P e r o v s k i t e M n o x i d e s h a v e b e e n s t u d i e d i n re la ti on to th e co lo ss al ma gn et or es is ta nc e ( CM R ) w h i c h i s a h u g e d e c r e a s e i n e l e c t r i c r e s i s t a n c e u n d e r a m a g n e t i c f i e l d . R e c e n t l y , t h e d o u b l e - la ye re d ma ng an it e La 2-2 x Sr 1+ 2x Mn 2 O 7 ha s be co me of sp ec ia l in te re st , be ca us e it sh ow s mu ch la rg er CMR tha n the bas e com pou nd La 1-x Sr x MnO 3 . As shown in Fig. 1 , the crystal structure has a common feature in perovskite manganites that the Mn ion is octahedrally surrounded by O ions. In this crystal f ie ld , th e en er gy le ve ls of Mn 3 d or bi ta ls (w hi ch is 5 -hold degenerated in a free atomic state) split into a triply degenerate t 2g and a doubly degenerate e g states. When a hole is doped in this system, which is introduced by Sr 2 + ion doping, it goes into the e g orbital. That makes e g electrons hop around t h e M n s i t e s . T h e h o p p i n g a l s o c a u s e s f e r r o m a g n e t i c a l i g n m e n t o f t h e M n s p i n s t h r o u g h t h e s t r o n g H u n d ’ s c o u p l i n g w i t h l o c a l i z e d t 2 g s p i n s . T h i s i s w h a t w e c a l l t h e d o u b l e e x c h a n g e ( D E ) mechanism. It can explain both the coexistence of m e t a l l i c c o n d u c t i o n a n d f e r r o m a g n e t i s m i n m a n g a n i t e s [ 1 ] . H o w e v e r , r e c e n t e x p e r i m e n t a l re su lt s ha ve re ve al ed th at th e ma gn it ud e of CM R and complicated magnetic phase diagrams cannot be explained only by the simple DE mechanism [2- 4]. The importance of the orbital degree of freedom is pointed out as well as the charge and spin ones. T h i s m e a n s t h a t t h e p o p u l a t i o n s o f x 2 – y 2 and 3 z 2 – r 2 o r b i t a l s i n t h e e g s t a t e p l a y a k e y r o l e i n un de rs ta nd in g th e tr an sp or t an d ma gn et ic pr op er ti es of this system. W e h a v e i n v e s t i g a t e d t h e o r b i t a l s t a t e i n L a 2 - 2 x S r 1 + 2 x M n 2 O 7 b y m a g n e t i c C o m p t o n p r o f i l e ( MCP ) measurement [5]. The MCP measurement Orbital State Study of Mn in Colossal Magnetoresistance Material La 2-2x Sr 1+ 2x Mn 2 O 7 by Magnetic Compton Profile Measurement [001] [110] [100] Fig. 1. The crystal structure of La 2-2x Sr 1+ 2x Mn 2 O 7 . ha s be en us ed as a un iq ue me th od to de te rm in e t h e e l e c t r o n - s p i n m o m e n t u m d e n s i t y i n f e r r o m a g n e t i c m a t e r i a l s . I n a d d i t i o n , i t h a s t h e f o l l o w i n g a d v a n t a g e s t o d e f i n e t h e o r b i t a l o c c u p a t i o n ; t h a t is , MCP changes its shape depending on the orbital st at e oc cu pi ed by ma gn et ic el ec tr on s, an d it al so depends on the direction of the scattering vector of X-ray s with respe ct to the cryst allin e axis. These f e a t u r e s e n a b l e u s t o d i f f e r e n t i a t e t h e e l e c t r o n population in x 2 – y 2 and 3 z 2 – r 2 orbitals together with t 2g state through the measurement of MCP by using a s i n g l e c r y s t a l l i n e s a m p l e . E x p e r i m e n t s h a v e b e e n m a d e a t b e a m l i n e B L 0 8 W u s i n g c i r c u l a r l y p o l a r i z e d X - r a y s o f 2 7 0 k e V . T h e M C P ’ s w e r e m e a s u r e d a l o n g [ 1 0 0 ] , [ 1 1 0 ] a n d [ 0 0 1 ] d i r e c t i o n s for La 2-2x Sr 1+ 2x Mn 2 O 7 with x = 0.35 and 0.42. La, Sr Mn O 38 [001] 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5 6 P z J mag (p z ) 0.8 0.6 0.4 0.2 0 J mag (p z ) 0 1 2 3 4 5 6 P z [110] 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5 6 P z exp. total t 2g x 2 – y 2 3 z 2 – r 2 [100] J mag (p z ) Figures 2 and 3 show respectively the MCP’s of x = 0.35 and 0.42 samples obtained at 10 K. The clear anisotropy of MCP reflects the orbital state of magnetic electrons on Mn site. These MCP’s were explained by theoretical Compton profiles obtained from an ab initio molecular orbital calculation for the ( MnO 6 ) 8- cluster which takes the hybridization effect between Mn 3 d and O 2 p orbitals into account. The th eo re ti ca l an al ys is of th e or bi ta l st at e wa s ma de u s i n g t h e s e f o l l o w i n g c o n d i t i o n s : E a c h M C P i s nor mal ize d by the mag net ic ele ctr on num ber s per site estimated from the hole concentration x . The t 2 g o c c u p a t i o n n u m b e r i s f i x e d t o t h r e e p e r s i t e because it is fully occupied. The remainder is fitted by the profiles of x 2 – y 2 and 3 z 2 – r 2 orbitals so that t h e a r e a o f f i t t e d p r o f i l e c o i n c i d e s w i t h t h a t o f ex pe ri me nt al on e. Th e re su lt s ar e al so sh ow n in Fig. 2 and Fig. 3 with the dashed red line and dash- d o t t e d b l u e l i n e . S i n c e t h e a r e a o f a p r o f i l e i s p r o p o r t i o n a l t o t h e n u m b e r o f e l e c t r o n s p i n s i n a state, the occupation numbers of x 2 – y 2 and 3 z 2 – r 2 orbitals can be thus obtained as 0.47 and 0.18 for x = 0. 35 re sp ec ti ve ly , wh il e th ey ar e 0. 46 an d 0. 12 for x = 0.42. These results show that the e g orbital state is dominated by the x 2 – y 2 -type orbital with almost constant occupation, while the occupation in 3 z 2 – r 2 -type orbital decreases with the increase in t h e h o l e c o n c e n t r a t i o n x . T h i s c o n c l u s i o n w o u l d e x p l a i n t h e c o n t i n u o u s c h a n g e o f m a g n e t i c s t r u c t u r e f r o m f e r r o m a g n e t i s m v i a c a n t e d a n t i f e r r o m a g n e t i s m t o A - t y p e a n t i f e r r o m a g n e t i s m with an increase of x . The decrease of population i n 3 z 2 – r 2 o r b i t a l w e a k e n s t h e f e r r o m a g n e t i c coupling between MnO 2 layers through e g electron hopping. The superexchange coupling between t 2g s p i n s g r a d u a l l y o v e r c o m e s t h e f e r r o m a g n e t i c coupling resulting in the antiferromagnetic structure at high x values. Fig. 2. The magnetic Compton profiles along the [100], [110] and [001] directions in La 2-2x Sr 1 + 2x Mn 2 O 7 with x = 0.35. Experimental data (solid circles) are shown with fit (solid gray line) using the MnO 6 cluster orb ital s. Also sho wn are the t 2g orb ital (dot ted gree n line ), x 2 –y 2 orb ital (das hed red line ) and 3z 2 –r 2 orbital (dash-dotted blue line) contributions. 39 0 1 2 3 4 5 6 P z [001] 0.8 0.6 0.4 0.2 0 J mag (p z ) 0 1 2 3 4 5 6 P z [110] 0.8 0.6 0.4 0.2 0 J mag (p z ) 0.8 0.6 0.4 0.2 0 J mag (p z ) 0 1 2 3 4 5 6 P z [100] exp. total t 2g x 2 – y 2 3 z 2 – r 2 Akihisa Koizumi Himeji Institute of Technology E-mail: akihisa @ sci.himeji-tech.ac.jp Fig. 3. Same as Fig. 2 but for x = 0.42. References [1] C. Zener, Phys. Rev. 82 (1951) 403. [2] Y. Moritomo et al. , Nature (London) 380 (1996) 141. [3] K. Hirota et al. , J. Phys. Soc. Jpn. 67 (1998) 3380. [4] M. Kubota et al. , J. Phys. Soc. Jpn. 69 (2000) 1606. [5] A. Koizumi, S. Miyaki, Y. Kakutani, H. Koizumi, N. Hiraoka, K. Makoshi, N. Sakai, K. Hirota and Y. Murakami, Phys. Rev. Lett. 86 (2001) 5589. 40
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