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Isotope effect on the Neel temperature of hydrated manganese chloride crystals Yue, Chung Leung 1970

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ISOTOPE EFFECT ON THE NEEL TEMPERATURE OF HYDRATED •MANGANESE CHLORIDE CRYSTALS CHUNG LEUNG YUE •B.Sc.(Special) University of Hong Kong, ' 1 9 6 7 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1 9 7 0 In p r e s e n t i n g t h i s t h e s i s in 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 an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e 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 s t u d y . I f u r t h e r a g r e e t h a p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f 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 a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depar tment o f The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8 , Canada 11 ABSTRACT The Neel temperatures of both the hydrated and 96% deuterated single crystal specimen of antiferromagnetic manganese chloride, have been compared. The sample was placed in the tank c i rcu i t of a radio-frequency osc i l la tor; the inductance of the c o i l and hence the frequency of osc i l la t ion thus depended on the suscepti-b i l i t y of the specimen. As the crystal in the l iqu id helium bath was warmed through the Neel temperature, the osc i l la t ion frequency was monitored by a frequency counter. By this method, the Neel temperature could be deduced to change by - 2 . 3 % when the crystal was 96% deuterated. This result is comparable to the measurements on CoClg^H^O and CuCl2.2H_0. A semi-quantitative explanation proposes an intimate relationship between the superexchange interaction and the hydrogen bond strength. i i i TABLE OF CONTENTS Page ABSTRACT „ i i TABLE OF CONTENTS i i i LIST OF TABLES iv LIST OF FIGURES v ACKNOWLEDGMENT v i CHAPTER 1 : INTRODUCTION 1 Theory of Antiferromagnetism 5 Measurement of Dif ferent ia l Susceptibi l i ty 9 CHAPTER 2 : APPARATUS AND SPECIMEN PREPARATION . . . . . . . 1 2 Crystal Structure of .MnCl_ ' ^ 2 ° 1 2 Crystal Growing 1 6 Crystal Mounting 1 9 Coaxial Cable 2 0 Sample Holder 2 1 Low Temperature Equipment 2 1 Automatic Manostat 2 5 Electronic Circui try 2 7 CHAPTER 3 : EXPERIMENTAL RESULTS 3 0 CHAPTER 4 : DISCUSSION 3 7 CHAPTER 5 : CONCLUSION ^ REFERENCE ^ 5 iv LIST OF TABLES Page Table I : Experimental data of a typical run of a '96% deuterated sample of MnClg.^HgO single crys ta l . 3 1 Table II : Experimental data of a typical run of a hydrated sample of MnClg.^ -HgO single crystal 3 2 . Table III : Neel temperatures of hydrated and deuterated MnCl,.4H 90 3 5 V LIST OF FIGURES Page Fig 1 : Variation of the suscept ibi l i ty of an antiferromagnetic material with temperature . 2 Fig 2 : Simple antiferromagnetic spin arrangement . . . 3 Fig 3 '• Superexchange in MnO 3 Fig • k i Mn ions in MnO b Fig 5 ' Temperature dependence of the susceptibi l i ty of an antiferromagnetic crystal 8 Fig 6 : Atomic arrangement in MnClg.^HgO 1 3 Fig 7 : Alignment of M n + + spins in MnClgJ+H 0 in the antiferromagnetic phase . . ° 1 5 Fig 8 : Coaxial cable 2 2 Fig 9 ' Teflon sample holder 2 3 Fig 1 0 : Automatic manostat 26 Fig 1 1 t Block diagram 2 9 Fig 1 2 : Typical run of a S6% deuterated sample of MnCl .J+H 0 single crystal 3 3 2 2 Fig 1 3 » Typical run of a hydrated sample of MnCl„.^H 0 single crystal 3 ^ ACKNOWLEDGMENT I wish to express my sincerest appreciation to Dr. B. Gc T u r r e l l for his constant supervision and assistance throughout this work. This research was supported through a grant of the National Research Council of Canada. CHAPTER 1 INTRODUCTION The concept of antiferromagnetism was f i r s t suggested by Neel ( 1 ) in 1 9 3 2 in connection with his study of the paramagnetic susceptibi l i ty of transit ion metals such as Pt, Pd, Mn, Cr and their al loys . The temperature dependence of the susceptibi l i ty of an antiferromagnet is characterised by the occurrence of a kink in the 4r~T curve at the Neel temperature (fig 1 ) . The A-reason for this is that below this temperature, T^, magnetic order sets in , and an ant iparal le l spin arrangement is y established. A simple antiferromagnetic system in which spins align para l l e l and ant iparal le l to each other is shown in f ig 2 . In such an antiferromagnet, the tendency to be magnet is by an external f i e l d is opposed by a strong interaction acting between adjacent spinso The coupling of individual spins to an external H is much weaker than the interaction between the spins; hence the susceptibi l i ty decreases with a decrease in temperature, contrary to the behaviour in the paramagnetic phase (fig 1)« Above the Neel point, the spin arrangement • becomes random, so that the susceptibi l i ty now decreases with an increase of temperature, just as in the paramagnetic case. 2 F i g 1 Variation of the susceptibi l i ty of an ant i -ferromagnetic material with temperature 3 Fig 3 Superexchange in MnO 4 Fig 4 Mn ions in MnO. diagram). (After (Only Mn ions are shown in the Shul l , Strauser and Wollan (2) ) 5 THEORY OF ANTIFERROMAGNETISM MnO is a representative antiferromagnetic material of NaCl-type of crystal structure. The Mm ions in this lat t ice form a f . c . c . structure and their spins are aligned a n t i -para l l e l to one another as shown in f ig This alignment of spins was determined by neutron dif fract ion techniques and was observed by Shull and Smart ( 3 ) « The magnetic ions in such an oxide are separated by oxygen ions. Therefore the direct exchange interaction . between magnetic ions resulting from the overlap of 'magnetic' electronic wavefunctions is considered to be weak. But in spite of this fact, there seems to be strong exchange inter-action between the magnetic ions, as shown by the re lat ive ly high value for the Neel temperature. This fact was f i r s t explained by Kramers Anderson ( 5 ) has subsequently discussed antiferromagnetism in these types of materials in terms of the so-called superexchange interaction. An authori-tative account on i t has been given by Anderson ( 6 ) in 1 9 ^ 3 • By superexchange we mean that the spins of the metal ions on opposite sides of an oxygen ion interact through the p-orbit of the oxygen ion. Consider the system composes of two metal ions M^ and M separated by an oxygen ion 0. The ground state of the oxygen ion w i l l have the electronic 2 2 6 * configuration of neon, i . e . Is 2 s 2 p . In this state, no spin 6 couplings with the metal ions are possible. But when one of the two electrons of the doubly negatively charged 0~~ ion is excited; and transferred to the neighbouring metal ion M]_, in which the strong exchange interaction tends to direct the spin of the transferred electron in a direction such that the ion has a maximum spin magnetic moment, because of the Hund's rule . Therefore, i f the metal ion M]_ with transferred electron has less than five 3 d electrons, a l l the 3 d electron spins tend to align themselves para l l e l to each other; while, i f the 3 d electronic level is more than h a l f - f i l l e d , the transferred electron must have i ts spin pointing ant iparal le l to the resultant magnetic moment of the ion. At the same time, the unpaired electron left in the p-orbit of the 0 ion w i l l be coupled with the other metal ion M2 in which the transferred electron should interact with the M2 electrons in a similar manner. But, by Pauli 's exclusion, pr inc ip le , the two electrons in the p-orbit of the 0 ion must have opposite spins, both metal ions should have ant iparal le l magnetic moments in order to f u l f i l l Hund's rule for both ions. Such a superexchange interaction is expected to be strongest when M2-O-M2 l i e along a straight l ine , because in this configuration the p-orbit of the 0 ion w i l l be able to get the maximum overlap with the metal ions. If Mj-0-M2 makes an angle, then the superexchange "is consequently smaller. 7 For MnO, the superexchange mechanism is given schematically in f ig 3 » In this case the electronic con-figuration of Mn+H" is 3&5, i . e . with a l l the spins para l le l to each other in the 3 d l eve l . Since an antiferromagnetic arrangement of spins of the same kind of magnetic ions cancel'each other out, there is no net spontaneous magnetism, i . e . i t is not ferromagnetic. The tendency to maintain the ant iferromagnetic arrangement of spins, however, opposes the magnetisation due to the application of an external f i e ld and accordingly gives rise to a characteristic temperature dependence of the suscepti-b i l i t y . Thus, contrary to paramagnetism where the suscepti-b i l i t y increases with decrease of temperature; antiferro-magnetic substances show a decrease of susceptibi l i ty with decrease of temperature below the transit ion temperature, the Neel temperature, or when the material is in the ant i -ferromagnetic regime. This situation is represented by X/( in f ig 5 a » when the magnetic f i e l d is applied para l le l to the spin. When the magnetic f i e ld is applied perpendicular to the spin, magnetisation takes place by the rotation of each spin from its or ig inal direct ion. Then the suscepti-b i l i t y becomes independent of the temperature as shown by the curve X±. in f ig 5 a . In a polycrystal , the susceptibi l i ty is the average between the two cases, and is shown by the Xpely curve in f ig 5 a « 5 Temperature dependence of the susceptibi l i ty of an antiferromagnetic. crystal 9 These curves show quali tat ively the behaviour of the suscept ibi l i ty as a function of temperature. For a given specimen, the quantitative behaviour of w i l l depend on the detailed magnetic character of the system. However, we are interested only in one specific point on this curve, v i z . the Neel temperature, T^, which is defined to be the point where the specific heat is at a sharp maximum discontinuity. Also, we are interested only in a comparison measurement, i . e . measuring a change in T N . Sykes and Fisher (7) have shown that the susceptibi l i ty , ")C » versus temperature, T, plot for an ant i f erromagnet should have a ver t i ca l tangent (fig 5 ° ) at the same temperature as the specific heat anomaly occurs; or at T^. Hence, experimentally, T^, would correspond to the point of maximum positive gradient in the % versus T curve; and may not necessarily correspond to the point of maximum suscept ibi l i ty . MEASUREMENT OF DIFFERENTIAL SUSCEPTIBILITY In the present study of the difference in the Neel temperatures of MnClg.^HgO and i ts deuterated form, we made use of an experimental setup which consist of, in essence, a marginal o sc i l l a tor , the inductive load of which was a c o i l wound around the specimen. The resonant frequency was 10 monitored by means of a Hewlett Packard 5 2 ^ 5 L frequency counter. The method was or ig inal ly due to Gorter (11), and has been used f a i r l y recently by Sawatzky and Bloom (12). The inductance of the co i l is given by:-L = L 0 ( l + 4 n f X ( T ) ) where L Q is the inductance in the absence of the sample, f is the ' f i l l i n g factor' of the sample in the c o i l , and X(T) is the d i f ferent ia l suscept ibi l i ty of the sample. But the resonant frequency of the r . f . osc i l la tor is given by:-2 -1 _ i V = (LC) or v = (LC) 2 Hence » = (LC)"* = (LQC )"*(l+^irfX(T) )"* = y 0 ( l + 4irfX(T) where v>0 is the osc i l la tor frequency with the sample removed, and C is the capacitance in the c i rcu i t of the r . f . o sc i l la tor . The capacitance w i l l actually change when the sample is placed in the c o i l , but provided that we are only interested in measuring relative suscept ib i l i t i e s , and in part icular , the maximum in suscept ibi l i ty , i . e . the minimum in frequency, this correction w i l l be unnecessary. A sl ight variation in the temperature of the sample, e.g. by a millidegree, when i t is in the antiferromagnetic regime, w i l l give a change in resonant frequency by about ±20Hz, which w i l l be readily monitored. 1 1 This kind of technique is much more easily performed than typical n.m.r. methods used, for example, by Sahri ( 1 3 » 14) in the measurement of the isotope shift in CoClg^HgO. The reason is that this method monitors the electronic magnetisation, while the n.m.r. detects this v ia the hyperfin interaction. The nuclear signals are of course much weaker. The experimental setup used is much simplif ied, and the only c r i t i c a l cr i ter ion on the apparatus for satisfactory operation is a stable r . f . o sc i l l a tor . 12 CHAPTER 2  APPARATUS AND SPECIMEN PREPARATION CRYSTAL STRUCTURE OF MnCl?. JIHoO G r o t h i n 1 9 0 8 ( 1 5 ) r e p o r t e d t h a t M n C l 2 . 4 H 2 0 has two m o n o c l i n i c c r y s t a l m o d i f i c a t i o n s . One form i s m e t a s t a b l e a t room t e m p e r a t u r e and i s isomorphous w i t h F e C l 2 . 4 H 2 0 . The o t h e r i s s t a b l e a t room t e m p e r a t u r e and i s the form t h a t would be s t u d i e d h e r e . . C r y s t a l l i n e MnCl^.^HgO e x h i b i t s the t y p i c a l p i n k c o l o u r t h a t c h a r a c t e r i s e s Mn s a l t s . I t has a m o n o c l i n i c p r i s m a t i c s t r u c t u r e and the u n i t c e l l edges are a = 1 1 . 1 8 6 K f b = 9 * 5 1 3 and (5 = 9 9 ' 7 4 ° . The space group i s ?2^/n w i t h f o u r f o r m u l a u n i t s p e r u n i t c e l l . A c c o r d i n g t o Z a l k i n , F o r r e s t e r and Templeton ( 1 6 ) , X-ray d i f f r a c t i o n s t u d y o f t h i s c r y s t a l shows t h a t the s t r u c t u r e c o n s i s t s o f d i s c r e t e o c t a h e d r a o f f o u r oxygen atoms and two c h l o r i n e atoms about the manganese, and w i t h the c h l o r i n e atoms a d j a c e n t t o each o t h e r . The f o u r Mn - 0 d i s t a n c e s a re n e a r l y e q u i d i s t a n t , b e i n g 2.224, 2 . 2 0 9 , 2 . 1 8 5 and 2 . 2 0 6 X . . Only f o u r o f t h e e i g h t hydrogen atoms form hydrogen bonds. W i t h r e f e r e n c e t o f i g 6 , we have: 1 3 Fig 6 Atomic arrangement of MnCl ?.4H Cu (According to Zalkin , Forrester and Templeton ( 1 6 ) ) 0 ( 1 ) - H ( l ) l 0(2) - H(2)l 0(2) - H(2)2 — 0(4) - H(4)l - — Three of the hydrogen bonds are between oxygen and chlorine, and one between two water molecules. Each unit c e l l has four formula weights with the Mn + + metal ions at the centres and corners of i ts b - c surfaces. The structure is octahedral in shape about the metal ions. Unlike the structure of CoC^^HgO, the two chlorine atoms are adjacent to each other on the octahedron, whilst the four oxygen atoms from water occupy the remaining four apexes. In the antiferromagnetic phase, the spins are aligned in the c-axis, and they belong to the symmetry group P2^/a', according to Spence and Nagarajan ( 1 7 ) . The layers of spins para l l e l to the b - c plane are stacked together so that i f in one layer a l l the spins point paral le l to the c-axis, then the spins in the next layer are a l l ant iparal le l to the c-axis (fig 7 ) . The oppositely directed spins that are adjacent to each other are linked by superexchange. A l l the possible paths of exchange involve the use of hydrogen bonds. - C l ( l ) - Cl(2) - 0 ( 1 ) - C l ( l ) 3 - 1 ? X 3 - 1 ? X 2 . 9 3 £ 3 . 2 9 X 1 5 c a Fig 7 Alignment of Mn + + spins in MnClg.^HgO in the antiferromagnetic phase. (according to Spence and Nagarajan ( 1 7 ) ) 16 CRYSTAL GROWING Sl ight ly different techniques are used for growing the hydrated and the deuterated crystals . For the hydrated crysta l , enough hydrated crystals of reagent grade MnC.^^H-pO supplied by Fisher Scient i f ic Co. were dissolved in d i s t i l l e d water in a beaker, so that a saturated solution was obtained at 35°C. The excess amount of undissolved salt was removed by f i l t e r i n g through fine-pore f i l t e r paper, in a funnel warmed on the outside by .a hot-air blower, so as to minimise any substantial drop in the temperature of the solution during f i l t r a t i o n ; otherwise,•the so lubi l i ty would be lowered, and less salt would be available later for crystal formation. The f i l t r a t e was-stored in a stoppered flat-bottomed flask, which was put inside a crysta l -growing apparatus which had thermostatic control . The temperature was allowed to f a l l at a rate of 1°C per day unt i l a number of well-formed seeds were produced in the flask. The seeds were then removed by f i l t r a t i o n , and then dried between f i l t e r papers. The best ones were selected as the seeds for the growing of the large crystals required. The solution was warmed again to i t s i n i t i a l temperature of 35°C and a seed was suspended in the solution by a piece of human hair . The piece of human hair was f i r s t cleaned by dipping into dilute NaOH to remove a l l the greases and fats, treated 1 7 with excess dilute n i t r i c acid to neutralise the a l k a l i , and f ina l ly washed in d i s t i l l e d water a number of times to remove a l l the excess acid; and i t was then dried under an infra-red lamp. The temperature of the water bath in the crys ta l -grower was lowered at the rate of 1 ° C per day once again, and the crystal grew slowly unt i l a crystal of a size that was s l ight ly larger than the sample-holding-cavity in the sample-holder was obtained. The crystal was then removed and dried between f i l t e r papers and kept in a sealed jar u n t i l i t was needed for the experiment. The size of the actual crystal that was used was about 1 . 2 cm in length and 0 . 7 cm at i ts widest. To prevent the formation of a polycrystall ine mass on the walls of the flask or on the seed i t s e l f , we took the precaution to remove any solids that might be present in the vessel or on the seed by the following methods: (a) The flask was washed thoroughly and then heated under an infra-red lamp or over a flame. (b) At the s tart , the solution was kept s l ight ly unsaturated. This dissolved any microscopic seeds present on the main seed. Care was taken to lower the temperature of the flask after a short while so that the main seed did not dissolve in.the solution completely. 18 The preparation of the deuterated crystals was f i r s t attempted by making, a saturated solution of anhydrous MnCl^* supplied by A l l i e d Chemicals L t d . , in heavy water, supplied by Merck, Sharp and Dolme Ltd. But contrary to what is suggested by Mellor (18), the anhydrous salt dissolved in • the heavy water and then hydrolysed to a dirty brown precipitate of manganese hydroxide. Preparing the saturated solution in an acidic medium using deuterated hydrochloric acid was considered, but since this was not available at the time, the method of successive deuteration was used instead. By t r i a l and error, i t was found that when crystals of MnClg.^HgO supplied by Fisher Scient i f ic Co. were warmed slowly over a flame in - a crucible , the crystals dissolved in the water of crysta l l i sat ion that was given off, and MnC^.^H^O was converted to the lower hydrates. Some of this water of crys ta l l i sa t ion was driven off as. steam and lost . More and more of this water could be removed in this way, leaving an amorphous mass behind. The resultant mass, when cooled to room temperature, could be dissolved in water without hydrolysis, as long as the process of heating was not carried beyond the stage where more than 80% of a l l the available water of crys ta l l i sa t ion was driven out. The heat-treated MnCl£ was then redissolved in heavy water, and crystals formed from cooling this solution would 1 9 be more than 80% deuterated. The heating process was applied once again.to the deuterated crystals and the resulting mass was dissolved again in pure heavy water. The crystals grown from this solution were used for the experiment. The actual.percentage'composition of deuteration was determined by heating the deuterated crystal strongly in a closed retort , to drive out a l l the water of crysta l l i sat ion in the crys ta l . The water vapor was condensed at the other end of the retort , and the percentage of deuterium oxide in the condensate was measured using a 6 0 MHz Varian n.m.r. spectrometer, b^y courtesy of the Chemistry Department, U..B.C. The water composition was determined by comparing the intensity of the proton signal in the condensate with that of an equal volume of d i s t i l l e d water. This measurement gave the percentage of ordinary water in the condensate to be h%. Thus the crystal was 96% deuterated. To make sure that the specimens grown were single crystals , von Laue patterns of these specimens were taken on a X-ray machine. Doubtful specimens were rejected. CRYSTAL MOUNTING To prevent any introduction of strains to the crys ta l , they were carefully handled to avoid a l l types of shocks. A cy l indr ica l specimen that would f i t snugly into the sample 2 0 holder was prepared by dissolving the crystal with a brush wetted by ordinary or heavy water, as the case might require. The specimens were cooled slowly during experiments to prevent the introduction of strains due to uneven cooling. The crystals were mounted with the c-axis para l l e l to the axis of the r . f . co i l enclosing the sample. The c-axis is the axis of easy magnetisation ( 1 7 ) . Hence the suscepti-b i l i t y that is measured is %f/ (fig 5 a ) , and a minimum in the susceptibi l i ty occurs when the temperature corresponds to the Neel temperature. The c-axis of single crystal MnCl^.^HgO was quite easi ly ident i f ied, as i t was given by the line of intersection of the a and m planes ( 1 5 ) ° COAXIAL CABLE The coaxial cable was made from a piece of stainless steel tubing of three-eighth inch diameter, and of a length of about thirty-three inches to allow the sample holder to s i t at the t ip of the t a i l of the inner helium dewar. The sample holder was made from teflon and was t ightly f i t ted to one end of the coaxial cable. The other end of the stainless steel tubing was soldered to a copper cylinder 21 which formed an a irt ight seal . The coaxial line assembly is shown in f ig '8 . The inside of the coaxial line consisted of a normal double CPH Amphenol P,G 22/u coaxial cable, whose outer metallic sheath was removed to decrease the rate of heat o conduction along the l ine . The two wires in the cable were e l e c t r i c a l l y connected to the outside osc i l la tor through the double covar seal and an Amphenol U G - I 0 3 / U plug. At the other end of-the coaxial line was soldered the tank co i l which was wound around the waist of the sample holder. SAMPLE HOLDER The sample holder shown in f ig 9 consisted of a hollow teflon cylinder with a screw-on end. Around the outside of this sample holder was wound the r . f . c o i l . To ensure thorough thermal equilibrium between the helium bath and the specimen, a small hole was d r i l l e d in the screw-on end so that the sample was in physical contact with the helium batho LOW TEMPERATURE EQUIPMENT The low temperatures were produced by using a conventional double-dewar glass cryostato Temperatures from 22 lo Marginal Oscillator -Brass CyUnder Covar Seal % Stainless Steel TuUng /eicuum ocreu 0 - Rinc J I ! i i • ' i—. Teflon Sample Holier L 3 a Fig 8 Coaxial Cable 2 3 F i g 9 Teflon Sample Holder 24 1 . 4 - 4 . 2 K can be easily obtained by pumping on the helium l i q u i d . The-dependence of temperature on the equilibrium vapor pressure of boi l ing helium is known very accurately. (The 1 9 5 8 Helium Pressure-Temperature Scale ( 1 9 ) ) The vapor pressure of the helium was measured by a manometer system that consisted of a mercury arm and a d i f ferent ia l o i l arm. The o i l used was n-dibutyl phthalate supplied by Fisher Sc i ent i f i c . The density of the o i l was obtained from the average of several methods. The density was measured by cal ibrat ing the o i l manometer against the mercury column by means of a cathetometer, and then by using the specific gravity bottle method, and was checked against standard data sheets. The values agreed very well and were consistent. By this method, the height of the mercury column or the difference in level of the o i l manometer was measured, and the corresponding value of the temperature was found from the vapor pressure versus temperature tables. To provide sufficient time for a thermal equilibrium to be attained in the dev/ar, i t was required that the pumping rate be so regulated that the temperature could be maintained constant to about 1 millidegree for 1 0 minutes. This was a'chieved by connecting an automatic manostat in series with the pumping system. The temperature was stablised by maintaining a constant vapor pressure with the automatic 2 5 manostat. It is fortunate that the Neel temperature of MnClg'^HgO is below, the X.-point of helium. 'This means that there is alv/ays good thermal equilibrium between the specimen and the bath. AUTOMATIC MANOSTAT The vapor pressure of the helium bath could be controlled by the pumping rate which was adjusted roughly to a constant speed by the large overhead gas valves in the system. But any fine adjustments that-would keep the temperature constant to part of a millidegree or better in ten minutes, had to be effected by the manostat shown in f ig 10. .The automatic manostat worked on the principle of negative feedback. A standard pressure was maintained in the brass bellows B which controlled the size of the mouth of the tube through which a l l the gas that was pumped must passed through. An excess of pressure in the cryostat compressed the brass bellows B and hence the mouth of the tube was increased, and the pumping rate was increased as well . This continued u n t i l the pressure in the cryostat started to drop and approached that in the bellows. The reverse operation would happen when the pressure inside the bellows was higher than that inside the cryostat. Using this device, millidegree 10 Automatic Manostat 2 7 s tab i l i t y could be maintained over a period of 1 0 minutes or more. Slow continuous variation of vapor pressure could be obtained by adjustments on the needle valve lb shown in f ig 1 0 . A better thermal s tab i l i ty could be obtained by using one of the many temperature control c ircui ts given, for example by Bjarke ( 2 0 ) , or Venegas and Finegold ( 2 1 ) . In either of these c i r c u i t s , the temperature of the helium bath can be maintained to within 1 0 . 0 ju-K over a period of 2 0 minutes. This is an improvement that could be u t i l i z ed in future experiments on other magnetic systems. ELECTRONIC CIRCUITRY The r . f . resonant c i rcu i t consisted of a marginal o sc i l l a tor , supplied by Alpha Electronics (model AL 6? n.m.r. spectrometer and gaussmeter), and the coaxial line with the tank c o i l at i ts end. The osc i l la tor was designed for detectin n.m.r. signals. However i t can also be used equally well in our experiment. The dimensions of the tank co i l were such that with the osc i l la tor and the coaxial line that had been b u i l t , resonant frequencies between 3 - MHz could be easily obtained by changing the value of the tuning capacitor. In this frequency range the best compromise between the 28 frequency, r . f . level and s tab i l i ty could be obtained. In each individual setting of the tuning capacitor, the maximum r . f . level that would s t i l l give a perfect sinusoidal waveform on the C.R.O. from the r . f . c i rcu i t as observed at the buffer stage output was used. This y/as necessary because i f the \. waveform in the r . f . c ircui t contained some prominent harmonics, then the frequency recorded by the Hewlett Packard 5 2 4 5 L frequency counter would become less stable. . The r . f . frequency that corresponded to a particular temperature was recorded on the Hewlett Packard frequency counter. The recorder print-out supplied a continuous record of the frequencies. The accuracy of this determination depended on the s tab i l i ty of the marginal osc i l la tor and the temperature s t a b i l i t y . With the experimental setup described, a local • s tab i l i ty of ±10 Hz was obtained. The dr i f t of the osc i l lator frequency with time- was very small, being about ±10 Hz during a normal experimental run. For increased accuracy, i t would be necessary to use a more stable osc i l la tor , for example, a Robinson osc i l la tor (22), or a non-marginal o sc i l l a tor . 29 F R E G L C O U N T E R DIGJTAL RECORSE& Fig 11 Block Diagram 3 0 CHAPTER 3  EXPERIMENTAL .RESULTS Sykes and. Fisher (7) have shown that in ant i -ferromagnetic material, whereas the specific heat reaches a maximum at the Neel temperature, the susceptibi l i ty need not do so. In hydrated antiferromagnetic materials, because of the short range magnetic order, the susceptibi l i ty versus temperature curve has a rounded maximum at a temperature above T N . This was discussed by Nakamura ( 2 3 ) . Lasheen, van den Broek and Gorter (24) have shown that the Neel temperature, as defined by specific heat measurements occurs at that temperature at which the suscepti-b i l i t y decreases suddenly. This is due to the rapid increase at the Neel temperature T^ , of the high anistropy f i e ld in a non-cubic antiferromagnet. Accordingly, in our experiments, we define T^ for MnCl .^H^O as that temperature at which the frequency increases rapidly as the temperature is decreased. For example, in an actual run (f ig 1 3 ) » i t was found that in region I, the experimental points adjacent to, and lower in temperature than T N rose 1 5 Hz in 5 millidegrees, whereas the TABLE I . Experimental data of a typical run of a 96% deuterated sample of MnCl J+H 0 single crystal . (Plotted in f ig 1 2 ) Height of o i l manometer (cm) Temperature ' ( ° K ) Frequency (Hz) 5 . 3 0 1 . 5 2 7 3 , 2 3 4 , 4 6 4 5 . 6 0 1 . 5 3 9 3 , 2 3 4 , 1 7 8 5 . 7 0 1.542 3 , 2 3 4 , 0 2 9 5 o 9 0 1 . 5 5 0 3 , 2 3 3 , 8 7 0 6 . 5 0 1 . 5 7 1 3 , 2 3 3 , 7 6 3 6 o ? 0 1 . 5 7 8 3 , 2 3 3 , 7 5 4 7 . 0 0 1 . 5 8 7 3 , 2 3 3 , 7 3 1 7 . 2 0 1 . 5 9 4 3 , 2 3 3 , 7 3 3 V . 3 0 1 . 5 9 7 3 , 2 3 3 , 7 3 7 7 c 5 0 I . 6 0 3 3 , 2 3 3 , 7 3 9 7 . 7 0 1.611 3 , 2 3 3 , 7 4 9 80 0 0 1.618 3 , 2 3 3 , 7 6 6 8 . 3 0 1.62? 3 , 2 3 3 , 7 7 6 8 „ 5 0 1.634 3 , 2 3 3 , 7 9 7 9 « 0 0 1.648 3 , 2 3 3 , 8 2 0 9 . 3 0 I . 6 5 6 3 , 2 3 3 , 8 4 1 9 c 9 0 1.671 3 , 2 3 3 , 8 6 6 1 cm of.Hg = 1 2 . 9 6 cm of n-dibutyl phthalate (S.G. = 1 . 0 4 9 ) 3 2 TABLE II Experimental data of a typical run of a hydrated sample of M n C l ? . 4 H ? 0 single crystal.. (Plotted in f ig 1 3 ) Height of o i l manometer (cm) Temperature (°K) Frequency (Hz) 6 . 3 5 1 . 566 3 , 2 1 2 , 1 2 2 6 . 6 0 1 . 5 7 6 3 , 2 1 1 , 8 6 2 606O 1 . 5 7 6 3 , 2 1 1 , 8 6 2 7 . 0 0 1 . 5 8 9 3 , 2 1 1 , 4 3 3 7 - . ^ 5 1 . 6 0 3 3 , 2 1 0 , 8 4 8 7 . 7 0 1 . 6 1 0 3 , 2 1 0 , 5 4 2 8.00 1 . 6 1 8 3 , 2 1 0 , 4 0 2 8 . 2 0 1 . 6 2 4 3 , 2 1 0 , 3 9 0 8 . 3 5 1 . 6 2 8 3 , 2 1 0 , 3 8 7 8 . 5 0 1 . 6 3 4 3 , 2 1 0 , 3 8 3 8 . 7 0 I 0 6 3 8 3 , 2 1 0 , 3 8 5 9 . 0 0 1 . 6 4 8 3 , 2 1 0 , 4 0 4 9 . 3 0 I . 6 5 6 3 , 2 1 0 , 4 1 4 9 . 6 0 l o 6 6 4 3 , 2 1 0 , 4 3 5 9 - 8 0 1 . 6 6 8 3 , 2 1 0 , 4 4 8 1 0 . 1 0 I . 6 7 6 3 , 2 1 0 , 4 7 3 1 0 . 4 0 I . 6 8 3 3 , 2 1 0 , 5 0 5 1 0 . 9 0 1 . 6 9 4 3 , 2 1 0 , 5 4 5 1 1 . 1 5 1 . 7 0 0 3 , 2 1 0 , 5 7 6 1 1 . 4 5 1 . 7 0 7 3 , 2 1 0 , 5 9 7 1 cm of Hg = 1 2 o 9 6 cm of n-dibutyl phthalate ( S . G . = 1 . 0 4 9 ) X >- 3,234,500 o z: U J Z D O L U (T Li. O < o cn o 3,234,000 3,233,500 1.50 1.55 1.60 1.65 TEMPERATURE- (°K) Pig 12 Typical run of a 9 6 % deuterated sample of MnCl ?.4H 0 single crystal u> OSCILLATOR FREQUENCY Hi 3 5 TABLE III Neel temperatures of hydrated and deuterated MnCl^.^-H 0 Hvdrated Samnle Deuterated Sample Run T N (°K) Run T N (°K) 1 1 . 6 2 5 1 1 . 5 9 1 2 I . 6 3 0 2 1 . 5 8 9 3 1 . 6 2 8 3 1 . 5 8 2 4 1 . 6 2 4 4 1 . 5 8 3 5 1 . 6 2 3 5 1 . 5 9 5 6 1 . 5 8 7 Average 1 . 6 2 6 + 0 . 0 0 2 Average 1 . 5 8 8 + 0 . 0 0 2 3 6 curve a t h i g h e r t e m p e r a t u r e s i n r e g i o n I I changed by l e s s than 1 0 Hz o v e r a tem p e r a t u r e i n t e r v a l o f 2 0 m i l l i d e g r e e s . The measurements o f N e e l t e m p e r a t u r e , d e f i n e d i n t h i s way, o b t a i n e d from s e v e r a l r u n s agreed v e r y w e l l , as can be seen i n t a b l e I I I . Any s y s t e m a t i c e r r o r i n T N a r i s i n g as a r e s u l t o f our d e f i n i t i o n o f the N e e l temperature s h o u l d d i s a p p e a r when comparing the c r i t i c a l t e m p e r a t u r e s o f the h y d r a t e d and d e u t e r a t e d s a l t s . F u r t h e r m o r e , the average v a l u e o f T^ f o r MnCl2«4H,>0 was found t o be 1 . 6 2 6 ± 0 . 0 0 2 ° K which compares v e r y w e l l w i t h the v a l u e 1.62°K o b t a i n e d by F r i e d b e r g and Wasscher ( 2 5 ) by means o f s p e c i f i c heat measurements, and a l s o by Lasheen, van den Broek and G o r t e r ( 2 4 ) . .From T a b l e I I I , v/e can see t h a t the N e e l temperature o f the h y d r a t e d s a l t i s 1.626 + 0 . 0 0 2 ° K , w h i l s t t h a t o f the 9 6 $ d e u t e r a t e d sample i s I . 5 8 8 ± 0 . 0 0 2 ° K . Hence, t h e r e i s a change o f - 2 . 3 $ i n the c r i t i c a l t e m perature on 9 6 $ d e u t e r a t i n g M n C l 2 . 4 H 2 0 . S a h r i ( 1 3 , 14) ob s e r v e d a change o f + 6 $ on d e u t e r a t i o n o f C o C l 2 « 6 H 2 0 ; w h i l s t B e n o i t , D r o c o u r t , Legrand, Renard ( 2 6 ) measured a change o f - 3 $ i n T^ on d e u t e r a t i n g C u C l 2 . 2 H 2 0 . T u r r e l l and Yue ( 2 7 ) o b s e r v e d a change o f + 0 . 8 $ i n the C u r i e t e m p e r a t u r e o f the f e r r o m a g n e t i c C u ( N H ^ ) 2 B r ^ . 2 H 2 0 on complete d e u t e r a t i o n . A l l t h e s e s a l t s are o r d e r e d t h r o u g h hydrogen bonds i n t h e i r r e s p e c t i v e l a t t i c e s and a s e m i -q u a n t i t a t i v e e x p l a n a t i o n l i a s been a t t e m p t e d i n Ch a p t e r 4. 37 CHAPTER 4 • • DISCUSSION MnCl2»4H20 is a typical antiferromagnet containing hydrogen bonds and is magnetically ordered by superexchange interaction through the path of hydrogen bonds. The super-exchange interaction can be expressed by a Heisenberg-Dirac Hamiltonian of the form:-$c — — J i ^ s - . s . x 3 - i ~3 where S^ and S_. are the total spin operators associated with magnetic ions M- and M. respectively, and J- • is the exchange integral associated with and resulting from the interaction v ia non-magnetic ions intermediate in position between Mi and M . . Often i t can be assumed that = 0 1 3 1 J . except for nearest neighbours. For a ferromagnetic inter-action between and M. , J . . > 0; for an antiferromagnetic interaction, J . . < 0. The Neel temperature, at which magnetic ordering sets in can give a good measure of the strength of the interaction. , In hydrated salts with crystal structures that order magnetically, of which MnClg.^HgO is a typical and good example, the superexchange interaction often can be assumed 3 8 t o a c t through the m o l e c u l e s o f w a t e r o f c r y s t a l l i s a t i o n , s i n c e the ' p a t h ' t h r o u g h t h e s e m o l e c u l e s c o n s t i t u t e the s h o r t e s t d i s t a n c e between the n e i g h b o u r i n g magnetic i o n s . In r/inCl 2 .^HgO, a c c o r d i n g t o Z a l k i n , e t a l ( 1 6 ) , the f o u r hydrogen bonds t h a t e x i s t are g i v e n i n P.14. I t i s mentioned i n the I n t r o d u c t i o n ( P . 5 ) t h a t an a u t h o r i t a t i v e account o f the superexchange i n t e r a c t i o n has been g i v e n by Anderson ( 6 ) . He d emonstrates t h a t the m i x i n g up o f e x c i t e d s t a t e s produced by e l e c t r o n t r a n s f e r i n the p u r e l y i o n i c ground s t a t e s l e a d s t o a magnetic i n t e r a c t i o n ( u s u a l l y a n t i f e r r o m a g n e t i c ), between n e i g h b o u r i n g m agnetic i o n s . P i m e n t e l and M c C l e l l a n (28) c o n s i d e r s t h a t i n hydrogen b o n d i n g , i n a d d i t i o n to the predominant c o n t r i b u t i o n o f e l e c t r o s t a t i c a t t r a c t i o n between the i o n s f o r m i n g the hydrogen bond; c o v a l e n t b o n d i n g , i n v o l v i n g e l e c t r o n t r a n s f e r i s a l s o v e r y i m p o r t a n t . F o r the t y p i c a l hydrogen bond A - H B, the w a v e f u n c t i o n can be w r i t t e n , assuming the p o s s i b i l i t y o f the f o r m a t i o n o f v a l e n c e bond s t r u c t u r e s by: where the H"s r e p r e s e n t the f o l l o w i n g s t a t e s : 3 9 ^ 2 A - H B covalent A-H bond ^ 2 A~ H + . . B ionic bond (no charge transfer) A~ H - B + covalent H-B bond (with charge transfer) S'ij, A + H~ . . B ionic bond (no charge transfer) z A H~ . . B + covalent A-B bond (with charge transfer) J i 1 The quantities a^(i = 1 , 2 , . . . 5 ) are admixture coefficients. Of a l l these contributions to the tota l wavefunction probably only the f i r s t three are important, and of these the third is smallest according to Coulson and Danielson ( 2 9 ) . They estimate that for a 2 . 8 X hydrogen bond, OJ^ = )a]_| 2 = 0 . 5 7 - 0 . 6 2 , 6o2 = U 2 I 2 = 0 . 2 ? - 0 . 3 1 and CJ j = la^l 2 = 0 . 0 4 - 0 . l 6 . Since a supe.rexch.ange interaction across the hydrogen bond w i l l involve charge transfer, i t w i l l be the contribution of Cj^ which w i l l be responsible for the magnetic interaction in the bond r/l^A-H . . . . BM2« Thus we require an estimate of the change in the weight of this contribution resulting from deuteration i f we want to explain the isotope sh i f t . Ubbelohde and Gallagher ( 3 0 ) have shown.that deuteration does affect the hydrogen bond. In strong bonds where the distance R between A and B is ~ 2 . 5 X , there is an expansion in bond length ~0.04 X . In weaker bonds (R ~ 3.0 X ) the effect is-much smaller, and may be positive or negative. 40 Sahri and Bloom (14) have attempted to explain the result in CoClg^HgO by suggesting that J^2> ' t n e superexchange interaction between M^ and Mg, is l inearly related to the potential energy, V, of the proton in the hydrogen bond, i . e . . -—— = constant However, they then assumed that the change in hydrogen bond strength was given by the difference in the 0 - H bonding strength 'on deuteration. This assumption appears incorrect since we. know experimentally that the hydrogen bond usually weakens on deuteration. This results since the deuteron has a smaller zero-point energy than the proton so that i t is more strongly bonded to the A atom, but more weakly bonded to the B atom resulting in a weaker A - B bond and a consequent increase in the A - B length. We assume then that the relationship between J and V proposed by Sahri and Bloom is correct, provided we take V as a measure of the covalent contribution to the A - B bond energy, since we believe the charge transfer process to be important as discussed above. We need to calculate then the change in covalent energy, A v c , resulting from deuteration. Re id ( 3 1 ) has offered a semi-empirical treatment of the hydrogen bond. His complete expression for the potential energy of the proton is: 41 V ( r , R ) = U j . ^ ) + ^z^Z1 + W ( R ) ' where r ^ , r ^ and R = r-^ + r ^ are the A - H, H .. B, and A - B bond l e n g t h s r e s p e c t i v e l y . and are m o d i f i e d L i p p i n c o t t and S c h r o e d e r p o t e n t i a l s ( 3 2 ) , and W i s a term i n c l u d i n g i o n i c b o n d i n g , van der Waals r e p u l s i o n and the z e r o - p o i n t e n e r g y . Re i d i s a b l e t o c a l c u l a t e how each energy term and hence the t o t a l energy depends on R f o r a g i v e n bond. He can the n c a l c u l a t e the change i n R, AR, on d e u t e r a t i o n t o o b t a i n a r e s u l t i n agreement w i t h e x p e r i m e n t . U s i n g h i s c u r v e s we e s t i m a t e ( - f t - ) a and Thus f o r s t r o n g bonds ( R e : 2 . 5 A*; R a 0.04 A ) , we estimate ^4 = — £ a - 4 . 3 x 0.04 = -17% c i n e x c e l l e n t agreement w i t h the e x p e r i m e n t a l r e s u l t i n HCrOg ( 3 3 ) , c o n s i d e r i n g the s i m p l i c i t y o f the model. F o r o weaker bonds (R ~ J.O A ) , and assuming an e x p a n s i o n AR — 0.001 - X , we o b t a i n A J - 14 x 0.001 = -1.4%. 42 Of course in this case the change AR may be negative, yielding a small positive shift in J . An alternative approach to the problem is to use the CW) estimates of Coulson and Danielson who find that the weight of the structure ^ ^ changes considerably with bond length while the values of tu^ and to^ remain f a i r l y constant. They assume the relat ion r , - r ? _ 1 - exp ( ^ - ^ ) where C is a constant with value C = 0.3 A*. Since (O^ is re lat ive ly constant (changing from 0 . 6 0 to O . 6 5 for a change in bond length from 2 . 5 X to 2 . 8 X according to the estimates of Coulson and Danielson), we can write r l " r 2 u>^_ constant x exp ( Q ) If we assume that the change in u>_, w i l l cause a change A j in the superexchange interaction, we obtain A J - " 3 A r l ~ A r 2 — / V ^~ — J - W - C where Ar^ and A r _ are the changes in r^ and r^ on deuteration. V/e expect A r ^ < 0 because of the smaller zero point energy of the deuteron, and expect that usually A r 2 > 0 (certainly for strong bonds). For a strong bond, Reid estimates A r , —' - 0 . 0 1 and — + 0«>05 A* since the bond expands 0.0H- % overalls Thus for strong bonds A J 0 . 0 6 _ 9 f w _ _ = _____ ._. - 2 0 % , again in good agreement with the experimental result for HCr0 2 (33). 44 CHAPTER 5  CONCLUSION We have found that the effect of deuteration in a magnetic crystal can be quite readily measured by monitoring the frequency of an osc i l la t ing r . f . c i r c u i t , in which the tank c o i l contains the specimen. Owing to the need for accurate temperature measurements, and the res tr ic t ion on refrigerant l iquids; only crystals whose Neel temperatures for ant i f erromagne t i c substances,, and Curie temperatures for ferromagnetic substances, that l i e in the range of 1.4 - 4 .2°K can be studied by the above method. Hence i t is advisable to i n s t a l l an additional experimental setup, i . e . a variable temperature cryostat, operational between the boi l ing point of helium and room temperature, so as to study the deuteration effects on other ferromagnetic and ant iferromagnetic salts , e.g. FeCl o4H 0 , NiCl . 6 H ? 0 ; and also to study isotopic 18 substitutions, e.g. 0 in MnO. Furthermore, variations in the value of A j / j for different substances w i l l result from different chemical structures and bond-lengths when the electronegative end of the hydrogen bond involves Br~ instead of C l ~ . Hence a study of the isotope shift of MnBr ? . 4H 2 0 w i l l perhaps lead to a better understanding of the superexchange interaction. REFERENCE L. N e e l , Ann. P h y s i q u e 18, 5 ( 1 9 3 2 ) . C. G. S h u l l , V/. A. S t r a u s e r and E. 0. W o l l a n , Phys. Rev. 83_, 3 3 3 ' ( 1 9 5 D « C. G. S h u l l and J . S. Smart, Phys. Rev. _6, 1 2 5 6 ( 1 9 4 9 ) . H. A. 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