Lectures on magnetism at the Fudan University, Shanghai October 2005

Transcription

1 Lectures on magnetism at the Fudan University, Shanghai October 2005 Klaus Baberschke Institut für Experimentalphysik Freie Universität Berlin Arnimallee 14 D D Berlin-Dahlem Germany 1

2 Introduction These lectures will cover the recent development of magnetic nanostructures, which are of tremendous interest, be it for technological applications or for the fundamental understanding of magnetism. Magnetism in the past has mostly been discussed as a macroscopic function of the free energy. Today s magnetic cluster and films of nanometer scale combined with UHV technique offer a new point of view to discuss magnetism in a microscopic atomistic picture. 1. Introduction a) Orbital and spin magnetic moments b) Which experimental technique measures what? 2. Magnetic Anisotropy Energy (MAE) a) Ferromagnetic resonance (UHV-FMR) b) ab initio calculations 3. ac Susceptibility?,? in UHV a) T C, critical phenomena b) Oscillatory Curie temperatures c) Higher harmonics?(n? ) 4. Trilayers a prototype of multilayers a) Optical and acoustic modes in the spin wave spectrum b) Interlayer exchange coupling (IEC) 5. X-ray magnetic circular dichroism (XMCD) a) Element specific XMCD, induced magnetism b) Sum rules and advanced theory c) Importance of strong spin spin correlations in 2D-magnets 6. Spin Dynamics a) Magnon-magnon scattering and Gilbert damping b) Spin pumping 2

3 Acknowledgement Synchrotron (BESSY, ESRF): H. Wende, C. Sorg, N. Ponpandian, (M. Bernien, A. Scherz, F. Wilhelm), Luo Jun (AvH fellow) Lab. Experiments (FMR, SQUID, c ac, STM): K. Lenz, (T.Tolinski, J. Lindner, E. Kosubek, C. Rüdt, R. Nünthel, P. Poulopoulos, A. Ney) Support: BMBF (BESSY), DFG (lab.) 3

4 1a Orbital and spin magnetic moments d 1 +λl S L Z S Z L ± S + _ The orbital moment is quenched in cubic symmetry 2- L Z 2- = 0, but not for tetragonal symmetry ψ 2 1/ 2 (2) { 2 2 } 2 4

5 Orbital magnetism in second order perturbation theory H '= µ B H L + λl S anisotropic µ L MAE MAE x LS Bruno ( 89) µ L 4µB 5

6 Direct Observation of Orbital Magnetism in Cubic Solids W.D. Brewer, A. Scherz, C. Sorg, H. Wende, K. Baberschke, P. Bencok, S. Frota-Pessôa Phys. Rev. Letters 93, (2004) Standard exercise in solid state physics: cubic symmetry L z =0 Is the orbital moment of 3d impurities in noble metal hosts completely quenched? XMCD investigations of Cr, Mn, Fe, Co in Au ab initio calculations of orbital moment 6

7 Motivation atoms large µ L (Hund s rules) 3d impurities in noble metal hosts: 1970 s: indirect evidence for surviving orbital moments (HF measurements) here: first direct evidence (electronic structure) by X-ray absorption spectroscopy (XMCD) metals µ L mostly quenched (Fe, Co, Ni: µ L /µ S ~5-10%) 7

8 impurity concentration in Au host: 1.0 at. % ESRF ID8: 7 T, 7-18 K Brewer et al., ESRF Highlights 2004, p 96 8

9 (K) dramatic increase of orbital moment for Co impurity (~4 times larger than Co bulk) 9

10 Fe in Ag: weak hybridization µ L survives Fe in Au: strong hybridization: µ L quenched subtle effect of hybridization and band-filling S. Frota-Pessôa, PRB 69 (2004)

11 11 Conclusion first direct experimental evidence for orbital moments in cubic symmetry text book arguments: weak Spin-Orbit coupling, distinct separation of t 2g and e g, no intermixing comparison to ab initio calculations: delicate balance hybridization between local impurity and host and the filling of the 3d states of the impurity future works on Kondo systems, e.g. with STM, may include surviving orbital moment description beyond pure spin magnetism (e.g. Kondo-like Hamiltonian JS σ)

12 12 1b Which experimental technique measures what? Orbital- and spin- magnetic moments at surfaces and interfaces of ferromagnetic nanostructures 1. µ L + µ S in UHV - SQUID 2. µ L, µ S in UHV - XMCD 3. µ L / µ S in UHV - EPR / FMR

13 13 Design of the UHV-SQUID magnetometer

14 Sensitivity 14

15 The effect of temperature 15 The magnetization of Co/Cu(001) vs the inverse film thickness at different temperatures. The bulk values for 4K (full line) and 300K (dashed line) are indicated.

16 16 m tot Co moment distribution msurf + minter 2 = mvol + (linear with 1/d) d Theory: Hjortstam et al., PRB 53, 9204 (1996) Pentcheva et al., PRB 61, 2211 (2000) A. Ney et al. Europhys. Lett. 54, 820 (2001)

17 X-ray Magnetic Circular Dichroism 17

18 Orbital and spin magnetic moments deduced from XMCD 18

19 Deconvolution into spin (µ S ) and orbital (µ L ) moments 19 The total magnetic moment (squares) of Co/Cu(001) vs the inverse film thickness and its separation into spin (down triangle) and orbital (diamonds) contribution. The bulk value is indicated (dashed line). For comparison experimental results using PND and XMCD are given by the open symbols.

20 FMR in ferromagnetic nanostructure In situ UHV-FMR set up pressure: 10-11mbar temperature: 20K - 500K 295 K 1.6 ML Gd/W(110) 318 K lhe cryostat 7.2 ML Ni/Cu(001) T=297 K thermocouple cavity sample M. Zomak et al., Surf. Sci. 178, 618 (1986) J. Lindner, K.B. J. Phys.: Cond. Matt 15, R193 (2003) UHV quartzfinger electromagnet K. Baberschke FU Berlin W. Platow, Ph.D. thesis (1999) Lectures on magnetism #1, Fudan Univ. Shanghai, Oct

21 21 Landau-Lifshitz-Gilbert-Equation Magnetic resonance (ESR, FMR) + = t M M M G H M t M S eff 2 2 ) ( 1 γ γ

22 22 Determination of g-tensor components 2 ω 2 K 4K 4 K 4 K 2K = H + H M M 2 4 0,[100] 4π 2 2 4π ,[100] γ M M M M M,[100] ω γ,[001] with γ ( K + K ) 2 = H M , 4π M = g h µ l µ s µ B = g 2 2 C. Kittel, J.Phys. Radiat. 12, 291 (1951 ) or f (GHz) f 2 (GHz 2 ) 0 0 g,[001] g,[100] / [110] H 0 (koe)

23 Ferromagnetic resonance on Fe n /V m (001) superlattices 23 MAE (µev/ atom) Fe b) 0.0 MAE=E [001] -E [110] a=3.05 Å (+0.8%) a=2.83 Å (-1.3%) [100]Fe/V [110] MgO MgO T/T C a) K K 2,K 4 (µev/atom) K 4 K 4II Fe V T (K) K4 II (µev/atom) XMCD Integral (arb. units) prop. µ S prop. µ L L 3 L 2 XMCD V x5 Fe µ S µ L µ S µ L g<2 g> Photon Energy (ev) A.N. Anisimov et al. J. Phys. C 9, (1997) and PRL 82, 2390 (1999) and Europhys. Lett. 49, 658 (2000) g g µ / µ L S XMCD: µ L / µ S(Fe) FMR: µ L / µ S (Fe+V) µ L / µ S(V) 40nm Fe Fe Fe4/V 4 Fe 2 /V 5 µ/µ L S µ(µ ) /V 2 bcc (001) Fe/V superlattice 2 5 µ(µ ) L B S B bcc Fe-bulk 0.10 FMR bulk Fe XMCD MAE µev/atom

24 24 Summary Distinguish between: 1. Magnetic anisotropy energy = f(t) 2. Anisotropic magnetic moment f(t) 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 onto spin space Quenching of <L Z > is oversimplified argument