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Hyperfine magnetic fields in Fe/Ag magnetic multilayers probed with low energy spin polarized ⁸Li Keeler, Todd Allan 2006

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Hyperfine Magnetic Fields in F e / A g Magnetic Multilayers Probed with Low Energy Spin Polarized 8 L i by T o d d A l l a n Keeler H . B . S c . , Lakehead Univers i ty , 2003 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F Master of Science i n T h e F a c u l t y of G r a d u a t e Studies (Physics) T h e Univers i ty O f B r i t i s h C o l u m b i a A p r i l 20, 2006 © T o d d A l l a n Keeler 2006 Abstract T h i s thesis is a presentation of experiments examining the induced hyperfine magnet ism i n the nonmagnetic layers of two t h i n f i lm magnet ic mult i layers , A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) and A u ( 4 0 A ) / A g ( 8 0 0 A ) / F e ( 2 0 A ) grown on G a A s ( O O l ) single crysta l substrates. T h e m a i n technique used i n this s tudy was beta-detected nuclear magnetic resonance ( / 3 N M R ) conducted at T R I -U M F laboratories i n Vancouver , B r i t i s h C o l u m b i a . / 3 N M R makes N M R mea-surements on radioact ive 8 L i + ( r=1.21 sec) nuclei that are imp lanted d irec t ly into the sample. Resonant / 3 N M R experiments showed strong induced m a g -net ism i n the non-magnet ic A g layer due the magnetic Fe. C o m p a r i s o n of a theoret ical model to exper imental results on the A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) sample suggest that the induced hyperfine magnet ism decays w i t h distance into the A g layer from the magnet i c /nonmagnet i c interface l ike x ~ 1 , 8 4 f rom a m a x i m u m of ~ 0 . 3 T at the magnet i c /nonmagnet i c interface. Contents A b s t r a c t i i Contents i i i List of Tables v List of Figures v i Acknowledgements i x 1 Introduct ion 1 2 T h e o r y 9 2.1 Induced Hyperf ine F ie lds i n F e / A g (001) 9 2.2 Pr inc ip les of / 3 N M R 19 2.3 M o d e l i n g the / 3 N M R lineshape i n F e / A g (001) 25 3 E x p e r i m e n t 31 3.1 8 L i + P r o d u c t i o n 31 3.2 Po lar izer 38 3.3 / 3 N M R H i g h - F i e l d Spectrometer 45 3.4 B e a m optics and B e a m Spot 55 3.5 8 L i stopping d istr ibut ions and T R I M Ca l cu la t i ons 55 3.6 F i t t i n g Procedure 60 3.7 Sample P r e p a r a t i o n 60 4 Results 65 4.1 T R I M . S P results 65 5 C o n c l u s i o n 82 B i b l i o g r a p h y List of Tables 4.1 Gauss ian fit parameters of T R I M . S P s topping profiles at 2.5 and 3.0 k e V i m p l a n t a t i o n energy i n the A g layer of A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s sample 77 4.2 Free parameters values obtained from f i t t ing the theoret ical l ineshape to resonant lines measured i n A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s at i m p l a n t a t i o n energies 2.5 and 3.0 k e V , r o o m t e m -perature, and Ho ~ 4 . 5 T 77 List of Figures 1.1 Bas i c / ? N M R setup 5 1.2 T y p i c a l / 3 N M R spectrum for a resonance experiment 6 1.3 T y p i c a l / 3 N M R spectrum for re laxat ion experiment 7 2.1 F e r m i structure of face centered cubic latt ice , a n d c r i t i ca l spanning vectors for (001) direct ion 11 2.2 F e r m i structure of face centered cubic latt ice , and c r i t i ca l spanning vectors for (001) direct ion 13 2.3 Wedged structure and results of a Scanning E l e c t r o n Microscopy w i t h P o l a r i z a t i o n A n a l y s i s ( S E M P A ) experiment that mea-sures I E C per iod 15 2.4 Shows the effect of al iasing on the per iod of I E C 16 2.5 Schematic of osci l lations i n the induced hyperfine fields i n F e / A g i n an external magnetic field Bext 17 2.6 M o d e l d i s t r ibut i on of magnetic fields expected for for a os-c i l la tory hyperfine fields i n an external fields B e x t = 3 T and assuming a Gauss ian 8 L i stopping d i s t r ibut i on 18 2.7 Schematic of the induced hyperfine fields w i t h osci l lat ions sur-p a s s e d i n F e / A g i n an external magnetic field Bext 20 2.8 T h e upper l i m i t of the distance from the F e / A g interface, x ; , where the internal field could be B^ 27 2.9 Integrat ion of the Gauss ian stopping profile, n(x) 28 2.10 M o d e l of the / 3 N M R lineshape expected from theoret ical hy -perfine field d i s t r ibut i on and stopping d i s t r i b u t i o n 30 3.1 F i g u r e of target used at IS A C 32 3.2 F igure of surface ion source used at IS A C 33 3.3 F i g u r e of IS A C target module 34 3.4 F i g u r e of the layout of the mass separator at I S A C 36 3.5 I S A C exper imental h a l l 37 3.6 / ? N M R beamline at I S A C 39 3.7 Po lar izer section of the / 3 N M R beamline 40 3.8 G r a p h of 7 L i + current vs. Temperature of N a neutra l i za t i on cel l 41 3.9 D l t rans i t i on i n neutra l 8 L i 42 3.10 A s y m m e t r y vs. N a deceleration plate voltage 46 3.11 E m i t t a n c e of beam at the H e cell reionizer 47 3.12 / 3 N M R high field spectrometer 48 3.13 E l e c t r i c potent ia l map of the spectrometer deceleration region 51 3.14 P o t e n t i a l step of the deceleration region along the beam axis . 52 3.15 Face centered cubic (fee) latt ice of A g 53 3.16 / ? N M R spectra taken at temperatures between 15 K and r o o m temperature showing the shift f rom the octahedral to the sub-s t i t u t i o n a l sites i n a t h i n A g f i lm grown on a M g O substrate . 54 3.17 8 L i + beamspot 56 3.18 Surface plot of 8 L i + b e a m s p o t 56 3.19 Implantat i on profiles generated by T R I M . S P for beam ener-gies of 500 e V , 5 k e V , 10 k e V , and 30 k e V 57 3.20 8 L i d i s t r ibut i on w i t h i n a sample as funct ion of i m p l a n t a t i o n energy. 58 3.21 Schematic d iagram showing how the unsatisfied surface b o n d orbi ta ls are dist inguished i n unreconstructed G a A s ( O O l ) for the Ga(001) and As(001) surfaces 63 3.22 X - r a y di f fraction ( X R D ) spectrum of A u ( 4 0 A ) / A g ( 8 0 0 A ) / F e ( 2 0 A ) / G a A s 64 4.1 / 3 N M R spectra of A u ( 4 0 A ) / A g ( 8 0 0 A ) / F e ( 2 0 A ) / G a A s taken at r oom temperature i n magnetic field Ho ~ 4 . 1 T 67 4.2 T R I M . S P calculated stopping d is tr ibut ions i n A u ( 4 0 A ) / A g ( 8 0 0 A ) / F e ( 2 0 A ) / G a A s 68 4.3 T R I M . S P calculations of percentance of imp lanted 8 L i stop-p ing i n each layer as funct ion of energy i n A u ( 4 0 A ) / A g ( 8 0 0 A ) / F e ( 2 0 A ) / G a A s 69 4.4 / 3 N M R spectrum taken at room temperature i n magnet ic field Ho ~ 4 . 5 T i n A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s 71 4.5 T R I M . S P calculated stopping d is tr ibut ions i n A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s 72 4.6 T R I M . S P calculations of percentance of i m p l a n t e d 8 L i stop-p ing i n each layer as funct ion of energy i n A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s 73 4.7 A r e a of Lorentz ian fits to resonance lines showing m i n i m u m signal 75 4.8 Gauss ian fit to T R I M . S P calculted d i s t r ibut ions i n the A g layer of A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s 78 4.9 F i t of theoret ical l ineshape to spectra taken i n A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s at r o o m temperature and H o ~ 4 . 5 T . . . 79 4.10 F o r m of the induced hyperfine fields i n the A g layer as deter-mined from the f i t t ing procedure 80 Acknowledgements I wou ld l ike to thank the many people, w i thout w h o m the work presented i n this thesis would never have been completed. F i r s t of a l l I wou ld l ike to t h a n k m y supervisor, D r . Rober t K ie l f , for his guidance thoughout this project . I wou ld l ike to t h a n k D r . Zaher S a l m a n for his invaluable assistance w i t h analysis of d a t a and computer programming thoughout th is project . I wou ld l ike to t h a n k D r . B r e t He inr i ch and his students, O leksandr Mosendz and B a r t K a r d a s z , at S i m o n Fraser Univers i ty for prepar ing the samples that were used i n these experiments. I wou ld l ike to thank the other members of the / 3 N M R group at T R I U M F , D r . A n d r e w M a c F a r l a n e , D r . K i m C h o w , M a s r u r Hossain , Terry P a r o l i n and D o n g W a n g for their assistance i n conduct ing these experiments as wel l as D r . B a s s a m H i t t i , D r . S y d K r e i t z m a n , and R a h i m A b a s a l t i for their technical assistance. I wou ld also l ike to thank m y fami ly and friends for a l l your support d u r i n g this project . T h a n k you a l l . I wou ld also l ike to thank the N a t i o n a l Science and Eng ineer ing Research C o u n c i l ( N S E R C ) for their f inancial support . Chapter 1 Introduction W e assume the matter our macroscopic wor ld is comprised of w i l l always display the properties we observe i n our everyday life. For example , i f one were to cut a block of some mater ia l i n half, we expect each piece to exhib i t the same properties that the whole d id . If one were to repeat this procedure over and over, however, eventually one would be left w i t h a piece so smal l that any further d iv is ion would change the mater ia l ' s intr ins ic properties. T h i s is the boundary between the macroscopic wor ld of our existance and the nanoscopic wor ld , where length is measured i n nanometers (b i l l i onth of a meter) , of atoms and molecules. T h e approx imat i on that any a t o m is surrounded by an inf inite number of other atoms i n a l l direct ions is no longer va l id because on the scale of nanometers the mater ia l w i l l on ly be made up of a few atoms. T h e "bu lk " properties of the mater ia l are reduced, and the "surface" properties become much more i m p o r t a n t , since on average an a t o m is more l ikely to be near the surface as the t o t a l number of atoms is reduced. W e can engineer structures i n a way that exploits th is , and use i t to s tudy specific effects i n u l t r a smal l scale systems. B y growing " u l t r a t h i n f i lms" only several atoms th ick , we have effectively reduced the number of dimensions of this system from three to two where nearly every a t o m is at the surface and surrounded by many atoms on a l l sides but very few above or below. T h e effect of low-dimensional i ty on magnetic mater ia ls is par t i cu lar ly s t r ik ing . U l t r a - t h i n magnetic films act like giant magnet ic molecules w i t h their own unique magnetic properties [1]. In 1986 G r u n b e r g et al. [2] made the unusual discovery that when two u l t r a t h i n f i lms of Fe were separated by a t h i n C r layer of certain thickness, the magnet izat ion d irec t ion of the Fe films a l ign anti ferromagnetical ly i n the absence of any external magnet ic field. T h i s led to the independent discoveries i n 1988 by Fert and G r u n b e r g [3, 4] that the res ist iv i ty across these layers would decrease d r a m a t i c a l l y when the coupl ing of the Fe layers changed from anti ferromagnetic ( A F ) to ferro-magnet ic ( F M ) . T h i s effect, which has been a t t r i b u t e d to sp in dependent scattering of conduct ion electrons at the magnet i c /nonmagnet i c interfaces, is much larger t h a n the conventional magneto-resistance described by the Lorentz force, and was thus given the name giant magneto-resistance ( G M R ) . T h i s phenomenon was quick ly adopted for use h a r d disk read heads, great ly increasing their sensit ivity, thus enabl ing the r a p i d increase seen i n h a r d disk b i t density. In 1990 it was found that interlayer exchange coupl ing ( I E C ) of magnet ic layers oscillates as a funct ion of spacer thickness for certa in m a g -netic mult i layer ( M M L ) structures [5, 6, 7], later this phenomenon was shown to occur i n almost any system of magnetic layers separated by a t rans i t i on meta l spacer, and that they a l l oscillate w i t h approx imate ly the same per i od , ~ 1 0 A [8]. These magnetic structures ho ld great promise i n the burgeoning spintronics i n d u s t r y which involves engineering electronic devices, such as sp in transistors and magnetic r a n d o m access memory ( M R A M ) , which u t i -lize electron sp in as wel l as charge by specif ically ta i l o r ing of a mater ia l ' s magnet ic and electric properties. T h i s osc i l lat ion between F M and A F coupl ing of the magnet izat ion i n magnet ic t h i n f i lms seems counter intuit ive based on our everyday exper i -ences. For example, we know that a compass needle w i l l always a l ign itself i n the same d irect ion , paral le l to the E a r t h ' s magnet ic field regardless of the distance i t is f rom the E a r t h ' s surface. Based on th is , i t wou ld seem r i d i c u -lous to t h i n k that the or ientat ion of two magnetic f i lms wou ld depend on their seperation distance, however this is what has been observed i n m a g -netic mult i layered structures as the thickness of the non-magnet ic spacer layer is increased. Several theories have had success i n describing the I E C of ferromagnetic layers i n these M M L systems. T h e most well k n o w n of these models is a n extension of the R u d e r m a n - K i t t e l - K a s u y a - Y o s i d a ( R K K Y ) mode l developed independently i n the 1950's by M . A . R u d e r m a n and C . K i t t e l [9], T . K a s u y a [10], and K . Y o s i d a [11] describing the effect of a magnet ic i m p u r i t y a t o m on the conduct ion electrons of a nonmagnetic host meta l . O t h e r models , treats the conduct ion electrons of the nonmagnetic layer as partic les i n a q u a n t u m wel l w i t h sp in dependent potent ia l barriers at the magnet ic a n d nonmagnet ic interfaces. T h e observed osci l lations are the result of the allowed s tanding wave solutions to the electronic density w i t h i n the nonmagnet ic layer. These models are able to y ie ld ana ly t i ca l results due to their relative s impl i c i ty and they b o t h relate the per iod of osc i l lat ion to the F e r m i surface of the bu lk spacer mater ia l i n the l i m i t of thick spacer layer [12], w h i c h is v a l i d for spacers thicker t h a n ~ 1 0 monolayers (a monolayer is a layer one a t o m th ick and is denoted by M L ) . Exper imenta l l y , I E C has been investigated p r i m a r i l y by prob ing the fer-romagnetic layers. W h i l e these types of experiments al low one to make mea-surements such as the coupl ing or ientat ion between two magnet ic layers as a funct ion of spacer thickness, they do not probe the mechanism of this cou-p l ing , the induced po lar i za t i on w i t h i n the non-magnet ic layer, direct ly . T h e smal l ampl i tude of the induced electronic po lar i za t i on due to r a p i d decay away from the magnetic layer, as wel l as the physical size of t y p i c a l samples (spacer thicknesses typ i ca l l y of only a few hundred angstroms) makes mea-surements of the induced po lar i zat ion of conduct ion electrons w i t h i n the n o n -magnet ic spacer layer very difficult. M o s t methods that make quant i tat ive measurements of po lar i zat ion w i t h i n the spacer mater ia l are either measur-ing average po lar i za t i on across the entire spacer, or probe nonmagnet ic layers grown on a ferromagnetic substrate. These two methods don ' t provide any in format ion about the per iod of osc i l lat ion of the conduct ion electron po lar -i za t i on . T h e signal obtained w i t h the first method , which can be done w i t h X - r a y magnetic c ircular d ichro ism ( X M C D ) [ 1 3 ] , is dominated by the first few monolayers ( M L ) close to the magnetic -nonmagnetic interface. T o make measurements of the per iod of osc i l lat ion requires a technique that measures po lar i za t i on of conduct ion electrons loca l ly w i t h i n the spacer. Techniques such as Mossbauer spectroscopy[14], per turbed angular correlation[15], and nuclear orientation[16, 17] provide methods of m a k i n g loca l measurements, however their l i m i t e d sensit iv i ty restricts t h e m to measurements close the magnet ic -nonmagnet ic interface where induced fields are strongest. In order to probe the behaviour deep w i t h i n the nonmagnetic layer effectively requires a technique that can make sensitive measurements of the loca l po lar i za t i on . T h e technique we have used to do this is beta-detected nuclear magnet ic resonance ( / 3 N M R ) . / 3 N M R is a technique very closely related to conventional nuclear m a g -netic resonance ( N M R ) . T h e y differ i n that the / 3 N M R signal is generated by u t i l i z i n g the /3-decay properties of radioact ive nuclei (~10 8 ) that have been imp lanted d irec t ly into the sample, whereas N M R requires measurements on a large number (~10 1 8 ) of the sample 's own nuclei to generate a s ignal . / 3 N M R conducted at T R I U M F ' s I S A C (Isotope Separator and Accelerator) fac i l i ty uses radioact ive 8 L i , a sp in 2 nucleus w i t h a mean l i fet ime of 1.21 s. In the /3-decay of a po lar ized radioactive 8 L i nucleus, a h igh energy electron is emi t ted preferentially along the direct ion of its nuclear po lar i za t i on d u r i n g the decay process 8 L i —*• 8 B e + e~ + ve. T h e 8 B e produced i n this process quick ly decays into two a l p h a particles, and do not contaminate the sample. I S A C has the capaci ty to produce a h ighly po lar ized low energy beam of 8 L i . Fur thermore , the i m p l a n t i o n energy can be adjusted i n the range 0.1-30 k e V , corresponding to mean i m p l a n t a t i o n depths of between 2 and 200 n m from the sample surface. T h i s ab i l i ty to conduct N M R experiments at either the surface, or into the bu lk region of t h i n f i lm nanostructures is what dis -tinguishes / 3 N M R from conventional , as wel l as related (such as m u o n spin r o t a t i o n / r e l a x a t i o n ( / iSR)) N M R techniques. / 3 N M R experiments are conducted by p lac ing the sample i n a spectrom-eter. A schematic of the setup used i n / 3 N M R experiments can be seen i n F i g 1.1. T h e most basic requirements for a / ? N M R spectrometer is a set of be ta detectors placed i n front and behind the sample i n this geometry. T h o u g h not required, the sample is usual ly s i tuated i n a large l ong i tud ina l magnet ic f ield, Ho, produced by a superconduct ing solenoid. A s m a l l osci l lat -ing magnet ic field, H i which lies i n the plane perpendicular to the po lar i za t i on direct ion is appl ied by a smal l co i l located near the sample. In conventional N M R , the s ignal intensity scales as the square of the resonance /osc i l lat ion frequency, u>2. T h i s is because b o t h the nuclear po lar i za t i on i n the sample and the induced electromotive force ( E M F ) i n the induc t i on coils scale w i t h to. Since the 8 L i beam is h ighly polar ized before be ing imp lanted i n the sample, and the measurements are not made w i t h induced E M F , the / 3 N M R signal is independent of appl ied magnetic field and could , i n fact, be carr ied out i n the absence of any Ho, provided that po lar i za t i on is not lost too qu ick ly to sp in latt ice re laxat ion . However it w i l l be shown that conduct ing / 3 N M R experiments w i t h a large l ong i tud ina l field does have certa in advantages. There are two observables i n / 3 N M R experiments related to the stat ic and d y n a m i c properties of the local magnetic environment. Resonant experiments are carr ied out by moni tor ing the po lar i zat ion of a cont inuously imp lanted beam of 8 L i whi le scanning through a range of frequencies of the osc i l lat ing perpendicular field ( H i i n F i g 1.1). Loss of po lar i za t i on occurs when the frequency, ui, matches the L a r m o r frequency of the 8 L i nuclei i n the sample. T h e d y n a m i c magnetic properties of a sample can be probed by i m p l a n t i n g a pulse of 8 L i and moni tor ing the re laxat ion of po lar i za t i on , i n the absence of the perpendicular field, as a funct ion of t ime. R e l a x a t i o n of nuclear spins i n a meta l is usual ly dominated by scattering of conduct ion electrons at the F e r m i surface off of the nuclear spins mediated by the hyperfine coup l ing between the electron and the nuclear sp in [18]. T y p i c a l resonance and re laxat ion spectra can been seen i n F igs 1.2 & 1.3. F i g u r e 1.1: Bas i c setup of a / 5 N M R experiment. Rad ioac t ive ions enter through a hole i n the backward detector and are imp lanted into sample which sits i n a l ong i tud ina l magnetic field, Ho- T h e asymmetry between the backward and forward detector counts are moni tored as a funct ion of H i osc i l lat ing magnetic field frequency, ui. Figure 1.2: T y p i c a l / 3 N M R spectrum obtained f rom a resonance experiment taken at T = 2 9 0 K and H 0 = 4 . 1 T i n G a A s . 0.18n Time (ms) F i g u r e 1.3: T y p i c a l / 3 N M R spectrum obtained from a re laxat ion experiment taken at T = 2 9 0 K and H 0 = 4 . 1 T i n G a A s . T h e purpose of the project that is presented i n this thesis was to use the / 3 N M R technique to measure the hyperfine field d i s t r i b u t i o n induced i n a nonmagnet ic Ag(OOl) due to an adjacent magnetic Fe (001) f i lm grown w i t h molecular beam epi taxy ( M B E ) on a G a A s (001) substrate. T h e d a t a collected was compared w i t h models based on current theories, as wel l as w i t h results of experiments conducted on F e / A g M M L w i t h the s imi lar , but compl imentary technique of low energy m u o n spin ro ta t i on ( L E - / i S R ) [ 1 9 ] . W e begin by first reviewing the relevant theory of induced hyperfine fields i n F e / A g M M L , and how we use this to generate a mode l for the resonant spec trum we would measure i n an experiment i n C h a p t e r 1. N e x t the exper-imenta l setup that is used, inc lud ing to product ion and po lar i za t i on of the radioact ive probe nuclei and the spectrometer used i n m a k i n g our / 3 N M R measurements, as wel l as how the F e / A g M M L samples were prepared is discussed i n deta i l i n C h a p t e r 2. F i n a l l y the results of the / 3 N M R resonance experiments conducted on these samples and the form of the hyperfine cou-p l i n g that we extract from comparison of the measured spectra w i t h our mode l is presented is given i n C h a p t e r 3. Chapter 2 Theory In this chapter we introduce the model which allows us to calculate the / 3 N M R frequency spec trum observed i n F e / A g M M L s . T h e mode l depends on the d is tr ibut ions of implanted 8 L i and hyperfine fields w i t h i n the A g layer. S topp ing d is tr ibut ions used i n the model come from M o n t e - C a r l o s imulat ions of 8 L i + i m p l a n t a t i o n into the sample. T h e spat ia l d i s t r ibut i on of hyperfine fields i n the nonmagnet ic layer come from predict ions based on the theoret ical calculat ions that have been done i n these systems. C r e a t i n g a mode l resonant l ineshape of / ? N M R measurements i n these systems requires understanding of the hyperfine coupl ing between the nonmagnetic A g a n d ferromagnetic Fe layers,as well as the physics of nuclear magnet ic resonance, and / 3 N M R specifically. A review of these areas w i l l be given first before discussing how we use t h e m to generate a model of the / 3 N M R frequency spectrum. 2.1 Induced Hyperfine Fields in F e / A g (001) T h e osci l latory nature of the coupl ing between ferromagnetic layers separated by a non-magnet ic layer has been theoret ical ly examined by several different methods. A t t e m p t s have been made to calculate the coupl ing between m a g -netic layers by a t t r i b u t i n g the difference i n the t o t a l energy of the system for ferromagnetic and antiferromagnetic orientations, either ab initio [21] or using t ight b ind ing approximat ions [22]. O b t a i n i n g conclusive results i n this manner is difficult because the energy difference between the orientations is t yp i ca l l y several orders of magnitude smaller t h a n the t o t a l energy itself and they also give very l i t t l e understanding of the phys ica l mechanism of the osc i l latory nature of the coupl ing. O t h e r models that have been proposed as a possible mechanism for this coupl ing are based on q u a n t u m confinement of the conduct ion electrons i n the nonmagnet ic layer [12, 23]. In these models, sp in dependent reflection ampl i tudes at the magnet i c /non-magnet i c interfaces, a long w i t h the finite thickness of the nonmagnet ic layer lead to a s i tuat ion analogous to a q u a n t u m well . T h e q u a n t u m interference due to mul t ip le reflections at the interfaces leads to modi f i cat ion of the electron density of states i n the form of s tand ing waves. T h e mechanism to describe the osc i l latory I E C i n M M L structures that has had the most success has its or ig in i n the theory w h i c h describes the interact ion of a magnetic i m p u r i t y w i t h the conduct ion electrons of the host meta l i n which it sits, known as the R u d e r m a n , K i t t e l , K a s u y a , and Y o s h i d a ( R K K Y ) interact ion [9, 10, 11]. In the case of a magnet ic i m p u r i t y i n a nonmagnet ic host meta l , hybr id i za t i on between the s-p conduct ion electrons of the host meta l and the d electrons of the magnetic impur i t i es results i n an effective exchange interact ion at the site of the impur i ty . T h e t y p i c a l coupl ing for s - p / d hybr id i za t i on is anti ferromagnetic , and the surrounding conduct ion electrons at tempt to screen the i m p u r i t y spin . T h e electrons close to the i m p u r i t y over-screen the sp in by a l igning ant i -para l l e l , the electrons further out a l ign paral le l to the i m p u r i t y which over-compensates the over-screened region, so the electrons further s t i l l a l ign ant i -para l l e l again , and so on out rad ia l l y to in f in i ty w i t h decreasing ampl i tude . In three dimensions, the ampl i tude of these osci l lations decays away like r - 3 , where r is the rad ia l distance away from the impur i ty . T h e spherical shells of a l ternat ing po lar i zat ion arise due to the cutoff i n k values for an electron i n a meta l . T h e occupied k-vectors extend f rom zero to the F e r m i wave vector, k p , i n the Fourier k-space of the host meta l . A de l ta funct ion for local ized screening i n real space requires a l l k-vectors: However, on ly electrons w i t h k-vectors up to k p are available for screen-ing w h i c h means the host conduct ion electrons cannot possibly screen the i m p u r i t y sp in perfectly to the atomic scale, result ing i n osci l lat ions of the electronic po lar i za t i on [25]. T h e per iod of osc i l lat ion is determined by the F e r m i surface of the of the host meta l , which should be expected as these osci l lations originate because of the sharp cut-off i n occupied k-states at the F e r m i energy. T h e per iod of the osc i l lat ion i n the electron po lar i za t i on , A ^ , is given by ir d iv ided by the wave-vector(s) that define the F e r m i surface of the host meta l , k p . T h e theoretical coupl ing of an electron to a magnet ic i m p u r i t y can be seen i n F i g 2.1. T w o impur i t i es w i l l interact w i t h each other when they are close enough to al low appreciable overlap of the screening po lar i za t i on regions. If the Figure 2.1: T h e osc i l latory coupl ing strength as a funct ion of d istance (mea-sured i n mult ip les the unitless quant i ty k^r) between a host conduc t i on elec-t r o n and a magnet ic i m p u r i t y predicted by R K K Y theory. T a k e n f rom [25] second i m p u r i t y is s i tuated such that i t is i n the region where the induced po lar i za t i on of the electrons is spin-down (wi th respect to the first i m p u -r i t y sp in direct ion) , i t is favoured to orient itself opposite to the po lar i za t i on directions, result ing i n ferromagnetic coupl ing between the two impur i t ies . A l ternat ive ly , the impur i t ies w i l l couple ant i ferromagnetical ly i f one i m p u -r i t y finds itself i n a region where the other has induced sp in -up electronic po lar i zat ion . E x t e n s i o n of the R K K Y theory of magnetic impur i t i es to M M L have shown that these systems share many characteristics w i t h the theory de-scr ib ing magnetic impuri t ies . However, these structures present a more com-pl icated s i tuat ion since the superposit ion of the interactions of conduct ion electrons w i t h the atoms i n the bu lk of the magnetic layer as wel l as the inter -face is necessary to proper ly describe the behavior of the entire system. T h e interface atoms w i l l have the largest effect on the interact ion as these atoms are most strongly coupled to the conduct ion electrons of the spacer layer, and i t is therefore reasonable to include only the first few magnet ic layers i n the theory [25]. Ca l cu la t i ons carr ied out assuming a spherical F e r m i surface (free electron approx imat ion) have led to the same relat ionship between the per iod of osc i l lat ion and the F e r m i surface of the spacer, but the ampl i tude of the osci l lations decay as r - 2 away from the magnet ic layer [24]. In real metals the F e r m i surface has a much more compl icated shape t h a n the s imple sphere predicted i n this approx imat ion . T h e characterist ic k-vectors that define the per iod of osc i l lat ion are cal led the critical spanning vectors. Spann ing vectors are defined as vectors para l le l to the interface n o r m a l that connect two points on the F e r m i surface, one point hav ing a posit ive component of the velocity i n the interface d i rec t ion and the other a negative component. A c r i t i ca l spanning vector is a spanning vector that connects two points of the F e r m i surface where its gradient is perpendicular to the interface, meaning that the c r i t i ca l spanning vector(s) connects para l le l regions of the F e r m i surface[27]. For the (001) d irect ion of a face centered cubic (fee) meta l , such as A g , there are two c r i t i ca l spanning vectors which span the "neck" and "be l ly" regions of the F e r m i surface and give rise to long and short per iod osci l lations, respectively. T h e F e r m i surface and c r i t i ca l spanning vectors can be seen i n F i g 2.2. There was i n i t i a l l y some confusion as to whether the osci l lat ions were ac tua l ly related to the F e r m i surface, as the periods predicted by this theory were smaller t h a n those measured i n experiment [29]. T h i s prob lem was resolved by considering an effect cal led aliasing. A l i a s i n g arises from the F i g u r e 2.2: F e r m i surface and spanning vectors of a fee latt ice . T h e F e r m i surface in the first B r i l l o u i n Zone is shown on the r ight , w i t h the "necks" i n the (111) region shown in grey. T h e repeated cross section ( taken through the slice represented by the dashed rectangle) is shown on the left, w i t h the F e r m i surface shown by the dark curves. T h e rec iprocal la t t i ce vector i n the (001) d i rec t ion is given by the white arrow, whi le the c r i t i c a l spanning vectors, qj_ spanning the " b e l l y " and q^ spanning the "neck" regions are given by the grey arrows. Taken from [29] fact that the thickness of a sample is not continuous on an a tomic scale. T h e spacer thickness must increase i n unit thicknesses of ha l f the latt ice constant, as this is the thickness of a single atomic layer. Since the thickness w i l l increase i n a tomic units , experiments effectively sample the osc i l lat ions at discrete intervals determined by the thickness of a single monolayer ( M L ) , D 0 . A l i a s i n g gives rise to longer periods t h a n predicted by s imple theory as can be seen i n F i g 2.4. T h e coupl ing per iod of two magnet ic layers can be measured by growing a wedge of nonmagnetic metal on a ferromagnetic substrate, then covering the wedge w i t h another ferromagnetic layer. T h e per i od of osc i l lat ion is determined by measuring the or ientat ion of the magnet i za t i on across the top ferromagnetic layer using Scanning E l e c t r o n Mic ros copy w i t h P o l a r i z a t i o n A n a l y s i s ( S E M P A ) , which w i l l oscil late due to the increasing spacer thickness of the wedge seperating i t f rom the b o t t o m ferromagnetic layer. Results of an experiment of this k i n d can be seen i n F i g 2.3. T a k i n g al ias ing into considerat ion brings theoret ical and exper imental periods into better agreement w i t h each other [30, 31] and confirms that the osci l lat ions real ly are determined by the F e r m i surface of the nonmagnet ic spacer. W h e n one takes al iasing into consideration the theoret ical ly predicted periods using c r i t i ca l spanning vectors from de Haas -van A l p h e n results for A g (2.38 and 5.58 M L , or 4.8 A and 11.3 A[26]) agree very wel l w i t h ex-per imenta l ly determined periods measured w i t h S E M P A are 2.37±0.007 and 5.73±0.05 M L (4.8±0.1 A and 11.6±0.1 A)[32] for F e / A g ( 0 0 1 ) . F r o m this descr ipt ion, we would expect the hyperfine fields i n the non -magnet ic layer away from the magnet i c /nonmagnet i c interface resul t ing f rom the induced electron po lar i zat ion to be of the form: Bhf(x) = B0J2CiXaisin(2irx/\i + fa) (2.1) i where x is the perpendicular distance into the A g , A; are the osc i l lat ion wavelengths given above, C* and fa are the ampl i tude and phase of each osc i l lat ion, and at are the power law exponents determining how the osc i l la -t ions decay away from the interface. For fee A g , the s u m w o u l d be carr ied out over the two periods determined from the c r i t i ca l spanning vectors (ie: i = l , 2 ) . T h i s form of the induced fields i n F e / A g is shown i n F i g 2.5 Theoret i ca l descriptions that predict coherent osci l lat ions i n the electronic po lar i za t i on of the spacer layer are based on perfectly flat and sharp inter -faces. E v e n w i t h the sophist icated techniques for growing t h i n films, such as molecular beam epi taxy ( M B E ) , ideal ly perfect samples w i t h flat, sharp interfaces are impossible. A model of what we expect the d i s t r i b u t i o n of m a g -net ism fields i n the A g layer based on this ideal osc i l latory form i n an external field of Bext=3 T and assuming a Gauss ian 8 L i s topping d i s t r i b u t i o n is shown i n F i g 2.6. It shows sharp peaks that correspond to the peaks and troughs of the osc i l lat ing hyperfine fields seen i n F i g 2.5. T h e two major peaks on either side of the external field are due to the region far f rom the A g / F e inter-face where there is less damping between adjacent peaks / t roughs , whi le the satell ite peaks at h igher / lower fields t h a n the Bext are due to peaks / t roughs closer to the interface where the fields are larger i n magnitude . Imperfections at the interface due to steps, interdif fusion, and s t r a i n have been examined i n the context of the R K K Y model by several groups and a l l have found that deviations from ideal interfaces greatly reduce the osci l lations 2 m m 12 n m Figure 2.3: Shows the wedged structure used to measure I E C per i od i n F e / A u / F e , as wel l as results for the per iod osc i l lat ion of the coup l ing be-tween the magnet ic layers obtained using Scanning E l e c t r o n M i c r o s c o p y w i t h P o l a r i z a t i o n A n a l y s i s ( S E M P A ) . Taken from[29]. z / Z ) Q Figure 2.4: Shows the effect discreet layer thickness, resul t ing i n the mea-sured per iod of osc i l lat ion being longer than theoret ical predict ions . T h e dot-ted l ine shows the short per iod oscil lations predicted by R K K Y , the squares shows the values taken at discreet thicknesses, and the longer per i od osci l -lat ions that wou ld be observed is shown w i t h the so l id l ine. Taken from [29] Figure 2.5: Schematic of oscil lations in the induced hyperfine fields i n F e / A g i n an external magnet ic field Bext based on the R K K Y theory of magnet ic impur i t ies i n a nonmangnet ic host. 0.02 0.018 2.92 2.94 2.96 3.02 3.04 3.06 M a g n e t i c F i e l d ( T ) F i g u r e 2.6: M o d e l d i s t r ibut i on of magnetic fields expected for for a osc i l la -t o ry hyperfine fields i n an external fields B e x t = 3 T a n d assuming a G a u s s i a n 8 L i s topping d i s t r i b u t i o n . T h e sharp peaks at h igher / lowers fields t h a n Bext correspond to peaks / t roughs i n the induced hyperfine fields, w i t h the two large, central peaks coming from the region far f rom the A g / F e interface where d a m p i n g is smallest. 3.12 [12, 34, 37]. Roughness as a result of atomic terraces separated by steps has been show to wipe out the short wavelength osci l lations [38] since there wou ld no longer be a well defined x i n E q . (2.1). Furthermore a vert i ca l m i s m a t c h between atomic planes, as l i t t l e as 0.8% for F e / A g ( 0 0 1 [39], can lead to suppression of b o t h the long and short wavelengths. For reasons that w i l l be discussed i n section 3.7 of the next chapter on Sample P r e p a r a t i o n , we feel that the F e / A g interface of the samples being studied is disordered enough that coherent osci l lations w i l l not be present over that latera l distances we measure over. W e predict that th is w i l l act to "smear" the fields between the ± x ~ Q envelope. T h e form of hyperfine field predicted by R K K Y theory is divergent at the F e / A g interface, whi ch is unphysica l . Ca l cu lat ions of the induced hyperfine field i n the A g layer closest to the interface have been done[40] w h i c h give a value of ~ 3 0 0 k G for the hyperfine field at the site of the A g nucleus closest to the interface. However, i n general, A g and L i w i l l have couple differently to the hyperfine fields of the Fe. In our experiment we wou ld expect the fields to approach the hyperfine coupl ing of 8 L i i n Fe, w h i c h we expect to be on the order of a few k G , based on measurements of the induced hyperfine field at the site of a L i i m p u r i t y i n a subst i tut iona l site of Fe [41]. W e have therefore chosen to use a form: where Ai?=27r/kp is taken as the long per iod F e r m i wavelength of A g (11.6 A) makes x/\p a unitless quantity. T h i s form behaves l ike x~a far f rom the F e / A g , but avoids the asymptot i c behavior at smal l x . T h i s f orm of hyperfine coupl ing can be seen i n F i g 2.7 2.2 Principles of /?NMR / 3 N M R is a technique that exploits the phenomenon of nuclear magnet ic reso-nance ( N M R ) to make measurements of local in terna l electronic and magnet ic environments. N M R techniques can be employed on any part ic le w i t h non -zero magnet ic moment. T h e magnetic moment of a nucleus, /2, is d i rec t ly propor t i ona l to i ts sp in , fi=^/hl, where / is the sp in of the nucleus, and 7 is k n o w n as the gyromagnetic rat io and is a propor t i ona l i ty constant specific to any nucleus. For 8 L i 7=6301 k H z / T . S imple classical e lectrodynamics tells Distance F i g u r e 2.7: Schematic of the induced hyperfine fields w i t h coherent osci l -lat ions supressed by interface roughness in F e / A g result ing i n a "smearing out" of the induced magnet ism over the shaded area i n the A g . us that i n the presence of an external magnetic field, H, jX w i l l experince a torque given by p x H [20]. Since torque is defined as the rate of change of angular m o m e n t u m , which can be expressed i n terms of magnet ic moment , we have the equation of mot ion : ^ = pxiH (2.3) T h i s implies that the instantaneous change i n p is perpendicular to b o t h p, and H. If H is a stat ic field, p w i l l sweep out a cone shape as i t precesses around the magnet ic field direct ion. T h e rate of this precession is k n o w n as the L a r m o r frequency, U>L and is found by solving the equation of m o t i o n above. A convenient way to solve this equation is to consider a r o t a t i ng frame of reference where p is at the or ig in , and H lies along the z-axis. If this reference frame rotates w i t h instantaneous angular velocity then it can be shown that i n this reference frame d / I /d t can be w r i t t e n as [18]: | = | + n x , ( ,4> M a k i n g this change i n E q . (2.3) gives: ^• + Q,xp = pxjH (2.5) ot or 5l = Px(jH + n) (2.6) T h i s equation of mot i on i n the ro tat ing frame is ident ica l to the equation i n the lab frame (non-rotat ing) , except we now have an "effective f i e ld " : He = H + Q/j (2.7) For a given external field, H=rloZ, we can f ind U>L of p by m a k i n g 0,—UL-Since this means that our frame of reference and p are r o t a t i n g at the same rate around p, we have Sfi/5t=0. F r o m our equation of m o t i o n i n this frame, this requires that H e = 0 , which implies that Q,=-^H=-'yr\oz. T h i s tells us that the L a r m o r frequency must be w^=7Ho. N o w , if we appl ied a magnetic field, H i , that rotates i n the xy -p lane of the laboratory frame at the L a r m o r frequency, i n our r o t a t i ng frame this w i l l be a stat ic field that the sp in w i l l begin to precess about , whi ch results i n an osc i l lat ing nuclear po lar i za t i on along the z d i rect ion i n the lab frame. W h e n there are many nuclei w i t h r a n d o m i n i t i a l phase angles, then this precession is seen as a loss of z po lar i za t i on , since we observe that average a l l nuclei . One can arrive at this very same result by approaching this prob lem using q u a n t u m mechanics. W h e n a magnetic moment is i n the presence of a magnetic f ield, H, it w i l l experience an Zeeman interact ion energy given by -/j, • H. T h e H a m i l t o n i a n that describes a nucleus i n the presence of an external magnet ic field is: H = -jhHQIz (2.8) where we take the external field to lie along the z -direct ion, and have m a g -n i tude Ho- W e can see that the magnetic field lifts the degeneracy of the lz eigenvalues, m / , whi ch are the projections of / along the z -direct ion: mi — —I, —I + 1 , / T h e energy levels are given by, E = -jhHomi (2.9) T h i s tells us that i n the presence of a magnetic field a non-zero sp in nucleus is i n a lower energy state when it is al igned w i t h that field. Q u a n t u m mechanics tells us that by in troduc ing a t ime dependent per turbat i on , i n the form of an a l ternat ing magnetic field perpendicular to the stat ic field H, transit ions can occur between adjacent levels i f the angular frequency of the per turbat i on is equal to 7H0. T h i s is exact ly the value of the frequency we found for the ro ta t ing magnetic field that would result i n loss of po lar i za t i on along z, us ing a classical descript ion above. In real mater ia ls , the loca l magnetic environment of the sp in is a super-pos i t ion of the external appl ied field w i t h the internal magnet ic field due to the surrounding nuclei and electrons. These internal magnet ic fields shift the L a r m o r frequency f rom the frequency one would get w i t h just the external magnet ic field. In a non-magnetic meta l the frequency shift is due to the P a u l i paramagnet ic susceptibi l i ty of the conduct ion electrons and is k n o w n as the K n i g h t shift. T h e external magnetic field causes po lar i za t i on i n the electrons, w h i c h produces an internal magnetic field, A H . A H scales w i t h the strength of the appl ied field, H , however the rat io A H / H is a constant characterist ic of the host meta l [18]. In F e / A g , the presence of the Fe layer w i l l induce po lar i za t i on of the conduct ion electrons i n the A g layer. Since electrons have a relat ively large magnetic moment , this po lar i za t i on leads to a d i s t r ibut i on of internal magnetic fields w i t h i n the n o r m a l l y nonmagnet ic A g which w i l l lead to a d i s t r ibut i on of L a r m o r frequencies of the nuclei i n this region. In conventional N M R , nuclear po lar i zat ion is generated by the app l i ca t i on of a large magnet ic field. T h e d i s t r ibut i on of m / sp in projections is given by the B o l t z m a n n d i s t r ibut i on . T h e perpendicular magnetic field osc i l lat ing at frequency u> is appl ied us ing induc t i on coils i n the xy -p lane . In t y p i c a l N M R experiments the L a r m o r frequency is i n the radio-frequency ( R F ) range, so i t is c ommon to refer to the perpendicular osc i l lat ing magnet ic field as s imp ly an R F field. A f t e r some t ime the R F field is shut off and for CJ=LUL, the coils w i l l pick up the induced voltage caused by the precessing spins i n an excited state as they relax back to equ i l ibr ium. Because the magnetic moment of an i n d i v i d u a l nucleus is smal l , a large number of spins (~10 1 8 ) are required to generate a s ignal . Since the po lar ized nuclei represent a s m a l l f ract ion of the t o t a l sample, conventional N M R is generally l i m i t e d to studies of the bu lk properties of large samples where many nuclei are available. / 3 N M R , whi le based on the same pr inc iple as N M R , is quite different f rom conventional N M R i n several ways. Instead of measuring the resonance of po lar ized nuclei of the sample itself, we measure the resonance of imp lanted po lar ized radioact ive nuclei w h i c h emit a h igh energy electron (/3-particle) preferential ly along their sp in axis. M e a s u r i n g resonance i n this way great ly increases the s ignal to noise rat io which means that only ~ 1 0 8 spins are required to generate a typ i ca l / 3 N M R spectrum. T h i s also means that the restrict ions of conventional N M R on the size of a sample do not app ly to samples i n / 3 N M R experiments. It is possible to imp lant 8 L i i n samples w i t h thicknesses from as t h i n as a few tens of angstroms grown on substrates less t h a n 2-3 m m , and w i t h latera l dimensions larger t h a n the 8 L i beam spot, w h i c h has a diameter of ~ 4 m m . A l s o , since the imp lanted nuclei have a h igh degree of po lar i za t i on (60%), the large magnetic field characterist ic of conventional N M R is unnecessary, which means it is possible to measure only the interna l magnet ism of a sample. In / 3 N M R experiments, we app ly a continuous wave ( C W ) R F at one frequency whi le constantly i m p l a n t i n g 8 L i into the sample. T i m e integrated counts (NF/B) are made i n the front (F) and back (B) (5 detectors shown i n F i g 1.1 for a per iod of t ime (on the order of several 8 L i l i fet imes) , then the R F is stepped to the next frequency and this procedure is repeated throughout the range of frequencies we are interested i n . T h e counts i n each detector for a par t i cu lar R F , Np/B is the t ime averaged integral of the z component of the 8 L i po lar i za t i on weighted by the decay of the radioact ive 8 L i . W e observe the t ime averaged po lar i za t i on since the /3-particle is emi t ted along the sp in d irect ion of the radioact ive nuclei at the t ime it decays. T h e f o rm of this is given by[35]: NF/B = NF/Bjo -e-r[l + AF/BGzz(t)]dt (2.10) where N°F/B is determined by the intesity and po lar i za t i on of the 8 L i beam as wel l detector geometry, r is the 8 L i l i fet ime, Ap/B is the a s y m m e t r y p a -rameter for the part i cu lar dector / sample geometry, and Gzz(t) is the t ime dependent po lar i za t i on along the z d irect ion for 8 L i i n a stat ic magnet ic field also directed along z. T h e funct ion G z z ( t ) is a funct ion of the populat ions and sp in dynamics at the 8 L i sites, as wel l as transi t ions and any other i n -teract ion that would affect the po lar i za t i on over t ime. T h e po lar i za t i on of the implanted 8 L i is moni tored the asymmetry be-tween the front and back detectors at a part i cu lar R F frequency by combin ing the counts i n the two detectors i n the fol lowing way: A = N F ~ N B . (2.11) Np + NB y ' Off resonance, the ma jo r i t y of 8 L i w i l l be po lar ized i n the +z d i rec t ion , result ing i n more counts i n the front detector, however, on resonance we ex-pect a loss i n the asymmetry since the 8 L i is just as l ike ly to be p o i n t i n g i n the -z d irect ion as the +z d irect ion when it decays. Ideally the off resonance asymmetry , cal led A 0 , would take the values of ± 1 , depending on the po lar -i za t i on d irect ion of the implanted 8 L i , since a l l the counts are i n either the front or back detectors. W h e n the R F is on resonance we expect the t ime averaged po lar i za t i on along the z to be zero result ing i n a loss of asymme-try. In pract ice A is not ± 1 on resonance, and zero off as i t is a funct ion of the geometry of the detectors as wel l as the po lar i za t i on and nuclear decay properties of the 8 L i . In the absence of any quadrupolar sp l i t t ing , such is the case for A g , the form of the z-component of the po lar i za t i on , P z , can be determined s imi lar to the po lar i za t i on of implanted muons i n /xSR w h i c h can be found i n Refs [35, 36]. To do this we take a reference frame t h a t is r o ta t ing about the z axis w i t h the same angular frequency as the appl ied R F , u>. T h e effective field, Heff, that results from this is the modif ied z component f rom E q . (2.7), as wel l as the R F field Hx i n the {xR,yR) plane, where (xR,yR,z) are the uni t vectors of the rotated reference frame: ^ e / / = ^ — - Z + HM) iLi where UJ0 = 7£ i#o is the L a r m o r frequency and p = XR c o s 4> + VR s in <f>. <f> is the angle between Hi and the x-axis i n the ro ta t ing frame, XR. W i t h H e / / d irected along f — zcosO + psin.9, and assuming i n i t i a l po la r i za t i on along the z d i rect ion , the t ime evolut ion of P z as a funct ion of ui is: Pz = cos 2 6 + s i n 2 9 c o s ( w e / / t ) (2.12) where o> e// = y^(cJo — ^ ) 2 + is the precession frequency i n the effective field, u>i = 'jLiHi is the precession i n the R F field and cot# = (u>o — u)/u\. T h e t ime depedence of P z is i n the cos(o; e / /t) t e r m , so the t ime averaged po lar i za t i on w i l l be the form of the Laplace t ransform of cos: r Jo e'st cos at = -= r (2.13) COO r s t cos at = + az T h i s form is what w i l l be found for the asymmetry i n the F / B detec-tors under R F exc i tat ion by tak ing E q . (2.10) w i t h P z ( t ) incorporated into the funct ion Gzz{t). A p p l y i n g this to E q . (2.11), one obtains a L o r e n t z i a n l ineshape for the R F induced asymmetry. where ARF is the peak ampl i tude , and A 2 = ^ + u>\2 is the hal f w i d t h at hal f m a x i m u m . 2.3 Modeling the /?NMR lineshape in F e / A g (001) G i v e n the internal magnetic field d i s t r ibut i on i n the A g layer as a funct ion of distance from the F e / A g interface, as wel l as the 8 L i s topping d i s t r i b u t i o n i n the A g layer, one can generate a phenomenological / 3 N M R l ineshape that one might expect to measure i n an experiment. One can approx imate the d i s t r ibut i on of 8 L i stopping i n the A g layer w i t h a G a u s s i a n d i s t r i b u t i o n because the profiles of 8 L i calculated by M o n t e - C a r l o software, T R I M . S P , fits extremely wel l to this form. T h e model l ineshape based on this in format ion can be used i n a fitting rout ine to find the induced field parameters that most closely replicates the exper imental data . T h e mode l l ineshape we want to make is a d i s t r ibut i on of the number of 8 L i that w i l l stop i n the presence of internal magnetic field B , n ( B ) . For stat ic (t ime-independent) internal fields, the resonance l ineshape is closely related to the internal magnetic field d i s t r ibut i on , n ( B ) . In a / 3 N M R resonance ex-periment , the 8 L i po lar i zat ion is monitored while a p p l y i n g a perpendicular magnet ic field at frequency u, as explained i n the previous section. A s was shown, the resonant frequency of a nucleus is propor t i ona l to the magni tude of the loca l magnetic field. T h i s means that the n ( B ) of our mode l should be propor t i ona l to the n(u>) measured i n the experiment. T h e magnet ic fields i n the A g layer that the imp lanted 8 L i experience is the induced hyperfine field, B ^ / , and the l ong i tud ina l field of Bext ~ 4 . 1 Tesla (T) appl ied n o r m a l to the surface of the sample. It has been found by L o w -Temperature Nuc lear Or ienta t i on ( L T N O ) [16, 17] that i n the presence of such a magnetic field directed out of the surface plane, the Fe magnet izat ion as wel l as the induced hyperfine fields i n the A g layer, are also directed out of the plane. T h e t o ta l internal magnetic field w i l l be the induced posit ive and negative hyperfine fields centered on the large external field. B{x) = Bext + Bhf (2.15) T h e "smearing" effect of Bhf due to sample imperfections means that the magnet ic field at a given x can lie anywhere between the m a x i m u m and m i n i m u m fields given by: Bo Bmax{x) = Bext + ^ ^ (x/\p)a' (2-16) + {x/\F)a T h i s d i s t r ibut i on of fields is shown i n F i g 2.7. W e isolate x i n this equation to obta in : ' B — Bext x(B) = XF Bo (2-17) Figure 2.8: Xj is the upper l i m i t of the distance from the F e / A g interface where the internal field could have the value B ; . B y integrat ing the s topping d i s t r ibut i on from x = 0 to x = x ; gives the number of 8 L i that cou ld stop i n a region of magnetic field B j T h i s funct ion tells us that a l l the 8 L i which stops between the F e / A g interface (x=0) and x ( B ) could be at a site where the magnet ic field is a part i cu lar value of B . F i g 2.8 shows this schematically. T h e relative number of 8 L i that lie i n this range can be found by integrat ing the normal i zed Gauss ian of the s topping d i s t r ibut i on , see F i g 2.9: x c and T are the center and the fu l l w id th - ha l f m a x i m u m of the s topping d i s t r ibut i on , and are determined by s imulat ing i m p l a n t a t i o n of 8 L i at a given energy. Repeat ing this through a range of B values centered around the appl ied magnetic field B e x t w i l l generate the model l ineshape. T h i s can be seen i n F i g 2.10. In / 3 N M R experiments we measure a loss of po lar i za t i on along the z d i rec t ion , we expect m a x i m u m signal at frequencies w h i c h relates to where n ( B ) is sma l l , since few 8 L i w i l l be i n resonance here. Therefore when we compare exper imental results to this model , we construct the funct ion T h e baseline, A 0 , is the off resonance po lar i za t i on , and a is a constant that relates the ampl i tudes of the model and the exper imental signals. One question that arises is whether this "stat ic f ield" p ic ture is va l id , or i f sp in- latt i ce re laxat ion w i l l skew the results by "magni fy ing" slower re-l ax ing lines, such as i n the A g layer far from the Fe , over faster re lax ing lines, such as i n and near the Fe layer. P r e l i m i n a r y results from / 3 N M R re laxat ion experiments suggest that , while sp in- latt i ce re laxat ion at r o o m temperature is approx imate ly twice as fast i n the A g of these magnet ic sam-ples ( 1 / T i ~ 0 . 6 s~) compared to a s imi lar A g f i lm grown on a nonmagnet ic substrate ( 1 / T i ~ 0 . 3 s~), this re laxat ion is slow enough that this "stat ic field" approx imat ion is va l id . (2.18) A = A0[l - axn(ui)] (2.19) F i g u r e 2.10: B y t a k i n g many values for B , centered around B e x t generates the d i s t r i b u t i o n n ( B ) , whi ch is our model of the / 3 N M R lineshape expected from theoret ical hyperfine field d i s t r ibut i on and s topping d i s t r ibut i on . Chapter 3 Experiment T h e technique of / ? N M R is d ist inct f rom conventional N M R i n that po lar ized radioact ive ions are implanted d irect ly into the sample and used as the probe rather t h a n the host nuclear spins. A radioact ive ion beam ( R I B ) of po lar -ized 8 L i is the N M R probe used i n / 3 N M R experiments at T R I U M F ' s IS A C facil ity. T h e R I B is produced using, what is cal led, the isotope separat ion on -l ine ( I S O L ) technique. T h e I S O L system, comprised of a p r i m a r y p r o d u c t i o n beam, a t a r g e t / i o n source, mass separator, and a separated beam transport and acceleration system, is capable of produc ing very intense ( > 1 0 8 s~) R I B of 8 L i suitable for / ? N M R experiments [42, 43]. 3.1 8Li+ Production I S A C exper imental h a l l , where / 3 N M R experiments are conducted, is housed i n a separate b u i l d i n g from T R I U M F ' s cyc lo tron h a l l . A pro ton beam line ( B L 2 A ) carries the high-energy protons from the cyc lo tron to one of the two target stations housed i n the I S A C bui ld ing . T h i s pro ton beam is what drives the i on product ion i n the I S O L method . B L 2 A is capable of de l iv -ering a 100 iik proton beam extracted from T R I U M F ' s 500 M e V H ~ cy-c lotron. T h e I S O L target is composed of a mater ia l of large a tomic mass such as s i l icon-carbide (S iC) or T a n t a l u m (Ta). M a n y different isotopes are produced through nucleosynthesis when the target is bombarded w i t h h igh energy protons. T y p i c a l l y the h igh energy protons cause fragmentat ion of the nuclei w i t h i n the target. T h e target is heated un i f o rmly to h igh t e m -peratures (~2000 °C) to enhance diffusion to the target 's transfer tube (see F i g 3.1 i n a t ime comparable to the radioact ive l i fet ime of the nuclei created [44, 45]. T h e target temperature is h igh enough to efficiently release the ex-otic nuclei , but not so h igh that the target mater ia l itself is desorbed through evaporation. T h e free radioact ive nuclides are ionized by coming into contact w i t h a heated tungsten extract ion tube. T h e target is he ld at h igh voltage so that the extracted ions leave the target at an energy of 30 k e V , typ ica l ly , I S A C target and Surface Ion Source concept Side view Front view Figure 3.1: F i g u r e of 20 m m diameter target cy l inder and transfere tube. T h e pro ton beam enters from the left i n the front v iew and bombards the target cy l inder . T h e radioact ive ions diffuse out of the heated target m a t e r i a l , then ionized a n d extracted by the transfer tube, ex i t ing to the r ight i n the side view. [49]. and w i t h a very s m a l l energy spread (1-2 e V ) , w h i c h is an i m p o r t a n t feature of the surface i on izat i on sources used at I S A C . H a v i n g an i o n b e a m w i t h a narrow energy d i s t r ibut i on greatly increases the efficiency for t ranspor t i on and generating nuclear po lar izat ion . T h e entire target assembly can be seen i n F i g 3.2 T h e large operat ional and residual rad ia t i on fields produced by pro ton bombardment on the target mater ia l requires that the target stat ions be housed in a shielded target h a l l that is isolated from the exper imenta l ar-eas. A l l h igh ly act ivated and potent ia l ly contaminated components , i n c l u d -ing produc t i on targets, ion sources, and beam d u m p as wel l as the decontam-inat i on and storage fac i l i ty are located i n the target h a l l . I S A C uses remote hand l ing of the target modules to al low quick access to the p r o d u c t i o n t a r -get which have h igh levels of residual ac t iv i ty and cou ld be contamined w i t h F i g u r e 3.2: F i g u r e of I S A C surface ion source. T h e target a n d transfer tube i n F i g 3.1 can be seen i n the center left part of the d i a g r a m , w i t h the system that extracts the ions shown to the right. C o o l i n g lines prevent components from overheating. [49]. S h u t t e r V a l v e F i g u r e 3.3: F i g u r e of removable target module used i n I S A C ' s I S O L m e t h o d for ion product ion . T h e surface ion source, F i g 3.2 is housed i n the b o t t o m most part of the module . T h e module is designed to be hand led remotely, a l lowing targets to be changed w i t h very l i t t le downtime. [48] mobi le act iv i ty . T h e target h a l l was also designed w i t h two target stat ions, a l lowing the pro ton beam to be sent from one target s ta t ion to the other, which greatly reduces the amount of t ime the R I B is off when targets need to be changed or maintenance on the target s tat ion is required. T h e t a r -get module is made of a 2 m long shielding p lug on the b o t t o m of which is mounted the target, i on source and extract ion system, as shown i n F i g 3.2 [47], see F i g 3.3. In order to extract a beam of pure 8 L i from the large number of different isotopes produced at the target, a l l the ions from the ion source must be passed through a mass separator. T h e layout of the mass separator used at I S A C can been seen i n F i g 3.4. T h e mass separator consists of three m a i n sections. T h e first section of the mass separator transports the beam from the target s ta t ion to the mass separator. E lec trostat i c quadrupoles focuse the beam hor izonta l ly at H F 1 and vert i ca l ly i n the center of B l . T h e second section, between H F 1 and H F 2 , serves as a coarse mass separator. T h i s section consists of a 60 degree bending element that accepts beam entering from either the east or west target. T h i s bender is basical ly a region w i t h a constant magnet ic field oriented vert i ca l ly that bends the p a t h of the ions. A n i on mov ing through this region of stat ic transverse magnetic field w i l l experience a Lorentz force perpendicular to b o t h the ions velocity and the magnetic field, result ing i n c i rcular mot i on i n the plane normal to the vert ica l magnet ic field d irect ion . Since the radius of curvature of the ion's c ircular p a t h is p ropor t i ona l the charge /mass rat io , the beam emerging from the bender w i l l have dispersion. If a l l particles of the beam are s ingly ionized, then this dispersion separates the partic les of different mass. Inserting sl its into the beam at th is point allows only the ions w i t h i n a desired range of dispersion through . T h e final section, l y i n g between H F 2 and H F 4 , is a h igh-reso lut ion mass separator. B y passing the beam through 2 pairs of ident i ca l 60 degree bend -ing magnets high-resolut ion separation of masses is achieved. T h e sections between H F 3 and H F 4 and between H F 2 and H F 3 ( F i g 3.4) are identicle ex-cept that they bend the beam i n opposite directions causing the dispersion of each to add . T h e dispersion of this last section is 5.2 c m per percent A M / M , and the t o t a l dispersion of the entire mass separator is 5.8 and 4.6 c m per percent A M / M for the Eas t and West targets, respectively. Here M is the mass of the desired part ic le to be separated. T h i s mass separator is designed to have mass resolution of up to 10,000 (mass resolution is defined as M / A M , where M is that mass of interest) [50]. Such mass resolution is more t h a n is F i g u r e 3.4: F igure of the layout of the mass separator at I S A C . [50] ISAC at TRIUMF F i g u r e 3.5: I S A C exper imenta l h a l l , showing the Target H a l l , and mass spectrometer underground , a n d the m a i n exper imenta l area where the / 3 N M R area is s i tuated . required for separating l ight ions such as 8 L i ( M here would be 8 a tomic mass uni ts (amu) ) , but does become necessary for separation of a specific isomer w i t h much larger atomic weight that are used i n other experiments carr ied out at I S A C . T h e 8 L i beam ex i t ing the mass separator is t ransported into the exper i -menta l h a l l where i t is first po lar ized and then delivered to the / 3 N M R spec-trometer. T h e target h a l l , mass separator and exper imental area at I S A C can be seen i n F i g 3.5. 3.2 Polarizer T h e layout of the polarizer and the / 3 N M R spectrometers are shown i n F i g 3.6. A f t e r passing through the mass separator the nearly monoener-getic (30 keV) R I B of 8 L i + is e lectrostatical ly guided to the / 3 N M R beamline i n the low-energy exper imental area. Before the R I B can be used i n / ? N M R experiments, nuclear po lar i zat ion must be generated i n the "opt i ca l p u m p i n g region" section (see F i g 3.6) of the polarizer. T h e N a neutra l i za t i on and H e re - ionizat ion cells, make up what is called the polar izer , w h i c h is shown i n deta i l i n F i g 3.7. Nuc lear po lar i zat ion i n the 8 L i R I B is achieved by opt i ca l ly p u m p i n g of the t o t a l sp in states ( F = 5 / 2 , 3/2) i n neutra l paramagnet ic 8 L i w i t h a beam of c i r cu lar ly po lar ized laser l ight coll inear w i t h the i on beam. Since the incoming beam is comprised of 8 L i + ions, the first step i n th is process is to neutral ize the beam by passing it through a N a vapour cel l . 8 L i + has a large cross section for charge exchange w i t h N a (>10~ 1 5 c m 2 ) so by passing the beam through this cel l we are able to achieve up to 9 0 % neutra l i za t i on w i t h very l i t t l e change i n the beam emittance of 87r m m m r a d , however neutra l i za t i on under typ i ca l exper imental condit ions is more l ike 50-70%. T h e N a cel l , w h i c h confines the N a vapour , is kept at a temperature of ~ 4 5 0 °C. T h i s is the temperature that maximizes neutra l i zat ion of the beam, see F i g 3.8. U p o n ex i t ing the N a cell the neutra l beam then enters the dri ft region where the neutra l 8 L i is polar ized by opt i ca l p u m p i n g , and remain ing ions are removed by charged plates [51, 52]. T h e neutra l beam travels for 1.7 m through a drift region where 6 He lmho lz coils keep a constant magnetic field of 1 m T col l inear w i t h the beam, which defines the axis of po lar i zat ion . It is i n this region that a tomic exc i ta t ion of the 8 L i by a counter-propagating c i r cu lar ly po lar ized laser beam produces Osaka exp. F i g u r e 3.6: / 3 N M R beamline at I S A C . A n unpolar ized 8 L i b e a m enters on the far left then passes through the polarizer before be ing sent to one of the three exper imental areas: the low or h igh field / 3 N M R spectrometers, or the Osaka Univers i ty experiment. y u M ^ m y monitor P | a i e s restriction Figure 3.7: Po lar i zer section of the / 3 N M R beamline where unpo lar i zed 8 L i + enters from the left and is neutral ized i n the N a vapour cell . O p t i c a l p u m p i n g by the laser achieves nuclear po lar izat ion in the beam w h i c h is then re- ionized i n the He gas re- ionizer before ex i t ing to the r ight . 0 100 200 300 400 500 600 Na reservoir temperature (°C) F i g u r e 3.8: G r a p h of 7 L i + current vs. N a vapour temperature . T h e loss of current i n this figure (~90%) is due entirely to neutra l i za t i on of the stable 7 L i ions. [51] OPTICAL PUMPING SCHEME FOR °U F i g u r e 3.9: D l atomic t rans i t i on of 8 L i that is opt i ca l ly p u m p e d i n the polarizer . A b s o r b t i o n of a c i r cu lar ly polarized photons always adds one uni t of angular m o m e n t u m ( A m ^ = l ) , while re laxat ion results can either a d d or subtract one un i t , or have no change ( A n i F = 0 , ± l ) . M a n y cycles w i l l result i n atoms being i n the h ighly polar ized F = 5 / 2 , m ^ = + 5 / 2 state. nuclear po lar i zat ion . T h e laser is tuned such that i t opt i ca l ly excites the D l atomic t rans i t i on , 2s 2 Si /2—>2p 2 Pi /2 in 8 L i , which occurs at A=671 n m . A schematic of this electronic t rans i t ion is shown i n F i g 3.9. Sp in -orb i t coupl ing between the nucleus and the valence electron i n the neutra l 8 L i a t o m breaks the degeneracy of the t o ta l sp in states, F = 5 / 2 and 3 /2 . T h e h igh po lar i zat ion of the 8 L i beam is achieved by p u m p i n g b o t h of these hyperfine levels by two laser lines separated by 382 M H z , w h i c h cor-responds to the energy difference between the two t o t a l sp in states of the valence electron. E x c i t a t i o n by absorpt ion of a c i r cu lar ly po lar ized pho ton w i t h posit ive hel ic i ty requires A r n p = + 1 so that overall angular m o m e n t u m is conserved (c ircular ly po lar ized photons are i n state S = l , m = l ) . T h e a t o m w i l l decay back to the ground state by spontaneous emission of a photon , obeying the selection rule A r n p = 0 , ± l since the emit ted photon m a y have any allowed spin pro ject ion. T o t a l sp in po lar i za t i on , and therefore nuclear po lar i za t i on , is thus increased as the number of opt i ca l cycles increases. T h e short l i fet ime of the excited electron state (27 ns) compared to the t rans i t t ime (2 ms) means that many opt ica l cycles occur as the neutra l 8 L i drifts through th is region [53]. Therefore, the beam that reaches the H e cell is i n the h igh ly polar ized t o ta l sp in state ( F = 5 / 2 , r n p = + 5 / 2 ) corresponding to the m / = + 2 nuclear sp in state, whi ch is directed opposite to the propagat ion d irect ion of the beam itself. T h e beam can also be po lar ized i n the opposite d irect ion i n exact ly the same manner using laser l ight of the opposite hel ic-ity. T h e beam po lar i za t i on can be switched very qu ick ly between the two helicities by insert ing a quarter wave plate into the laser optics system. T h e laser used for opt i ca l p u m p i n g d u r i n g these experiments was a Spectra -Phys ics 3900S s tanding wave T i : sapphire (T iS ) laser p u m p e d by an 18 W argon ion laser, though this system has since been updated by replac ing the T i S laser w i t h a dye laser. L a s i n g at A=673 n m is accomplished by f i t t ing the laser cav i ty w i t h a rear m i r r o r opt imized for this wavelength and an R = 9 9 % output coupler. T h e cavity length is designed so that l ong i tud ina l cav i ty modes are separated by 382 M H z and a 1 m m thick , R = 1 0 % intra - cav i ty etalon restricts operat ion to just the two modes. T h e resultant output is two laser lines required to p u m p the two electronic states, each w i t h a power of ~ 1 0 0 m W . These two modes have instantaneous l ine w id ths of ~ 1 M H z which are broadened to ± 2 0 M H z on the timescale of 1 s due to acoustic noise, whi ch is s t i l l much narrower t h a n the ~ 1 0 0 M H z absorpt ion b a n d -w i d t h of the incoming beam at 30keV. T h i s absorpt ion b a n d w i d t h is due the energy spread of the neutra l 8 L i beam, typ i ca l ly a few e V as a result of the inherent spread of the ion source (~2 eV) as wel l as coll isions w i t h N a atoms i n the neutra l i zat ion cell [51, 53]. 8 L i atoms that pass through the polarizer at s l ight ly different energies w i l l "see", i n each atom's frame of reference, pho-tons of s l ight ly higher/ ( lower) frequency, and therefore s l ight ly higher (lower) energy due to what is known as the Doppler effect. T h e Dopp ler w i d t h has the form: SE ov = uQ-'V2Em0c2 For 8 L i the resonant frequency is ^ O = 4 . 4 7 x l 0 1 4 H z , a n d for the b e a m at I S A C , w i t h energy E (30 keV) and w i d t h SE (2 e V ) , 5u has a value of about 42 M H z [46]. Not i ce that this w i d t h is proport iona l to E - 1 / 2 , wh i ch , for ther-m a l energies, wou ld be enormous. T h u s , the beam is accelerated to 30 k e V to narrow the Doppler w i d t h , a l lowing efficient opt i ca l po lar i za t i on of the beam to become feasible. T h e power of each laser l ine must be spread over this absorpt ion w i d t h on a ms timescale, this being the t ime scale for 8 L i to pass through opt i ca l p u m p i n g section of the polarizer . Resonant e lectro-opt ical modulators ( E O M ) of 19 M H z and 28 M H z i n series are used to produce laser sidebands spaced at ~ 1 0 M H z intervals, effectively broadening the l i n e w i d t h of the laser . T h i s spacing was found to p u m p the beam the most efficiently, w i t h closer spacing only result ing i n a minor increase i n po lar i za t i on . A t N a temperatures of ~ 4 3 0 °C (high vapour density, and therefore more broaden-ing) , the E O M s gives almost 5 0 % increase i n po lar i za t i on , and near ly 7 0 % at 370 °C[53]. To efficiently polarize the beam using this method it is c ruc ia l that the laser frequency remains extremely stable. E v e n slight changes i n laser fre-quency can result i n t o t a l loss of po lar izat ion . Dr i f t s are prevented by using a feedback system w i t h a 2 G H z free-spectral-range spec t rum analyzer to moni tor and m a i n t a i n the frequency difference between the one of the T i S modes and a single-mode frequency stabi l ized H e - N e laser reference l ine. A n y change i n frequency w i l l automat i ca l ly be corrected by ad just ing the cav i ty length by means of a piezo-mounted rear T i S mirror . Frequency s tab i l i ty is ± 1 0 M H z on average. T h i s feedback system also monitors the number of T i S modes, and any extraneous modes are corrected for by adjustments to the in t ra - cav i ty etalon [51]. A f t e r the laser has been tuned and stabi l ized , fine-tuning of the po lar i za t i on is done by s l ight ly decelerating the beam by a p p l y i n g a bias voltage to the neutra l i zat ion cel l . F i g 3.10 shows /3-decay asymmetry versus N a cell voltage, found by integrated (3 count measure-merits for 10 s at each voltage. T h e three peaks seen are due to scanning 2 hyperfine lines across 2 equally spaced laser modes, w i t h the central peak hav ing the largest asymmetry ampl i tude corresponding to p u m p i n g of b o t h hyperfine levels [51]. T h e final section of the polarizer is a H e gas cel l that re-ionizes the po lar -ized neutra l beam to al low the 8 L i to be steered and focused e lectrostat ical ly onto the sample. Because the ionizat ion cross-section of 8 L i w i t h H e is more t h a n an order of magnitude smaller t h a n for neutra l i zat ion by N a the b e a m emerges w i t h a larger emittance from the He cel l , and means elements down-stream must have a larger acceptance accordingly. F i g 3.11 shows scatter ing effect of the beam for no flow and 3 t imes the flow of He required for o p t i m u m ion izat ion . It can be seen that He flow has very l i t t l e effect on the center of the beam profiles, however the transverse m o m e n t u m profile is s igni f icantly broadened f rom passing through the He cell [52]. A n electrostatic bender placed after the He cell redirects the ionized beam by 45° towards another bender that then directs i t to one of three exper i -menta l areas (the h igh and low field / 3 N M R spectrometers, and the Osaka experiment, see F i g 3.6), while the undeflected neutra l beam passes straight through to a neutra l beam monitor . T h e i on flux that reaches the sample is ~ 1 0 7 s~. 3.3 /3NMR High-Field Spectrometer A f t e r being po lar ized and re- ionized, the beam can be sent to the spectrome-ter where i t is used for / 3 N M R experiments. T h e / 5 N M R spectrometer, shown i n F i g 3.12, is where the ac tua l / 3 N M R experiment takes place. T h e now po-lar ized 8 L i + beam enters from the left, passing through a hole cut out of the back detector before entering the last E i n z e l lens at the entrance of a h igh homogeneity 9 T superconduct ing solenoid. T h e profile of the beam on the sample, or "beam spot " , is extremely sensitive to the beam energy as wel l as the voltage on the E i n z e l lens, and the magnet ic field w i t h i n the solenoid. T h e beam spot is moni tored using a C C D camera and imag ing a piece of s c int i l la t ing plast ic located at the sample pos i t ion . M o r e thorough discussion of beam optics and beam spot w i l l be given later on , but elements are tuned such that the beam spot is 3 -4mm i n diameter at the sample. T h e 8 L i ions are implanted into the sample which is pos i t ioned i n the center of the solenoid. Sample dimensions are t yp i ca l l y 8 m m by 10mm and 0.10 0.05 + 0.00 ¥ - 0 . 0 5 «... -0.10 460 470 480 490 500 510 520 530 Beam deceleration (volts) Figure 3.10: A s y m m e t r y at 380°C for each laser he l i c i ty as a funct ion of the voltage on the N a cell deceleration plates. T h e three peaks are due to scanning two hyperfine lines across two equally spaced laser modes, w i t h the central peak corresponding to pumping b o t h hyperfine levels. T h e dr i f t ing offset is due to the beam shift ing posit ion on foi l . [51] - 5 - 3 - 1 1 3 5 - 5 - 3 - 1 1 3 5 m m m m Figure 3.11: M e a s u r e d emittance from He cell ex t rapo lated back to the center. Shows no H e flow on left, and He flow of 0.029 T o r r l i t r e / s on right . 10 contours are equal ly spaced from 5% to 9 5 % of m a x i m u m phase space density [5 2] HV Isolator & Einzel Lens 9 CO I a. § Figure 3.12: / 3 N M R h i g h field spectrometer. 8 L i ions enter f rom the left, through a hole i n the backward detector, and are i m p l a n t e d into the sample s i tuated at the center of 9 T superconduct ing solenoid. GO l i m i t e d to a thickness of a few m m by the necessity of be ta part ic les , emit ted i n the radioact ive decay of 8 L i , to pass out through the sample and make it to the detector. T h e r m a l contact w i t h a He cold finger cryostat w i t h an operat ional temperature range of 2-500 K allows the temperature control of the sample. Since m a n y of the experiments carr ied out w i t h this spectrometer are at cryogenic temperatures, the sample must be kept i n an u l t r a h igh v a c u u m ( U H V ) environment. Otherwise residual gases wou ld condense and b u i l d up on the sample surface. T h i s would be enough to prevent near ly a l l incident 8 L i from stopping w i t h i n the sample at low energies. A l s o , the beam is not energetic enough to pass through a t h i n window, therefore the entire f inal leg of the beam line must also be U H V compat ib le . Di f ferent ia l p u m p i n g w i t h large cryopumps reduces the pressure of 10~ 7 T o r r upstream of the spectrometer, to the order of 1 0 - 1 0 T o r r i n the m a i n U H V chamber. T h e cryostat is mounted on a large bellows w i t h a smal l motor so that it may be w i t h d r a w n from the magnet bore i n order to change the sample through a load lock located on the top of the m a i n v a c u u m chamber. T h i s obviates the need to vent the entire vacuum chamber to atmospheric pressure d u r i n g sample changes. T h e spectrometer is designed longi tudinal ly , such that the b e a m axis , 8 L i po lar i za t i on , and magnetic fields are a l l coaxial . A transverse field would act to beam the beam away from the sample, whi le the large l o n g i t u d i n a l magnet ic fields, several Tesla, used i n the h igh field spectrometer act to focus the ions on the sample. Incoming ions and outgoing beta partic les are strongly confined along the beam axis by the large magnet ic fields i n the spectrometer when the magnetic solenoid is on. T h e /3-detectors are made of B i c r o n B C 4 1 2 plast ic sc int i l lator and are approx imate ly 0.6 c m thick . T h e front detector ( located beh ind the sample, w i t h respect to the incoming ions) is approx imate ly 4 c m i n diameter and is centered on the b e a m / m a g n e t i c field axis a few c m downstream of the sample. Confinement of the emit ted betas inside the magnet bore means that the backward detector, approx imate ly 20 c m by 14 c m by 0.6 c m thick must be posit ioned further upstream, outside of the solenoid, to ensure that the outgoing betas w i l l be detected whi le s t i l l a l lowing the incoming beam to pass through a 1.8 c m slot cut out of the sc int i l la t ing plastic . E a c h detector and its U V T plast ic l ight guide is held i n stainless steel housing w i t h t h i n stainless steel windows that al low transmiss ion of the h igh energy betas whi le iso lat ing the detectors f rom the U H V chamber which allows t h e m to be easily d u r i n g bake outs. L i g h t guides t ransport the photons, produced when a beta part ic le strikes the s c int i l la t ing plast ic , to the photomult ip l ier tubes. T h e photomult ip l i er tubes convert the l ight from the sc int i l la t ion to an electric pulse that is sent to the electronic counters. In this geometry, the detectors w i l l subtend very different sol id angles i n the absence of magnetic field produced by the solenoid, however their efficiencies are very s imi lar under exper imental condit ions due to the focusing effect of the solenoid. T h e h igh field / 3 N M R spectrometer has the ab i l i t y to vary the i m p l a n -t a t i o n energy of the beam anywhere from 100 e V to 30 k e V , w h i c h i n t u r n , varies the mean stopping depth of 8 L i f rom just a few n m from the sample 's surface to as deep as 200 n m into the bulk . T h i s feature makes / 3 N M R a very useful t oo l for studies of t h i n film nanostructures. E n e r g y of i m p l a n t a -t i o n is adjusted by p lac ing the spectrometer, magnet, cryostat and a l l other electronics on a ground insulated, h igh voltage p la t f o rm w h i c h creates an electrostatic potent ia l step up to 30 k e V that the 8 L i + i on must " c l i m b " before i m p l a n t i n g itself into the sample. In F i g 3.12 everything located to r ight the " H V Isolator" is always at ground potent ia l , whi le everything to the left lies on the h igh voltage p la t f o rm and w i l l be at h igh voltage when the p lat form is biased. T h e b e a m passes through a grounded tube surrounding the last E i n z e l lens and extends into the magnet bore. Decelerat ion of the beam occurs i n the smal l space between this gold p lated E i n z e l lens and the sample. F i g 3.13 shows an electric po tent ia l m a p of the region between the grounded tube (light grey) and the sample at h igh voltage (dark grey), and F i g 3.14 shows the potent ia l step along the beam axis (r=0) i n th is region for an appl ied bias of 30 k V . T h i s allows the energy of imp lanta t i on of the beam to be selected so that the m a j o r i t y of 8 L i + stops at different distances from the magnet ic interface i n these samples, to b u i l d up a profile of the magnetic environment w i t h i n a sample. It has been shown that 8 L i + implanted into fee A g w i l l come to rest i n one of two possible sites, the subst i tut iona l (S) and octahedral (O) sites, see F i g 3.15. A t low temperatures, most of the 8 L i stops i n the O site, but as the sample is warmed to room temperature the 8 L i + ions occupy most ly the S site, as can be seen i n F i g 3.16, showing / 3 N M R spectra taken i n a 500 A A g film grown on S r T i 0 3 [55, 56]. Potent ia l M a p o f the Dece lerat ion R e g i o n S o l e n o i d B o r e Heatshield Bore 50 nun 100 mm Cooled Einzel Sample Position _ l- . . , , c r w - * x Crvostat Aperture Lens (EL3) Magnet Centre ^ Snout Figure 3.13: E l e c t r i c potenia l m a p of the deceleration region of the spec-trometer for p l a t f o r m bias of 30 k V . D a r k grey shows the region t h a t is at 30 k V , while l ight grey shows the region that is at ground (0 kV).[54] T t i g - D ^ ^ ax is ) ' J _ _ _ L I 5Q ; . 100 _ 130':, . ;2Qf : Ajiial 'Distance Z(mm) '250 F igure 3.14: E lec t r i c potenia l step along the beam axis (r=0) i n the decel-erat ion region of the spectrometer when p lat form is biased to 30keV.[54] Figure 3.15: F C C latt ice of A g w i t h three possible sites for 8 L i to stop i n ; subst i tut iona l (S), oc tahedra l (O) , and tetragonal(T).[55] T = 1 5 K 18896 18901) 18904 18908 Frequency (kHz) 18912 F igure 3.16: / 3 N M R spectra taken at temperatures between 15 K a n d room temperature showing the shift f rom 8 L i ions s topping at the oc tahedra l site at low temperatures to the subst i tut ional site at i n a t h i n A g f i lm grown on a M g O substrate. [55] 3.4 Beam optics and Beam Spot Ideally, one would l ike a wel l - co l l imated beam w i t h as smal l a beam spot as possible for / 3 N M R experiments. To achieve this the beam must be focused on the sample by t u n i n g the various focusing elements upstream. It was shown i n F i g 3.11 that emittance of the beam is larger u p o n ex i t ing the H e gas cell . Before reaching the sample it is focused by three E i n z e l lenses and three adjustable co l l imators . These beam opt i ca l elements are located i n the f inal section of the beam line between, the two 45° benders and the spectrometer. A l l beam opt ic devices are electrostatic to ensure that po lar i za t i on d irect ion is preserved whi le the beam is focused. T h e beam spot at the sample pos i t i on is a very sensitive to the E i n z e l lens voltage, magnetic field, and b e a m energy. P o t e n t i a l maps, such the one seen i n F i g 3.13, are used to predict how the beam w i l l travel through the beamline, and to estimate the t u n i n g parameters of the various focussing elements that w i l l give best beam spot on the sample. Steering of the beam through the 8 m m square opening i n the copper heat shield of the cryostat and focussing of the beam on the sample is done by m o n i t o r i n g the beam spot by using a low-noise C C D camera (Starl ight Express , M X 5 1 6 ) to image the l ight emitted when the 8 L i ions enter a 0.25 m m th i ck B i c r o n B C 4 1 2 plast ic sc int i l lator at the sample pos i t ion . F i g 3.17 of a t y p i c a l beam spot image shows fa int ly the 8 m m square window of the cryostat w i t h the beam spot i n the center. T h e camera is mounted outside the U H V chamber and views the s c in t i l -lator near ly on the beam axis v i a a front surface m i r r o r placed upstream that bends the l ight nearly 90° through a view port . T h e low dark current of the C C D allows long exposures to be made, w i t h ~ 1 0 seconds exposure typ i ca l l y being sufficient to image the beam under normal i on flux condit ions. T h e image may be further analyzed to gain more quant i tat ive in format ion on the beam intensity peak shape. However for t u n i n g the beamline d u r i n g an ex-periment , what is of interest is seeing a smal l , focused beam spot centered on the sample. A surface plot of the entire image can be seen i n F i g 3.18. 3.5 8 L i stopping distributions and T R I M Calculations H a v i n g knowledge of the 8 L i + s topping d i s t r ibut i on i n the sample is very impor tant to the understanding of the d a t a collected i n / 3 N M R experiments Figure 3.17: T y p i c a l beamspot image of a 5 k e V 8 L i beam focussed on B i c r o n plast ic sc int i l lator taken w i t h Star l ight Express C C D camera. 8 m m square hole i n the copper heat sheild can be seen, as wel l as the focussed b e a m spot i n the center. [54] F igure 3.18: Surface plot of beamspot image seen i n F i g 3.17. Au Ag Fe GaAs 0 1000 2000 3000 Distance (A) Figure 3.19: Top : N u m b e r of implanted 8 L i + as a funct ion of depth from the surface at 500 e V , 5 k e V , 10 k e V , and 30 k e V i m p l a n t a t i o n energies i n A u ( 4 0 A ) / A g ( 8 0 0 A ) / F e ( 2 0 A ) / G a A s , generated by M o n t e - C a r l o s imulat i on of 100,000 ions using T R I M . S P software. * denotes 10 k e V and 30 k e V d a t a scaled by factor of 10 to show deta i l . B o t t o m : shows distances further t h a n 1000 A for highest i m p l a n t a t i o n energy -ST - \ GaAsv(001) | . / ^Ag (800A) \ > • "c 1 \ /Au (40 A) Fe (20 A) ~> 1 1 I ' I I I 1 1 1 1— 5 10 15 20 25 30 Energy (keV) F i g u r e 3.20: 8 L i d i s t r ibut i on at various energies, by precent i n the layers of A u ( 4 0 A ) / A g ( 8 0 0 A ) / F e ( 2 0 A ) / G a A s , generated by M o n t e - C a r l o s imulat i on of 100,000 ions using T R I M . S P software. on M M L . Since the layers are on the order of just tens of nanometers th i ck and the hyperfine field at each 8 L i + depends on the distance away f rom the magnet ic layer that each ion stops from, knowing the relative number of ions s topping i n each layer, as wel l as the stopping d i s t r i b u t i o n profile w i t h i n the layers is essential i n order to analyze the d a t a once its collected. Stop-p ing d is tr ibut ions are generated using the M o n t e - C a r l o s imulat i on software T R I M . S P . T h i s software, developed by W . Ecks te in at the M a x P l a n c k Inst i -tut fur P l a s m a p h y s i k i n Garching,[58] simulates the i m p l a n t a t i n of a suitable large number of particles, usual ly on the order of 10 5 . T h e sample is defined beforehand by entering the thickness, elemental compos i t ion , and molar den-sity for each layer. T h e d a t a that is generated f rom these s imulat ions is then exported to s tandard graphing software, such as O r i g i n , where s topping pro -file as a funct ion of depth can be p lot ted , and the profile i n the layers fit to a Gauss ian d i s t r ibut i on (see F i g 3.19). T R I M . S P d a t a output also allows one to p lot the percentage of 8 L i + that stops i n each layer as a funct ion of i m p l a n t a t i o n energy ( F i g 3.20). In our / 3 N M R experiments we want to implant at energies such that we are measuring the s ignal from the A g layer, so knowing the percentage of 8 L i + s topping i n each layer at a part i cu lar energy is required. K n o w i n g the amount of 8 L i + s topping i n different layers for given i m p l a n t a t i o n energy allows us to determine the energies that w i l l result i n the m a x i m u m number of ions, and therefore m a x i m u m signal , i n the layer of interest, w h i c h is A g i n our case. T h i s in format ion also tells us what signals to expect, as wel l as the relative intensities. T h i s is extremely impor tant when ana lyz ing the exper imental d a t a which may contain / 3 N M R signals from several different layers of our sample. A pecu l iar i ty that shows up i n these calculations is the d iscont inui ty i n the s topping d i s t r ibut i on at the A g / F e interface. T h e density of Fe (p=7.87 g / c m 3 ) is lower t h a n that of A g (p=10 .5g / cm 3 ) , so in tu i t i ve ly one would expect a higher stopping power i n the A g t h a n i n the Fe, however the spike that is observed i n F i g 3.19 suggests otherwise. T h i s d i spar i ty m a y be re-solved by examin ing the electronic structure of Fe compared to A g . T h e conduct ion electron densities i n these metals are very different. In uni ts of n u m b e r ( x l O 2 2 ) / c m 3 the conduct ion electron densities are 17.0 for Fe and 5.86 for A g [59]. A t the relat ively low i m p l a n t a t i o n energies we use the i n c i -dent 8 L i + ions lose energy p r i m a r i l y through ion izat ion of the loosely b o u n d host atoms ' electrons, since the 8 L i + is not energetic enough to excite core electrons. T h i s effect was confirmed by r u n n i n g T R I M s imulat ions w i t h the Fe layer replaced by B e and Cs . B e has a very low density (p=1.85 g / c m 3 ) but an extremely large valence electron density, ( 2 4 . 7 x l 0 2 2 / c m 3 ) , whi le the C s has a very s imi lar density (p=1.87 g / c m 3 ) but a much smaller valence electron density ( 0 . 9 1 x l 0 2 2 / c m 3 ) . T h e T R I M s imulat ions showed that a large number of 8 L i stopped i n the B e layer, whi le the C s h a r d l y stopped any at a l l . T h i s suggests that the observed d iscont inuity i n the s topping d i s t r ibut i on at the A g / F e interface is a result of the difference i n the valence electron density of the two materials . Once the stopping profiles, n (x ) , for various i m p l a n t a t i o n energies are generated they can be used w i t h the assumed hyperfine field d i s t r i b u t i o n i n A g , B ( x ) , to generate the d i s t r ibut i on of fields, n ( B ) . T h i s is essentially the measurement that is made i n a resonance l ineshape / 3 N M R experiment. 3.6 Fitting Procedure W i t h the s topping d is tr ibut ions calculated w i t h T R I M . S P , and the theoret-ica l internal magnetic field d i s t r ibut i on , it is possible to generate the mode l / 3 N M R lineshape for a part i cu lar i m p l a n t a t i o n energy. T h i s l ineshape is used i n the fitting rout ine bui l t into O r i g i n 7.5 graphing software and fit to d a t a collected i n / 3 N M R experiments. O r i g i n fits d a t a using a regression method based on the Levenberg -Marquardt ( L M ) a lgor i thm w h i c h is the most wide ly used a lgor i thm i n nonl inear least squares fitting [60]. It is possible to fit sev-eral spectra at the same t ime , and share parameters of the magnet ic field d is tr ibut ions . T h i s means we can take several spectra taken at different i m -p lanta t i on energies, hav ing different 8 L i s topping d is tr ibut ions , and fit t h e m to the same magnetic d i s t r ibut i on . T h i s f i t t ing rout ine gives the parameters for the induced hyperfine field d i s t r ibut i on that brings the mode l and the exper imental spectra into best agreement. 3.7 Sample Preparation F e / A g heterostructures studied i n these experiments were prepared using molecular beam ep i t ix ia l ( M B E ) at Bre t Heinr i ch ' s surface physics labo -ratory located at S i m o n Frasier Univers i ty . A sample is prepared by first loading a G a A s (001) single crysta l into an U H V chamber and c leaning the surface by He ion sputter ing before thermal ly anneal ing the clean surface to form large, flat terraces, suitable for prepar ing F e / A g mult i layers . T h e substrate is then moved into the M B E growth chamber where Fe and A g layers are al ternately grown on the substrate by deposi t ing mater ia l by ther-m a l evaporat ion of a heated elemental source sample. O p e n i n g a shutter that separates the furnace from the growth chamber exposes the substrate to the evaporated atoms emerging rad ia l ly f rom the source and condensing on the substrate surface. T h e f inal step is to grow a t h i n 10 M L A u capping layer that suppresses ox idat ion of the surface. F i l m thickness is moni tored d u r i n g growth by counting peaks i n reflected high energy electron di f fract ion ( R H E E D ) osci l lations as wel l as using a quartz crysta l moni tor , ca l ibrated to take into account of the different subtended sol id angle of the sample a n d quartz monitor . G r o w t h rates were approx imate ly 1-2 M L per minute . T h e strength of this technique is the constant low energy of the deposited atoms, compared w i t h other techniques, a l lowing the ep i tax ia l growth of extremely wel l ordered, crystal l ine samples w i t h sharp interfaces[61]. In order to produce films w i t h sharp interfaces i t is necessary to have close match ing of in -p lane latt ice parameters between the substrate and the epi -t a x i a l layer[62]. GaAs (OOl ) is a suitable substrate due to the smal l m i s m a t c h (-1.4%) between the latt ice spacing of base-centered cubic (bcc) Fe (a.F e = 2.87 A ) and face-centered cubic (fee) G a A s (acaAs= 5.65 A ) , remember ing that i n G a A s has a 2 a tom basis. It is impor tant that the Fe layer is grown first on the G a A s substrate for several reasons. T h e latt i ce larger m i s m a t c h (2.2%) between G a A s and A g (a^ s =4.09 A ) leads to a larger s t ra in t h a n i n the case of Fe. It has also been found that A g grows ep i tax ia l ly i n two orientations (001) and ( O i l ) on (001)GaAs[64]. G a A s ( O O l ) has two different surfaces, either a l l G a or A s atoms, and for an unreconstructed surface, each surface a t o m has two unsatisfied bonds oriented along the [110] d irect ion for G a surface atoms or [110] direct ion for A s surface atoms, see F i g 3.21 [63]. T h e As - s tab i l i zed surface leads to (011) A g or ientat ion , while G a - s t a b i l i z e d surface gives rise to (001) or ientat ion of Ag[64]. Roughness i n real samples means that there w i l l w i l l be domains of G a and A s surfaces, w h i c h wou ld lead to domains of different or ientat ion for A g grown on G a A s , leading to low qua l i ty f i lms, whi le Fe always follows the (001) or ientat ion for b o t h G a and A s terminated surfaces. T h i s , along w i t h the close match ing of latt ice spacing allows the growth of bbc Fe into very ordered layers[63]. A g grown on the Fe(001) surface has (001) or ientat ion and fee s tructure , w i t h latt ice rotated by 7r/2[65]. T h e A g or ientat ion on the Fe i n our samples was conf irmed w i t h x -ray di f fract ion experiments, whi ch can be seen i n F i g 3.22 for the A u ( 4 0 A ) / A g ( 8 0 0 A ) / F e ( 2 0 A ) / G a A s sample. It can be seen that a l l the major peaks for A g were paral le l to the (001) plane, thus conf i rming (001) or ien-t a t i o n of A g . T h e "satel l i te" peaks that can be seen on either side of the Ag(002) peak can be accounted for by considering the the finite thickness effect of the A g layer[66]. S i m i l a r peaks for the smaller Ag(004) peak cannot be d ist inguished f rom the noise. Since there are on ly 14 monolayers ( M L ) of Fe, compared w i t h 400 M L of A g i n the sample, and just 20 M L of A u on the surface, the s ignal peaks from the Fe and A u are very diff icult to pick out from the noise, so i t isn ' t possible to make any conclusive arguments about the s tructure of these layers from the x - ray di f fract ion, however their (001) or ientat ion was confirmed by R H E E D measurements d u r i n g growth. G a O O Q ) As( tOO) o . o . o o o Ok o o O O ° o ° O D ° P 0 JP o a ^ o o o o o F i g u r e 3.21: Schematic d iagram showing how the unsatisfied surface b o n d orbi ta ls are dist inguished i n unreconstructed GaAs (OOl ) for Ga(OOl) and As(OOl) t erminated surfaces. Roughness i n real samples w i l l have domains of G a and A s , m a k i n g growth of wel l ordered A g fi lms d irec t ly on G a A s difficult [63]. n • 1 • 1 1 r~ 40 60 80 100 2-Theta (degrees) Figure 3.22: X R D spectrum of A u ( 4 0 A ) / A g ( 8 0 0 A ) / F e ( 2 0 A ) / G a A s show-ing peaks from planes paral le l to (001) i n b o t h A g and G a A s , conf irming their (001) or ientat ion. Chapter 4 Results T h e s topping d i s t r ibut i on of 8 L i is a cruc ia l part of the procedure to extract the spat ia l dependence of the hyperfine fields i n the A g spacer layer i n a magnetic mult i layer . It is therefore necessary to verify that the results of the T R I M . S P s imulat ions for i m p l a n t a t i o n m a t c h the / 3 N M R d a t a collected at various i m p l a n t a t i o n energies. In this section we w i l l review the results obta ined from T R I M . S P calculations and how they are used i n the analysis . T h e n results of f i t t ing the model l ineshape to / 3 N M R spectra w i l l be pre-sented, along w i t h the parameters for the spat ia l dependence of the induced hyperfine fields i n the A g layer. 4.1 T R I M . S P results In order to verify that the i m p l a n t a t i o n s imulat ions produced us ing the T R I M . S P software are accurate we compare the predicted s topping d i s t r i b u -tions for various energies of ion i m p l a n t a t i o n w i t h the / 3 N M R spectra taken i n two different M M L samples, A u ( 4 0 A ) / A g ( 8 0 0 A ) / F e ( 2 0 A ) / G a A s , and A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s . Based on knowledge gained i n pre-vious experiments to characterize the / 3 N M R resonances of 8 L i i n the various layers, A u [55], A g [56], and G a A s [67] we determine the relative number of 8 L i that stop i n each layer from the relative ampl i tude of each layers' char-acteristic peak, and compare this to the d i s t r ibut i on that results f rom the T R I M s imulat i on at the same energy. A t r o o m temperature the implanted 8 L i stops p r i m a r i l y at a subst i t i ona l site i n b o t h A u and A g result ing i n very narrow / 3 N M R resonances that have intr ins ic l inewidths on the order of just a few hundred H z . These resonant lines are also shifted by a smal l characterist ic amount as a result of the electronic environment w i t h i n the sample. T h i s is cal led the K n i g h t shift and is a result of the smal l po lar i zat ion i n conduct ion electrons at the F e r m i surface of metals due to the presence of the external magnet ic field. T h e hyperfine interact ion between the po lar ized electrons and the 8 L i gives rise to T h e K n i g h t shifts i n A u and A g . Measured relative to insulator M g O resonance, these shifts are +60(20) and +120(12) p p m respectively[55]. T h e / 3 N M R resonance that is measured i n the semiconductor substrate G a A s , has no K n i g h t shift , but is considerably broader (3-4 k H z ) t h a n either A u or A g due to the n a t u r a l abundance of sizable nuclear moments of 6 9 G a , 7 1 G a , and 7 5 A s isotopes [67]. T h e large internal hyperfine fields experienced by the 8 L i s topping i n the Fe layer implies that the resonance i n Fe is wel l outside the frequency range used i n these experiments. Furthermore , any 8 L i that stops i n Fe at r oom temperature shows a very fast spin- latt ice re laxat i on rate relative to the 8 L i hal f life due to scattering of magnetic exc i tat ions i n the Fe. T h i s w i l l have the effect of reducing the off resonance asymmetry . F i g 4.1 shows the / 3 N M R spectra taken i n the A u ( 4 0 A ) / A g ( 8 0 0 A ) / F e ( 2 0 A ) / G a A s sample at four energies of i m p l a n t a t i o n between 500 e V a n d 30 k e V . T h e spectra, which have been normal ized to the off resonance ampl i tude , A o , were carr ied out at r o o m temperature (~285 K ) i n a l o n g i t u d i n a l field of H 0 ~ 4 . 1 T . T h e stopping profiles, calculated w i t h T R I M . S P at these same four energies can be seen i n F i g 4.2. F i g 4.3 shows the percentage of imp lanted 8 L i that stops i n a par t i cu lar layer as a funct ion of energy for this sample. T h e m a i n resonant peak of the first spectrum, F i g 4.1(a), is most p r o m i -nent i n on ly the spec trum taken at the lowest energy of i m p l a n t a t i o n , E = 5 0 0 e V . T h i s peak is shifted by ~ + 8 0 p p m relative to the G a A s , which is i n good agreement w i t h the K n i g h t shift measured previously for A u , and is therefore a t t r i b u t e d to most of the 8 L i stopping i n the 40 A A u capping layer. T h i s is supported by the T R I M . S P results that show nearly a l l of the 8 L i s topp ing i n this layer at this energy, F igs 4.2(a) and 4.3. T h i s resonant peak, a t t r i b u t e d to A u , diminishes r a p i d l y for i m p l a n t a t i o n energies above 500 e V , also pre-d ic ted by the T R I M . S P results. A l s o a second l ine, w i t h larger frequency shift t h a n the A u , increases at these energies, F i g 4.1(b). T h i s peak is shifted by ~ 1 2 0 p p m relative to the G a A s , i n very good agreement w i t h the K n i g h t shift measured i n A g . T h i s narrow line has a w i d t h that is comparable to the A g line observed i n A g films grown on nonmagnet ic substrates, w h i c h would indicate that most of the 8 L i is stopping i n the A g close to the A u / A g interface farthest f rom the Fe layer where the hyperfine coupl ing to the m a g -netic Fe is negl igibly smal l . However this l ine does appear to have a broad base result ing f rom the hyperfine fields experienced by the smal l amount of 8 L i that stops close to the A g / F e interface. T h i s s i tuat ion is supported by the T R I M . S P stopping profile for i m p l a n t a t i o n energy of 5 k e V , F i g 4.2(b), which shows that 8 L i is predominant ly located i n the A g layer close to the \ f (a) 500 eV 25820 25830 25840 25850 25860 Frequency (kHz) Figure 4.1: j3 spectra taken at room temperature i n a l o n g i t u d i n a l field of H 0 ~ 4 . 1 T i n A u ( 4 0 A ) / A g ( 8 0 0 A ) / F e ( 2 0 A ) / G a A s at (a) 500 ev, (b) 5 k e V , (c) 10 k e V , and (d) 30 k e V i m p l a n t a t i o n energy. T h e error bars i n the spectra are s tat i s t i ca l , but the noise i n the spectra is systematic . Figure 4.2: T R I M . S P calculated stopping d is t r ibut ions i n A u ( 4 0 A ) / A g ( 8 0 0 A ) / F e ( 2 0 A ) / G a A s at energies (a) 500 e V , (b) 5 k e V , (c) 10 k e V , a n d (d) 30 k e V . To - \ GaAs (001) g . . / x A g ( 8 0 0 A ) \ ^ - Q I • CD • H- | \ / A u ( 4 0 A ) Fe (20 A) i i i • i • i • i 10 15 20 25 30 Energy (keV) Figure 4.3: T R I M . S P calculated stopping d is tr ibut ions i n each layer as a funct ion of energy for A u ( 4 0 A ) / A g ( 8 0 0 A ) / F e ( 2 0 A ) / G a A s . A u (400 A f rom the Fe layer). A s the i m p l a n t a t i o n energy is increased, the 8 L i ions stop deeper into the sample and therefore closer to the F e / A g interface. A t 10 k e V , F i g 4.1(c) shows the A u l ine now completely gone, and the A g line has been s igni f icantly broadened at frequencies on b o t h the h igh and low frequency sides, suggesting the presence of large posit ive and negative hyperfine fields i n this region. T h e peak also shows asymmetry which could be the result of an emerging G a A s peak at lower frequencies. A g a i n , T R I M . S P profiles ca lculated at E = 1 0 k e V i m p l a n t a t i o n , F i g 4.2(c), supports this interpretat ion . It can be seen that most of the 8 L i stops i n the region w i t h i n 400 A of the F e / A g interface, as wel l as a smal l amount ending up i n the G a A s substrate. A t fu l l i m p l a n t a t i o n energy, E = 3 0 k e V , a broad peak is observed that we at t r ibute to the G a A s substrate, F i g 4.1(d) since the T R I M . S P calculat ions for fu l l i m p l a n t a t i o n energy shows that the m a j o r i t y of the 8 L i stops i n the G a A s substrate, F i g 4.2, w i t h some s t i l l s topping i n the A g close to the Fe, w h i c h would account for the asymmetry i n this l ine, w i t h more weight on the h igh frequency side of the spectrum. A second sample (Au(40 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s ) was also com-pared to T R I M . S P calculated d istr ibut ions . Exper iments on this sample were also conducted at r oom temperature (~285 K ) , but the l o n g i t u d i n a l field was H 0 = 4 . 5 T , w h i c h is why the resonances are at a higher frequencies i n F i g 4.4 compared to F i g 4.1. These spectra have not been normal i zed by Ao for reasons that w i l l be explained later. T h e T R I M . S P calculated d is tr ibut ions i n this sample are shown i n F igs 4.5 and 4.6. T h e / 3 N M R spectra taken at 2.5 and 5.5 k e V (see F i g 4.4) b o t h show a broadened A g l ine, w i t h the 2.5 k e V line being slight asymmetr i c due a smal l A u l ine at lower frequency. T h e T R I M . S P calculated profiles, see F i g 4.5 of this this energy range show that the 8 L i is p r i m a r i l y s topp ing i n the 200 A A g layer at these two energies, closer to the A u / A g interface at 2.5 k e V , and the A g / F e interface at 5.5 k e V as expected. It can be seen i n F i g 4.6 that i n this sample, w i t h a much thicker Fe layer t h a n the previous sample, that quite a bit of 8 L i stops i n the Fe layer at 5.5 k e V , compared w i t h 2.5 k e V . However this has l i t t l e effect on the shape of the spectrum. W h i l e the spectra i n F i g 4.1 were normal ized by the off resonance asymmetry , the spectra i n F i g 4.4 were not normal ized to show the loss i n off resonance asymmetry , Ao- One can see how Ao is reduced at 5.5 k e V from the fast re laxat ion of 8 L i s topping i n and near the Fe layer. A t the ful l i m p l a n t a t i o n energy of 29.5 0.16-0.12-0.08-0.04 (a) 2.5 keV (b) 5.5 keV (c) 9.5 keV f (d ) 29.5 keV 28280 28320 28360 28400 Frequency (kHz) Figure 4.4: / 3 N M R spectrum taken at room temperature i n magnet ic field H 0 ~ 4 . 5 T i n A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s at i m p l a n t a t i o n energies (a) 2.5 k e V , (b) 5.5 k e V , (c) 9.5 k e V , and (d) 29.5 k e V . T h e error bars i n the spectra are s tat i s t i ca l , but the noise i n the spectra is systematic . D i s t a n c e ( A ) F i g u r e 4.5: T R I M . S P calculated stopping d is t r ibut ions i n A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s for implantat i on energies (a) 2.5 k e V , (b) 5.5 k e V , (c) 9.5 k e V , and (d) 29.5 keV . Inset: shows further range into substrate for highest i m p l a n t a t i o n energies. 80 J 60 A Au (40 A) Ag (200 A) Fe(140 A) GaAs 1 40 J 20 J 0 10 15 20 25 30 Energy [keV] F i g u r e 4.6: T R I M . S P calculations of percentance of imp lanted L i s topping i n each layer as funct ion of energy i n A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s . k e V we see a very narrow G a A s that comes from 8 L i s topping deep w i t h i n the substrate, inset F i g 4.4. A t imp lanta t i on energies around 9.5 k e V , the / 3 N M R spec t rum has an intermediate appearance between the spectra of 5.5 and 29.5 k e V . It can be seen, F i g 4.6, that i m p l a n t a t i o n energies close to 10 k e V results i n nearly equal d i s t r ibut i on between the A g , Fe, a n d G a A s layers. Since we get no s ignal f rom Fe, we would expect that the s ignal wou ld be almost equal parts G a A s substrate and A g . A s was shown i n C h a p t e r 2, i n many cases the resonance lines can be described by a Lorentz ian shape: A(u) = A 0 - ARF{0) (u0 - to)2 + A 2 where AQ is the off resonance asymmetry and A is the hal f w i d t h at hal f the m a x i m u m ampl i tude , and UJQ is the resonance frequency. A l t h o u g h the Lorentz ian fits do not provide details about the decay of i n -duced hyperfine magnet ism away from the magnet i c /nonmagnet i c interface, i t does provide an easy way to follow general trends i n the data . T h e w i d t h of the L o r e n t z i a n gives us an idea of the average induced hyperfine fields i n the A g layer. It makes sense that larger d is tr ibut ions of induced magnet ism w i l l give rise to broader d is tr ibut ions . T h e area of the L o r e n t z i a n gives us a measure of the t o t a l s ignal strength, so i f we real ly are los ing s ignal f rom fast re laxat ion of 8 L i stopping i n Fe we should see a m i n i m u m i n the s ignal strength at the m a x i m u m i m p l a n t a t i o n i n Fe. F i g 4.7 shows the area under the Lorentz ian fits to the resonance l ine w h i c h shows a m i n i m u m i n the s ignal for i m p l a n t a t i o n energies around 5 k e V . T R I M . S P calculat ions predicts the m a x i m u m amount of 8 L i s topp ing the the Fe layer at s l ight ly higher i m p l a n t a t i o n energy of ~ 7 . 5 k e V , F i g 4.6. T h i s could be interpreted as the T R I M . S P g iv ing s l ight ly shallower i m p l a n t a t i o n at a par t i cu lar energy t h a n is observed. It has been observed i n previous studies that the T R I M . S P calculations predict s l ight ly deeper i m p l a n t a t i o n for 8 L i at s imi lar energies t h a n is observed[68]. It is also l ike ly that 8 L i s topping i n the A g very close to the A g / F e interface also relaxes faster t h a n i n A g away from the interface. T h i s would also lead to a s l ight ly lower value for the i m p l a n t a t i o n energy of the m i n i m u m i n signal strength. These results qua l i ta t ive ly conf irm that the M o n t e - C a r l o T R I M . S P soft-ware accurately calculates the 8 L i s topping d i s t r i b u t i o n i n this sample. It is therefore reasonable to use the results of these calculat ions as the stop-p ing profile of 8 L i i n the A g layer i n the model ing of our / 3 N M R lineshape 0.06-£ 0.04 c 03 2 0.02 < 0.00 0 ~r 5 10 15 Implantation Energy (keV) Figure 4.7: T h e area under the Lorentz ian fits of / 3 N M R resonances l ines, showing a m i n i m u m at i m p l a n t a t i o n energy of ~ 5 k e V , resul t ing f rom fast 8 L i re laxat ion i n the presence of large hyperfine fields i n and close to the magnet ic Fe layer. as discussed i n C h a p t e r 2. It also indicates the presence of large posit ive and negative hyperfine fields induced i n the A g close to the Fe, but f rom the spectra taken i n the 800 A th ick A g sample, these induced fields become negligible at distances greater t h a n approx imate ly 400 A away f rom the Fe. In this region, far from the magnetic layer, the spectra appear to have very s imi lar w idths to spectra taken i n A g t h i n films grown on a non-magnet ic substrate at r o o m temperature , F i g 3.16. In order to use the fitting procedure described i n chapter 3 to extract the parameters of the hyperfine coupl ing i n the A g layer, we need spectra that have been taken w i t h i m p l a n t a t i o n energies such that a l l , or most of the s ignal comes f rom 8 L i stopping i n the A g close to the Fe layer. U n f o r t u n a t e l y at higher i m p l a n t a t i o n energies the 8 L i range straggl ing is largest. T h i s presents a prob lem i n the A u ( 4 0 A ) / A g ( 8 0 0 A ) / F e ( 2 0 A ) / G a A s sample, where at energies sufficiently h igh to stop an appreciable amount of 8 L i i n the region close the the A g / F e interface, a significant amount of 8 L i stops i n the G a A s substrate. T h i s distorts the s ignal and makes f i t t ing to our model diff icult. T h e A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s sample is more promis ing . Since the Fe layer is much thicker and the A g is th inner most of the observed s ignal comes from the A g close to the interface. Implantat i on energies of 2.5 and 3.0 k e V were determined to be the best spectra, since s ignal f rom the A u layer become significant at i m p l a n t a t i o n energies lower that 2.5 k e V , and the G a A s substrate has already become significant at i m p l a n t a t i o n energy of 5 k e V . T h e stopping d istr ibut ions calculated for these energies w i t h T R I M . S P were fit i n just the A g layer to a Gauss ian d i s t r ibut i on , to determine the center and w i d t h of the stopping profile. T h e results of th is fit can be seen i n F i g 4.8, and the values obtained are given i n Table 4.1. U s i n g these values for the stopping d i s t r ibut i on , the two spectra were fit together to the funct ion we derived i n C h a p t e r 2: A = A0(l - an(u>)) where n(tu) is based on the Gauss ian stopping d i s t r ibut i on and the d i s t r i b u -t i o n of magnetic fields: i + (x/\Fy Bmin(x) - Bext i + ^ ° x ^ a w i t h the free parameters u0 (which is related to Bo by 7) and a be ing shared, whi le uext (which is related by 7 to B e x t ) , a, and Ao were independent for each energy. T h e result of the best fit can be seen i n F i g 4.9. Energy (keV) Center (A ) W i d t h ( A ) 2.5 160 168 3.0 145 190 Table 4.1: Gauss ian fit parameters of T R I M . S P s topping profiles at 2.5 and 3.0 k e V i m p l a n t a t i o n energy i n the A g layer of A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s sample. Energy a (shared) VQ (kHz) (shared) a ( x l 0 - 5 ) A 0 i>ext (kHz) 2.5 k e V 1.84 ± . 0 5 1942 ± 266 (3 ± 0.4) 0.1236 ±0.0001 28358 ± 1 8 3.0 k e V 1.84 ± . 0 5 1942 ± 266 (2 ± 0 . 3 ) 0.1277 ±0 .0001 28363 ± 2 2 Table 4.2: Free parameters values obtained from f i t t ing the theoret ical l ine-shape to resonant lines measured i n A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s at i m p l a n t a t i o n energies 2.5 and 3.0 k e V , room temperature , and Ho ~ 4 . 5 T . D i v i d i n g u0 by 7=6301 k H z / T gives the result B 0 = 0 . 3 8 ±0 .04 T for the hyperfine coupl ing of 8 L i at the F e / A g interface. T h i s is fortui tous ly close the calculated value of 0.300 T [40] for the induced hyperfine field at the first A g layer from the F e / A g interface. T h e decay constant, a=1 .84 ±0 .05 , agrees reasonably well w i t h the theoret ical value of 2, however is much larger t h a n the values a = 0 . 4 ( l ) and 0.8(1) measured i n Fe(40 A ) / A g ( 3 0 0 0 A ) (001) and Fe(40 A ) / A g ( 2 0 0 A ) / F e ( 4 0 A) (001) samples, respectively, us ing the c o m p l i -mentary technique of L o w Energy M u o n S p i n Resonance ( L E - / x S R ) [19, 69]. T h e spectra i n F i g 4.9 show a sharp peak that is missed by the f i t t ing funct ion , which shows a "flat t o p " . T h e flat top of the f i t t ing funct ion i n -dicates that the induced hyperfine fields have not completely decayed away i n the A g furthest from the Fe, which is 200A i n this case. T h e sharp peak that is missed is most l ikely due to the smal l amount of L i that stops i n the A u cap at these energies, as seen i n the F igs 4.2 &; 4.3. 0 100 200 300 400 500 Depth [A] Figure 4.8: G a u s s i a n fit (dotted line) to T R I M . S P ca lcu lated d is t r ibut ions (solid line) i n the A g layer of A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s for 2.5 k e V and 3.0 k e V i m p l a n t a t i o n energies CO 0.128 0.126-0.124-_ d 0.122-1 CO ^ 0.120-"S 0.118-E E 0.116-1 co < 0.114-1 28300 28325 28350 28375 28400 28425 Frequency (kHz) F i g u r e 4.9: F i t of the theoret ical l ineshape (solid line) to / 3 N M R spectra (points) taken at room temperature and H 0 ~ 4 . 5 T i n A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s for 2.5 k e V and 3.0 k e V implantat i on energies CD CO c 1— B c Distance (A) F i g u r e 4.10: F o r m of the induced hyperfine fields i n the A g layer as deter-m i n e d from the fitting procedure. Inset shows expanded distance to show deta in far f rom the F e / A g interface. T h i s f orm for the induced hyperfme fields can be seen i n F i g 4.10. It shows that the induced fields are fa ir ly large near the F e / A g interface, but the inset shows that the induced magnet ism is very smal l at distances of ~ 4 0 0 A , as was observed i n the A u ( 4 0 A ) / A g ( 8 0 0 A ) / F e ( 2 0 A ) / G a A s sample. Chapter 5 Conclusion T h e results of the experiments on two F e / A g heterostructures, A u ( 4 0 A ) / Ag(800 A ) / F e ( 2 0 A ) / G a A s and A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s , show that / 3 N M R is wel l suited to s tudy ing the induced interna l magnet i sm i n M M L structures. W e have shown that by contro l l ing the i m p l a n t a t i o n energy of the radioact ive 8 L i + N M R probes, i t is possible to profile the in terna l magnet ic environment of t h i n f i lm samples from w i t h i n 40 A f rom the sample surface to depths of 2000 A , w h i c h is wel l into the sample bulk . W e have demonstrated that / 3 N M R is capable of measuring the internal magnet ic environment of these magnet i c /nonmagnet i c t h i n films, and w i l l be a very useful t oo l as i n -dustry begins to manufacture devices on nanoscopic scales, and p a r t i c u l a r l y w i t h the sp in properties of charge carriers becoming ut i l i zed i n spintronic devices. W e have introduced a mode l / 3 N M R lineshape based on the theories of induced hyperfine coupl ing into a nonmagnetic layer adjacent to magnet ic layer. These theories were developed by extending the R K K Y theory de-scr ib ing the sp in po lar i zat ion i n the host metal ' s conduct ion electrons i n the region of a magnetic i m p u r i t y atom. W e ant ic ipated that the coherent osc i l la -t ions of the electronic po lar i za t i on i n the nonmagnet ic layer should be w iped out over the latera l distances of a few m m determined by the beam spot of the 8 L i beam due to roughness at the interface. T h e result of this is that we don ' t measure the sharp features characterist ic of coherent osci l lations, and that the hyperfine magnet ism is instead "smeared o u t " . T h e mode l l ineshape was found to fit very wel l to / 3 N M R resonances measured by i m p l a n t i n g 8 L i into the A g layer of of a A u ( 4 0 A ) / A g ( 2 0 0 A ) / F e ( 1 4 0 A ) / G a A s sample at energies 2.5 and 3.0 k e V , which confirmed our predic t ion for the f o rm of the induced hyperfine fields, and yielded values for the hyperfine d i s t r ibut i on . T h e fits show that the value of the m a x i m u m hyperfine fields at the A g / F e interface is B 0 = 0 . 3 8 ±0 .04 T , and that the induced magnet i sm decays away from the interface fol lowing the power law (x /Ai?)^- 8 4 " 1 " 0 - 0 5 ) . T h e hyperfine d i s t r ibut i on that was extracted from the fits was shown i n F i g 4.10. T h e hyperfine field at the interface agrees wel l w i t h theoret ical predict ions [40], as wel l as exper imental values for the hyperfine coupl ing of L i i n Fe [41]. Some ways to improve the method of measuring the induced magnet i sm were discovered d u r i n g the course of these experiments. It can be seen f rom the T R I M . S P calculated stopping d is tr ibut ions that as the energy of i m -p lanta t i on is increased, the w i d t h of the d i s t r ibut i on also increases. In the samples examined i n these experiments, the A g / F e interface, w h i c h is the region of interest, was 240 A and 840 A f rom the sample surface. T h e i m -p lanta t i on energy required to implant 8 L i i n this region results i n a s topping d i s t r ibut i on that is very wide. T h i s wide d i s t r ibut i on makes i t diff icult to ob ta in a c lean s ignal from just A g close to the F e / A g interface since much of the 8 L i is being stopped i n other layers such as the G a A s substrate, to get around this prob lem we to have several samples of vary ing A g thicknesses of 5 0 A , lOOA, and 150A, but ident ica l Fe and A u layers between samples. T h i s would al low us to implant at low energies (~1 keV) i n a l l samples, w h i c h would result i n a very narrow stopping d i s t r ibut i on but s t i l l a l low depth pro -filing of the induced hyperfine magnet ism. T h i s w i l l have the advantage of sampl ing very narrow slices of the induced magnet ism i n only the A g layer at various distances away from the F e / A g interface, whi ch we expect w i l l al low better character izat ion of the spat ia l depedence of the induced magnet ism. 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