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 Universität Berlin spin-waves in 2D, Colorado July 27 1

2 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.) Freie Universität Berlin spin-waves in 2D, Colorado July 27 2

3 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) Freie Universität Berlin spin-waves in 2D, Colorado July 27 3

4 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 M (arb. units) U. Bovensiepen et al., PRL 81, 2368 (1998) T Co C = 34 K T* Ni = 38 K C T (K) Freie Universität Berlin spin-waves in 2D, Colorado July 27 4

5 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) The large shift of T C Ni can NOT be explained by the static exchange field of Co. Freie Universität Berlin spin-waves in 2D, Colorado July 27 5

6 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 MF Co/Cu/Ni trilayer.9 Tyablikov (or RPA) decoupling 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) Freie Universität Berlin spin-waves in 2D, Colorado July 27 6

7 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 Freie Universität Berlin spin-waves in 2D, Colorado July 27 7

8 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) 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) [11] M sat M sat 2 AFM M Ni Temperature (K) [1] easy M Co [11] ext H, k easy M Ni L. Bergqvist, O. Eriksson J. Phys. Conds. Matter 18,1 (26) Freie Universität Berlin spin-waves in 2D, Colorado July 27 8

9 Freie Universität Berlin spin-waves in 2D, Colorado July 27 9

10 Freie Universität Berlin spin-waves in 2D, Colorado July 27 1

11 Freie Universität Berlin spin-waves in 2D, Colorado July 27 11

12 J inter (µev/atom) FMR Cu/ Ni/ Cu/ Ni/ Cu(1) XMCD Co/ Cu/ Ni/ Cu(1) FMR Ni/ Cu/ Co/ Cu(1) Theory d ) a ) b ) c ) d (ML) Cu 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) Freie Universität Berlin spin-waves in 2D, Colorado July 27 12

13 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) Freie Universität Berlin spin-waves in 2D, Colorado July 27 13

14 S. Schwieger, W. Nolting, PRB 69, (24) Freie Universität Berlin spin-waves in 2D, Colorado July 27 14

15 PRB 75, (27) J(T) 1- A(d)T n, with n 1.5 A(d) const. A(d) linear function A(d) osc. function (interface) (electronic bandstructure) (spin wave excitation) Freie Universität Berlin spin-waves in 2D, Colorado July 27 15

16 3. Gilbert damping versus magnon-magnon scattering. In nanoscale magnetism path 2 has been discussed very very little. Mostly an effective damping (path 1) was modeled/fitted. Freie Universität Berlin spin-waves in 2D, Colorado July 27 16

17 Landau-Lifshitz-Gilbert equation(1935) dm = γ dt m H eff dm +α m dt Gilbert damping M =const. M spirals on a sphere into z-axis 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. Freie Universität Berlin spin-waves in 2D, Colorado July 27 17

18 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 Which FMR-publication has checked (disproved) quantitatively this analytic al function? S Freie Universität Berlin spin-waves in 2D, Colorado July 27 18

19 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 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) Freie Universität Berlin spin-waves in 2D, Colorado July 27 19

20 HPP(Oe) Oe! 4 8 HF FMR K. Lenz et al. PRB 73, (26) f (GHz) two-magnon scattering observed in Fe/V superlattices J. Lindner et al., PRB 68, 612(R) (23) 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 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) Freie Universität Berlin spin-waves in 2D, Colorado July 27 2

21 Angular- and frequencydependent FMR on Fe 3 Si binary Heusler structures epitaxially grown on MgO(1) d = 4nm Kh. Zakeri et al. preprint 27 Angular dependence at 9 and 24 GHZ γγ (26 53) 1 7 sec -1, anisotropic G sec -1, isotropic Freie Universität Berlin spin-waves in 2D, Colorado July 27 21

22 Spin pump effects, s-d-exchange between spin wave and s-electron R.H. Silsbee, A. Janossy, P. Monod, PRB 19, 4382 (1979) Y. Tserkovnyak, A. Brataas, G.E.W. Bauer, PRB 66, (22) Landau-Lifshitz equation + extension precession Gilbert-damping spin-pump current d M G d M = γ M Heff + M 2 d t γ M S dt + γ M S V S I pump (5) Precession drives spin current into NM NM-substrate acts as spin-sink I S back = I S pump = h 4π torque is carried away d M Ar M dt A d M dt Gilbert damping enhanced by spin-pump effect! i Freie Universität Berlin spin-waves in 2D, Colorado July 27 22

23 acoustical mode optical mode M M M M at point of contact compensation of pumped currents decrease the linewidth B. Heinrich et al., PRL 9, (23) s d NM λ SF no spin-accumulation I back = Gilbert-damping enhanced by spin-pump effect compensation, if both films precess simultaneously (H res1=h res2) only Gilbert contribution remains! K. Lenz et al., Phys. Rev. B 69, (24) Freie Universität Berlin spin-waves in 2D, Colorado July 27 23

24 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 damping into the thermal bath; Todays advanced experiments and analysis result in: G» isotropic dissipation and G» anisotropic spin wave scattering Freie Universität Berlin spin-waves in 2D, Colorado July 27 24