TEMPERATURE VARIATION OF SPIN- AND ORBITAL-MAGNETIC FORM FACTOR OF HOLMIUM IRON GARNET BY X-RAY MAGNETIC DIFFRACTION X - r a y m a g n e t i c d i f f r a c t i o n w i t h t h e u s e o f e l l i p t i c a l l y p o l a r i z e d s y n c h r o t r o n r a d i a t i o n i s a u n i q u e t o o l w h i c h e n a b l e s u s t o t a k e s e p a r a t e m e a s u r e m e n t s o f s p i n - a n d o r b i t a l - m a g n e t i c m o m e n t s o f f e r r o m a g n e t s [ 1 ] . T h e s e m a g n e t i c mom ent s are fun dam ent al phy sic al qua nti tie s and give us essential knowledge regarding magnetism. To date, the white beam method [2-5] which utilizes e l l i p t i c a l l y p o l a r i z e d w h i t e X - r a y s o f b e n d i n g - m a g n e t r a d i a t i o n , h a s b e e n t h e m o s t e x t e n s i v e l y employed technique. In the present experiment we h a v e a d o p t e d a n a d v a n c e d m e t h o d b y u t i l i z i n g a monochromatic beam. This method utilizes highly brilliant undulator radiation and a phase plate. One advan tage of the monoc hroma tic beam metho d is its capability of more precise measurements, as it is n o t s u b j e c t t o f l u o r e s c e n t X - r a y s a n d m u l t i p l e scattering as much as the white beam method. The monochromatic beam method was applied to a determination of the spin- and orbital-magnetic form factor of Holmium Iron Garnet, Ho 3 Fe 5 O 12 , at v a r i o u s t e m p e r a t u r e s b e t w e e n 6 0 K a n d 3 0 0 K . T h i s c o m p o u n d i s a f e r r i m a g n e t w i t h a c o m p e n s a t i o n temperature ( Tc ) of approximately 130 K, at which t h e t o t a l m a g n e t i z a t i o n v a n i s h e s . T h e t o t a l m a g n e t i z a t i o n i s c o m p o s e d o f t h e m a g n e t i c m o m e n t s o f H o a n d F e a t o m s . T h e d o m i n a n t component of the total magnetization, which is the H o m o m e n t b e l o w t h e T c , i s b e l i e v e d t o b e switched to the Fe moment above the Tc. In this experiment, we aim to determine how the spin- and o r b i t a l - m a g n e t i c m o m e n t s o f t h i s c o m p o u n d v a r y through the compensation temperature. The experiment was performed at the undulator be am li ne BL 39 XU , wh er e a ph as e pl at e ma de of diamond crystal is installed [6] . The phase plate is a n X - r a y o p t i c a l d e v i c e u t i l i z e d t o c o n t r o l t h e p o l a r i z a t i o n of synchrotron radiation and to generate elliptically po la ri ze d ra di at io n. Th e ph as e pl at e sy st em ha s be en su cc es sf ul ly ap pl ie d to MC D me as ur em en ts a t t h i s b e a m l i n e [ 7 ] , a n d t o t h e X - r a y m a g n e t i c diffraction measurement [8] . The present study is the first case in which a phase plate was applied in t h e X - r a y m a g n e t i c d i f f r a c t i o n , t o g e t h e r w i t h t h e third-generation undulator radiation. T h e p r e p a r e d s i n g l e c r y s t a l s p e c i m e n o f t h e c o m p o u n d w a s m a d e b y t h e L P E m e t h o d . E l l i p t i c a l l y p o l a r i z e d X - r a y s o u t o f t h e p h a s e p l a t e w e r e i r r a d i a t e d o n t h e s p e c i m e n a n d t h e d i f f r a c t i o n in te ns it y of th e (8 80 ) re fl ec ti on pl an e wa s me as ur ed using an APD detector [9] . The scattering angle to t h e s p e c i m e n w a s s e t a t t h e 9 0 d e g r e e s . T h e specimen was kept in a refrigerator to maintain the desired temperature between 60 K and 300 K. The specimen was also kept under a magnetic field of 0 . 6 T e s l a b y a n e l e c t r o m a g n e t . T h e d i f f r a c t i o n i n t e n s i t i e s w e r e m e a s u r e d b y r e v e r s i n g t h e magnetization direction (referred to as a magnetic effe ct or a flip ping rati o). The magn etic fiel d was a p p l i e d i n t w o w a y s ; ( i ) a l o n g t h e i n c i d e n t b e a m a n d ( i i ) a l o n g t h e d i f f r a c t i o n b e a m . T h e f o r m e r m e a s u r e m e n t g i v e s u s t h e o r b i t a l - m a g n e t i c f o r m f a c t o r a t t h e 8 8 0 r e c i p r o c a l l a t t i c e p o i n t , μ L ( 8 8 0 ) , a n d t h e l a t t e r m e a s u r e m e n t g i v e s u s t h e t o t a l magnetic form factor (orbital+spin), μ L +2 S (880). In Fig. 1 , the observed values of the μ L (880) and Fig. 1. Temperature variation of orbital-magnetic form factors (solid circles) and total magnetic form factors (solid squares) of Holmium Iron Garnet at the 880 reciprocal lattice point, μ L (880) and μ L +2S (88 0), res pec tiv ely . Ope n cir cle s and ope n squ are s rep res ent abs olu te val ues of the f o r m f a c t o r s a b o v e t h e c o m p e n s a t i o n t e m p e r a t u r e T c ( 1 3 0 K ) . S o l i d l i n e s a n d d a s h e d l i n e s represent the fitted cubic curves for the absolute values of μ L (880) and μ L +2S (880), respectively. Thicker lines are drawn for the data represented by solid circles and squares. the μ L +2 S (880) are shown between 60 K and 300 K. S o l i d c i r c l e s a n d s o l i d s q u a r e s r e p r e s e n t t h e μ L ( 8 8 0 ) a n d t h e μ L + 2 S ( 8 8 0 ) , r e s p e c t i v e l y . A b o v e the compensation temperature, which is 130 K, the absolute values of the μ L (880) and the μ L +2 S (880), are shown by the open circles and open squares, respectively. It is noted in Fig. 1 that (i) the signs of b o t h μ L ( 8 8 0 ) a n d μ L + 2 S ( 8 8 0 ) a r e r e v e r s e d a t t h e compensation temperature, ( ii ) the absolute values o f t h e b o t h μ L ( 8 8 0 ) a n d μ L + 2 S ( 8 8 0 ) d e c r e a s e mon oto nic all y as the tem per atu re inc rea ses . The es ti ma te d st at is ti ca l er ro r ba rs , wh ic h ar e no t sh ow n in the figure, are about the same as the size of data po in t. Th e so li d li ne s an d da sh ed li ne s in Fi g. 1 r e p r e s e n t t h e f i t t e d c u b i c c u r v e s f o r t h e a b s o l u t e v a l u e s o f t h e μ L ( 8 8 0 ) a n d t h e μ L + 2 S ( 8 8 0 ) , r e s p e c t i v e l y . F r o m t h e s e f i t t e d c u r v e s t h e s p i n - m a g n e t i c f o r m factor μ 2 S ( 8 8 0 ) w a s d e r i v e d a s μ 2 S ( 8 8 0 ) = μ L + 2 S ( 8 8 0 ) – μ L ( 8 8 0 ) and is plo tte d in Fig . 2 . We see , tha t the si gn of th e μ 2 S (8 80 ) is opp os it e to tha t of the μ L (8 80 ) a n d t h e absolute value of the μ 2 S (880) decreases monotonically as the temperature increases. This i s t h e f i r s t m e a s u r e m e n t o f t h e t e m p e r a t u r e v a r i a t i o n i n t h e s p i n - a n d o r b i t a l - m a g n e t i c f o r m factor of this compound. Both Ho and Fe atoms contribute to the total magnetic form factor of this compound. Assuming t h a t t h e o r b i t a l m o m e n t o f F e i s q u e n c h e d , a s i s almost the case for 3 d transition-metal atoms, the t o t a l m a g n e t i c f o r m f a c t o r i s c o m p o s e d o f t h e following three components; (a) the orbital moment of Ho, (b) the spin moment of Ho, and (c) the spin moment of Fe. The μ L (880) would come from the orbital-magnetic form factor of Ho. The change in t h e s i g n o f t h e μ L ( 8 8 0 ) a t t h e c o m p e n s a t i o n temperature directly indicates the direction reversal o f t h e m a g n e t i c m o m e n t o f H o . T h e μ 2 S ( 8 8 0 ) i s c o m p o s e d of the spin moments of Ho and Fe. In μ L (880) μ L +2 S (880) absolute values above T c Temperature (K) Magnetic Form Factor 0 100 200 300 0 -1 1 2 Fig. 2. Orbital-magnetic form factor μ L (880) (solid lines) a n d s p i n - m a g n e t i c f o r m f a c t o r μ 2S ( 8 8 0 ) ( d a s h e d l i n e s ) . μ 2S (880) are derived from the fitted curves of μ L (880) and μ L +2S (880), as μ 2S (880) = μ L +2S (880) – μ L (880). M a s a h i s a I t o a , E t s u o A r a k a w a b a n d Hiroshi Maruyama c (a) Himeji Institute of Technology (b) Tokyo Gakugei University (c) Okayama University E-mail: itom @ sci.himeji-tech.ac.jp References [1] M. Blume and D. Gibbs, Phys. Rev. B 37 (1988) 1779. [2] D. La un dy et al . , J. Ph ys. Co nd en s. Mat ter 3 (1991) 369. [3] S. P. Collins et al. , Philos. Mag. B 65 (1992) 37. [4] M. Ito et al. , J. Phys. Soc. Jpn. 64 (1995) 2333. [5] D. Laundy et al. , J. Synchrotron Rad. 5 (1998) 1235. [6] M. Ito, E. Arakawa, M. Suzuki, N. Kawamura, K. H i r a n o , S . K i s h i m o t o , H . M a r u y a m a a n d K . N a m i k a w a , in preparation. [ 7 ] H . M a r u y a m a e t a l . , J . S y n c h r o t r o n R a d . 6 (1999) 1133. [8] M. Ito and K. Hirano, J. Phys. Condens. Matter 9 (1997) L613. [ 9 ] S . K i s h i m o t o e t a l . , t o b e p u b l i s h e d i n N u c l . Instrum. Meth. in Phys. Res. A (2001). order to separate Ho and Fe contribution in th e sp in -m ag ne ti c fo rm fa ct or , fu rt he r ex pe ri me nt s an d/ or an al ys es ar e ne ed ed . T h e r e f o r e w e p l a n t o o b t a i n t h e s p a t i a l d i s t r i b u t i o n o f t h e s p i n a n d o r b i t a l moments of Ho and Fe in the compound. In conclusion, (i) the spin- and orbital- m a g n e t i c f o r m f a c t o r s o f t h e H o l m i u m Ir on Ga rn et at th e 88 0 re ci pr oc al la tt ic e point were measured between 60 K and 3 0 0 K f o r t h e f i r s t t i m e ; ( i i ) b o t h t h e ma gn et ic fo rm fa ct or s sh ow th e ch an ge i n t h e s i g n a t t h e c o m p e n s a t i o n t e m p e r a t u r e w h i c h i s t h e d i r e c t o b s e r v a t i o n o f t h e r e v e r s a l o f t h e m a g n e t i c m o m e n t d i r e c t i o n ; a n d ( i i i ) t h e a b s o l u t e v a l u e s o f b o t h m a g n e t i c fo r m fa c t o r s in d i c a t e a m o n o t o n i c decrease as the temperature increases. 0 100 200 300 0 -1 1 2 Temperature (K) Magnetic Form Factor μ L (880) μ 2 S (880)
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