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Heat capacity measurements on manganese, nickel- and cobalt-lanthanum-double nitrate
Volume 25A, number 4
PHYSICS LETTERS
Then the e l e c t r o n i c p o r t i o n of the i n t e r a c t i o n m a y be r e p l a c e d by an e f f e c t i v e m a g n e t f i e l d at the nucleus p r o p o r t i o n a l to ( i IJI i). The H a m i l t o n i a n then b e c o m e s ~ = g n ~nHeff" I , which p r o d u c e s 21+1 equally s p a c e d n u c l e a r Z e e m a n l e v e l s . The c r y s t a l f i e l d l e v e l s of the 4I~ m u l t i p l e t of E r in e r b i u m e t h y l s u l p h a t e have ~een m e a s u r e d [4]. F r o m this it is known that at 4 . 2 o K only the l o w e s t K r a m e r ' s doublet i s occupied. Taking into account the C3h s y m m e t r y and u s i n g an effective s p i n S ' =½ the H a m i l t o n i a n f o r the doublet m a y be r e w r i t t e n : ~ = A~ S~Iz + + A.L (Sxl x + S ' I y ); A J~ and A , have b e e n c a l c u l a t e d using g~ = 1 . 5 ~ ± 0 . 0 5 , g ± = ~ 7 7 + 0 . 0 3 [2], gn = = 0.318~0.010 [5] and (~-3)eff = 10.60 a.u. [6]. Since no m a g n e t i c f i e l d is p r e s e n t to s p l i t the doublet and A£ i s l a r g e , the effective f i e l d a p p r o x i m a t i o n i s not v a l i d and a l a r g e d e v i a t i o n f r o m equal s p a c i n g i s o b s e r v e d . Using the above A , and A ± the line p o s i t i o n s c a l c u l a t e d f r o m the equation f o r ~ a g r e e with the o b s e r v e d ones within e x p e r i m e n t a l e r r o r . The n u c l e a r q u a d r u pole i n t e r a c t i o n c a l c u l a t e d f r o m c r y s t a l f i e l d d a t a [4] is n e g l i g i b l e , a s i s the i s o m e r shift [5]. A f u r t h e r c o n s e q u e n c e of the l a r g e g± is that the
HEAT
28 August 1967
s p i n - s p i n r e l a x a t i o n i s f a s t in m a g n e t i c a l R c o n c e n t r a t e d m a t e r i a l s . T h i s e x p l a i n s the difficulty is o b s e r v i n g v i o l a t i o n s of the e f f e c t i v e f i e l d a p p r o x i m a t i o n . F u r t h e r d e t a i l s w i l l be r e p o r t e d e l s e w h e r e [7]. The authors wish to thank Dr. Ursel Zahn for preparation of the absorbers and Dr. A. Meyer from Siemens A G Forschungslaboratorium Miinchen for providing the HoAl 2.
Refe~'~ces 1. H.H.Wickman, M.P.K1eh~ and D.A.Shlrley, Phys. Rev. 152 (1966) 345, and references therein. 2. G.H. Larson and C.D.Jeffries, Phys. Rev. 141 (1966) 461.
3. A. Abragam and M . H . L . P r y e e , Proc. Roy. Soc. (London) A205 (1951) 135. 4. J.C. Hfil and R.G.Wheeler, Phys. Rev. 152 (1966) 482. 5. E. MUnck, D.Quitrnann and S. Htffner, Z. Naturfor~ sch. 21A (1966) 847. 6. B. Bleaney, in Proc. 3rd Int. Symp. on Quantum electronics, Paris (1963), p. 595 ft. 7. Zeitschr. f. Physik, to be published.
CAPACITY MEASUREMENTS ON MANGANESE, NICKELCOBALT-LANTHANUM-DOUBLE NITRATE
AND
K. W. MESS, E. LAGENDIJK and W. J. H U ~ K A M P Kamerlingh Onnes Laboratory, Leiden, The Netherlands Received 7 July 1967
Heat capacity measurements of Mn-, Ni-, and Co-lanthanum-nitrate have shown singularities at T N = = 0.230°K, T N = 0.393°K and T N = 0.181°K respectively, which are due to magnetic long range order.
In t h i s l e t t e r we r e p o r t on the p h a s e t r a n s i t i o n of La2Mn3(NO3)1224H20, La2Ni3(NO3)1224H20 and La2Co3(NO3)1224H20, which show s i n g u l a r i t i e s in the h e a t c a p a c i t y below l ° K . The m e t h o d of m e a s u r e m e n t h a s been d e s c r i b e d in an e a r l i e r p u b l i c a t i o n [1]. The h e a t c a p a c i t y d a t a a r e shown in fig. 1, a f t e r s u b t r a c tion of e m p t y c a l o r i m e t e r h e a t c a p a c i t y and of the h y p e r f i n e s t r u c t u r e i n t e r a c t i o n c o n t r i b u t i o n . The l a t t e r m a y be e s t i m a t e d a c c o r d i n g to Ch.f.s./R
=
if(I+I)A2S2/k2T 2
in which the h.f.s, coupling p a r a m e t e r i s known f r o m E P R - m e a s u r e m e n t s [2] in i s o m o r p h o u s L a - M g - n i t r a t e o r B i - M g - n i t r a t e . By e x t r a p o l a tion of C a c c o r d i n g to a T - 2 - d e p e n d e n c e a t high T and a c c o r d i n g to a m o l e c u l a r f i e l d a p p r o x i m a t i o n at low T one can e s t i m a t e the t o t a l e n t r o p y y i e l d of the h e a t c a p a c i t y a n o m a l y . The r e s u l t s a r e given in t a b l e 1, f r o m which it i s s e e n that r e a s o n a b l e a g r e e m e n t with the v a l u e R i n (2S+ 1) i s o b t a i n e d in the t h r e e c o m pounds, h e n c e the h e a t c a p a c i t y m a y be e x p l a i n e d e n t i r e l y in t e r m s of m a g n e t i c o r d e r i n g of the electronic spins. 329
Volume25A. number 4
PHYSICS LETTERS
28 August 1967
Table 1 TN(OK)
AS/R
- ln(2S + 1)
(Soo-S c)/R
Eto t / R
-E c / E t o t
CT2/R
La2Mn3-nitrate
0.230
1.75
1.79
1.135
0.436
0.62
0.060
La2Ni 3 -nitrate
0.393
1.07
1.10
0.225
0.388
0.41
0.045
La2Co 3 -nitrate
0.181
0.680
0.693
0.291
0,150
0.61
0.0160
By i n t e g r a t i o n of C one obtains f r o m the data a l s o the e n e r g y yield, E c , above the t r a n s i t i o n point and a l s o the t o t a l e n e r g y y i e l d E t o t. The q u a n t i t i e s E c and Ec/Eto t have a l s o been l i s t e d in table 1. S u s c e p t i b i l i t y m e a s u r e m e n t s , u t i l i z i n g the s a m e a p p a r a t u s , have shown that in the M n - and C o - c o m p o u n d s X d e c r e a s e s s t r o n g l y at the t r a n s i t i o n point, when the m e a s u r i n g f ie ld is p a r a l l e l to the c r y s t a l l o g r a p h i c c - a x i s , w h e r e a s X is a p p r o x i m a t e l y constant below the t r a n s i t i o n point when the m e a s u r i n g f i e l d is p e r p e n d i c u l a r to the c - a x i s . F o r the N i - c o m p o u n d , h o w e v e r , no such d e c r e a s e i s o b s e r v e d , and on b a s i s of the s u s c e p t i b i l i t y m e a s u r e m e n t s only, it i s not e x c l u d e d that the N i - s a l t i s f e r r o m a g n e t i c . T he m a g n e t i c a n i s o t r o p y m a y be r e l a t e d to c r y s t a l l i n e f i el d e f f e c t s , which a r e e x p r e s s e d by the p a r a m e t e r D in the s p i n - H a m i l t o n i a n t e r m D{S2z-~S(S +1)}. F o r Mn D/k = -0.0310OK f o r one t h i r d of the ions and D/k = -0.0070°K f o r the r e m a i n i n g two t h i r d s [2,3]. Hence c r y s t a l l i n e fie ld e f f e c t s a r e a l s m o s t n e g l i g i b l e f o r the a n a l y s i s of the heat c a p a c i t y data of the M n - s a l t e.g. they c o n t r i b u t e about 4% to the heat c a p a c i t y at T >> T N. F o r the N i - c o m p o u n d at low T a v a l u e D/k = +0.29°K has been found [4]. T h i s v a l u e is in r e a s o n a b l e a g r e e m e n t with what can be e s t i m a t e d f r o m the r e s u R s of E P R - m e a s u r e m e n t s of Hoskins et al. [5] in i s o m o r p h o u s L a - M g , L a - Z n , B i - M g and B i - Z n - d o u b l e n i t r a t e s . It is u n c e r tain w h e t h e r the D - v a l u e p e r t a i n s to }, } or a ll N i - i o n s , but we will a s s u m e that a ll ions have D/k = +0.29. In any c a s e a c o n s i d e r a b l e c o n t r i b u tion to the heat capacity at T >> TN has to be e x p e c t e d and m ay acco u n t f o r at m o s t about one t h i r d of the m e a s u r e d CT2/R v a l u e . S i m i l a r l y , in the L a - N i compound, the e n e r g y y i e l d is not e n t i r e l y due to m a g n e t i c i n t e r a c t i o n s but roughly half the e x p e r i m e n t a l v a l u e has to be a t t r i b u t e d to c r y s t a l l i n e f i e l d e n e r g y . F r o m the e x p e r i m e n t a l data and f r o m the e qua t i o n s
E/R qS2j/k,
CT2/R=2qS2(S+I)2j2/3k 2
w h e r e J i s the H e i s e n b e r g e x c h a n g e constant and q is the n u m b e r of n e a r e s t n e i g h b o u r s , one m a y
330
4O i
i Co
I Mn
I
I
I
06
08
Ni
oz 2O
10
2
1 01
T
02
0.3
04
lO°K
Fig. 1. Heat capacity Cmag, of Mn-. Ni- and Co-lanthanum double nitrate as a function o f t on a double logarithmic scale. obtain a value of the c o o r d i n a t i o n n u m b e r q. Such a c o m p a r i s o n l e a d s to low q ( ~ 2). F o r the C o - s a l t the above f o r m u l a e would give q ~ 6, but f o r the a n i s o t r o p i c C o - i o n s it would not be r e a s o n a b l e to c o m p a r e the r e s u l t s with the H e i s e n b e r g m o d e l . It i s known that f o r o t h e r C o - s a l t s the heat capacity ab o v e T N i s c o m p a r a t i v e l y s m a l l ; t h e o r e t i c a l l y , taking the Ising m o del, this r e d u c t i o n (at constant qJ, o r e q u i v a l e n t ly TN or m o l e c u l a r field) is a f a c t o r of t h r e e and would then alSO lead to q ~. 2. T h i s m ay not be u n r e a s o n a b l e in v i e w of the c r y s t a l s t r u c t u r e [6], f r o m which it is found that e v e r y m a g n e t i c ion
Volume25A, number 4
PHYSICS LETTERS
has at l e a s t t h r e e n e i g h b o u r s at 7.15.~, but § have one neighbour at 5.2A and the r e m a i n i n g -~ have t h r e e m o r e n e i g h b o u r s at 7.15/~. It is quite p o s s i b l e that the i o n - p a i r s at 5.2 A distance have a relatively strong magnetic interaction. In this c o n n e c t i o n we m e n t i o n additional e x p e r i m e n t a l r e s u l s . When an e x t e r n a l m a g n e t i c field was applied a d i a b a t i c a l l y to the M n - s a l t , the t e m p e r a t u r e change along an i s e n t r o p e could be m e a s u r e d and was found to show two distinct ext r e m a , the l a t t e r one p r o b a b l y close to the p a r a m a g n e t i c - a n t i f e r r o m a g n e t i c t r a n s i t i o n r e g i o n in the H-T phase d i a g r a m [1]. The l a t t e r m i n i m u m was found at low T to o c c u r at 5 kOe. F r o m the e n e r g y y i e l d in the L a - M n - s a l t one d e r i v e s on b a s i s of m o l e c u l a r field theory that at T = 0 the m o l e c u l a r field would be only 2250 Oe. It may t h e r e f o r e be s u g g e s t e d that the e x p e r i m e n t a l v a l u e of 5 kOe r e f e r s to the field r e q u i r e d for b r e a k i n g the a n t i f e r r o m a g n e t i c coupling between two M n - i o n s and this would a l s o b e t t e r a g r e e with the r e l a t i v e l y l a r g e entropy y i e l d above TN in the M n - c o m p o u n d . Quite s i m i l a r r e s u l t s were seen in the N i - c o m p o u n d , where a field of 5.7 kOe i s r e q u i r e d . We m e n t i o n f u r t h e r a l s o n u c l e a r o r i e n t a t i o n e x p e r i m e n t s on 54Mn i n c o r p o r a t e d in the L a - M n n i t r a t e s i n g l e c r y s t a l . The a n i s o t r o p y of the e m i t t e d g a m m a r a y s was o b s e r v e d with the aid of two c o u n t e r s , p a r a l l e l and p e r p e n d i c u l a r to the applied m a g n e t i c field, w h e r e a s the t e m p e r a t u r e could be kept at a c o n s t a n t value of about 0.05°K while v a r y i n g the m a g n e t i c field s t r e n g t h or d i r e c t i o n . When the field was along the c-axis it was found that the n u c l e a r s p i n s were p r e f e r e n t i a l l y a l i g n e d a l o n g the c - a x i s . However, t h e r e was a t r a n s i t i o n r e g i o n b e t w e e n 2.5 and 4 kOe, where the n u c l e a r s p i n s m u s t have been t u r n e d
28 August 1967
away f r o m the c - a x i s to a c o n s i d e r a b l e extent, i.e. r e d u c i n g the g a m m a a n i s o t r o p y n e a r l y to zero. When the field was p e r p e n d i c u l a r to the c - a x i s and s m a l l e r than about 3.2 kOe, the n u c l e a r s p i n s r e m a i n e d a l i g n e d along the c - a x i s . However, for fields above at l e a s t 4 kOe the n u c l e a r spins were p o l a r i z e d i n the m a g n e t i c field d i r e c t i o n ( ± caxis). On b a s i s of other e x p e r i m e n t a l r e s u l t s [7] on 54Mn n u c l e a r o r i e n t a t i o n in such r e l a t i v e l y s t r o n g fields it m a y be deduced that the n u c l e a r s p i n s r e a s o n a b l e r e p r e s e n t the b e h a v i o u r of the e l e c t r o n i c s p i n s , hence f r o m the e x p e r i m e n t a l r e s u l t s we conclude: 1) the M n - i o n s have a n i s o t r o p i c exchange coupling and the c - a x i s i s the p r e f e r r e d d i r e c t i o n of a n t i ferromagnetic alignment 2) t h e r e i s a s p i n - f l i p r e g i o n between 3 and 4 kOe. We c o n c l u d e t h a t L a - M n - n i t r a t e , and L a - C o n i t r a t e b e c o m e a n t f f e r r o m a g n e t i c at T N = = 0 . 2 3 0 ° K , and TN = 0.181°K r e s p e c t i v e l y , while L a - N i s h o w s a c o m b i n a t i o n of f e r r o m a g n e t i c and antiferromagnetic interactions.
Refe~'e~ces 1. K.W.Mess, E. Lagendijk, D. Curtis and W.J. Huiskamp. Physica 34 (1967) 126. 2. B.M. Brandt, D. van Ormondt and T. Thalhammer, Phys. Letters 19 (1965) 549. 3. K.D. Bowers and J.Owen, Rep. Progr. Phys. 18 (1955) 304. 4. L. Niesen and J. Lubbers, private communication. 5. R. H~Hoskins, R.C. Pastor and K.R. Trigger, J. Chern. Phys. 30 (1959) 1630. 6. A. Zalkin, J.D. Forester and D. H. Templeton, J. Chem. Phys. 39 (1963) 2881. 7. J. Lubbers and W.J.Huiskamp, Physiea 34 (1967) 166,212.
* * * * *
331
PHYSICS LETTERS
Then the e l e c t r o n i c p o r t i o n of the i n t e r a c t i o n m a y be r e p l a c e d by an e f f e c t i v e m a g n e t f i e l d at the nucleus p r o p o r t i o n a l to ( i IJI i). The H a m i l t o n i a n then b e c o m e s ~ = g n ~nHeff" I , which p r o d u c e s 21+1 equally s p a c e d n u c l e a r Z e e m a n l e v e l s . The c r y s t a l f i e l d l e v e l s of the 4I~ m u l t i p l e t of E r in e r b i u m e t h y l s u l p h a t e have ~een m e a s u r e d [4]. F r o m this it is known that at 4 . 2 o K only the l o w e s t K r a m e r ' s doublet i s occupied. Taking into account the C3h s y m m e t r y and u s i n g an effective s p i n S ' =½ the H a m i l t o n i a n f o r the doublet m a y be r e w r i t t e n : ~ = A~ S~Iz + + A.L (Sxl x + S ' I y ); A J~ and A , have b e e n c a l c u l a t e d using g~ = 1 . 5 ~ ± 0 . 0 5 , g ± = ~ 7 7 + 0 . 0 3 [2], gn = = 0.318~0.010 [5] and (~-3)eff = 10.60 a.u. [6]. Since no m a g n e t i c f i e l d is p r e s e n t to s p l i t the doublet and A£ i s l a r g e , the effective f i e l d a p p r o x i m a t i o n i s not v a l i d and a l a r g e d e v i a t i o n f r o m equal s p a c i n g i s o b s e r v e d . Using the above A , and A ± the line p o s i t i o n s c a l c u l a t e d f r o m the equation f o r ~ a g r e e with the o b s e r v e d ones within e x p e r i m e n t a l e r r o r . The n u c l e a r q u a d r u pole i n t e r a c t i o n c a l c u l a t e d f r o m c r y s t a l f i e l d d a t a [4] is n e g l i g i b l e , a s i s the i s o m e r shift [5]. A f u r t h e r c o n s e q u e n c e of the l a r g e g± is that the
HEAT
28 August 1967
s p i n - s p i n r e l a x a t i o n i s f a s t in m a g n e t i c a l R c o n c e n t r a t e d m a t e r i a l s . T h i s e x p l a i n s the difficulty is o b s e r v i n g v i o l a t i o n s of the e f f e c t i v e f i e l d a p p r o x i m a t i o n . F u r t h e r d e t a i l s w i l l be r e p o r t e d e l s e w h e r e [7]. The authors wish to thank Dr. Ursel Zahn for preparation of the absorbers and Dr. A. Meyer from Siemens A G Forschungslaboratorium Miinchen for providing the HoAl 2.
Refe~'~ces 1. H.H.Wickman, M.P.K1eh~ and D.A.Shlrley, Phys. Rev. 152 (1966) 345, and references therein. 2. G.H. Larson and C.D.Jeffries, Phys. Rev. 141 (1966) 461.
3. A. Abragam and M . H . L . P r y e e , Proc. Roy. Soc. (London) A205 (1951) 135. 4. J.C. Hfil and R.G.Wheeler, Phys. Rev. 152 (1966) 482. 5. E. MUnck, D.Quitrnann and S. Htffner, Z. Naturfor~ sch. 21A (1966) 847. 6. B. Bleaney, in Proc. 3rd Int. Symp. on Quantum electronics, Paris (1963), p. 595 ft. 7. Zeitschr. f. Physik, to be published.
CAPACITY MEASUREMENTS ON MANGANESE, NICKELCOBALT-LANTHANUM-DOUBLE NITRATE
AND
K. W. MESS, E. LAGENDIJK and W. J. H U ~ K A M P Kamerlingh Onnes Laboratory, Leiden, The Netherlands Received 7 July 1967
Heat capacity measurements of Mn-, Ni-, and Co-lanthanum-nitrate have shown singularities at T N = = 0.230°K, T N = 0.393°K and T N = 0.181°K respectively, which are due to magnetic long range order.
In t h i s l e t t e r we r e p o r t on the p h a s e t r a n s i t i o n of La2Mn3(NO3)1224H20, La2Ni3(NO3)1224H20 and La2Co3(NO3)1224H20, which show s i n g u l a r i t i e s in the h e a t c a p a c i t y below l ° K . The m e t h o d of m e a s u r e m e n t h a s been d e s c r i b e d in an e a r l i e r p u b l i c a t i o n [1]. The h e a t c a p a c i t y d a t a a r e shown in fig. 1, a f t e r s u b t r a c tion of e m p t y c a l o r i m e t e r h e a t c a p a c i t y and of the h y p e r f i n e s t r u c t u r e i n t e r a c t i o n c o n t r i b u t i o n . The l a t t e r m a y be e s t i m a t e d a c c o r d i n g to Ch.f.s./R
=
if(I+I)A2S2/k2T 2
in which the h.f.s, coupling p a r a m e t e r i s known f r o m E P R - m e a s u r e m e n t s [2] in i s o m o r p h o u s L a - M g - n i t r a t e o r B i - M g - n i t r a t e . By e x t r a p o l a tion of C a c c o r d i n g to a T - 2 - d e p e n d e n c e a t high T and a c c o r d i n g to a m o l e c u l a r f i e l d a p p r o x i m a t i o n at low T one can e s t i m a t e the t o t a l e n t r o p y y i e l d of the h e a t c a p a c i t y a n o m a l y . The r e s u l t s a r e given in t a b l e 1, f r o m which it i s s e e n that r e a s o n a b l e a g r e e m e n t with the v a l u e R i n (2S+ 1) i s o b t a i n e d in the t h r e e c o m pounds, h e n c e the h e a t c a p a c i t y m a y be e x p l a i n e d e n t i r e l y in t e r m s of m a g n e t i c o r d e r i n g of the electronic spins. 329
Volume25A. number 4
PHYSICS LETTERS
28 August 1967
Table 1 TN(OK)
AS/R
- ln(2S + 1)
(Soo-S c)/R
Eto t / R
-E c / E t o t
CT2/R
La2Mn3-nitrate
0.230
1.75
1.79
1.135
0.436
0.62
0.060
La2Ni 3 -nitrate
0.393
1.07
1.10
0.225
0.388
0.41
0.045
La2Co 3 -nitrate
0.181
0.680
0.693
0.291
0,150
0.61
0.0160
By i n t e g r a t i o n of C one obtains f r o m the data a l s o the e n e r g y yield, E c , above the t r a n s i t i o n point and a l s o the t o t a l e n e r g y y i e l d E t o t. The q u a n t i t i e s E c and Ec/Eto t have a l s o been l i s t e d in table 1. S u s c e p t i b i l i t y m e a s u r e m e n t s , u t i l i z i n g the s a m e a p p a r a t u s , have shown that in the M n - and C o - c o m p o u n d s X d e c r e a s e s s t r o n g l y at the t r a n s i t i o n point, when the m e a s u r i n g f ie ld is p a r a l l e l to the c r y s t a l l o g r a p h i c c - a x i s , w h e r e a s X is a p p r o x i m a t e l y constant below the t r a n s i t i o n point when the m e a s u r i n g f i e l d is p e r p e n d i c u l a r to the c - a x i s . F o r the N i - c o m p o u n d , h o w e v e r , no such d e c r e a s e i s o b s e r v e d , and on b a s i s of the s u s c e p t i b i l i t y m e a s u r e m e n t s only, it i s not e x c l u d e d that the N i - s a l t i s f e r r o m a g n e t i c . T he m a g n e t i c a n i s o t r o p y m a y be r e l a t e d to c r y s t a l l i n e f i el d e f f e c t s , which a r e e x p r e s s e d by the p a r a m e t e r D in the s p i n - H a m i l t o n i a n t e r m D{S2z-~S(S +1)}. F o r Mn D/k = -0.0310OK f o r one t h i r d of the ions and D/k = -0.0070°K f o r the r e m a i n i n g two t h i r d s [2,3]. Hence c r y s t a l l i n e fie ld e f f e c t s a r e a l s m o s t n e g l i g i b l e f o r the a n a l y s i s of the heat c a p a c i t y data of the M n - s a l t e.g. they c o n t r i b u t e about 4% to the heat c a p a c i t y at T >> T N. F o r the N i - c o m p o u n d at low T a v a l u e D/k = +0.29°K has been found [4]. T h i s v a l u e is in r e a s o n a b l e a g r e e m e n t with what can be e s t i m a t e d f r o m the r e s u R s of E P R - m e a s u r e m e n t s of Hoskins et al. [5] in i s o m o r p h o u s L a - M g , L a - Z n , B i - M g and B i - Z n - d o u b l e n i t r a t e s . It is u n c e r tain w h e t h e r the D - v a l u e p e r t a i n s to }, } or a ll N i - i o n s , but we will a s s u m e that a ll ions have D/k = +0.29. In any c a s e a c o n s i d e r a b l e c o n t r i b u tion to the heat capacity at T >> TN has to be e x p e c t e d and m ay acco u n t f o r at m o s t about one t h i r d of the m e a s u r e d CT2/R v a l u e . S i m i l a r l y , in the L a - N i compound, the e n e r g y y i e l d is not e n t i r e l y due to m a g n e t i c i n t e r a c t i o n s but roughly half the e x p e r i m e n t a l v a l u e has to be a t t r i b u t e d to c r y s t a l l i n e f i e l d e n e r g y . F r o m the e x p e r i m e n t a l data and f r o m the e qua t i o n s
E/R qS2j/k,
CT2/R=2qS2(S+I)2j2/3k 2
w h e r e J i s the H e i s e n b e r g e x c h a n g e constant and q is the n u m b e r of n e a r e s t n e i g h b o u r s , one m a y
330
4O i
i Co
I Mn
I
I
I
06
08
Ni
oz 2O
10
2
1 01
T
02
0.3
04
lO°K
Fig. 1. Heat capacity Cmag, of Mn-. Ni- and Co-lanthanum double nitrate as a function o f t on a double logarithmic scale. obtain a value of the c o o r d i n a t i o n n u m b e r q. Such a c o m p a r i s o n l e a d s to low q ( ~ 2). F o r the C o - s a l t the above f o r m u l a e would give q ~ 6, but f o r the a n i s o t r o p i c C o - i o n s it would not be r e a s o n a b l e to c o m p a r e the r e s u l t s with the H e i s e n b e r g m o d e l . It i s known that f o r o t h e r C o - s a l t s the heat capacity ab o v e T N i s c o m p a r a t i v e l y s m a l l ; t h e o r e t i c a l l y , taking the Ising m o del, this r e d u c t i o n (at constant qJ, o r e q u i v a l e n t ly TN or m o l e c u l a r field) is a f a c t o r of t h r e e and would then alSO lead to q ~. 2. T h i s m ay not be u n r e a s o n a b l e in v i e w of the c r y s t a l s t r u c t u r e [6], f r o m which it is found that e v e r y m a g n e t i c ion
Volume25A, number 4
PHYSICS LETTERS
has at l e a s t t h r e e n e i g h b o u r s at 7.15.~, but § have one neighbour at 5.2A and the r e m a i n i n g -~ have t h r e e m o r e n e i g h b o u r s at 7.15/~. It is quite p o s s i b l e that the i o n - p a i r s at 5.2 A distance have a relatively strong magnetic interaction. In this c o n n e c t i o n we m e n t i o n additional e x p e r i m e n t a l r e s u l s . When an e x t e r n a l m a g n e t i c field was applied a d i a b a t i c a l l y to the M n - s a l t , the t e m p e r a t u r e change along an i s e n t r o p e could be m e a s u r e d and was found to show two distinct ext r e m a , the l a t t e r one p r o b a b l y close to the p a r a m a g n e t i c - a n t i f e r r o m a g n e t i c t r a n s i t i o n r e g i o n in the H-T phase d i a g r a m [1]. The l a t t e r m i n i m u m was found at low T to o c c u r at 5 kOe. F r o m the e n e r g y y i e l d in the L a - M n - s a l t one d e r i v e s on b a s i s of m o l e c u l a r field theory that at T = 0 the m o l e c u l a r field would be only 2250 Oe. It may t h e r e f o r e be s u g g e s t e d that the e x p e r i m e n t a l v a l u e of 5 kOe r e f e r s to the field r e q u i r e d for b r e a k i n g the a n t i f e r r o m a g n e t i c coupling between two M n - i o n s and this would a l s o b e t t e r a g r e e with the r e l a t i v e l y l a r g e entropy y i e l d above TN in the M n - c o m p o u n d . Quite s i m i l a r r e s u l t s were seen in the N i - c o m p o u n d , where a field of 5.7 kOe i s r e q u i r e d . We m e n t i o n f u r t h e r a l s o n u c l e a r o r i e n t a t i o n e x p e r i m e n t s on 54Mn i n c o r p o r a t e d in the L a - M n n i t r a t e s i n g l e c r y s t a l . The a n i s o t r o p y of the e m i t t e d g a m m a r a y s was o b s e r v e d with the aid of two c o u n t e r s , p a r a l l e l and p e r p e n d i c u l a r to the applied m a g n e t i c field, w h e r e a s the t e m p e r a t u r e could be kept at a c o n s t a n t value of about 0.05°K while v a r y i n g the m a g n e t i c field s t r e n g t h or d i r e c t i o n . When the field was along the c-axis it was found that the n u c l e a r s p i n s were p r e f e r e n t i a l l y a l i g n e d a l o n g the c - a x i s . However, t h e r e was a t r a n s i t i o n r e g i o n b e t w e e n 2.5 and 4 kOe, where the n u c l e a r s p i n s m u s t have been t u r n e d
28 August 1967
away f r o m the c - a x i s to a c o n s i d e r a b l e extent, i.e. r e d u c i n g the g a m m a a n i s o t r o p y n e a r l y to zero. When the field was p e r p e n d i c u l a r to the c - a x i s and s m a l l e r than about 3.2 kOe, the n u c l e a r s p i n s r e m a i n e d a l i g n e d along the c - a x i s . However, for fields above at l e a s t 4 kOe the n u c l e a r spins were p o l a r i z e d i n the m a g n e t i c field d i r e c t i o n ( ± caxis). On b a s i s of other e x p e r i m e n t a l r e s u l t s [7] on 54Mn n u c l e a r o r i e n t a t i o n in such r e l a t i v e l y s t r o n g fields it m a y be deduced that the n u c l e a r s p i n s r e a s o n a b l e r e p r e s e n t the b e h a v i o u r of the e l e c t r o n i c s p i n s , hence f r o m the e x p e r i m e n t a l r e s u l t s we conclude: 1) the M n - i o n s have a n i s o t r o p i c exchange coupling and the c - a x i s i s the p r e f e r r e d d i r e c t i o n of a n t i ferromagnetic alignment 2) t h e r e i s a s p i n - f l i p r e g i o n between 3 and 4 kOe. We c o n c l u d e t h a t L a - M n - n i t r a t e , and L a - C o n i t r a t e b e c o m e a n t f f e r r o m a g n e t i c at T N = = 0 . 2 3 0 ° K , and TN = 0.181°K r e s p e c t i v e l y , while L a - N i s h o w s a c o m b i n a t i o n of f e r r o m a g n e t i c and antiferromagnetic interactions.
Refe~'e~ces 1. K.W.Mess, E. Lagendijk, D. Curtis and W.J. Huiskamp. Physica 34 (1967) 126. 2. B.M. Brandt, D. van Ormondt and T. Thalhammer, Phys. Letters 19 (1965) 549. 3. K.D. Bowers and J.Owen, Rep. Progr. Phys. 18 (1955) 304. 4. L. Niesen and J. Lubbers, private communication. 5. R. H~Hoskins, R.C. Pastor and K.R. Trigger, J. Chern. Phys. 30 (1959) 1630. 6. A. Zalkin, J.D. Forester and D. H. Templeton, J. Chem. Phys. 39 (1963) 2881. 7. J. Lubbers and W.J.Huiskamp, Physiea 34 (1967) 166,212.
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