10 P [110] ( a.u ) Profile –10 0 5 –5 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 P [100] ( a.u ) Profile –10 0 5 10 –5 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 P [110] ( a.u ) Profile 0.25 0.2 0.15 0.1 0.05 0 –10 0 5 10 –5 P [100] ( a.u ) Profile –10 0 5 10 –5 0.3 0.25 0.2 0.15 0.1 0.05 0 P [001] ( a.u ) Profile –10 0 5 10 –5 0.25 0.2 0.15 0.1 0.05 0 –10 0 5 10 –5 P [001] ( a.u ) Profile 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 [1 1 0] direction [1 0 0] direction [1 0 0] direction [1 1 0] direction [0 0 1] direction [0 0 1] direction (a) (b) P h a s e S e p a r a t i o n b e t w e e n E l e c t r o n - r i c h F e r r o m a g n e t i c a n d E l e c t r o n - p o o r A n t i f e r r o m a g n e t i c R e g i o n s o n S t u d i e d b y M a g n e t i c C o m p t o n P r o f i l e M e a s u r e m e n t P h a s e S e p a r a t i o n b e t w e e n E l e c t r o n - r i c h F e r r o m a g n e t i c a n d E l e c t r o n - p o o r A n t i f e r r o m a g n e t i c R e g i o n s o n La 2-2x Sr 1+ 2x Mn 2 O 7 S t u d i e d b y M a g n e t i c C o m p t o n P r o f i l e M e a s u r e m e n t P e r o v s k i t e M n o x i d e s h a v e a t t r a c t e d m u c h interest because of the colossal magnetoresistance ( CMR ) which appears just above its metal-insulator transition temperature T c . The ferromagnetism and me ta ll ic co nd uc ti vi ty be lo w T c ha ve be en in te rp re te d in terms of the double-exchange (DE) mechanism, w h e r e e g o r b i t a l e l e c t r o n s g o a r o u n d M n s i t e s throu gh hybri diza tion with O 2 p orbi tals, and alig n the localized t 2g spins by the strong Hund’s coupling [ 1 ] . H o w e v e r , t h e C M R p h e n o m e n o n c a n n o t b e e x p l a i n e d b y t h e s i m p l e D E m e c h a n i s m . I t i s c u r r e n t l y p o i n t e d o u t t h a t t h e o r b i t a l d e g r e e o f fr ee do m is im po rt an t , as ar e th e ch ar ge an d sp in Fig. 1. Directional Compton profiles of (a) x 2 – y 2 and (b) 3z 2 – r 2 atomic orbitals. ones. The determination of e g e g ( x 2 – y 2 and 3 z 2 – r 2 or bi ta ls ) an d t 2g or bi ta l oc cu pa ti on in Mn 3 d st at e will provide a clue for the clear understanding of the CMR phenomenon existing in this system. T h e s e o r b i t a l s t a t e s c a n b e d i s t i n g u i s h e d o n a m a g n e t i c C o m p t o n p r o f i l e ( M C P ) b y t h e i r characteristic line shapes. For instance, directional C o m p t o n p r o f i l e s o f x 2 – y 2 a n d 3 z 2 – r 2 a t o m i c or bi ta ls are sho wn in Fi g. 1(a ) and 1( b) , re sp ec ti ve ly . This feature makes it possible to determine the and t 2g orbital occupation separately [2]. Recently, t h e t e m p e r a t u r e d e p e n d e n c e o f M C P h a s b e e n measured on a single crystal of La 2-2x Sr 1 + 2x Mn 2 O 7 41 Fig. 2 References [1] C. Zener, Phys. Rev. 82 (1951) 403. [2 ] A. Ko iz um i et al . , Ph ys . Re v. Le tt . 86 (2 00 1) 5589. [3] A. Koizumi, T. Nagao, Y. Kakutani, N. Sakai, K. Hirota and Y. Murakami , submitted in Phys. Rev. Lett. [4] A. Moreo et al. , Science 283 (1999) 2034. Akihisa Koizumi Himeji Institute of Technology E-mail: akihisa @ sci.himeji-tech.ac.jp at x = 0.42 along the c -axis [3]. Experiments were ma de on be am li ne BL 08 W us in g ci rc ul ar ly po la ri ze d X-rays at 174 keV. MCP’s measured at 10 and 150 K are shown in . The area of each MCP is no rm al iz ed to th e ma gn et ic mo me nt me as ur ed at ea ch te mp er at ur e , an d i t sh ou ld be no te d th at T c lies in between these temperatures. Thus MCP at 15 0 K re fl ec ts a fi el d - in du ce d fe rr om ag ne ti c st at e above T c . Significant change in shape is observed in a low m o m e n t u m r e g i o n ; t h e d i p i s s h a l l o w e r a t 1 5 0 K than at 10 K. Sinc e the magn etic mome nt of the s a m p l e a l m o s t o r i g i n a t e s i n t h e s p i n s i n M n 3 d orbitals, this behavior means that the ratio of e g spin t o t 2 g i n c r e a s e s a b o v e T c , b e c a u s e t h e e g - o r b i t a l profile shows a peak at p z =0, while the t 2g -one has a dent. To evaluate the spin magnetic moments in t h e r e s p e c t i v e o r b i t a l s , a f i t t i n g a n a l y s i s o f e a c h MCP was carried out using theoretical profiles of t 2g a n d e g t y p e o r b i t a l s o b t a i n e d f r o m a n a b i n i t i o m o l e c u l a r o r b i t a l c a l c u l a t i o n f o r t h e ( M n O 6 ) 8 – cluster. In the case of manganites, it is reasonable to assume that the electron number in each orbital i s p r o p o r ti o n a l to th e n u m b e r o f s p i n s d u e to th e strong Hund’s coupling between t 2g and g spins. If we assume that all Mn ions have the same electron number, that is, t 2g and g orbital occupations are 3 and 0.58, respectively, the e e e g / t 2g ratio is expected to be 0.193. However, the ratio at 10 K deduced from t h e f i t t i n g r e s u l t i s 0 . 2 3 4 , w h i c h i s s l i g h t l y l a r g e r t h a n t h e e x p e c t e d r a t i o , a n d t h e r a t i o a t 1 5 0 K shows an even large r value of 0.306. This can be i n t e r p r e t e d i n t e r m s o f t h e p h a s e s e p a r a t i o n b e t w e e n e l e c t r o n - r i c h f e r r o m a g n e t i c a n d e l e c t r o n - p o o r a n t i f e r r o m a g n e t i c r e g i o n s [ 4 ] , b e c a u s e t h e MC P me as ur em en t on ly ob se rv es th e fe rr om ag ne ti c c o m p o n e n t i n t h e s a m p l e . F r o m t h e r a t i o s , i t i s found that the e g electrons are highly segregated in the ferromagnetic region above T c . Fig. 2. The magnetic Compton profiles of La 2-2x Sr 1 + 2x Mn 2 O 7 with x = 0.42 measured at (a) 10 K and (b) 150 K. Experimental da ta an d th e fi tt in g re su lt ar e sh ow n wi th s o l i d c i r c l e s a n d s o l i d l i n e , r e s p e c t i v e l y . T h e g r e e n l i n e r e p r e s e n t s t h e t 2 g o r b i t a l contribution. The red and blue lines are for the x 2 – y 2 and 3z 2 – r 2 contributions in the e g orbital state, respectively. 42 T = 1 0 K J m a g ( p z ) ( m B / a . u . ) ( a ) 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 T = 1 5 0 K 0 0 . 0 5 0 . 1 0 . 1 5 J m a g ( p z ) ( m B / a . u . ) ( b ) 0 1 2 3 4 5 6 p z ( a . u . )
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