Paramagnetic dispersion in some copper and silver salts

P h y s i c a X l I I , no 8

S e p t e m b e r 1947

PARAMAGNETIC DISPERSION IN SOME COPPER AND SILVER SALTS by

L. J. F.

B R O E R and J. KEMPERMAN

Communication from the Zeeman-laboratoriunl of the University of Amsterdam

Summary T h e p a r a m a g n e t i c d i s p e r s i o n of s o m e c o p p e r salts a n d Ag(CsHsN)4 (NO3) 2 has been m e a s u r e d . The o c c u r e n c e of d i s p e r s i o n is in a g r e e m e n t w i t h t h e o r y , b u t t h e specific h e a t s of t h e spin s y s t e m in all cases are m u c h t o o large to be a c c o u n t e d for b y m a g n e t i c i n t e r a c t i o n . The diffic u l t y m e t in c o m p a r i n g t h e caloric, m a g n e t o s t a t i c and r e l a x a t i o n d a t a on c o p p e r s u l p h a t e is discussed.

Introduction. CUS04.5 H20 was one of the salts in which T e un i s s e n 1) could not detect any dispersion. Later G r 0 e n d ij k and G 0 r t e r (unpublished measurements) found dispersion phenomena in Cu(NH4) 2 . (S04) 2 . 6 H20. The accuracy obtainable with their apparatus however did not permit the determination of the characteristic constants 0 and F. As the magnetic and caloric behaviour of copper salts at very low temperatures presents soms interesting features we thought it justified to repeat and extend these experiments. Owing to some improvements in the experimental technique 2) we succeeded in obtaining the relaxation constants of some salts, albeit that the accuracy was not very good. This is caused by the low susceptibility of copper salts, the copper ion having only one spin. 1. Theorelical considerations. According to the theory of C as i m i r and d u P r 6 3) the paramagnetic dispersion is described by the formulae: ;( F --= (I--F) (1) ZO ' 1 -~- 02V2 .~2 F =

--

Physica XIII

n~ + n 2 465

(2)

--

30

466

L. J. F. BROER AND J. KEMPERMAN

The constant H h is connected to the specific heat of the spin system b/Tzby the relation H~=b/C, where C is the C u r i e constant. The object of the investigation is the determination of b and O. Both constants have been the subject of some theoretical considerations. The general theory of the specific heat of the spin system is dueto Van Vleck and H e b b and P u r c e l l 4 ) . T h e y g i v e the expansion of the specific heat in powers of T -1. We are concerned here only with the first term bT-2. Two contributions are to be taken into account, viz. the splitting of the levels of one single ion b y the electrostatic field caused by the surroundings and the magnetic interaction of the spins. As the copper ion has only one spin (configuration 3d 9) presumably there are no small electrical splittings, so only the magnetic interaction is left and b is easily calculated. As we are only interested in the order of magnitude here we shall suppose that the arrangement of the ions is cubical and neglect the contribution of the.orbital moment to C. It is then found b y evaluating V a n V 1 e c k's formulae that:

3,25. H,, =

v

10 4

(3)

where V is the molar volume. The theory of the relaxation constant e is also due to V a n V 1 e c k 5). A very rough explanation of the complicated procedure has been given b y one of the authors e). The detailed calculations were made for chromium and titanium alum only. But, Ti +++, configuration 3d, being in magnetical respects rather analogous to Cu ++, configuration 3d 9, (and Ag ++, configuration 4d 9) some conclusions can be drawn from the theory for our purposes. The lowest level of the ions under consideration is 2D. When the five-fold orbital degeneration is removed b y a field of nearly cubical symmetry we get two groups of two and three orbital levels, respectively. The distance between the groups is of the order of 20.000 cm - t . In Ti-alum the splittings within each group are only a few hundred cm -1 as the deviations of cubical symmetry are very small here. Under these circumstances the calculated value of ~ at liquid air temperatures is only of the order of 10-9 sec which is b y far too small to be observable with the means at our disposal. When the deviations of cubical symmetry increase the distance of

PARAMAGNETIC

DISPERSION

IN SOME COPPER AND SILVER SALTS

467

the lowest orbital level from the other level (s) of its group increases. Because the expression for 0-~ contains this distance as a resonance denominator (0 actually depends on the sixth power of the distance), o will be larger in this case. We are therefore faced with the somewhat curious conclusion that here a large crystalline asymmetry is favorable for the observation of dispersion in contrast to what we are used to e.g. for chromium and iron salts. In these salts increase of asymmetry has little influence on 0, which is of observable magnitude in the cubical case too, whereas it causes such high values of H h that the dispersion cannot be detected with our magnet, which permits fields up to 3200 Oersted only. In copper salts on the contrary 0 increases strongly with increasing asymmetry as the lowest orbital level is degenerate in a field of cubical s y m m e t r y . On the other hand there is no electrical splitting here, therefore no influence of the asymmetry of the crystalline field on H h need to be feared. Now it has been shown by P o l d e r S ) that the data on the susceptibility and the magnetic anisotropy of copper sulphate and copper potassium sulphate can be interpreted quite naturally by assuming a very large deviation from cubical symmetry. According to his calculations the distance from the lowest level to the others is about 12.000cm -1 in these salts. This conclusion is strongly supported by X-ray structural analysis. Occurence of paramagnetic dispersion in these substances at frequencies of 106-107 Hz is therefore not, as T e u n i s s e n 1) thought, in contradiction to theory.

2. Experimental results. We will present our data in the form of tables of Q and F, omitting all graphs for the sake of briefness. Cu(NH4) 2"(S04) 2 . 6 H20. ' The sample was prepared by crystallisation from a mixture of molar aequivalent solutions of copper sulphate (d e H a e n) and potassium sulphate (S c h e r i n g and K a h 1 b a u m ) . The results of the measurements are collected in Table I. TABLE I '

I I

Values of ~ a n d F for Cu(NH4) 2 . SO4).., . 6 H~O

400

0,47

8°° I

6,59

2400

I

o,s7

0,28

/

I

o,33

0,40

0,47

0,77

o,gs

468

L.J.F.

BROER AND J. KEMPERMAN

From the values of F we obtained Hh = 425 Oersted, b/C = 0,18.106 Oersted 2. D ij k s t r a 8), observing the paramagnetic absorption, gives nearly the same values of 0, but his F values are somewhat larger, resulting in H h = 375 Oersted. CUK2(SO4)2.6 H20. This sample was prepared in exactly the same way as the former. The experimental data are collected in Table II. TABLE I[ Values of Q and F for CuK=(SO,)=. 6 H,O H

0 . 10s (770 )

0 . 106 (90o)

F

400 800 2400

0,66 0,80 0,90

0,43 0,48 0,54

0,57 0,81 0,95

From the values of F we obtained H h =: 345 Oerstedl b/C---0,12.106 Oersted 2. This value is in good agreement with experiments in Leiden on relaxation and adiabatic cooling, which yielded H h = 355 Oersted ~). CUSO4.5 H20. Some measurements were performed on a sampl e obtained from d e H a e n. It turned out that the relaxation constant was so small that only the beginning of the dispersion curves was observable. The minimal value of Z'/Zo was 0,87 at 13,2.106 Hz, 3200 Oersted and 77°K. As Z is rather small here it is hardly possible to draw conclusions from these observations as F cannot be determined with any certainty. V o 1 g e r 10) made extensive observations on the paramagnetic absorption of this salt. 'Unfortunately the values of F cannot be inferred from this work either as the difference between the spin and lattice relaxation constants is too small at liquid a i r temperatures. His conclusion is that b/C will be probably between I0 and 20.106 Oersted 2. As our measurements agree somewhat better with the first value we will, rather arbitrarely, adopt it. The values of 0 and F concluded to from t h a t assumption are collected in table III. TABLE I f [ Values of Q and F for CuSO,. 5 H=O with b/C = 10. 10' Oersted z, H h = 3200 Oersted. H

O. 10a(77°)

O. 108(90°)

2400 3200

5,2 5,7

4~5 5,0

F 0,22 ~ 0,34

PARAMAGNETIC D I S P E R S I O N IN SOME COPPER AND S I L V E R SALTS

469

T h e values of ~ are somewhat larger t h a n those given b y V o ig e r. E v e n t u a l l y we stress t h a t neither V o 1 g e r's nor our measu r e m e n t s do prove the v a l i d i t y of (2). T h e specific heat of CUS04.5 H 2 0 has been studied b y A s hm e a d 11) and D u y c k a e r t s 1~.). W e wil~ discuss their results in the n e x t section in connection with the relaxation data. Cu(CsHsN)4.(NO3) 2. This sample and the n e x t one were p u t at our disposal b y the L a b o r a t o r y for Inorganic Chemistry t h r o u g h the kind offices of Mr P. F. v a n V e 1 d e n, chem. drs. The d a t a on the r e l a x a t i o n constants are here still less accurate t h e n in the other cases, p a r t l y because these constants t u r n e d out to be r a t h e r high, p a r t l y because of the e x t r e m e l y low v o l u m e susceptibility of the compounds. T h e last fact w a s the more i n c o n v e n i e n t as the glass tilbes containing the samples could be m o l t e n to only when p a r t i a l l y filled as these substances are inflammable and r a t h e r unstable. W e will therefore mention only here t h a t H h is approxim a t e l y 500 Oersted (b/C -~ 0,25.106 Oersted2), whereas at 77°K q is a b o u t 4 . 1 0 - 6 sec at H ---- 800 Oersted. Ag(CsH~N)4.(NQ) 2. T h e s a m e d i f f i c u l t i e s as in the former case are met here to a slightly less extend. Here we f o u n d H h = 1600 Oersted (b/C -~ 2,5.106 Oersted 2) and 0 a b o u t 3,5 and 3 . 1 0 - 6 sec at 77°K and H - - - 2 4 0 0 resp. 1600 Oersted. In passing we m a y mention the fact t h a t the two pyridine compounds change colours u p o n cooling m u c h more t h a n a n y other salt we h a v e investigated. The deep blue copper salt is of a bright violet at 77°K, whereas the yellow-brown silver salt turns to orange. Cu(BrO3) 2. 6 H20. Cu(NH3)4SO4. H20. W e could not detect a n y dispersion in these salts at 77°K u p to v = 13,2.106 H z and H := 3200 Oersted. 3. D i s c u s s i o n . In section 1 we showed t h a t the t h e o r y of V a n V 1 e c k leads to the e x p e c t a t i o n t h a t copper salts will show relaxation in our f r e q u e n c y range only when the crystalline fields strongly deviate from cubical s u m m e t r y . F r o m the work of P o 1d e r this is k n o w n to be the case with the three first substances m e n t i o n e d in section 2. D a t a on the s t r u c t u r e and the magnetic

470

L.J.F.

BROER

AND J. KEMPERMAN

anisotropy of the pyridine nitrate seem to be lacking. However, as this compound shows a very strong dichroism *) it is probable that here too the non-cubical terms in the potential are strong. On the other hand the macr0scopical symmetry of the bromate is cubical, so it is hardly to be expected that in this salt the crystalline potential will differ much from cubical s y m m e t r y as it seems plausible t h a t the copper ion here is surrounded by an octahedron of water molecules. On the ammonia sulphate, which is rhombic, we are somewhat less certain but nevertheless we can say that our experiments in general agree with theory in this regard. The lack of dispersion in the bromate might be due to a very large value of Hh, but, as the molar volume of the bromate (165) is much larger than t h a t of the sulphate (110) we do not think this very probable. The silver pyridine nitrate is, as far as we are aware, the first instance known of a salt of an ion not belonging to the iron or the rare earth groups, which shows relaxation. Often the salts of the palladium and platinum groups do not show normal paramagnetism, the susceptibility then is lower than would be expected according to B o s e-S t o n e r (free spins). It seems however that bivalent silver complexes have about the Same susceptibility as copper salts 13). This was confirmed by a rough measurement on the silver pyridine nitrate at 290°K and 77°K by Messrs F. H. Fischer and J . W . E . V o s in this laboratory. They found a magneton number of 1,7 at both temperatures. There is no reason therefore that these salts would not show relaxation phenomena analogous to those in copper salts. Next we turn to the discussion on the ~pecific heat constants b. The experimental data are collected in table IV. T A B L E IV V a l u e s of V a n d

•

Substance

V

Cu(NH4)s (SO4)2.6 H20 C u K 2 . (SO~) 2 . 6 H 2 0 C u S O 4 . 5 H~O Cu(CsH6N)4(NOa),. A g ( C s H s N ) 4 . (NOa). . . . . . . .

206 198 110 310 310

The theoretical values of

,

b/C are

b/C

lO-e'b/C (theor.)

10- s . b/C (exp.)

bexp'/bth"

0,025 0,026 0,09 0,011 0,011

0,18 0,12 10-20 0,25 2,5

7 4,5 110-220 23 230

obtained from formala (3). The

*) T h i s w a s k i n d l y p o i n t e d o u t t o us b y D r C . H . M a c

Gillavry.

PARAMAGNETIC

DISPERSION

IN SOME COPPER

AND SILVER

SALTS

471

molar volume of the copper pyridine nitrate was taken from a preliminary measurement by Mr. J. L. d e V r i e s (Laboratory for Inorganic Chemistry). For the silver compound we can safely assume the same value. It is seen from table IV that the magnetic interaction cannot account even for the order of magnitude of b/C. This was known already for CUK2(SO4)2.6 H20 from the Leiden measurements 9). Appearently this discrepancy is rather frequent with copper salts. Usually an explanation is sought for in the direction of a superexchange interaction between the copper ions as has been discussed by K r a m e r s 14). It is not yet clear however if the order of magnitude of b can really be explained in this way. In this connection we mention that an exchange coupling of the magnitude of the magnetic interaction perhaps could have escaped notion in chromium, iron and gadolinium salts. The values of the electric splitting of the spin levels of these ions would be lowered somewhat in this case. Eventually we will consider the data on the specific heat of CuSO 4 . 5 H20 at low temperatures. When at higher temperatures the specific heat is represented by the formula bT -2 it will in general show a maximum at a temperature of the order of z--: ~v/b/R. Now, if the specific heat of the lattice according to D e b ij e is subtracted from the curves given by A s h m e a d 1~) and D u y ck a e r t s 12) the resulting plot shows two maxima, viz. at about 0.1°K and I°K. If both of these were connected with the spin system b would presumably be so high as to prevent observation of the paramagnetic dispersion with our means. In this way one is tempted to assume that the second maximum has nothing to do with the spins. A further argument for this assumption is that, when the entropy is computed by 'graphical integration from the corrected curve, about 1,2 R is obtained. (The temperature range of A s h m e a d's measurements is not quite extended enough on the lower side to give an exact result). As the large magnetic anisotropy indicates that no electrical splittings of the order of 1 cm -1 are present 4) we would" expect 0,7 R. This amount seems reconcilable with the curve obtained by omitting the second maximum too *). *) I n a r e c e n t discussion w i t h Dr. A s h m e a d it a p p e a r e d t h a t on this g r o u n d he t o o w a s led to s u p p o s e t h a t t h e s e c o n d m a x i m u m w a s n o t c a u s e d b y the spins.

.472

P A R A M A G N E T I C D I S P E R S I O N IN SOME C O P P E R A N D S I L V E R S A L T S

A difficulty of the hypothesis mentioned would be to imagine what can happen in the crystal at about I°K apart from static spin interaction to cause this extra entropy. Furthermore it might be hard to reconcile it (at least together with P o 1 d e r's theory) with the measurements of R e e k i e 15) who found that the powder susceptibility obeys the C u r i e - W e i s s law down to helium temperatures with 0 as high as 0,7°.K. However, according to recent measurements of d e K 1 e r k 9), in CuK2(SO4) 2. 6 H20 0 =-- 0,05 oK. The ratio of b and 0 therefore seems to be approximately the same in both salts. (The magnitude of this ratio is in accordance with the assumption of superexchange). As the specific heat of the po.tassium sulphate obeys the b T - z law between 0.2 and 0,8°K it might very well be that the value of 0 in the sulphate could be explained without referring to the second maximum of the specific heat. The authors are very much indebted to Prof. dr. C. J. G o r t e r for his stimulating interest in this work. Received May 1st, 1947

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14) 15)

P. T e u n i s s e 1 1 , Thesis, Groningen 1939. L. J. F. B r o e r and D . C . S c h e r i n g , Physica I0, 631, 1943. H. B. G. C a s i m i r and F. K. d u P r 6 , Physica 5, 507, 1938. J.H. Van Vleek, J, chem. Phys. 5, 320, 1937. M.H. Hebb a n d E . M. P u r c e l l , J. chem. Phys. 5 , 3 3 8 , 1937. J.H. Van Vleek, Phys. Rev. 57, 426,1940. L. J. F. B r o e r , P h y s i c a l 3 , 3 5 3 , 1947. D. P o l d e r , Physiea 9, 709,1942. L . J . D ij k s t r a, Thesis, A m s t e r d a m , 1943. D. d e K l e r k , Physiea 12, 513, 1946. J. V o 1 g e r, Thesis, Leiden, 1946. J. A s h m e a d , Nature 143, 853, 1939. G. D u y e k a e r t s , Bull. Soe. roy. Sei. Li~ge, 10,281, 1941. G.T. Mbrgan and S. S u g d e n , Nature 128,51, 1931. L. C a p a t o s andN. P e r o k i s , C . R . Aead. Seie. 202, 1773, 1936. W. K l e m m . Z. anorg, allg. Chem. 201, 32, 1931. H.A. Kramers, Physiea 1, 183, 1934. J. R e e k i e , Proe. roy. Soe.,173, 367, 1939.