WHY ARE SPIN WAVE EXCITATIONS ALL IMPORTANT IN NANOSCALE MAGNETISM?

Transcription

1 WHY ARE SPIN WAVE EXCITATIONS ALL IMPORTANT IN NANOSCALE MAGNETISM? Klaus Baberschke Institut für Experimentalphysik Freie Universität Berlin Arnimallee 14 D Berlin-Dahlem Germany 1. Element specific magnetizations and T C s in trilayers. 2. Interlayer exchange coupling and its T-dependence. 3. Gilbert damping versus magnon-magnon scattering. T C Co T C Ni J inter Co Cu Ni IEC Freie Freie Universität Berlin Berlin ICNM27, Istanbul June 28 1

2 A whole variety of experiments on nanoscale magnets are available nowadays. Unfortunately many of the data are analyzed using theoretical static mean field (MF) model, e. g. by assuming only magnetostatic interactions of multilayers, static exchange interaction, or static interlayer exchange coupling (IEC), etc. We will show that such a mean field ansatz is insufficient for nanoscale magnetism, 3 cases will be discussed to demonstrate the importance of higher order spin-spin correlations in low dimensional magnets. + Spin-Spin correlation function S i S j t z + z S i S j Si S j S i Si S j S isj S i+ RPA Physica B 384, 147 (26) 2

3 1. Element specific magnetizations and T C s in 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 3

4 2. 16 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 T * Ni T (K) P. Poulopoulos, K. B., Lecture Notes in Physics 58, 283 (21) M (ka/m) ML Cu 2.8 ML Ni Cu (1) T* C,Ni T C,Ni T C,Ni 38 K T (K) 2. ML Co 3. ML Cu 2.8 ML Ni A. Scherz et al. PRB 65, (25) Cu (1) 4

5 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) 5

6 d FM1 T C, Ni Evidence for giant spin fluctuations (A. Scherz et al. PRB 72, (25)) 2D spin fluctuations IEC ~ 1 2 d NM Jinter FM2 (Co) NM (Cu) FM1 (Ni) d NM 6

7 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 A. Scherz et al. J. Synchrotron Rad. 8, 472 (21) 7

8 2. IEC in coupled films measured withuhv-fmr pressure: 1-11mbar T= 2K - 5K theory lhe cryostat FMR thermocouple cavity sample exp. UHV quartzfinger electromagnet J. Lindner, K. B. Topical Rev., J. Phys. Condens. Matter 15, R193-R232 (23) Freie Universität Berlin ICNM27, Istanbul June 28 8

9 J =J Interlayer exchange coupling and its T-dependence. P. Bruno, PRB 52, 411 (1995) N.S. Almeida et al. PRL 75, 733 (1995) T/T inter inter, [ ] T= hv F / 2πkd B sinh(t/t) 3/2 J =J [ ] inter inter, 1-(T/T C ) Ni 7 Cu 9 Co 2 /Cu(1) T=55K - 332K J. Lindner et al. PRL 88, (22) (Fe 2 V 5 ) 5 T=15K - 252K, T C =35K J inter (µev/atom) 2 1 T=294K 8 v=2.8 1cm/s F 7 v=2.8 1cm/s F T 5/2 T 3/ T 3/2 J (µev/atom) inter /2 (T/T C) 6 v=5.3 F 1cm/s 3/2 (T/T C ) /2 (T/T C) 9

10 S. Schwieger, W. Nolting, PRB 69, (24) 1

11 PRB (27) in print J(T) 1- AT n, with n

12 3. Gilbert damping versus magnon-magnon scattering. 12

13 Landau-Lifshitz-Gilbert equation(1935) dm dt = γ m H eff dm +α m dt T ~ 1 αω Gilbert damping M =const. Bloch-Bloembergen Equation (1956) dm dt dm z dt x, y = γ ( m H = γ ( eff m H ) eff z ) x, y m z M T m 1 T x, y 2 S spin-lattice relaxation (longitudinal) spin-spin relaxation (transverse) M z =const. 13

14 FMR Linewidth - Damping Landau-Lifshitz-Gilbert-Equation 2-magnon-scattering 1 γ M t = _ (M H) G γm M eff + 2 ( M ) S t viscous damping, energy dissipation R. Arias, and D.L. Mills, Phys. Rev. B 6, 7395 (1999); D.L. Mills and S.M. Rezende in Spin Dynamics in Confined Magnetic Structures, edt. by B. Hillebrands and K. Ounadjela, Springer Verlag ω(k ) ϕ k > ϕ c ϕk < ϕ ω FMR c Gilbert-damping ~ω k Gil H ( ω) = G γ 2 M S ω H 2Mag ( ω) = Γarcsin 2 2 1/2 [ω +( ω/2) ] - ω / /2 [ω +( ω/2) ] + ω /2 ω = γ(2k2-4πm), S γ =( µ B/h)g K - uniaxial anisotropy constant 2 M- saturation magnetization S 14

15 Gilbert damping contribution: linear in frequency two-magnon excitations (thin films): non-linear frequency dependence H 2 magnon with ( ω) = Γ arcsin ω ω + ( ω + ( ω / 2) / 2) ω = γm eff R. Arias et al., PRB 6, 7395 (1999) ω + ω / 2 / 2 real relaxation no inhomogeneous broadening two-magnon damping dominates Gilbert damping by two orders of magnitude: 1/T 2 ~1 9 s -1 vs. 1/T 1 ~1 7 s -1 K. Lenz et al., PRB 73, (26) 2 H H H (Oe) 1 H * H 2-magnon H inhom H Gilbert + H inhom inhomogeneous broadening ω/2π (GHz) 15

16 Oe! two-magnon scattering observed in Fe/V superlattices H PP (Oe) J. Lindner et al., PRB 68, 612(R) (23) HF FMR K. Lenz et al. PRB 73, (26) f (GHz) Γ γ Γ G α H (koe) (1 8 s -1 ) (1 8 s -1 ) (1-3 ) (Oe) Fe 4 V 2 ; H [1] Fe 4 V 4 ; H [1] Fe 4 V 2 ; H [11] Fe 4 V 4 ; H [11] Fe 4 V 4 ; H [1] recent publications with similar results: Pd/Fe on GaAs(1) network of misfit dislocations G. Woltersdorf et al. PRB 69, (24) NiMnSb films on InGaAs/InP B. Heinrich et al. JAP 95, 7462 (24) 16

17 Conclusion Higher order spin-spin correlations are important to explain the magnetism of nanostructures. In most cases a mean field model is insufficient. A phenomenological effective Gilbert damping parameter gives very little insight into the microscopic relaxation mechanism. It seems to be more instructive to separate scattering mechanisms within the magnetic subsystem from the dissipative scattering into the thermal bath; Todays advanced experiments and analysis result in: G isotropic and Γ anisotropic. 17

18 Acknowledgement BESSY-crew: H. Wende, C. Sorg, A. Scherz, J. Luo, X. Xu Lab. experiments: K. Lenz, S. Kalarickal, X. Xu, E. Kosubek, J. Lindner, T. Tolinski Theory: H. Ebert, LMU; J.J. Rehr, UW; O. Eriksson UU; P. Weinberger, TU Vienna; R. Wu, D.L. Mills, UCI; P. Jensen + K.H. Bennemann, FUB; W. Nolting, HUB physik.fu-berlin.de/~.de/~bab Support: BMBF (BESSY), DFG (lab.) 18