Spin-spin absorption in chromic methylammonium alum and manganous chloride tetrahydrate at very low temperatures

Ambler, E. Hudson, R . P . 1956

Physica X X l I 866-868

LETTER

TO

THE

EDITOR

Spin-Spin Absorption in Chromic Methylammonium Alum and Manganous Chloride Tetrahydrate at Very Low Temperatures Spin-spin absorption measurements were carried o u t o n Cr2(CH3NH3) 2(SO4)424H.O at frequencies from 0.1'to 10 mc/s and temperatures from 0.06 to I°K. All measurements were made in zero steady external field and with r[ magnetic fields of amplitudes up to about 1 oersted. A large amount of work I)has been done previously on m a n y salts at higher temperatures where Curie's Law is obeyed and where Broer's 2) theory of spin absorption is

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Fig. l. Complex part of the magnetic susceptibility of chromic m e t h y l a m m o n i u m alum, Z ' , (emu/g.ion) plotted as a function of the ~'magnetic temperature", T a, for various frequencies: e, 0.1; o, 0.5; x, 1; ,',, 2; v, 4; o, 6; and ~ 10 mc/s. Dotted line shows course of real past of susceptibility in arbitrary unets. generally in satisfactory agreement with experimental results. A good deM of work has also been done in the range of temperature below I°K where strong absorption has been observed at audio frequencies 1)3). The present measurements provide a link between these extremes which, from the theoretical point view, are considered as being more or less distinct. They are distinct i n the sense that the very low temperature measurements seem to be associated with cooperative ordering; they are the same however, in the sense that they both have their origin entirely within the spin system, and both could be described, in principle, in terms of the function f(v) defined b y Broer. m

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SPIN-SPIN ABSORPTION AT VERY LOW TEMPERATURES

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The e x p e r i m e n t a l m e t h o d was to measure t h e complex p a r t of the susceptibility, Z ' , b y the absorption method. The results are plotted as a function of the " m a g n e t i c t e m p e r a t u r e " T* 4) in fig. 1. A close analysis shows t h a t at the higher t e m p e r a t u r e s Z"o~ v b u t a t lower t e m p e r a t u r e s the v a r i a t i o n becomes progressively slower; at 0. I ° K X"oL v°'83. A t I ° K the r e l a x a t i o n c o n s t a n t 0' = 2.6 × 10 -9 sec and is falling slowly wfth increasing t e m p e r a t u r e (compare the results of V o l g e r et al. s) on chromic p o t a s s i u m a l u m ; O' = 1.6 × 10 -9 at 77°K). If we i n t e r p r e t our d a t a in t e r m s o f / ( v ) we find t h a t this f u n c t i o n increases as the t e m p e r a t u r e decreases, and decreases for t h e higher frequencies. This comparison m a y be of limited v a l u e at these v e r y low t e m p e r a t u r e s since the theoretical calculation of the q u a n t i t y would be o v e r w h e l m i n g l y difficult. I t would be e x t r e m e l y v a l u a b l e to h a v e a t h e o r y of spin relaxation here, however, because of t h e light it m i g h t t h r o w on the n a t u r e of a n t i f e r r o m a g n e t i c transi-

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Fig. 2. Complex p a r t of the m a g n e t i c susceptibility divided b y the angular f r e q u e n c y of m e a s u r e m e n t , X"/w, for m a n g a n o u s chloride t e t r a h y d r a t e , p l o t t e d as a function of the absolute t e m p e r a t u r e , T : e, 1; ©, 2 and &, 4 mc/s. The d o t t e d curve shows roughly, and w i t h a r b i t r a r y o r d i n a t e scale, the course of the real p a r t of the susceptibility. tions. Perhaps a more useful a p p r o a c h would be found in t r e a t i n g the local m a g n e t i c field from the p o i n t of view of r a n d o m processes, as has been done already w i t h the t h e o r y of the widths of resonance lines. W e h a v e also m a d e m e a s u r e m e n t s on MnC12.4H20 which is k n o w n to h a v e a transition p o i n t 0) (almost certainly antiferromagnetic) at a b o u t 1.62°K. The values of Z" divided by the angular f r e q u e n c y of measurement, co, are p l o t t e d in fig. 2 as a function of t h e absolute t e m p e r a t u r e T . . I t will be seen t h a t a single c u r v e fits all points fairly well, showing t h a t Z"cc ~o. The m o s t striking features are the sharp m a x i m u m at about, 2.3°K, well a b o v e the transition t e m p e r a t u r e , To, and a p p a r e n t l y no a n o m a l y at To. Now it is known from specific h e a t m e a s u r e m e n t s 6) t h a t appreciable short-range order persists at t e m p e r a t u r e s a b o v e Tc. W e suggest t h a t our results show t h a t below

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SPIN-SPIN A B S O R P T I O N

AT VERY LOW

TEMPERATURES

the m a x i m u m in Z'" there is an appreciable r e d u c t i o n in a m p l i t u d e of the F o u r i e r c o m p o n e n t s of t h e local field w i t h frequencies higher t h a n t h e m e a s u r i n g frequency. Some slight evidence for this p o i n t is o b t a i n e d b y a close inspection of t h e X" vs T curves, where t h e curves for t h e higher frequencies h a v e m a x i m a a t progressively higher t e m p e r a t u r e s ; t h e effect, however, is v e r y small. W e h a v e tried also to m a k e a comparison w i t h Broer's t h e o r y a t t h e higher t e m p e r atures. U n f o r t u n a t e l y , the p r o b l e m is v e r y c o m p l i c a t e d in this salt because S t a r k splitting and dipolar, e x c h a n g e and hyperfine coupling are all i m p o r t a n t . A t 4°K, for example, t h e calculated v a l u e of X"/~ assuming only dipolar coupling is shown b y p o i n t D in fig. 2. P o i n t S shows the v a l u e w h e n S t a r k splitting is included. T h e effect of isotropic e x c h a n g e is to m o v e t h e p o i n t upwards, b u t t h e precise v a l u e is h a r d to calculate and a rough e s t i m a t e shows t h a t it will p r o b a b l y m o v e it s o m e w h a t a b o v e our e x p e r i m e n t a l curve; hyperfine coupling, on the o t h e r hand, w o u l d t e n d to bring it down. The points show, s o m e w h a t surprisingly, t h a t e v e n q u i t e close to the transition p o i n t the t h e o r y does n o t give values t h a t are in g r e a t d i s a g r e e m e n t w i t h experiment. W e hope to e x t e n d this t y p e of m e a s u r e m e n t to o t h e r substances; single crystals w i t h effective S = { and strong a n i s o t r o p y should produce interesting results, more a m e n a b l e to comparison w i t h theory. A c o m p l e t e description and discussion of these results is being s u b m i t t e d to The P h y s i c a l Review. E. AMBLER R. P. HUDSON Cryogenic Physics Section, National Bureau of Standards Washington 25, D.C. U.S.A. Received 14-8-56.

REFERENCES 1) Gorter, C. J., "Paramagnetic Relaxation", Elsevier, Amsterdam (1947). 2) Broer, L. J. F., Physica 10 (1943) 801. 3) See e.g. reviews by Ambler, E. and Hudson, R. P., Repts on Prog. in Phys.18 (1955) 251 or De Klerk, D. and S t e e n l a n d , M. J., "Progress in low Temperature Physics", Vol. I, Ed. C. J. Gorter, North-Holland Pub. Inc., Amsterdam (1955). 4) The T*-T relation has been given by Gardner, W. E. and Kurti, N., Proc. roy. Soc. A 2 2 3 (1954) 542. 5) Volger, J., De Vrijer, F. W. and Gorter, C. J., Physica 13 (1947) 635. 6) F r i e d b e r g , S. A. and Wasscher, J. D., Physica 19 (1953) 1072.