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Proton magnetic resonance in paramagnetic and antiferromagnetic single crystals of CoCl₂.6H₂O Sawatzky, Erich 1960

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PROTON MAGNETIC RESONANCE IN PARAMAGNETIC AND ANTIFERROMAGNETIC SINGLE CRYSTALS OF CoCl 2« 6H20 by E r i c h Sawatzky B.Sc, University of B r i t i s h Columbia, 1958. A thesis submitted i n p a r t i a l f u l f i l m e n t of the requirements f o r the degree of Master of Science i n the Department of Physics We accept t h i s thesis as conforming to the required standard The University of B r i t i s h Columbia, A p r i l , 1960 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head o f my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department o f VfiLfSICS The U n i v e r s i t y of B r i t i s h Columbia, Vancouver Canada. Date /3 #/>r/l; #60. i i Abstract Standard radio-frequency nuclear resonance spectroscopy techniques have been applied to study the f i n e structure of the proton magnetic resonance absorption l i n e i n single c r y s t a l s of CoC^'SI^O. Cobaltous Chloride i s a paramagnetic c r y s t a l at high temperatures and becomes antiferromagnetic at about 2.29°K. The pos i t i o n and number of "lines strongly depend on temperature and on the d i r e c t i o n of the externally applied magnetic f i e l d . Fewer l i n e s than the t h e o r e t i c a l number of twenty-four were always observed. At room temperature the proton resonance at 12 Mc/sec. i n a f i e l d of 2.82 K gauss consists of a single l i n e about si x gauss wide. A s p l i t t i n g of t h i s l i n e into a maximum of si x components has been observed at l i q u i d helium temperature. The maximum o v e r a l l separation at 4.2°K i s about 110 gauss. For each d i r e c t i o n of the externally applied magnetic f i e l d the separation between the l i n e s increases with decreasing temperature. The t r a n s i t i o n temperature i s measured and e f f e c t s due to short-range order above the t r a n s i t i o n are observed. Theoretical formulae f o r the positions of the component Tines are developed by considering the two-proton spin system within a water molecule of hydration immersed i n the — > homogeneous external f i e l d H and the inhomogeneous txme-i i i averaged f ie ld of the cobalt ions* Measurements in the antiferromagnetic state have been partially completed. i v Table of Contents Page Abstract i i L i s t of I l l u s t r a t i o n s v Acknowledgements v i i Chapter 1 - Introduction 1 Chapter 2 - Theory Underlying The Experiment 7 Chapter 3 - Apparatus And Experimental Procedure 13 Chapter 4 - Results A. - The CoCl 2»6H 20 Cr y s t a l 18 B. - Discussion Of Experimental Observations 20 i . Introduction 20 i i . Measurements In The Paramagnetic State 22 (a) H Q In The Plane J- a-axis 22 (b) H Q In a-c Plane 25 i i i . T r a n s i t i o n Temperature Measurements 35 i v . Measurements In The Antiferromagnetic State 37 Bibliography 39 V L i s t of I l l u s t r a t i o n s to follow Page Fi g . 1 Level of O s c i l l a t i o n at Frequency (0 o 2 F i g . 2 A General Line and i t s Derivative 3 F i g . 3 Block Diagram of the Apparatus 13 F i g . 4 Photographs of Apparatus 13 F i g . 5 Arrangement of C r y s t a l Mount 14 F i g . 6 Photograph of Three-Dimensional Cr y s t a l Model 19 F i g . 7 Proton Spectrum at 78°K 20 F i g . 8 Proton Spectrum at 4.2°K 20 F i g . 9 Relationship between Recorded Spectrum and i t s Integrated Line Shape 21 F i g . 10 Rotation at 78°K with Tf 0 i n plane Perpendicular to the a-axis 22 F i g . 11 Rotation at 78°K with H Q i n a-c Plane 25 F i g . 12 Rotation at 4.2°K with If 0 i n a-c Plane 25 F i g . 13 F i e l d Pattern of a Dipole 25 F i g . 14 Theoretical Line 27 F i g . 15 F i e l d Dependence of S p l i t t i n g at 78°K with H"q i n the Plane Perpendicular to the a-axis 27 F i g . 16 F i e l d Dependence of S p l i t t i n g at 78°K with H" i n the a-c Plane 27 o F i g . 17 Proton Spectrum at 2.5°K 35 F i g . 18 Transition Temperature 35 v i to follow Page F i g . 19 Proton Spectrum at 2.25°K 36 F i g . 20 Proton Spectrum at 2.21°K 36 F i g . 21 Proton Spectrum at 1.52°K 37 F i g . 22 Rotation at 1.52°K with H i n a-c Plane 37 v i i Acknowledgements The work described i n t h i s thesis has been supported i n part by research grants to Dr. M. Bloom and Dr. G.M. Volkoff from the National Research Council of Canada and through the award of a National Research Council Student-ship (1959-60). To Dr. M. Bloom, who suggested and supervised t h i s research, I wish to express my sincere appreciation for his constant i n t e r e s t , many illu m i n a t i n g discussions, and for his invaluable help i n int e r p r e t i n g the r e s u l t s . I also wish to express my appreciation to Dr. G.M. Volkoff for c r i t i c a l l y reading the manuscript of t h i s t h e s i s . My thanks are also due to Mr. W. Morrison, who constructed the magnet support. Chapter 1 Introduction The nuclear magnetic resonance technique provides a powerful method of studying the interactions between atomic nuclei and t h e i r magnetic environment both at high and low temper-atures. The work described i n t h i s thesis represents a preliminary survey of the proton magnetic resonance i n single c r y s t a l s of CoClg'SHgO i n the paramagnetic and a n t i - f e r r o -magnetic phases of t h i s substance. Results obtained here s h a l l serve as a guide for more det a i l e d investigations of hydrated cobaltous chloride planned f o r the near future. Chapter 2 of t h i s thesis i s a summary of the theory underlying the experimental work to be described and Chapter 3 i s a description of the experimental apparatus. Chapter 4 i s a report of the experimental observations on single c r y s t a l s of CoClg'BHgO i n external magnetic f i e l d s up to 3200 gauss and at temperatures down to 1.52°K. The experimental data so obtained y i e l d information on both the c r y s t a l structure and the el e c t r o n i c wave functions of the atoms comprising the c r y s t a l , and bring out some of the d i f f i c u l t i e s encountered i n paramagnetic c r y s t a l s with a r e l a t i v e l y large number of water molecules of hydration. In general, i f a sample containing non-interacting n u c l e i with spin I 0 and magnetic moment "j~T i s placed i n a uniform magnetic f i e l d H Q, the nu c l e i can each assume a maximum - 2 -number of 21 + 1 orientations with respect to H q. In t h i s work only the resonance spectrum of the protons i n the water molecules of hydration i s studied. Since the spin of a proton i s I = \ y only two orientations are possible, giving r i s e to two d i f f e r e n t energy l e v e l s separated by 2p,pHQ. Transitions between these energy l e v e l s may be induced by an externally applied r - f f i e l d at r i g h t angles to H Q and of angular frequency (jjQ = 2u. H / h . The c o i l around the sample i s part of the resonant c i r c u i t of an o s c i l l a t i n g detector. This c o i l produces the desired r - f f i e l d H^, and i n ab-sorption experiments i t usually also serves as the pick-up c o i l . Resonance may be observed by monitoring the l e v e l of o s c i l l a t i o n of the r - f o s c i l l a t o r as i t s frequency i s varied. A dip i n the l e v e l of o s c i l l a t i o n r e s u l t s when tr a n s i t i o n s are induced between the nuclear Zeeman l e v e l s , since then energy i s absorbed from the r - f f i e l d . As described l a t e r , t h i s resonance absorption, though peaked at the c l a s s i c a l Larmor frequency (n) Q = u.H0/In, occurs over a range of frequen-cies as indicated schematically i n figu r e 1. It i s often convenient, for signal-to-noise consider-ations, to modulate the magnetic f i e l d p e r i o d i c a l l y while sweeping the o s c i l l a t o r frequency through the resonance, and to use the method of phase s e n s i t i v e detection i n recording the r - f l e v e l of o s c i l l a t i o n . With a modulation amplitude smaller than the l i n e width the derivative of the resonance ^ 60 Fig. I. D ip in l e v e l of osc i l la t ion as the f r e q u e n c y of the oscil lator passes fhrough the Larmor frequency 6Jo . fo follow page 2. -3-l i n e i s observed as indicated schematically i n figure 2. The simple picture of non-interacting n u c l e i outlined above i s never s t r i c t l y true. Interactions with the sur-rounding magnetic moments are always present, although i n l i q u i d s and gases these interactions are averaged consider-ably, the l i n e widths usually being determined by inhomo-geneities i n the externally applied magnetic f i e l d . In the case of s o l i d s the picture changes considerably. We s h a l l consider only c r y s t a l l i n e s o l i d s . Here a l l n u c l e i , except for t h e i r thermal vibrations, are situated i n f i x e d positions and each nucleus experiences i n addition to the externally applied f i e l d s H Q and a l o c a l magnetic f i e l d due to the neighbouring magnetic dipoles. If the c r y s t a l contains paramagnetic ions, t h i s l o c a l f i e l d may be of the order of J H ^ Q c a j |c=- 1000 gauss; the l o c a l f i e l d due to other n u c l e i i s usually not larger than about 20 gauss. Since the n u c l e i and paramagnetic ions are each oriented i n 21 + 1 and 2S + 1 d i f f e r e n t ways respectively, the f i e l d produced by the surroundings at the s i t e s of d i f f e r e n t n u c l e i i n a unit c e l l may vary between about + ( H 2 0 c a j { and - j H ^ o c a i | . In the ease of non-paramagnetic single c r y s t a l s with only one type of nuclear magnetic moment present (those of the waters of c r y s t a l l i z a t i o n ) Pake* showed t h e o r e t i c a l l y and observed experimentally that the proton resonance l i n e i s s p l i t into two components by the dipole-dipole i n t e r a c t i o n between the proton-pair i n the water molecule. The separation of the l i n e s i n any given observation (a) Ahf Modulation ampli tude Fig. Z. F ie ld m o d u l a t i o n A H smaller t h a n line w i d t h (a) , derivat ive of l ine (b) . t o fo l low page3 - 4 -also depends on the orient a t i o n of the c r y s t a l with respect —»> to the external f i e l d H Q. If the sample i s a paramagnetic c r y s t a l , w e ^ i n addition to the interactions between the nuclear dipoles and the external f i e l d s and between the protons themselves, the interactions between the protons and the e l e c t r o n i c magnetic moments of the paramagnetic ions. This i n t e r a c t i o n gives r i s e to additional decomposition of the proton resonance l i n e . Such f i n e structures of the proton magnetic resonance l i n e were treated t h e o r e t i c a l l y 2 and observed experimentally by N. Bloembergen i n CuSO^'SHgO and by N.J. P o u l i s 3 ' 4 i n CuCl 2«2H 20. When observing the proton resonance i n paramagnetic c r y s t a l s we would expect a very broad l i n e because of the large magnetic interactions between the protons and the para-5 magnetic ions. But i t can be shown that i f exchange forces between the magnetic ions are present, t h i s broadening action of the magnetic ions may be considerably reduced. In the case of CoCl 2*6H 20 such exchange interactions are present and at room temperatures we observe a single l i n e about s i x gauss wide. As a f i r s t approximation the temperature dependence of the resonance spectrum may be obtained from the Curie law, which states that at high temperatures the mean magnetization of a magnetic ion i n a f i e l d I?0 at temperature T i s given by <H> - M.2HQ/3kT where the average i s over time. This mean magnetization gives -5-r i s e to a time-average l o c a l f i e l d which depends strongly on the space coordinates i n the c r y s t a l and on the orientation of the magnetic moments. The energy le v e l s of the proton magnetic moments are determined by the vector sum of t h i s l o c a l f i e l d with H q. However, i n paramagnetic resonance work, the l o c a l f i e l d i s usually much smaller than H Q, and we con-sider only the component i n the d i r e c t i o n of H Q of the l o c a l f i e l d . Thus a d i f f e r e n t t o t a l magnetic f i e l d i s produced at the d i f f e r e n t s i t e s i n a unit c e l l , and the d i f f e r e n t protons i n the unit c e l l have d i f f e r e n t Larmor frequencies. Assuming that H Q i s constant over the sample, the l o c a l f i e l d w i l l be the same for corresponding protons i n d i f f e r e n t unit c e l l s . Since the l o c a l f i e l d increases with decreasing temperature, the resonance l i n e s p l i t s into a number of component l i n e s as the temperature i s lowered. Therefore, the number of com-ponents observed depends on temperature, on the number of water molecules i n the unit c e l l and on the degree of symmetry possessed by the c r y s t a l . The i n t e r n a l f i e l d at a proton due to a magnetic ion a distance r away i s of order of magnitude (p.)/r . Since the r-dependence i s an inverse cube, only the near neighbours w i l l have any profound influence on the s p l i t t i n g and the shape of the l i n e s . Taking r = 2 x 10~ 8 cm and H Q = 3000 gauss, the s p l i t t i n g at 300°K i s about 1 gauss, at 78°K about 4 gauss, and at 4°K about 70 gauss. We therefore do not expect any res o l u t i o n of the resonance l i n e at room temperature. -6-Theory predicts that CoCl2*6H20 has a possible maximum number of 24 component lines each of which should be several gauss wide, so that we cannot expect a complete resolution in a f ie ld of 3000 gauss even at liquid helium temperatures. The maximum number of 24 lines was never observed. At 4.2°K only six lines were found. In order to calculate the positions of the lines as a function of crystal parameters, temperature, and the external f ie ld H Q , degenerate perturbation theory is applied to the Hamiltonian describing the system. To simplify matters, some approximations are made, since some of the terms in the Hamiltonian are much smaller than others. These calculations are summarized in Chapter 2. Chapter 2 Theory This part of the thesis consists of a summary of the theory of steady state nuclear resonance spectroscopy as applied to paramagnetic c r y s t a l s . Although none of i t represents o r i g i n a l work by the author, nevertheless, i t s i n c l u s i o n i s required to interpret the experimental work presented i n Chapter.4. We consider a paramagnetic c r y s t a l with one or more water molecules of hydration whose c r y s t a l structure i s at least p a r t i a l l y known. From X-ray investigations for instance, the oxygen positions can be determined, but not the proton positions. Both the proton magnetic moments with spin I = |- and the e l e c t r o n i c magnetic moments of the paramagnetic ions with spin S produce l o c a l magnetic f i e l d s throughout the c r y s t a l . The magnitude and d i r e c t i o n of t h i s l o c a l f i e l d at any given point depend on the orientation and separation of the moments at any given time, since both moments precess about the external magnetic f i e l d H Q. Thus we have a system of protons immersed i n the homogeneous external f i e l d H Q and the r a p i d l y varying inhomogeneous f i e l d produced by the paramagnetic ions. The en t i r e Hamiltonian describing t h i s system may be written i n the form ( 1 ) H = - I p k . g k . H Q + H s g + H e K S + H S I + H n - Z Y . h I.-"HQ -8-The quantities g k and |3 represent the g-factor of cobalt written as a tensor and the nuclear Bohr magneton respectively. The f i rs t term in H represents the Zeeman energy of the paramagnetic ions in the external f ie ld H Q , Hgs the magnetic interaction g between the paramagnetic ions themselves, H e x the exchange interaction between them; Hgj is the magnetic interaction be-tween the paramagnetic ions and the proton moments, H J J the magnetic interaction between the protons themselves, and ^ I-JHQ represents the magnetic interaction between the proton moments and the external f ie ld H Q . The proton magnetic moment is denoted by y f i f , where I is the spin operator and y the gyromagnetic ratio. This notation is customary in nuclear magnetic resonance work and keeps the nuclear and electron spins clearly separated. The term in equation (1) connecting the two spin systems is Hgj and may be written (2) « 3 I - ^ jr jfi l j - l lk _ SYitKfj'r^Xprk'rjk) ± k I r i k 3 r i k 5 where ptfc is the magnetic moment of the kth magnetic ion and Tjjj. is the radius vector connecting the i*h proton and the kth i o n a n ( j r ^ » |*"ik| • B u * Mlc varies rapidly in time due to the exchange coupling between the magnetic ions represented g by H e x . The exchange interaction causes a pair of antiparallel spins to f l i p simultaneously, i . e . if two spins are oriented as Tt|r and one reverses direction, the other also f l ips due to the exchange coupling. The exchange frequency is approxi-- 9 -mately given by h ^ e x = kT N, where T N i s the Neel temperature. For CoCl 2'6H 20, — 2°K, so t h a t \ > e x - 5 x 1 0 1 0 cycles/sec. The Larmor frequency for protons i n a f i e l d of 3000 gauss i s 12.8 Mc/sec. so that the protons cannot follow the rapid variations of the l o c a l f i e l d due to the cobalt ions. Thus the protons see only the time-average f i e l d of the cobalt ions. We therefore can use the time average ^ p t ^ of ji^. i n equation g (2). We s h a l l also neglect the term Hgg compared with H e x , since the exchange energy between a pair of cobalt ions i s about 100 times greater than th e i r magnetic energy. The time-average magnetization (pT^ of the kth cobalt ion can now be calculated i n p r i n c i p l e from the reduced Hamiltonian for the 7 cobalt system by the diagonal sum method described by Van Vleck . The e f f e c t of the time-average magnetization p.k on the proton resonance i s obtained from the Hamiltonian for the proton spin system, with T k^ replaced by i n H g I. Written out i n f u l l , the proton Hamiltonian becomes; (3) H = -^<y.nl. .lL +S-W.n x'x i o xk) rx T:<?k>_ 3 d i ^ i k ) ^ k > , i ? i k ) rxk 3 r i k 5 Since the dipole-dipole i n t e r a c t i o n i s proportional to j - , r i J the most important terms i n the proton-proton i n t e r -action are those representing the coupling between nearest -10-neighbours. Therefore, only interactions between the proton pair i n the same water molecule are considered. The i n t e r -actions with other protons and the time dependent part of the f i e l d due to the cobalt ions contribute only to the l i n e widths of the component l i n e s . We now have a two-proton system im-mersed i n the homogeneous f i e l d H Q and the s t a t i c inhomogeneous f i e l d of the cobalt ions. To f i n d the p o s i t i o n of the resonance l i n e s , equation (3) must be solved for i t s eigenvalues which give the energy l e v e l s of the system. Using t h i s Hamiltonian, 2 N. Bloembergen obtains f o r the energy l e v e l s to f i r s t order: —yn H Q + a + d -d + Vb 2 + d 2~ -d - fb2 + d 2 +yh H Q - a + d ^ y f i (H* + H 2) h* 0 £ - H 2) -I/4 Y 2fc 2 (1 - 3 c o s 2 0 1 2 ) r ^ | ^<M*k> ( 1 - 3 c o s 2 ° i k > r T k \ ( i = 1 ' 2 ) k / i and Et and EZ are the z-components of the f i e l d produced by the cobald ions at protons 1 and 2 re s p e c t i v e l y when 1 i s chosen p a r a l l e l to H 0. a and b are functions of temperature by v i r t u e 1 2 of H£ and H^ which are calculated from H$i with p.y, replaced by (4) where (5) *1 E2 E 3 E4 a b d "4 -11 • The energy levels of (4) give rise to four transition frequencies as follows: (6) h x = yhH0 - a + 2d + ^b 2 + d 2 h 2 = yhH0 - a - 2d - ]f ^ + cf* h 3 = Y h H 0 - a + 2d - J /V +J l h 4 = Y h H 0 - a - 2d + j/bx with corresponding intensities (b-d- tyb2 + d 2) I, = I 9 - - — 5 — ^ i r r , ,,• and 1 2 b 2 + d 2 - b/b*+cf (7) (b-d + /b ir+ci z- > 2 I s 1 4 b2+d2+b f ¥ W We thus have a maximum of four lines for each proton pair in every water molecule in the unit c e l l . The maximum number of proton lines in CoClg'SB^O should therefore be 4 x 6 (number of H2O molecules per formula) -f- 2 (because of reflection symmetry of the unit cell) x 2 (number of formula units per unit ce l l ) , which gives 24 lines. In this chapter we have followed the usual description of magnetic fields at nuclear positions in paramagnetic crystals and neglected the contribution to average magnetic f ie ld due to the average magnetization M per unit volume. If contributions of this sort are important as we later see that they are, the external f ie ld HQ which appears in this -12-chapter should everywhere be replaced by B* = HQ + (4TJ—N) I f , where N, the demagnetization factor for the crystal being 8 studied, must be calculated from the geometry of the crystal • If the crystal is not an ellipsoid, M w i l l be a function of position in the crystal and this non-uniformity wil l be equivalent to an inhomogeneity in the applied f ie ld in that i t wi l l also contribute to the nuclear resonance line width. -13-Chapter 3 Apparatus and Experimental Procedure. A standard steady state nuclear resonance spectrometer was used f o r the work reported i n t h i s t h e s i s . A block diagram of the apparatus i s shown i n figu r e 3, and photographs i n figu r e 4. The o s c i l l a t i n g detector used was a s l i g h t l y modified 9 version of a c i r c u i t of Watkins and Pound . The o r i g i n a l c i r c u i t i s described i n d e t a i l i n reference 9, and the modifications by H.H. Waterman 1 0 and s h a l l not be dealt with here. The narrow band amplifier and phase s e n s i t i v e detector were b u i l t and f u l l y described by H.H. Waterman 1 0. The remainder of the apparatus i s standard equipment and s h a l l not be described, except for i t s use i n t h i s work. The large magnetic f i e l d H^ , was supplied by an air-cooled iron-core electromagnet manufactured by Newport instruments Co., which has four inch diameter plane pole t i p s with adjustable air-gap. The cryostat was of such dimensions that the air-gap could not be less than 3.2 cm. With t h i s air-gap and a f i e l d of 3000 gauss the homogeneity was measured to be about 0.3 gauss per cm. The magnet i s mounted on a r o t a t i n g table provided with a c i r c u l a r brass scale graduated i n degrees and with a vernier arranged to measure the magnet orient a t i o n to one tenth of a degree. The whole support was constructed i n such a way that the magnet can conveniently be rotated through 360 degrees Freq. Meter iKl Radio Received Motor Sample Oscill. D etector Narro w Band Amplifier Broad Band Amplifier Oscill. De l Modulation Coils Scope Field Modulqt ion El ec t ro -M agnet Phase < Sen sitive c Detector Phase Shi f ter Williamson Ampl i f ie r M agnet Power ^ Recording ^Milliameter A u d i o Oscillator V a c u u m Pump Fig.3. BLOCK DIAGRAM OF APPARATUS. Figure 4 Photographs of Apparatus to follow page 13 14-without i n t e r f e r i n g with the r e s t of the apparatus* Cylinders about 1.5 cm long and 0.8 cm i n diameter were cut from f a i r l y large c r y s t a l s , which were of the same type described by P. G r o t h 1 1 . During t h i s operation great care was taken to make one of the c r y s t a l axes p a r a l l e l to the axis of the cylinder. The preparation of the c r y s t a l s proved to be a d i f f i c u l t task, mainly because CoClg'SI^O c r y s t a l s have a low melting point (86°C) and are quite b r i t t l e . Two such cylinders were cut, one with the a-axis and the other with the b-axis p a r a l l e l to the cylinder axis. In each case the c r y s t a l was attached to the end of a German s i l v e r tube 1 cm i n diameter and 80 cm long. The cylinders were mounted i n such a way that t h e i r axes were p a r a l l e l to the axis of the German s i l v e r tube. The r - f c o i l was wound d i r e c t l y on the c r y s t a l to give as high a f i l l i n g factor as possible. The number of turns i n the c o i l was chosen to give the r - f o s c i l l a t o r a frequency range of about 7.5 Mc/sec. (7 Mc/sec. - 14.5 Mc/sec.). When aligned, the c r y s t a l with c o i l and the end of the German s i l v e r tube were imbedded i n " P l a s t i c Wood" and then coated with glue to insure a permanent mount (see f i g . 5). During the mounting the d i r e c t i o n of the axis perpendicular to the cylinder axis (hence to one of the c r y s t a l axes) was marked on the brass piece at the top end of the German s i l v e r tube, so that the orientation of the c r y s t a l i s known with respect to the sup-—^ porting frame, and hence the magnetic f i e l d H Q. The angular Brass holder f f t f ing into dewar cap. der man silver t u b e . Co-ax connector Koi/ar seal O-r ing Luci te spacer Central lead Inner dew/ar Crysta l with coil "Plastic Wood" Fig. 5 . A r r a n g e m e n t of c r ys ta l m o u n t , to fol low page M--15-orient a t i o n of the c r y s t a l cylinder i n the plane of r o t a t i o n of the magnet i s not very c r i t i c a l , but the d i r e c t i o n of the cylinder axis should be as nearly perpendicular to H Q as possible. A deviation of t h i s axis from the i d e a l p o s i t i o n may introduce spurious l i n e s i n the resonance spectrum. It was estimated that the cylinder axis was v e r t i c a l to within about two degrees. The cryostat was a common double dewar system. The sup-porting frame of the dewar cap was provided with set screws so that the German s i l v e r tube could be adjusted to be v e r t i c a l and hence the cylinder axis (a- or b-axis of the c r y s t a l ) was always perpendicular to the f i e l d H Q (the d i r e c t i o n of H Q i s adjusted to be hor i z o n t a l ) . Thus and H*-^  are always perpen-dicul a r to each other. Temperatures lower than the b o i l i n g point of helium are obtained by pumping on the helium vapour. The lowest temper-ature obtained was about 1.52°K. The inner dewar has a capacity of about two l i t e r s and without pumping kept l i q u i d helium for approximately twelve hours. The temperature i s controlled by regulating the pumping speed and i t i s measured by observing the vapour pressure with a meniscus type eathetometer. A pair of c o i l s are mounted on the magnet pole pieces and are supplied from a Williamson type power amplifier. The sweep frequency i s provided by an a u d i o - o s c i l l a t o r which feeds into a phase s h i f t i n g network. To t h i s network are also connected the horizontal sweep of the oscilloscope and the reference -16-voltage input of the phase s e n s i t i v e detector, so that any phase r e l a t i o n s h i p between the three units i s possible. The oscilloscope i s used mainly for adjustment purposes but may be used for actual measurements i f only the frequency of the resonance l i n e s i s sought. When so used, the modulation amplitude i s a c t u a l l y larger than the l i n e width. To observe the derivative of the true l i n e shape with a recording m i l l i -ameter the modulation amplitude should be less than about 1/4 the l i n e width. Observations at such low modulation amplitudes are made with the aid of a narrow band amplifier and the phase se n s i t i v e detector. To decrease the noise generated i n the o s c i l l a t o r a f a i r l y long time constant i s inserted between phase s e n s i t i v e detector and recorder reducing the noise band pass. This, however, requires that the time of sweeping through a s i g n a l be at least several times the time constant. In t h i s way i t i s possible to run through a l i n e spectrum continuously and record l i n e s separated by many gauss on the same chart. To obtain the frequency at which resonance occurs, frequency markers are made on the chart at regular i n t e r v a l s by mixing the r a d i a t i o n from the o s c i l l a t o r with that of a B22-CA frequency meter and an ordinary radio receiver. The radio receiver and frequency meter are f i r s t set to zero-beat at the desired frequency. As the o s c i l l a t o r frequency passes through t h i s zero-beat, one terminal of the recorder i s momentarily grounded causing the needle suddenly to swing to one side. -17-The f ie ld HQ is determined by placing a water sample as close to the crystal as possible and measuring its resonance frequency with the aid of a second oscillating detector and the oscilloscope. The f ie ld is obtained from 00 0 = yB.0f where y is well: known for protons in water. The magnet current was regulated with a highly stable Varian magnet current power supply, which kept the f ie ld constant throughout an entire helium run. -18-Chapter 4 Results A. The CoCl 2«6H 20 C r y s t a l . Large c r y s t a l s (3 x 1.5 x 1 cm) were grown from a saturated aqueous solution of CoClg'SHgO by slowly evaporating i t at room temperature. CoC^'SI^O i s of the monoclinic prismatic type. P. G r o t h 1 2 gives for a : b : c = 1.4788 : 1 : 0.9452 with = 122°19*. Perfect cleavage occurs along the c | 0 0 l j face. X-ray studies of the single c r y s t a l were ca r r i e d out by J. Miguno 12 et a l . . These authors report two formula units per unit c e l l with space group determined as c | h - C2/m. The atomic positions are given i n the following table: Kind of Atom Co CI 0 T °II A photograph of a three-dimensional model of the c r y s t a l structure i s shown i n figur e 6. According to the authors of reference 12, the two C l ~ ions and four water molecules are arranged octahedrally about the C o + + ions to form the group GoC^^HgO,, and the other two Position X y z o r i g i n 0 0 0 4 ( i ) .278 0 .175 8(j) .0288 + .221 .255 4(j) .275 0 .700 -19-waters of the formula unit are located at somewhat greater distances from the cobalt ions. These s h a l l be termed " r e l a t i v e l y f r e e " waters. Hydrogen bonds of the type Oj ••• H - OJJ - H ••• Oj and Oj ••• H ••• CI seem to form the group linkages i n the plane p a r a l l e l to (001), which would lead to the perfect cleavage along (001) as reported by P. G r o t h 1 1 . Figure 6. Photograph of three-dimensional model of crystal-structure of CoCl 2»6H 20. White: C o + + ions Small Black: Cl~ ions Large Black: H20 molecules. to follow page 19 -20-B. Discussions of Experimental Observations,  i . Introduction. A complete analysis of the magnetic behaviour of CoC^'SI^O i s beyond the scope of t h i s t h e s i s . The work reported here i s a preliminary survey of the proton resonance i n CoClg'SHgO at various temperatures. It i s hoped that the r e s u l t s obtained w i l l serve as a guide for more det a i l e d investigations planned for the near future. These s h a l l be a continuation and ex-tension of the work reported here. The experimental r e s u l t s f a l l into three groups: (a) measurements i n the paramagnetic state, (b) observation of the phase t r a n s i t i o n , and (c) p a r t i a l l y completed measure-ments i n the antiferromagnetic state. In making the measurements the c r y s t a l was kept f i x e d while the orientation of H 0 was changed by r o t a t i n g the magnet. In one set of measurements H Q was oriented i n the a-c plane of the c r y s t a l , while i n another set i t was i n the plane perpen-di c u l a r to the a-axis. In the subsequent discussion zero angle s h a l l r e f e r to H Q perpendicular to the a-axis for the a-c r o t a t i o n and to l f 0 p a r a l l e l to the a-c plane f o r the ro t a t i o n i n the plane perpendicular to the a-axis. A recording of the spectrum at 78°K with H Q i n the a-c plane and at 160° i s shown i n figu r e 7. The corresponding spectrum at 4.2°K i s shown i n figure 8. Similar recordings Fig.7. Proton r e s o n a n c e spect rum in C o C I 2 - 6 H 2 0 a t T = 7 8 ° K . H o = 3 0 2 0 gauss . Ho at 160° and ro ta t ing in a - c plane. Freq. m a r k e d in 2 0 K c / s e c . steps. to follow page 20 Fig.8. Same da ta as in f ig .8. T=4.2°K. Freq.in 4 0 K c / s e c steps. to follow page 2.0 -21-were obtained i n each case for angular orientations between 0 and 180 degrees at 10 degree i n t e r v a l s . The r e s u l t s of the measurements of the angular dependence of the resonance l i n e positions are shown i n figures 10, 11, and 12. These corre-spond to rotations with H Q i n the plane perpendicular to the a-axis at 78°K, and to rotations with H Q i n the a-c plane at 78°K and 4.2°K respectively. The positions of the l i n e s are given i n the frequency scale. Each c r y s t a l p o s i t i o n i n these figures corresponds to a chart of the types i n figures 7 and 8. The positions of the proton l i n e s correspond to maxima i n the absorption spectra and hence to zeros i n t h e i r derivatives. Since most of the l i n e s overlap the absorption curve w i l l also contain minima, but only the 1st, 3rd, 5th, etc., zeros i n the derivative curves represent proton l i n e s (see fi g u r e 9). Due to t h i s overlapping of neighbouring l i n e s the observed maxima are s l i g h t l y s h i f t e d from th e i r true pos i t i o n s . No corrections have been made f o r such s h i f t s . Each point i n the graphs of figures 10, 11, and 12 corresponds to such a proton l i n e . In each of these figures the s o l i d v e r t i c a l l i n e represents the frequency of the protons i n water (from which H Q i s calculated) and s h a l l subsequently be termed the "free proton" resonance frequency. r e c o r d i n g mil l iameter. Ho in a-c plane at 160° . T * 4 . 2 ° K. ^ a ) (b) Spectrum of (a) redrawn on rectangular scale sec Resonance lines co r respond to "zeros" in derivative (c) Graph (b) integrated Fi<j. 9. Derivative of resonance line and actual line obtained by integrating (b) graphically . to follow page 21 -22-i i . Measurements i n the Paramagnetic State. The proton magnetic resonance spectrum was studied i n single c r y s t a l s of CoClg'SHgO i n a f i e l d H Q of about 3100 gauss. The maximum number of 24 l i n e s predicted by theory was never observed. In the paramagnetic region two complete rotations were made at 78° K, one with H Q i n the plane perpen-di c u l a r to the a-axis, the other with H Q i n the a-c plane. At 4.2°K one complete r o t a t i o n was made with I?0 i n the a-c plane. The c r y s t a l remained f i x e d i n space at a l l times, while the magnet was rotated about i t i n 10 degree i n t e r v a l s . From each of these graphs we can see d i r e c t l y that the spectra repeat themselves aft e r a 180-degree ro t a t i o n of H Q . Several checks were made at angles between 180 and 360 degrees, and these confirmed the 180-degree symmetry; consistent with paramagnetic measurements. This r e p e t i t i o n of the resonance spectrum a f t e r a 180-degree r o t a t i o n i s due to the 180-degree p e r i o d i c i t y of (3cos 2©-l). (a) H Q i n the Plane Perpendicular to the a-axis. Figure 10 represents the only r o t a t i o n with H Q i n the plane perpendicular to the a-axis. A maximum number of three l i n e s was observed, and they a l l overlapped strongly. It i s thus impossible to follow any i n d i v i d u a l l i n e through the whole ro t a t i o n . Figure 10 exhibits a general symmetry about the b-axis. This indicates that the protons are situated symmetri-2 0 0 180 160 140 CO 0> tu o> a> -o I c. o 120 IS 8 0 c a> T O a> > 60 c? 4 0 2 0 0 -10 © 0 © 0\ ® 8 0 0 .820 .& © \ ©* © © © © © © © Free pro ton frequency ^ © © © © A /O -860 .880 .900 92 O © ^ Freq. in Mc/sec » f © \ © © © / / © / 0 © © © © Fig. 10. Paramagnetic 'CoC42 6H 2 0 at 78°K H o rotat ing in plane perpendicular to a-axis t o follow page22 -23-c a l l y with respect to the b-axis which i s consistent with the c r y s t a l structure. When H Q i s p a r a l l e l to the b-axis, a l l the l i n e s occur above the free proton frequency. In t h i s p o s i t i o n the l o c a l f i e l d produced by the central cobalt ion i n an octahedron i s the same at a l l four surrounding oxygens Oj, and i s i n the same d i r e c t i o n as H Q (the c r y s t a l structure reveals t h i s (see fig u r e 13a); and the g-factor of Co i s p o s i t i v e ) . Therefore, i f we disregard the r e l a t i v e l y free waters and the neighbouring octahedra, the protons of the i s o l a t e d octahedron should have a resonance frequency greater than the free proton frequency at t h i s c r y s t a l p o s i t i o n . The minimum and maximum resonance frequencies occur simultaneously at 45° on either side of the b-axis. When HQ i s i n t h i s p o s i t i o n the l o c a l f i e l d i s almost —> i n the same d i r e c t i o n as H Q for two of the four waters, and opposite to H Q f o r the other two (see fi g u r e 13b), giving r i s e to resonance l i n e s above and below the free proton l i n e r e s pectively as exhibited by figur e 10. The points i n figure 10 not f a l l i n g on curves (1) or (2) may then be attr i b u t e d to the r e l a t i v e l y free waters. It i s of int e r e s t to examine some aspects of figure 10 quantitatively, since the plane perpendicular to the a-axis i s within about 20 degrees of the r e f l e c t i o n plane of the octahedron. For the angle 45°, H Q i s almost p a r a l l e l to the vector joining the central cobalt ion with two of the Oj atoms -24-(actually, cos© = 0.97 i f © i s the angle between H Q and the vector j o i n i n g the oxygen atoms and the cobalt ion), and exactly perpendicular to the vector from the cobalt ion to the other two Oj atoms i n the octahedron. Taking the protons to be near the Oj atoms and noting that the f i e l d due to the cobalt ion i s proportional to (3cos2©-l)r""3, we expect the s h i f t s of the proton frequencies due to these two groups of water molecules from the frequency corresponding to the 3cos 2© average t o t a l i n t e r n a l f i e l d to be i n the r a t i o or 1 8 -j- . C l e a r l y , i n order that t h i s be so, the average i n -ter n a l f i e l d must be taken to correspond to a proton resonance frequency approximately 19 Kc higher than the free proton value (see figu r e 10). We a t t r i b u t e t h i s to the contribution of (4TT - N)M "to the average f i e l d discussed at the end of chapter 2. —* Since H Q was applied perpendicular to the cylinder-axis of our sample which i s roughly a cylinder of length 1.6 times the diameter, N i s approximately equal to 1.6JT . Assuming CH that M — — 2 , where C i s the Curie constant f o r our c r y s t a l T and T2s78°K, we calculate C-0.014. The Curie constant i s given by _ N g 2 / 3 2 S(S + 1) 3 k where N i s the number of paramagnetic ions per cm , g,ft , and -25-S have been defined i n chapter 2, and k i s Boltzman's constant. 1 3 Putting g ^ 4 and guessing that S = -|, we obtain C ~ 0.016. The close agreement of these two calculations of C i s probably f o r t u i t o u s , but i t probably also indicates that our general interpretation i s correct. It w i l l now be in t e r e s t i n g i n future studies to measure the temperature dependence of M by t h i s method, and with the same geometry measure the temperature dependence of the maximum s p l i t t i n g of the l i n e s . The f i r s t i s proportional to the "space averaged" magnetization per unit volume while the second should be proportional to the time average magnetic moment of an i n d i v i d u a l cobalt ion. It would be surp r i s i n g i f they did not have the same temperature dependence. Never-theless, an experimental check i s of int e r e s t with respect to some fundamental ideas concerning i n t e r n a l magnetic f i e l d s . In the next section concerning the r o t a t i o n of H Q i n the a-c plane approximate v e r i f i c a t i o n of the above ideas i s observed, since there we also have data i n the paramagnetic state at l i q u i d helium temperatures. (b) H Q i n the a-c plane. Figure 11 represents the ro t a t i o n with I?0 i n the a-c plane at 78°K and fi g u r e 12 the same r o t a t i o n at 4.2°K. In figure 11 the number of l i n e s i s again small and the l i n e s are never completely resolved, so that l i n e i d e n t i f i c a t i o n i s R e l a t i v e o r i e n t a t i o n in d e g r e e s o o no Q Q TI O — * " Q -\ TJJ Q 3 Q ro 0 0 ne. gne X X — • -0 0 0 II OJ -\ 0 0 — • -Q 0 Ol — 0 5 ro • Q CD C X cn ro O Fig.ll. Pgramagnetic CoCl2-6H 20 at 78° K. Ho in a-c plane to follow page 2 5 Fig. 13. Field pattern of a dipole. to follow page Z5 -26-d i f f i c u l t . Again the spectra are repeated after a 180-degree rotation due to the periodicity of (3cos20-l), as explained in the previous section. Comparing figures 11 and 12 we can recognize a general similarity in the two plots. In figure 11 the maximum frequencies occur at 0 degrees and 180 degrees, whereas in figure 12 they occur at -19 degrees and 161 degrees. At these orientations H Q is in the plane of the four oxygens O j forming the reflection plane of the octahedron, and maxi-mum frequencies are expected. However, these maximum fre-quencies should occur at the same crystal orientations regard-less of temperature. Since different crystals were used for these rotations, the above discrepancy is probably due to faulty alignment of the sample for the rotation at 78°K. There must also be a slight misalignment of this sample rela-tive to figure 10, since the spectrum at 0 degrees in figure 11 does not quite agree with the 0-degree spectrum of figure 10. In figure 11 the majority of lines occur at frequencies below the free proton frequency, whereas in figure 12 the majority of lines occur above the free proton line. The ratio of the maximum frequency below the free proton line to that above in figure 11 is about 85 : 55, whereas in figure 12 the same ratio is about 165 : 305. In other words, at the lower temperatures the whole system of lines is shifted to higher frequencies. -27-Since the time averaged magnetic moment of the cobalt ions i s proportional to H Q, the s p l i t t i n g caused by the cobalt ions should be a l i n e a r function of H Q. The separation of extreme l i n e s was measured as a function of H Q at 78°K f o r H Q i n the a-c plane and with 160 degrees orientation, and also for H Q i n the plane perpendicular to the a-axis at 0 degrees ori e n t a t i o n . The r e s u l t s are shown i n figures 16 and 15 respec t i v e l y . In both cases the s p l i t t i n g i s found to be line a r i n H Q, but when extrapolated for H Q = 0 the s p l i t t i n g does not become zero. This i s to be expected, since the proton-proton i n t e r a c t i o n i s independent of the applied f i e l d . For H Q i n the a-c plane the s p l i t t i n g extrapolates to about 83 Kc or 19 gauss, and f o r EQ i n the plane perpendicular to the a-axis i t extrapolates to about 53.5 Kc or 12 gauss. The second of these values i s almost exactly the usual proton-proton s p l i t t i n g i n waters of hydration. The f i r s t value i s somewhat high to represent pure proton-proton interactions, but since we do not know the r e l a t i v e amplitudes of the quantities a and b i n formula 6, the slope of the l i n e i n figure 15 may ac t u a l l y change as H Q approaches zero. In view of the above r e s u l t s the ideas put forward at the end of the l a s t section concerning the rot a t i o n i n the plane perpendicular to the a-axis can now be checked roughly. For the angle -19° i n t h i s r o t a t i o n H" i s i n the r e f l e c t i o n plane of the octahedron and for the angle 71° l l 0 i s •9 *6 -7 -6 -5" -4 -3 -2 - I O I 2 3 4 5 Fig. 14. S e e t e x t . to follow page 27 Fig. 16. S a m e as f i g . 15. H e at 160° in a-c plane. T = 7 8 ° K +o follow page 2 7 -28-perpendicular to t h i s plane. Again, taking the protons to be near the Oj atoms, a l l the protons associated with the Oj atoms are magnetically equivalent for the a-c r o t a t i o n . C a l -culating the p o s i t i o n of t h i s l i n e as a function of orientation of H Q i n the a-c plane, we obtain curve (1) of fig u r e 14. The extreme positions of the l i n e above and below the average f i e l d are i n the r a t i o of 1 : 2 respectively. This means that the average i n t e r n a l f i e l d i n fig u r e 11 should be taken to correspond to a proton resonance approximately 20 Kc higher than the free proton value. Within experimental error t h i s i s i n agreement with the r e s u l t s for the r o t a t i o n with H Q i n the plane perpendicular to the a-axis. The extreme frequencies in curve (1) of figure 11 are about 12,427 Mc/sec. and 12,536 Mc/sec. which comes to a difference of 109 Kc. For the ro-t a t i o n at 4.2°K, considering curve (la) i n fig u r e 12, the average f i e l d should be taken to correspond to a proton frequency about 197 Kc higher than the free proton frequency. The extreme frequencies for l i n e l a i n t h i s figure are about 13,183 Mc/sec. and 13,657 Mc/sec.} a difference of 372 Kc. Therefore M - (4.2°K) „ 197 1 Q M (77.3°K) 20 and LL (4.2°K) 372 - 83 ~ ~ 11 Li (77.3°K) 109 - 83 -29-From these r e s u l t s we see that the "space averaged" magnetization M and the average value of the i n d i v i d u a l cobalt moment have the same temperature dependence within experimental accuracy. The dependence should not be expected to follow a simple Curie law. Usually one can approximate the temperature dependence of magnetic s u s c e p t i b i l i t i e s by a Curie-Weiss law. If we assume that M and < pl> are proportional to — g , where © i s the Curie temperature of the substance, then our r e s u l t s give approximately ' n 10.5 or Q ^3.4°K As described l a t e r , we have measured the Neel temperature of t h i s substance to be approximately TJJ — 2«28°K. Since Q i s normally greater than T N, t h i s r e s u l t seems reasonable. It should be emphasized, however, that we have not t r i e d to correct f o r the s h i f t i n the p o s i t i o n of the l i n e s due to overlap. With well resolved l i n e s and the proton positions known, the r a t i o of extreme frequencies for a p a r t i c u l a r l i n e below 2 —3 and above zero s h i f t due to (3cos 0 - l ) r could be obtained. In such a case the above ideas would, i n f a c t , provide a method for measuring the average magnetization I f . According to theory the s i x d i f f e r e n t water molecules of hydration i n CoCl^BHgO should lead to 24 l i n e s i n s i x groups of four. Each group of four should consist of two pairs, the centers of which are separated by a distance 2b (see formula 5), -30-and the separation between these two lines is 4 d . They should be of equal intensity (see formula 7). However, experiments on CoClg^^O never give 24 lines in a f ield of 3 K gauss. Thus, i t may be concluded that certain lines overlap even at liquid helium temperatures. At 4.2°K a system of six lines consisting of three pairs is observed. One of the major goals in this work is to find the positions of the protons in the unit c e l l . Since these are not yet known, we cannot give theoretical curves of the type of figure 12. However, an angular dependence of the form of figure 14 is obtained if we make the following assumptions: (i) disregard the two relatively free water molecules, (ii) assume that only the cobalt at the centre of the octahedron influences the four surrounding waters, ( i i i ) neglect the effects of cobalt ions in neighbouring octahedra, and (iv) assume that the two protons in a water molecule do not interact and are situated at the Oj positions. Curve 1 in figure 14 represents H z =» (3cos 2©-l)r""3 = (3sin2y3 c o s 2 G - l ) r ~ ^ as a function of ce, where y3 is the angle between the Co*"** - Oj vector and the projection of this line on the plane of rotation, and .a is the angle between HQ and the plane of the Ox atoms. For the a-c rotation /3 = 7r/4 and r i s , of course, a constant. Choosing an arbitrary amplitude, this curve can be fitted exactly to curve la in figure 12 when the angles of -31-rotation are chosen to coincide in the two figures. When HQ is perpendicular to the reflect ion plane of the octa-hedron, lines of lowest frequency are observed, since in this position the local f ie ld due to the central cobalt is opposite to the direction of HQ because cobalt has a positive g-factor (3 unpaired electrons in the 3d shell) . When I?0 is perpendicular to the axis of the octahedron, i . e . parallel to the reflection plane, lines of maximum frequency are ob-served. This is in agreement with figure 14. In reality, of course, the two protons are not at the oxygen positions and they do interact, but the fact that curve 1 in figure 14 and curves la and lb in figure 12 are almost exactly in phase means that one of the protons is located in the reflection plane of the octahedron. If we consider the octahedron as an isolated system, potential energy and symmetry considerations should cause the other proton also to be in this plane. But in the crystal one such octahedron is surrounded by many others, and the second proton in the waters may be twisted slightly out of this plane. Such a position would produce a pair of curves slightly out of phase with curves la and lb in addition to having different frequencies. Curves 2a and 2b are out of phase by about 30° with curves la and lb. The splitting in the pair 1 and 2 is of the order of 10-15 gauss, which is the usual splitting in a water mole-cule due to proton-proton interaction. It may be, then, that -32 the separation i n pairs 1 and 2 i s due to the proton dipole-dipole i n t e r a c t i o n . Curves l a and lb i n fig u r e 12 coalesce near <a = 71° when i s perpendicular to the r e f l e c t i o n plane of the octahedron. This implies that the proton-proton s p l i t t i n g i n curve-pair 1 i s zero at t h i s p o s i t i o n . There-fore, (3cos2©j2~]i) = 0 i n t h i s o rientation, where 9j2 *-s t h e angle between the vector connecting the two protons and i t s projection on the plane of r o t a t i o n of the magnet. If the s p l i t t i n g i s t r u l y zero, and more det a i l e d studies may reveal that i t i s not, then the d i r e c t i o n of the l i n e connecting the two protons could be determined. The s p l i t t i n g between the centres of pairs 1 and 2 i s therefore assumed to be caused by the central cobalt. In t h i s argument the e f f e c t of the neighbouring cobalts was neglected. Since the nearest cobalt-neighbours to any of the protons are about twice the distance of the central cobalt to any of i t s surrounding protons, t h e i r e f f e c t i s reduced by a factor 8 at least due to the -1^ behaviour of a dipole f i e l d , r 3 and so should produce only a s l i g h t change i n the curves of figure r . Curve 2 i n figure 14 represents the l o c a l f i e l d at the p o s i t i o n of an O J J due to i t s four nearest cobalt neighbours drawn to the scale of curve 1. This curve, however, i s not i n phase with curve-pair 3 i n figure 12, which merely indicates that the protons of the r e l a t i v e l y free waters are not located -33-at the O J J positions. The splitting in this pair of lines cannot definitely be accounted for. It is probably due to a proton-cobalt interaction, since i t is too large for a proton-proton interaction (about 30 gauss), unless these water molecules are greatly distorted. Quantitative results cannot be given at this time, since not sufficient data have been recorded. The work planned for the immediate future w i l l incorporate these qualitative arguments, and i t is hoped that i t wil l be possible to establish the proton positions. The f i rs t obvious extension of the work reported here is to repeat the measurements at much higher fields so that a better resolution is obtained. Probably more lines w i l l then appear and definite identification should be possible. A study of the splitting between certain pairs of lines as a function of f ie ld at given positions should reveal which splittings are caused by proton-proton interactions and which are due to the cobalt ions. It is also planned to perform double resonance ex-periments. With the aid of these i t should be possible to study line shapes even if the lines normally s t i l l slightly overlap. Crystals containing different concentrations of DgO should reveal some interesting phenomena, as i t should be possible to eliminate certain proton lines and to observe the lower frequency deuteron resonance lines. With the -34-results from these measurements and the completion of the observations in the antiferromagnetic state i t should be possible to completely describe the magnetic behaviour of CoCl o*6H o0. -35-i i i . T r a n s i tion Temperature Measurements. 14 15 T. Haseda and E. Kanda , and M. Leblanc independently found that CoClg^SHgO exhibits an antiferromagnetic behaviour below about 3°K. W.K. Robinson and S.A. Friedberg observed a lambda-type anomaly i n the s p e c i f i c heat of CoClg'SHgO at 2.29°K and assumed t h i s anomaly to be associated with a para-magnetic-antiferromagnetic phase t r a n s i t i o n . In t h i s work the t r a n s i t i o n temperature was measured by observing the change i n the proton spectrum. Figure 1? shows the proton spectrum at 2.5°K with H Q at 160° i n the a-c plane. The frequency of the o s c i l l a t o r was adjusted so that the recorder pen rode on the f i r s t maximum slope of the spectrum which corresponds to the f i r s t maximum in figure 17 as indicated. With the frequency held constant at t h i s point, the temperature was slowly decreased. As a re s u l t the graph of figure 18 was obtained. The temperature check points are marked on the graph by small pips i n the curve, and the corresponding temperatures are l i s t e d i n t h i s f i g u r e . Figure 18 shows that the onset of the t r a n s i t i o n occurs at s l i g h t l y above 2.28°K i n agreement with the s p e c i f i c heat measurements by Robinson and Friedberg. At thi s temperature the l i n e of the paramagnetic state disappears, but the change i s not abrupt. The t r a n s i t i o n takes place over a temperature Fig. 17. Proton spectrum at at T=2.5°K. Ho at 160° and in a-c plane. Freq.in 40 Kc /sec . steps fo follow page 3 5 -36-range of about 0.07° (pips 7 to 11). This range i s not caused by time e f f e c t s i n the recording system. Several such graphs were obtained with d i f f e r e n t rates of temperature change, and the range through which the t r a n s i t i o n takes place was about 0.07° i n each case. The error i n the temperature measurements may be as large as +0.03°, but temperature differences could be measured to a much higher degree of accuracy. The f a c t that the t r a n s i t i o n i s not sudden but takes place over a ce r t a i n temperature spread indicates that short-range magnetic order e f f e c t s are present. It was possible to keep the temperature constant at any point, and several recordings of the spectrum were made with the t r a n s i t i o n p a r t i a l l y completed. One such recording at 2.25°K i s shown i n figu r e 19. This spectrum s t i l l resembles that of figu r e 17 (recorded at 2.5°K), but a change i s e a s i l y recognizable. Recordings at lower temperatures within the t r a n s i t i o n range further deviate from figu r e 17, u n t i l the t r a n s i t i o n to the anti-ferromagnetic state i s complete. Figure 20 shows part of a spectrum at 2.21°K (just below the t r a n s i t i o n temperature). Other lines occur i n t h i s spectrum several Mc/sec. on either side of the part shown. T=2.25°K. Ho at 160° and in a-c plane. Freq. in 40 Kc/sec. steps. to rolioW paqe 3S -37-i v . Measurements i n the Antiferromagnetic State. As stated before, CoCl2*6H 20 becomes antiferromagnetic at about 2.28°K. Measurements i n the antiferromagnetic state are only p a r t i a l l y complete. These were ca r r i e d out at 1.52°K i n a f i e l d of 3100 gauss with H Q i n the a-c plane. A recording of the spectrum with I?0 at 20° i s shown i n figu r e 21. The r e s u l t s are shown i n f i g u r e 22. Figure 22 i s of the same type as fig u r e 12, the angular orientation being the same i n both graphs. These r e s u l t s exhibit some features s t r i k i n g l y d i f f e r e n t from the measurements i n the paramagnetic temperature region. The spectrum and the number of l i n e s change e s s e n t i a l l y i n passing from the paramagnetic to the antiferromagnetic region. Line s h i f t s of 7.5 Mc/sec. have so f a r been recorded. Probably these w i l l increase to about 15 Mc/sec. when the r o t a t i o n i s completed. The l i n e s are well resolved and generally much broader (of the order of 120 Kc/sec. or about 28 gauss). Figure 21 shows a t y p i c a l recording of the proton resonance at 1.52°K fo r a given orientation of H q. The data i n f i g u r e 22 are derived from such recordings. One s t r i k i n g and as yet unexplained feature i n a l l re-cordings i n the antiferromagnetic state i s the very strong l i n e approximately 30 Kc/sec. above the free proton frequency. This l i n e i s not affected by the orientation of ~EQ i n the R<j. 21. Proton resonance speirum. in Anti-ferromagnetic state at l.52°K. No in a-c plane at ZO°. to.follow paqe 37 -38-a-c plane* When the rotation in the antiferromagnetic state is completed, i t appears that the spectrum wil l be symmetric only with respect to 360° rotation instead of 180° as in the paramagnetic state. This result is expected, since in the antiferromagnetic state the magnetic ions are oriented with respect to the crystal axes rather than the — » external magnetic f ie ld H Q . -39-Bibliography 1. G.E. Pake, J. Chem. Phys. 16, 327 (1948). 2. N. Bloerabergen, Physica 16, 95 (1950). 3. N.J. Poulis, Physica 17, 392 (1951). 4. N.J. Poulis, Physica 18, 201 (1952). 5. J.H. Van Vleck, Phys. Rev. 74, 1168 (1948). 6. N. Bloembergen, E.M. Purcell, and R.V. Pound, Phys. Rev. 73, 679 (1948). 7. J.H. Van Vleck, J. Chem. Phys. 5, 320 (1937). 8. American Inst, of Physics Handbook, Chapter 5, p. 240. 9. D.G. Watkins, Ph.D. Thesis, Harvard University, Cambridge, Mass., u;S.A; (1952). 10. H.H. Waterman, Ph.D. Thesis, University of B.C. (1954). 11. P. Groth, Chemische Krystallographie, 1. T e i l , p. 248, Wilhelm Enzelmann Verlag, Leipzig (1906). 12. J. Mizuno, K. Ukai, T. Sugawara, J. Phys. Soc. Japan 14, 383 (1959). 13. M. Date, J. Phys. Soc. Japan 14, 1244 (1959). 14. T. Haseda, E. Kanda, j ; Phys. Soc. Japan JL2, 1051 (1957). 15. M. Leblanc, Ph.D. Thesis, University of B.C. (1958). 16. W.K. Robinson, S.A. Friedberg, Tech. Report No. 5, Carnegie Inst, of Tech., Dept. of Physics (1959). 

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