- Email: [email protected]
Critical magnetic behavior of EuO
15 June 1970
PHYSICS LETTERS
Volume 32A, number 2
The s t r o n g i n t e r a c t i o n b e t w e e n p o s i t r o n i u m and D P P H - z i n e and n i t r o b e n z e n e is r e p o r t e d f o r d i a m a g n e t i c o r g a n i c m o l e c u l e s f o r the f i r s t t i m e . T h i s i n t e r a c t i o n a p p e a r s to be c a u s e d by the p r e s e n c e of one or s e v e r a l NO 2 g r o u p s bound to an a r o m a t i c ring. The quenching by D P P H - z y l is p r o b a b l y caused a l s o by the p r e s e n c e of such NO 2 groups r a t h e r than by the u n p a i r e d e l e c t r o n . Indeed, n i t r o b e n z e n e is a s t r o n g a c c e p t e r of unp a i r e d e l e c t r o n s in f o r m a t i o n of a c o m p l e x with c h a r g e t r a n s f e r [5], and it a l s o r e a c t s s t r o n g l y with h y d r a t e d e l e c t r o n s [6]. F u r t h e r e x p e r i m e n t s a r e in p r o g r e s s at our laboratory.
CRITICAL
MAGNETIC
References [1] R. L. de Zafra, Phys. Rev. 113 (1959) 1547. [2] T. A. Pond, Phys. Rev. 94 (1954) 758. [3] J. Berko and A. J. Zuchelli, Phys. Rev. 102 (1956) 724. [4] V. I. Goldanskii, Atomic Energy Review 6 (1) IAEA, Vienna {1968). [5] P. E. Sagdeev and Yu. N. Molin, Zhurnal Structurnoi Khimii 7 {1966) 38. [6] E. J. Hart, I. Gordon and J. K. Thomas, J. Chem. Phys. 68 (1964) 1272.
BEHAVIOR
OF
EuO
G. GROLL
Physik-Department der Technischen Hochschule, Mi~nchen, Germany Received 4 May 1970
Combined recoilless y-resonance and magnetization measurements indicate the existence of critical spin fluctuations and of critical superparamagnetism in EuO.
Using r e c o i l l e s s 7 - r e s o n a n c e a b s o r p t i o n and m a g n e t i z a t i o n m e a s u r e m e n t , we have m a d e an e x t e n s i v e i n v e s t i g a t i o n of the c r i t i c a l m a g n e t i c b e h a v i o r of the n e a r l y - H e i s e n b e r g f e r r o m a g n e t EuO both below and above i ts C u r i e t e m p e r a t u r e , Tc = 69.2°K. M e a s u r e m e n t s w e r e done on a n u m b e r of EuO s a m p l e s of d i f f e r e n t o r i g i n in the t e m p e r a t u r e r an g e f r o m 63°K to 77°K with a t e m p e r a t u r e v a r i a t i o n of ± 0.01°K. The m a g n e t i z a t i o n m e a s u r e m e n t s w e r e p e r f o r m e d at v e r y s m a l l e x t e r n a l applied m a g n e t i c f i e l d s , H a < 20 Oe, for which the induced m a g n e t i z a t i o n M(T) was shown to be l i n e a r l y dependent on H a f o r all t e m p e r a tures. In the t e m p e r a t u r e r a n g e b e t w e e n 0.93 Tc and 0.98 Tc, the i n t e r n a l m a g n e t i c field at the nuc l e u s , Heft(T) , was d e t e r m i n e d f r o m the splitting of the 7 - r e s o n a n c e hyperfine s p e c t r u m . It was found that Heff(T ) f i t s the f a m i l i a r p o w e r law H e tf ~ (T c - T ) f l with fl = 0.34 ± 0.02. In r a i s i n g the t e m p e r a t u r e above 0.98 Tc, the h y p e r f in e s p e c t r u m began to c o l l a p s e into one s i n g l e b r o a d ened line. The linewidth d e c r e a s e d r a p i d l y when going to h i g h e r t e m p e r a t u r e s , but did not i n s t a n -
taneously attain its p a r a m a g n e t i c value ( m e a s ured w e l l above Tc); i n st ead it a p p r o a c h e d this value a s y m p t o t i c a l l y within a t e m p e r a t u r e r a n g e of s o m e p e r c e n t s of (T- Tc)/T c. T h e r e a r e two p o s s i b l e r e a s o n s f o r the a p p e a r a n c e of such a C u r i e tail in the 7 - r e s o n a n c e r e s u l t s : 1. I m p e r f e c t i o n s of the c r y s t a l , c a u s i n g l o c a l l y d i f f e r e n t C u r i e t e m p e r a t u r e s and t h e r e b y a s m e a r i n g out of the C u r i e point. 2. C r i t i c a l slowing down of the spin motion [ ! ] cau si n g line b r o a d e n i n g through r e l a x a t i o n effects. The effect of i m p e r f e c t i o n s is a p u r e l y static one and its c o n t r i b u tion to the C u r i e tail was d e t e r m i n e d by the m a g n e t i z a t i o n m e a s u r e m e n t s . B e c a u s e of the s t a t i s t i c a l nature of this effect we a s s u m e d a G a u s s i a n d i s t r i b u t i o n of C u r i e points around an a v e r a g e v a l u e , Tc, with a halfwidth, Lx, and fitted the e x p e r i m e n t a l r e s u l t s to the t h e o r e t i c a l l y computed c u r v e f o r M(T). F o r t h r e e d i f f e r e n t EuO s a m p l e s we found f o r the halfwidth of the C u r i e point d i s t r i b u t i o n A ~ 0.35OK, 0.65OK and 0.90°K. The a v e r a g e C u r i e t e m p e r a t u r e , Tc, h o w e v e r , was found within the e r r o r l i m i t to be the s a m e f o r all s a m p l e s , Tc = (69.19 + 0.02)°K. 99
Volume 32A, number 2
PHYSICS LETTERS
The r e s u l t s of the m a g n e t i z a t i o n m e a s u r e m e n t s showed, that the main contribution to the r e s o n a n c e line b r o a d e n i n g d i r e c t l y above the C u r i e point is due to the d y n a m i c a l b e h a v i o r of the spin s y s t e m . Us i n g W e g e n e r ' s r e l a x a t i o n model [2] we obtained f r o m the linewidth b r o a d ening the spin c o r r e l a t i o n t i m e T. F o r i T - Tc) >/ 2 ± ~"was found to obey the power law T ( T - Tc)~ with ~ = 1.2 + 0.2. C h a r a c t e r i s t i c v a l ues for T a r e 7 × 10 -11 s e c (E=0.0I) and 1.5 × 10 -11 s ec (E =0.03), w h e r e E stands f o r ( T - T c ) / T c. In o r d e r to get a t h e o r e t i c a l e s t i m a t e f o r the magnitude of T, we have used m o l e c u l a r field t h e o r y and the spin d i f f u s i o n p i c t u r e in analogy to H e l l e r ' s [3] computation of the NMR linewidth in the a n t i f e r r o m a g n e t MnF 2. R e a s o n a b l e a g r e e ment with the e x p e r i m e n t a l r e s u l t s was obtained by taking the r e l a x a t i o n t i m e outside the c r i t i c a l region (E >i 0.I) as 0.2 × 10-12 sec. The critical exponent ~ in the above theory is equal to 1.5 for the ferromagnet. If, however, one uses the well established values 7 = ~ and v = 2 [4] instead of the molecular field values for the critical exponents 7(susceptibility) and v(correlation range), which enter into the computation of T, one obtains ~ = 2 as an improved theoretical result. This is in clear disagreement with the experimental value of 1.2 + 0.2, indicating that the conventional diffusion picture is unsound in the critical region. On the other hand, the experimental result may be compared with Kawasaki's elaborate theory of "anomalous spin diffusion" [5] and the theory of dynamical scaling [6], both of which give ~ = I. In the ferromagnetic region, near Tc, the individual lines of the split hyperfine spectrum showed an increasing broadening approaching the Curie point. This effect of line broadening was much too great to be accounted for solely by c r i tical fluctuations or by the influence of the Curie point distribution. Moreover, the observation that the linewidths were almost independent of the line positions indicated a relaxation mechan-
100
15 June 1970
i s m with a c h a r a c t e r i s t i c t i m e v e r y much g r e a t e r than the i n v e r s e n u c l e a r L a r m o r f r e q u e n c y [7]. We w e r e t h e r e f o r e led to the conclusion that c r i t i c a l s u p e r p a r a m a g n e t i s m [8] o c c u r s in EuO. T h i s also b e c a m e evident through the o b s e r v a tion that f o r H < T c the hyperfine field, Heft(T) , d i f f e r s slightly for d i f f e r e n t s a m p l e s . A c o m p a c t way of d e s c r i b i n g this effect q u a n t i t a t i v e l y is to plot H3ff(T) v e r s u s T ( e m p i r i c a l l y a s t r a i g h t line), and to d e t e r m i n e an apparent C u r i e point TcM by e x t r a p o l a t i o n of H3ff v e r s u s 0. T M then is dependent upon the p a r t i c u l a r c r y s t a l under investigation. It was found that T M is r e l a t e d to the width of the C u r i e point d i s t r i b u t i o n , A, as TM ~ ~ c ( 1 - ~ / ~ ) . A may be taken as a q u a n t i ta~ive m e a s u r e o[ the deviation of the s a m p l e c r y s t a l s t r u c t u r e f r o m..that of an i d eal c r y s t a l . The r e l a t i o n b et w een T~e1 and A then i n d i c a t e s that c r i t i c a l s u p e r p a r a m a g n e t i s m is a p u r e effect of c r y s t a l i m p e r f e c t i o n . A full account of this work will appear in Z. Physik. The author would like to thank Prof. R. L. M S s s b a u e r f o r his i n t e r e s t in this work. He is a l s o v e r y much indebted to Dr. H. Pink, Dr. O. Vogt, Dr. E. Kaldis and Dr. M. W. Shafer for p r o v i d i n g him with EuO s a m p l e s .
References [1] w. Marshall and R. D. Lowde, Rep. Prog. Phys. 31 (1968) 705. [2] H. Wegener, Z. Physik 186 (1965) 498. [3] P. Heller in Critical phenomena, N.B.S. Misc. l:~bl. No. 273, eds. M. S. Green and J. V. Sengers (Washington: National Bureau of Standards) p. 58 (1966). [4] M. E. Fisher, Rep. Prog. Phys. 30 (1967) 615. [5] K. Kawasaki, J. Phys. Chem. Solids 28 (1967) 1277. [6] B. I. Halperin and P. C. Hohenberg, Phys. Rev. 177 (1969) 952. [7] F. van der Woude and A. J. Dekker, Phys. Star. Sol. 9 (1965) 775. [8] L. M. Levinson, M. Luban and S. Shtrikman, Phys. Rev. 177 (1969) 864.
PHYSICS LETTERS
Volume 32A, number 2
The s t r o n g i n t e r a c t i o n b e t w e e n p o s i t r o n i u m and D P P H - z i n e and n i t r o b e n z e n e is r e p o r t e d f o r d i a m a g n e t i c o r g a n i c m o l e c u l e s f o r the f i r s t t i m e . T h i s i n t e r a c t i o n a p p e a r s to be c a u s e d by the p r e s e n c e of one or s e v e r a l NO 2 g r o u p s bound to an a r o m a t i c ring. The quenching by D P P H - z y l is p r o b a b l y caused a l s o by the p r e s e n c e of such NO 2 groups r a t h e r than by the u n p a i r e d e l e c t r o n . Indeed, n i t r o b e n z e n e is a s t r o n g a c c e p t e r of unp a i r e d e l e c t r o n s in f o r m a t i o n of a c o m p l e x with c h a r g e t r a n s f e r [5], and it a l s o r e a c t s s t r o n g l y with h y d r a t e d e l e c t r o n s [6]. F u r t h e r e x p e r i m e n t s a r e in p r o g r e s s at our laboratory.
CRITICAL
MAGNETIC
References [1] R. L. de Zafra, Phys. Rev. 113 (1959) 1547. [2] T. A. Pond, Phys. Rev. 94 (1954) 758. [3] J. Berko and A. J. Zuchelli, Phys. Rev. 102 (1956) 724. [4] V. I. Goldanskii, Atomic Energy Review 6 (1) IAEA, Vienna {1968). [5] P. E. Sagdeev and Yu. N. Molin, Zhurnal Structurnoi Khimii 7 {1966) 38. [6] E. J. Hart, I. Gordon and J. K. Thomas, J. Chem. Phys. 68 (1964) 1272.
BEHAVIOR
OF
EuO
G. GROLL
Physik-Department der Technischen Hochschule, Mi~nchen, Germany Received 4 May 1970
Combined recoilless y-resonance and magnetization measurements indicate the existence of critical spin fluctuations and of critical superparamagnetism in EuO.
Using r e c o i l l e s s 7 - r e s o n a n c e a b s o r p t i o n and m a g n e t i z a t i o n m e a s u r e m e n t , we have m a d e an e x t e n s i v e i n v e s t i g a t i o n of the c r i t i c a l m a g n e t i c b e h a v i o r of the n e a r l y - H e i s e n b e r g f e r r o m a g n e t EuO both below and above i ts C u r i e t e m p e r a t u r e , Tc = 69.2°K. M e a s u r e m e n t s w e r e done on a n u m b e r of EuO s a m p l e s of d i f f e r e n t o r i g i n in the t e m p e r a t u r e r an g e f r o m 63°K to 77°K with a t e m p e r a t u r e v a r i a t i o n of ± 0.01°K. The m a g n e t i z a t i o n m e a s u r e m e n t s w e r e p e r f o r m e d at v e r y s m a l l e x t e r n a l applied m a g n e t i c f i e l d s , H a < 20 Oe, for which the induced m a g n e t i z a t i o n M(T) was shown to be l i n e a r l y dependent on H a f o r all t e m p e r a tures. In the t e m p e r a t u r e r a n g e b e t w e e n 0.93 Tc and 0.98 Tc, the i n t e r n a l m a g n e t i c field at the nuc l e u s , Heft(T) , was d e t e r m i n e d f r o m the splitting of the 7 - r e s o n a n c e hyperfine s p e c t r u m . It was found that Heff(T ) f i t s the f a m i l i a r p o w e r law H e tf ~ (T c - T ) f l with fl = 0.34 ± 0.02. In r a i s i n g the t e m p e r a t u r e above 0.98 Tc, the h y p e r f in e s p e c t r u m began to c o l l a p s e into one s i n g l e b r o a d ened line. The linewidth d e c r e a s e d r a p i d l y when going to h i g h e r t e m p e r a t u r e s , but did not i n s t a n -
taneously attain its p a r a m a g n e t i c value ( m e a s ured w e l l above Tc); i n st ead it a p p r o a c h e d this value a s y m p t o t i c a l l y within a t e m p e r a t u r e r a n g e of s o m e p e r c e n t s of (T- Tc)/T c. T h e r e a r e two p o s s i b l e r e a s o n s f o r the a p p e a r a n c e of such a C u r i e tail in the 7 - r e s o n a n c e r e s u l t s : 1. I m p e r f e c t i o n s of the c r y s t a l , c a u s i n g l o c a l l y d i f f e r e n t C u r i e t e m p e r a t u r e s and t h e r e b y a s m e a r i n g out of the C u r i e point. 2. C r i t i c a l slowing down of the spin motion [ ! ] cau si n g line b r o a d e n i n g through r e l a x a t i o n effects. The effect of i m p e r f e c t i o n s is a p u r e l y static one and its c o n t r i b u tion to the C u r i e tail was d e t e r m i n e d by the m a g n e t i z a t i o n m e a s u r e m e n t s . B e c a u s e of the s t a t i s t i c a l nature of this effect we a s s u m e d a G a u s s i a n d i s t r i b u t i o n of C u r i e points around an a v e r a g e v a l u e , Tc, with a halfwidth, Lx, and fitted the e x p e r i m e n t a l r e s u l t s to the t h e o r e t i c a l l y computed c u r v e f o r M(T). F o r t h r e e d i f f e r e n t EuO s a m p l e s we found f o r the halfwidth of the C u r i e point d i s t r i b u t i o n A ~ 0.35OK, 0.65OK and 0.90°K. The a v e r a g e C u r i e t e m p e r a t u r e , Tc, h o w e v e r , was found within the e r r o r l i m i t to be the s a m e f o r all s a m p l e s , Tc = (69.19 + 0.02)°K. 99
Volume 32A, number 2
PHYSICS LETTERS
The r e s u l t s of the m a g n e t i z a t i o n m e a s u r e m e n t s showed, that the main contribution to the r e s o n a n c e line b r o a d e n i n g d i r e c t l y above the C u r i e point is due to the d y n a m i c a l b e h a v i o r of the spin s y s t e m . Us i n g W e g e n e r ' s r e l a x a t i o n model [2] we obtained f r o m the linewidth b r o a d ening the spin c o r r e l a t i o n t i m e T. F o r i T - Tc) >/ 2 ± ~"was found to obey the power law T ( T - Tc)~ with ~ = 1.2 + 0.2. C h a r a c t e r i s t i c v a l ues for T a r e 7 × 10 -11 s e c (E=0.0I) and 1.5 × 10 -11 s ec (E =0.03), w h e r e E stands f o r ( T - T c ) / T c. In o r d e r to get a t h e o r e t i c a l e s t i m a t e f o r the magnitude of T, we have used m o l e c u l a r field t h e o r y and the spin d i f f u s i o n p i c t u r e in analogy to H e l l e r ' s [3] computation of the NMR linewidth in the a n t i f e r r o m a g n e t MnF 2. R e a s o n a b l e a g r e e ment with the e x p e r i m e n t a l r e s u l t s was obtained by taking the r e l a x a t i o n t i m e outside the c r i t i c a l region (E >i 0.I) as 0.2 × 10-12 sec. The critical exponent ~ in the above theory is equal to 1.5 for the ferromagnet. If, however, one uses the well established values 7 = ~ and v = 2 [4] instead of the molecular field values for the critical exponents 7(susceptibility) and v(correlation range), which enter into the computation of T, one obtains ~ = 2 as an improved theoretical result. This is in clear disagreement with the experimental value of 1.2 + 0.2, indicating that the conventional diffusion picture is unsound in the critical region. On the other hand, the experimental result may be compared with Kawasaki's elaborate theory of "anomalous spin diffusion" [5] and the theory of dynamical scaling [6], both of which give ~ = I. In the ferromagnetic region, near Tc, the individual lines of the split hyperfine spectrum showed an increasing broadening approaching the Curie point. This effect of line broadening was much too great to be accounted for solely by c r i tical fluctuations or by the influence of the Curie point distribution. Moreover, the observation that the linewidths were almost independent of the line positions indicated a relaxation mechan-
100
15 June 1970
i s m with a c h a r a c t e r i s t i c t i m e v e r y much g r e a t e r than the i n v e r s e n u c l e a r L a r m o r f r e q u e n c y [7]. We w e r e t h e r e f o r e led to the conclusion that c r i t i c a l s u p e r p a r a m a g n e t i s m [8] o c c u r s in EuO. T h i s also b e c a m e evident through the o b s e r v a tion that f o r H < T c the hyperfine field, Heft(T) , d i f f e r s slightly for d i f f e r e n t s a m p l e s . A c o m p a c t way of d e s c r i b i n g this effect q u a n t i t a t i v e l y is to plot H3ff(T) v e r s u s T ( e m p i r i c a l l y a s t r a i g h t line), and to d e t e r m i n e an apparent C u r i e point TcM by e x t r a p o l a t i o n of H3ff v e r s u s 0. T M then is dependent upon the p a r t i c u l a r c r y s t a l under investigation. It was found that T M is r e l a t e d to the width of the C u r i e point d i s t r i b u t i o n , A, as TM ~ ~ c ( 1 - ~ / ~ ) . A may be taken as a q u a n t i ta~ive m e a s u r e o[ the deviation of the s a m p l e c r y s t a l s t r u c t u r e f r o m..that of an i d eal c r y s t a l . The r e l a t i o n b et w een T~e1 and A then i n d i c a t e s that c r i t i c a l s u p e r p a r a m a g n e t i s m is a p u r e effect of c r y s t a l i m p e r f e c t i o n . A full account of this work will appear in Z. Physik. The author would like to thank Prof. R. L. M S s s b a u e r f o r his i n t e r e s t in this work. He is a l s o v e r y much indebted to Dr. H. Pink, Dr. O. Vogt, Dr. E. Kaldis and Dr. M. W. Shafer for p r o v i d i n g him with EuO s a m p l e s .
References [1] w. Marshall and R. D. Lowde, Rep. Prog. Phys. 31 (1968) 705. [2] H. Wegener, Z. Physik 186 (1965) 498. [3] P. Heller in Critical phenomena, N.B.S. Misc. l:~bl. No. 273, eds. M. S. Green and J. V. Sengers (Washington: National Bureau of Standards) p. 58 (1966). [4] M. E. Fisher, Rep. Prog. Phys. 30 (1967) 615. [5] K. Kawasaki, J. Phys. Chem. Solids 28 (1967) 1277. [6] B. I. Halperin and P. C. Hohenberg, Phys. Rev. 177 (1969) 952. [7] F. van der Woude and A. J. Dekker, Phys. Star. Sol. 9 (1965) 775. [8] L. M. Levinson, M. Luban and S. Shtrikman, Phys. Rev. 177 (1969) 864.