X-Ray Magnetic Dichroism. S. Turchini ISM-CNR
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1 X-Ray Magnetic Dichroism S. Turchini SM-CNR
2 Magnetism spin magnetic moment direct exchange: ferro antiferro superexchange 3d Ligand 2p 3d
3 Stoner model Rigid exchange between spin up and down bands ε F Criterium for ferromagnetism: n(ε f )>1
4 Symmetry breaking dichroism is due to the coupling of a chiral probe (circular polarized light, an asymmetric experimental geometry) with a sample that presents a breaking sysmmetry the dichroism is expressed as an asymmetry ratio between the intensities measured in two distinct experimental chiral geometries D = A A B B f there is a mirror reflection that makes the two experimental geometries superimposable there is no dichroism
5 hq M i left hq M i right D = right right left left
6 hq i M right hq M i right D = right right ( M ( M ) ) right right ( M ( M ) )
7 hq right D=0 left hq
8 E E M hq M hq E E hq hq D = E M E M E M E M
9 XMCD and XLMD XMCD is proportional to m in ferro(ferri)magnets XLMD is proportional to m 2 in ferromagnets and antiferromagnets
10 X-Ray absorption Spectroscopy One particle picture: L3 DOS d L2 2p 3/2 The absorption is proportional to the local density of state projected in angular momentum 2p 1/2
11 XMCD DOS 3p 2p 1s MOKE ntraband transition no chemical information Hard X-rays s-> p transition low lifetime (10 ev) VUV p->d transition high lifetime (0.1eV) no spin orbit Soft X-Rays p-d transition high lifetime (1 ev) Spin orbit
12 Multiplet Structure p 6 d 0 p 5 d 1 LS coupling initial state: 1S final state: 1 S, 1 P, 3 P, 3 D 1 S 1 P Only one line in the absorption spectrum
13 1 F 1 D ntermediate coupling mapping 1 P (LS) 1 P, 3 P, 3 D(jj) 1 P 3 F 3 D 3 P LS Two lines with branching ratio 2:1 (the triplets are degenerate) jj
14 Turning on 3d spin orbit interaction and d-d, p-d Coulomb interaction Ti4 ev Eav Splitting of the L3 and intensities strongly redistributed by the p-d Coulomb interaction LS(p) 3.78 LS(d) F 2 pd 6.30 G 1 pd 4.62 G 2 pd 2.63
15 Atomic XMCD atomic in jj coupling J=1,0,-1 T=0 K J1 -M1 -M-1 M=-1 J-1 J -M1 -M1 J -M M=1 Strong dichroism due to optical selection rules
16 Band XMCD model J. Stohr, JMMM, 200, 470 (1999)
17 Sum rules? m spin = spin spin = E< ε E> ε F ( ρ ρ ) de ( ρ F spin ρ spin ) de Lz A B Lifting quantum number s (ls,l-s) m spin A c pol B Different polarization between L3 and L2
18 Sum Rules 2p edges ) (10 ) ( 3 ) ( d L L L L orb n de de m = µ µ µ µ ) (10 ) ( ) ( 2 ) ( d L L L L z spin n de de de T m = µ µ µ µ µ µ C.T. Chen et al, PRL,75,152(1995)
19 m m orb neglecting T z spin = n h = 2n 4( A 3( h B) ) L 3 L 2 A 2B L 3 L 2 background subtraction (s states) isolating the edge contribution number of holes in the d band splitting of magnetic moment in orbital and spin part good values of m orb /m spin
20 T is the magnetic dipole operator T α = β Q αβ What is T z? S Assuming the magnetic saturation along α direction S α = S = i s i β i i Tα = s Qα i T reflects anisotropy in spin density T is zero when the charge is isotropic (cubic sysmmetry, policrystalline sample), otherwise is not negligible When summed over x,y,z directions T disappears
21 Electronic and magnetic structure of Sr 2 FeMoO 6 double perovskite ferrimagnetic compound half metallic state colossal magnetoresistance XAS and XMCD can answer important questions What is the valence state of Fe? By means of a configuration interaction multiplet calculation the valence state of Fe was found 3
22 s there a localized momentum on Mo? the Mo spin moment is negligible (<0.25µ b ), the ferrimagnetism is delocalized The half metallic state is destroyed by the mis-site disorder S. Ray, A. Kumar, D.D. Sarma, R. Cimino, S. Turchini, S. Zennaro and N. Zema, PRL,87,097204(2001)
23 Localized magnetic states of Fe, Co, Ni ML Fe/K ML Co/K 0.04 ML Ni/K Localized atomic states with d 7,d 8,d 9 P. Gambardella, S.S. Dhesi, S. Gardonio, C. Grazioli, P. Ohresser and C. Carbone, 88,047202(2002)
24 Hund s Rules for ground state maximum S maximum L (according to S) L and S parallel/antiparallel for a shell more/less then half filled R = 2 S z Lz 7 T z highly localized moments disappear increasing the coverage
25 FM-AFM manipulation The manipulation of FM-AFM interfaces has often led to the discovery of unexpected magnetic properties and to the possibility of interesting applications AFM FM a FM put directly in contact with an AFM 1956 Meiklejohn and Bean: fine particles of Co (FM) coated by CoO (AFM) FM-AFM in the thin film form is a better controllable system
26 Mn on Fe(100) Mn Fe 1ML of Mn on Fe LDA calculations the magnetic structure with the Mn moments out of plane is the most stable 0.35 mev/atom lower than the collinear structure
27 Competiting exchange interactions Unusual magnetic structures AFM monolayer on top of an FM solated atom: collinear structure Higher coverages: AFM interaction becomes more important This CAN lead to non collinear magnetic structures
28 Circular Dichroism results ntensity (arb. units) ntensity (arb. units) Mn 2p XAS σ 5 σ - 0 Mn 2p dichroism Fe 2p XAS 0.2 ML Mn 5 0 σ -5 σ Fe 2p dichroism Photon energy (ev) Photon energy (ev) Norm. Dichroism (%) Norm. Dichroism (%) Mn-Fe asymetry ratio from XMCD Antiparallel Mn-Fe exchange coupling Ferromagnetic Mn signal, decreasing with coverage and vanishing at 1 ML. We have an AFM monolayer of Mn O. Rader et al., Phys. Rev. B 56, 5053 (1997) J. Dresselhaus et al., Phys. Rev. B 56, 5461 (1997)
29 XMLD effects observed at Mn L 3,2 edges ntensity (arb. units) θ = 0 o θ = 60 o θ XMLD effects are observed at Mn L 3,2 edges near ML coverage with polar angle Photon Energy (ev) Difference spectrum Evidence for antiferromagnetic ordering of Mn. ntensity (arb. units) Experiment: µ XAS (60 ) - µ XAS (0 ) C. Grazioli, D. Alfè, S. R. Krishnakumar, S.S. Gupta, M. Veronese, S. Turchini, N. Bonini, A. Del Corso, D.D. Sarma, S. Baroni, and C. Carbone, PRL, 95,117201(2005) Photon Energy (ev)
30 Experimental and calculated Mn L 3,2 XMLD Atomic calculations including multiplet interactions ntensity (arb. units) (µ µ - ) E perpendicular to µ µ 0 E parallel to µ 3d 5 multiplet features AF-Mn moments are perpendicular to both Fe moments and to the film surface Photon Energy (ev) non-collinear spin-flop state N. C. Koon, Phys. Rev. Lett. 78, 4865 (1997) ntensity (arb. units) µ XAS (60 ) - µ XAS (0 ) Experimental µ 0 - (µ µ - ) Calculated Photon Energy (ev)
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