S t e r e o s c o p i c p h o t o g r a p h s o f a t h r e e - d i m e n s i o n a l a t o m i c a r r a n g e m e n t h a v e b e e n o b t a i n e d f o r t h e f i r s t t i m e [ 1 ] . T w o - d i m e n s i o n a l p h o t o e l e c t r o n diffraction patterns obtained by left and right helicity l i g h t c a n b e u s e d a s s t e r e o s c o p i c p h o t o g r a p h s wh en th e tw o pa tt er ns ar e si mu lt an eo us ly vi ew ed by the left eye and the right eye. Using a display- t y p e s p h e r i c a l - m i r r o r a n a l y z e r [ 2 ] , s t e r e o s c o p i c photographs can be obtained directly on the screen w i t h o u t u s i n g a n y c o m p u t e r - a i d e d c o n v e r s i o n process. Atomic arrangements, however, have not been y e t d i r e c t l y o b s e r v e d . S T M ( s c a n n i n g t u n n e l i n g m i c r o s c o p e ) o r T E M ( t r a n s m i s s i o n e l e c t r o n m i c r o s c o p e ) c a n p r o v i d e a t o m i c i m a g e s i n t w o - dimensional, but not in a three-dimensional atomic a r r a n g e m e n t . D e t a i l e d a t o m i c p o s i t i o n s c a n b e o b t a i n e d w i t h t h e u s e o f o t h e r t o o l s f o r s t r u c t u r e a n a l y s i s , s u c h a s L E E D ( l o w - e n e r g y e l e c t r o n diffraction) and X-ray diffraction, however requiring complicated analysis. When the kinetic energy of photoelectrons from t h e c o r e s t a t e i s a b o v e s e v e r a l h u n d r e d e V , t h e s c a t t e r i n g o f p h o t o e l e c t r o n s f r o m s u r r o u n d i n g atoms create an intensity modulation in the angular d i s t r i b u t i o n , k n o w n a s p h o t o e l e c t r o n d i f f r a c t i o n . The so-called forward focusing peaks appear in a t w o - d i m e n s i o n a l p h o t o e l e c t r o n d i f f r a c t i o n p a t t e r n along the direction connecting the emitter and the sc at te re r of ph ot oe le ct ro ns . Th e re ce nt re se ar ch has shown that, utilizing circularly polarized light for t h e e x c i t a t i o n o f p h o t o e l e c t r o n s , t h e s e f o r w a r d focusing peaks are rotated in the same direction as the electric vector of the incident circularly polarized light [3] . This was the first observation of the orbital a n g u l a r m o m e n t u m o f e l e c t r o n s . T h i s c i r c u l a r d i c h r o i s m o c c u r s f o r b o t h c h i r a l o r m a g n e t i c m a t e r i a l s and non-chiral and non-magnetic materials such as STEREOVIEW OF 3-D ATOMIC ARRANGEMENT BY CIRCULARLY POLARIZED-LIGHT PHOTOELECTRON DIFFRACTION Si(001) [3] or W(110) -O [4] surfaces. The rotation angle ∆φ of these forward focusing peaks around the photon incident axis is expressed by a simple formula: ∆ φ = m / kR sin 2 θ [3] , where m i s t h e m a g n e t i c q u a n t u m n u m b e r o f t h e p h o t o e l e c t r o n , k i s i t s w a v e n u m b e r , R i s t h e int ern ucl ear dis tan ce bet wee n the emi tter and the n e a r e s t - n e i g h b o r s c a t t e r e r , a n d θ i s t h e a n g l e betw een the dire ctio ns of inci dent phot on and the o u t g o i n g p h o t o e l e c t r o n . T h i s r o t a t i o n h a s b e e n ex pl ai ne d as be in g du e to th e tr an sf er of an gu la r m o m e n t u m o f t h e p h o t o n t o t h e p h o t o e l e c t r o n , w h e r e i t s z c o m p o n e n t a n g u l a r m o m e n t u m i s c h a n g e d b y 1 w h e n e x c i t e d b y t h e c i r c u l a r l y p o l a r i z e d l i g h t . T h e d i s c o v e r y o f t h i s r o t a t i o n pro per ty has cre ate d new fie lds in the ana lys is of a t o m i c , e l e c t r o n i c , a n d m a g n e t i c s t r u c t u r e o f surfaces. Stereomicroscopy of atomic structure we d e s c r i b e h e r e i n i s o n e o f t h e m o s t i m p o r t a n t applications of this phenomenon. We show an example in Fig. 1 , where (a) , (b) indicate the photoelectron diffraction patterns of W 4 f p h o t o e l e c t r o n s f r o m W ( 1 1 0 ) s u r f a c e a t t h e kinetic energy of 800 eV for left and right circularly polarized light, respectively. This experiment was p e r f o r m e d a t B L 2 5 S U u s i n g t h e h i g h - e n e r g y - resolution display-type spherical-mirror analyzer [5] . I t s e n e r g y r e s o l u t i o n i s 0 . 3 % o f t h e p a s s - e n e r g y , and the angular resolution is higher than 1 degree. When Fig. 1 (a) is looked with the left eye and (b) w i t h t h e r i g h t e y e , t h e t h r e e - d i m e n s i o n a l a r r a n g e m e n t of atoms can be viewed as shown in (c) : the A atom looks closer, the B and C atoms look farther, and the others look even farther. This image coincides with the real arrangement of W atoms viewed from t h e a t o m O , a s s h o w n i n F i g . 1 ( d ) . T h e m a g n i f i c a t i o n ratio is approximately 10 10 . T h e s e f i g u r e s c a n b e v i e w e d a s s t e r e o - p h o t o g r a p h s F i g . 1 . S t e r e o s c o p i c p h o t o g r a p h s o f W ( 1 1 0 ) c r y s t a l , w h i c h i s a c t u a l l y t h e t w o - d i m e n s i o n a l ci rc ul ar ly po la ri ze d- li gh t ph ot oe le ct ro n di ff ra ct io n pa tt er ns of W 4f fr om th e W( 11 0) su rf ac e. (a) , (b) show the resu lts for left and righ t circ ular ly pola rize d ligh t, resp ecti vely . The kine tic en er gy is 80 0 eV . Th e sm al l bl ac k ci rc le s in di ca te th e ca lc ul at ed di re ct io ns of ea ch fo rw ar d- focusing peak along the crystallographic axes shown in (c) . Looking at (a) with the left eye and (b) with the right eye, the three-dimensional arrangement of atoms shown in (d) can be viewed. (a) (b) O [ 0 0 1 ] 1 1 0 ] [ 1 1 1 ] [ 1 0 0 ] B C A B’ B C’ C A (c) (d) d u e t o t h e f o l l o w i n g r e a s o n s : t h e p h o t o e l e c t r o n s have orbital angular momentum, propagating from a p o i n t o f s o m e d i s t a n c e c a l l e d t h e i m p a c t parameter, not from the center of the emitter atom; t h e a n g u l a r m o m e n t u m i s t h e p r o d u c t o f t h e mo me nt um an d th e im pa ct pa ra me te r, th us wh en the angular momentum is plus (minus), the impact p a r a m e t e r i s a l s o p l u s ( m i n u s ) ; a n d t h e s e p l u s - m i n u s i m p a c t p a r a m e t e r s c o r r e s p o n d t o o u r r i g h t a n d l e f t e y e s , t h u s t h e o b t a i n e d p h o t o e l e c t r o n diffraction patterns are the same as the image seen by right and left eyes. More details are described in ref. [1] . Hiroshi Daimon Nara Institute of Science and Technology ( NAIST ) E-mail: daimon @ ms.aist-nara.ac.jp References [1] H. Daimon, Phys. Rev. Lett. 86 (2001) 2034. [2] H. Daimon, Rev. Sci. Instrum. 59 (1988) 545. [3] H. Daimon et al. , Jpn. J. Appl. Phys. 32 (1993) L1480. [4] H. Daimon et al. , Phys. Rev. B 58 (1998) 9662. [ 5 ] M . K o t s u g i , K . E n o m o t o , Y . M i y a t a k e , T . N a k a t a n i , Y . S a i t o h , T . M a t s u s h i t a , S . I m a d a , T . Furuhata, S. Suga, K. Soda, M. Jinno, T. Hirano, K. Hattori and H. Daimon, Rev. Sci. Instrum. (2001) - in press.
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