A15. Circular dichroism absorption spectroscopy and its application

Transcription

1 A15. Circular dichroism in X-ray X absorption spectroscopy and its application Klaus Baberschke Institut für Experimentalphysik Freie Universität Berlin Arnimallee 14 D Berlin-Dahlem Germany 1. Introduction to NEXAFS and XMCD. 2. Element specific magnetizations in trilayers. 3. Determination of orbital- and spin- magnetic moments; XMCD sum rules. 4. Magnetic Anisotropy Energy (MAE) and anisotropic µ L. 5. New developments, outlook. Freie Universität Berlin Hercules A15 / Grenoble /

2 See also other lectures 9 S.Pascarelli X-ray absorption spectroscopy A 13 J. Vogel XAS: theoretical basis A14 Y. Joly XAS: the monoelectronic approach A 16 F. Sirotti Magnetic dichroism A 17 M. Sacchi Soft X-ray magnetic dichroism This lecture see: Lectures Hercules 28 2

3 In this lecture we will not discuss the equipment/apparatus, but rather focus on application of XAS in magnetism. Concerning XAS-technique there exist many review articles e.g. J. Stöhr: NEXAFS Spectroscopy, Springer Series in Surface Science 25, 1992; H. Wende: Recent advances in the x-ray absorption spectroscopy, Rep. Prog. Physics 67, 215 (24). J. Stöhr, H.C. Siegmann: Magnetism, Springer 26 In the soft X-ray regime (VUV) one needs to work in vacuum. For nanomagnetism one wants to prepare and work anyway in UHV (in situ experiments). L-edges of 3d elements ( Mn, Fe, Co, Ni ) and K-edges of 2p elements ( C, N, O ) range between 1 and 1 ev 3

4 1. Introduction: XAS X-ray Absorption Spectroscopy is the most appropriate technique for element specific investigations. X-ray absorption cross section (arb. units) Fe Co L 3,2 edges of 3d elements Note: the intensity of the 2p 3d dipole transitions (E1) is proportional to the number of unoccupied final state (i.e. 3d- holes). Ni Cu Photon energy (ev) 4

5 XAS of 1 ML of Fe octaethylporphyrin on metal surface p* s Porphyrin molecule 5

6 XAS / NEXAFS and XMCD at Fe in OEP 6

7 eg t2g Freie Universität Berlin Hercules A15 / Grenoble /

8 X-ray Magnetic Circular Dichroism Faraday effect in the X-ray regime (Gisela Schütz, 1987) Norm. XMCD (arb. units) Norm. XAS (arb. units) L 3 L2 Fe M µ + µ µ continuum µ(e) =µ + µ (E) (E) (E) Spin up Spin down M k L 3 L 2 3d left right +h h 2p 2p E F 3d 3 2 3d Photon Energy (ev) XMCD signal is a measure of the magnetization p 1 2 2p 3 2 Many Reviews, e.g. H. Ebert Rep. Prog. Phys. 59, 1665 (1996) 8

9 The origin of MCD (after K. Fauth, Univ. Würzburg) Reviews e.g.: Lecture Notes in Physics Vol. 466 by H. Ebert, G. Schütz 9

10 X-ray magnetic circular dichroism (XMCD) 3d exchange 3d 3d E F µ s = (n h n h )µ B σ + σ 62.5% 37.5% σ + σ 2p spin orbit 25% 75% 2p 3/2 2p 3/2 2p 1/2 1

11 2. Element specific magnetizations in trilayers T C Co T C Ni e- 3 e ev(l 3) 853 ev(l ) M M substrate J inter Co Cu Ni A trilayer is a prototype to study magnetic coupling in multilayers. What about element specific Curie-temperatures? Two trivial limits: (i) d Cu = direct coupling like a Ni-Co alloy (ii) d Cu = large no coupling, like a mixed Ni/Co powder BUT d Cu 2 ML? 11

12 Ferromagnetic trilayers norm. absorption (a.u) 4 2 Co L 3,2 x 1.72 Ni L 3,2 XMCD (arb.uunits) 29K Ni L 3,2 336K Co L 3,2 x K M Co 2.ML Co 2.8ML Cu -4 M Ni 4.3ML Ni 29K Cu (1) Photon energy (ev) XMCD (arb.uunits) ML Co 3.4 ML Cu 3.6 ML Ni Cu(1) h ν (ev) Cu(1) T = 14K U. Bovensiepen et al., PRL 81, 2368 (1998) T (K) M (arb. units) T C Co = 34 K T* C Ni = 38 K 12

13 Interlayer exchange coupling M (arb. units) ML Cu 4.8 ML Ni Cu(1) T C Ni = 275K 2.8 ML Co 2.8 ML Cu 4.8 ML Ni Cu(1) 37K P. Poulopoulos, K. B., Lecture Notes in Physics 58, 283 (21) T * Ni T (K) J inter (µev/atom) a FMR Cu/ Ni/ Cu/ Ni/ Cu(1) ) b XMCD Co/ Cu/ Ni/ Cu(1) ) c FMR Ni/ Cu/ Co/ Cu(1) ) Theory d ) d Cu (ML) a) J. Lindner, K. B., J. Phys. Condens. Matter 15, S465 (23) b) A. Ney et al., Phys. Rev. B 59, R3938 (1999) c) J. Lindner et al., Phys. Rev. B 63, (21) d) P. Bruno, Phys. Rev. B 52, 441 (1995) 13

14 Magnetization (arb. units) hν Magnetization (arb. units) H statisch +HV 281 K 265 K Remanence and saturation magnetization I P e _ 184 K Magnetic Field (Oe) C. Sorg et al., XAFS XII, June 23 Physica Scripta T115, 638 (25) 5 ML Cu 6 ML Ni Cu (1) Temperature (K) M (ka/m) M / (T = ) M C,Ni C,Ni ML Cu 2.8 ML Ni 1 T C,Ni T Cu (1) C,Ni 38 K T (K) 2. ML Co 3. ML Cu 2.8 ML Ni * TC,Ni 2D Cu (1) 3D T / T C,Ni d Ni (ML) Theory / Experiment

15 Enhanced spin fluctuations in 2D (theory) P. Jensen et al. PRB 6, R14994 (1999) Ni T / T C J inter 1 K 3 K =3 K Co/Cu/Ni trilayer.9 Tyablikov (or RPA) decoupling.6.3 MF d (ML) Ni + Spin-Spin correlation function S i S j t z + z S i S j Si S j S isi S j S isj S i+ RPA z + Si S j, mean field ansatz (Stoner model) is insufficient to describe spin dynamics at interfaces of nanostructures J.H. Wu et al. J. Phys.: Condens. Matter 12 (2) 2847 E=E AFM E FM (ev/ml) - T ( o K) T= o K T=25 o K T χ 1/ max E FM2 E NM E FM1 E TOT FM coupled AFM coupled (a) (b) (c) d NM Single band Hubbard model: Simple Hartree-Fock (Stoner) ansatz is insufficient Higher order correlations are needed to explain T C -shift 1/ χ max (arbitrary unit) 15

16 Evidence for giant spin fluctuations PRB 72, 54447, (25) d FM1 T C, Ni 2D spin fluctuations IEC ~ 1 2 d NM Jinter FM2 (Co) NM (Cu) FM1 (Ni) d NM 16

17 Crossover of M Co (T) and M Ni (T) Norm. XMCD Difference (arb.units) Co L 3,2 -edges Ni L 3,2 -edges 45K 2.1ML Cu 4ML Ni Cu(1) x Photon Energy (ev) 1.3ML Co 2.1ML Cu 4ML Ni Cu(1) Magnetization M (Gauss) [11] M sat M sat 2 AFM M Ni Temperature (K) [1] easy M Co [11] ext H, k easy M Ni Two order parameter of T C Ni and T C Co A further reduction in symmetry happens at T C low 17

18 3. Orbital magnetism in second order perturbation theory effective Spin Hamiltonian d 1 L Z S Z +λl S L ± S + _ ψ 2 1/ 2 (2) { 2 2 } 2 The orbital moment is quenched in cubic symmetry 2- L Z 2- =, but not for tetragonal symmetry W.D. Brewer, A. Scherz, C. Sorg, H. Wende, K. Baberschke, P. Bencok, and S. Frota-Pessoa Direct observation of orbital magnetism in cubic solids Phys. Rev. Lett. 93, 7725 (24) and W.D. Brewer et al. ESRF Highlights, p. 96 (24) 18

19 Determination of orbital- and spin- magnetic moments Which technique measures what? µ L, µ S in UHV-XMCD µ L + µ S in UHV-SQUID µ L / µ S in UHV-FMR per definition: 1) spin moments are isotropic 2) also exchange coupling J S 1 S 2 is isotropic 3) so called anisotropic exchange is a (hidden) projection of the orbital momentum into spin space For FMR see: J. Lindner and K. Baberschke In situ Ferromagnetic Resonance: An ultimate tool to investigate the coupling in ultrathin magnetic films J. Phys.: Condens. Matter 15, R193 (23) 19

20 Orbital and spin magnetic moments deduced from XMCD N d d (?µ L 3 2?µ L 2 ) de = ( 2 SZ + 7 TZ ) N d (?µ L 3 +?µ L 2 ) de = LZ nor m. X MCD (arb.unit s) L3 edge? Ni?? 2N 3N d h µ S d h L 2 edge µ S ( µ 2 L + µ L ) 3 µ L ( µ 2 L 2 µ L ) 3 de de µ L µ L / µ S XMCD Integral (arb. units) prop. µ S prop. µ L L 3 L Photon Energy (ev) XMCD: FMR: V x5 Fe µ S µ L µ S µ L g<2 g>2 µ µ L / S(Fe) µ L / µ S (Fe+V) bulk Fe Photon Energy (ev) H. Ebert Rep. Prog. Phys. 59, 1665 (1996) µ L / µ S(V) XMCD 4nm Fe Fe Fe /V 4 / V Fe 2 /V 5 2

21 spin moment only Sum rules orbital moment only 3d l z s z +1/2 1/2 3d l z s z +1/2 1/2 L 3 L 3 dichroism Dichroismus only nur m S m S L 2 dichroism Dichroismus only nur m L m L L 2 L 3 dichroism Dichroismus L 2 m S und S and m L m L Photonenenergie 21

22 absorption C n h L 3 L 2 right circular left circular step function 1. Summenregel: µ s = 1 C (A+ 2B) µ B difference integrated difference B (x 3) A A B A photon energy (ev) (P. Carra et al., PRL 7 (1993) 694) 2. Summenregel: µ l = 2 3C (A B) µ B (B. T. Thole et al., PRL 68 (1992) 1943) 22

23 23 Enhancement of Orbital Magnetism at Surfaces: Co on Cu(1) λ λ λ / 1 2)/ ( 3 1) / ( exp nd d n n D d n d D S L e C e B Ae M M = = Σ + Σ + = M. Tischer et al., Phys. Rev. Lett. 75, 162 (1995)

24 Giant Magn. Anisotropy of Single Co Atoms and Nanoparticles P. Gambardella et al., Science 3, 113 (23) Induced magnetism in molecules T. Yokoyama et al., PRB 62, (2) µ L ~531 ev e- O C 1ML Ni Cu µ n = number of atoms XMCD XMCD 24

25 4. Magnetic Anisotropy Energy (MAE) and anisotropic µ L 1. Magnetic anisotropy energy = f(t) 2. Anisotropic magnetic moment f(t) 5 [111] M (G) 3 1 [1] Ni [111] [1] 1 2 B (G) µ L ~.1 G 3 MAE =?M db ½?M?B ½ 2 2 G 2 MAE erg / cm 3.2 µev / atom Characteristic energies of metallic ferromagnets binding energy 1-1 ev/atom exchange energy mev/atom cubic MAE (Ni).2 µev/atom uniaxial MAE (Co) 7 µev/atom 1µeV/atom is very small compared to 1 ev/atom total energy but all important K. Baberschke, Lecture Notes in Physics, Springer 58, 27 (21) 25

26 Magnetic Anisotropy Energy MAE and anisotropic µ L anisotropic µ L MAE K V (µev/atom) Orbital moment ( µ /atom) B exp. SO+OP [1] SO+OP [11] SO (1] SO[11] bcc fcc 1.5 c/a O. Hjortstam, K. B. et al. PRB 55, 1526 ( 97) K V (µev) Ni c/a=.69 c/a=1.8 α =1 c/a=.79 α = Orbital moment (µ B) D= λ ge g; MAE g - g = g e λ(λ -Λ ) x LS µ L 4µ B Bruno ( 89) 26

27 effective Spin Hamiltonian d 1 L Z S Z +λl S L ± S + _ ψ 2 1/ 2 (2) { 2 2 } 2 The orbital moment is quenched in cubic symmetry 2- L Z 2- =, but not for tetragonal symmetry 27

28 L 2,3 XAS and XMCD of 3d TM s Sc Ti V Cr Mn Fe Co Ni Cu Zn normalized XAS, XMCD (arb. units) Ti V Cr x15 x1 x Fe Co Ni Photon Energy (ev) A. Scherz et al., XAFS XII June 23 Sweden, Physica Scripta T115, 586 (25) A. Scherz et al., BESSY Highlights p. 8 (22) 28

29 5. Full calculation of µ(e) norm. XAS (arb. units) norm. XMCD (arb. units) Experiment A. Scherz et al. a) E V L 3,2 edges E B C x2.23 b) Photon Energy (ev) A Fe 9 V 1 alloy Fe/V 3 /Fe trilayer D PRB 66, (22) XAS (arb. units) XMCD (arb. units) Theory J. Minar, D. Benea, H. Ebert, LMU a) b) B V L 3,2 edges C Energy (ev) Fe 9 V 1 alloy: L 3,2 edge Fe/V 3 /Fe trilayer L 2 edge x6 D 2. no oxygen! A theory exp. 29

30 Summary gap-scan technique systematic investigation of XAS, XMCD fine structure development double pole approximation correlation energies (Ti: M 11 =3.7 ev, M 22 =-.56 ev, M 12 =.54 ev) experiment theory failure of spin sum rule core-hole interaction correlation energies as input for theory future ab initio calculations must include core-hole correlation effects 1) intergral SR 2) MMA 3) calculation of full µ(e) see: Recent advances in x-ray absorption spectroscopy H. Wende, Rep. Prog. Phys. 67 (24)

31 All spectroscopic techniques do not restrict themselves to measure the intensity (area under the resonance) only. i.e.: integral sum rules. A resonance signal contains a resonance position, a width, an asymmetry profile, etc. The optimum is given if theory can calculate the full profile of the resonance, in our case µ(e) i.e. the spectral density. In many calculations the matrix elements for the transition probability have been taken f(e) now we have to pay attention even to the spin dependence A.L. Ankudinov, J.J. Rehr, H. Wende, A. Scherz, K. Baberschke Spin-dependent sum rules for x-ray absorption spectra Europhysics Letters 66, 441 (24) Recent advances in x-ray absorption spectroscopy H. Wende, Rep. Prog. Phys. 67, 215 (24) Handbook of Magnetism and Advanced Magnetic Materials (Wiley&Sons 28) Five volumes ; K. Baberschke Vol. 3 31

32 Conclusion, Future During last few years: enormous progress in Theory: Experiment: calculate µ(e), spin dependent spectral distribution full relativistic calculations real (not ideal) crystallographic structures higher E/E, detailed dichroic fine structure undulator, gap-scan technique, constant high P C element-selective microscopy, probe of non-magnetic constituents Future: core hole effects: change of branching ratio for early 3d elements effect on XMCD unknown! correct determination of µ L and MAE with XMCD (x3) correction for spin- and energy-dependence of matrix elements 32