1/23 Magnetism of ultrathin films: Theory and Experiment Klaus Baberschke Institut für f r Experimentalphysik Freie Universität t Berlin
2/23 New and fundamental aspects are found in nanomagnetism with no counterpart in bulk materials 281. WE-Heraeus-Seminar Spin-Orbit Interaction and Local Structure in Magnetic Systems with Reduced Dimensions June 22 in Wandlitz
3/23 For thin films the Curie temperature can be manipulated 6 4 Ni(1)/Cu(1) Paramagn. d=7.6 T=3K finite size M 2 M Ferromagn. 5 1 thickness (ML) P. Poulopoulos and K. B. J. Phys.: Condens. Matter 11, 9495 (1999) T T C ( ) TC ( d) 1/ C ( ) cd Yi Li, K. B., PRL 68, 128 (1992)
4/23 New artificial structures, like tetragonal (fct) Ni, Fe, Co are grown vacuum K S1 2 = -3.2% volume, and surface MAE K i = K i V S K + 2 i d C. Uiberacker et al. Phys. Rev. Lett. 82, 1289 (1999) Cu(1)/Ni 12 / Vac K S2 substrate 1 = +2.5% Ni 2.49 Å Cu 2.55 Å.1 E b (mev). -.1 -.2 Cu(1) substrate 12 ML Ni unrelaxed relaxed -2.5 % relaxed -5.5 % vacuum -.3 2 4 6 8 1 12 14 16 18 layer
Interlayer Exchange Coupling and f (T) Freie Universität Berlin UC Irvine 26.-28. May 21 5/23 full trilayer grows in fct structure T C Co T C Ni J inter Co Cu Ni IEC LEED I(V) Intensity (arb. units) x 1.5 Cu Ni 6 9 Ni 9 d=1.7 ij Cu(1) d ij=1.81 Å 2 4 Energy (ev) Ni Cu Ni 8 6 9 Å 6 R. Nünthel, PhD Thesis FUB 23 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?
6/23 2. 16 M (arb. units) 1.75.75.5.25 2.8 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 15 2 25 3 35 T (K) P. Poulopoulos, K. B., Lecture Notes in Physics 58, 283 (21) M (ka/m) 12 3 2 1 3. ML Cu 2.8 ML Ni Cu (1) T* C,Ni T C,Ni T C,Ni 38 K 3 6 9 12 15 18 21 24 T (K) A. Scherz et al. PRB 65, 24411 (25) The large shift of T C Ni can NOT be explained by the static exchange field of Co. 2. ML Co 3. ML Cu 2.8 ML Ni Cu (1)
7/23 Crossover of M Co (T) and M Ni (T) Norm. XMCD Difference (arb.units) 2-2 -4-6 Co L 3,2 -edges Ni L 3,2 -edges 45K 2.1ML Cu 4ML Ni Cu(1) x2 76 8 84 88 Photon Energy (ev) 1.3ML Co 2.1ML Cu 4 ML Ni Cu(1) Magnetization M (Gauss) 1 75 5 3 2 1 M sat M sat 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) AFM M Ni 4 8 12 16 2 24 Temper ature (K) L. Bergqvist, O. Eriksson J. Phys. Conds. Matter 18,4853 (26) [ 11] 2 [1] easy M Co [11] ext H, k easy M Ni
8/23 P. Bruno, PRB 52, 411 (1995); V. Drchal et al. PRB 6, 9588 (1999) N.S. Almeida et al. PRL 75, 733 (1995) J =J Interlayer exchange coupling and its T-dependence. inter inter, [ ] T/T T = hv F / 2 kbd sinh(t/t ) 3/2 J =J [ ] inter inter, 1-(T/T C )
9/23 in-situ FMR in coupled films IEC => f(t) in µev/ particle Advantage: FM and AFM theory FMR in-situ UHV-experiment J. Lindner, K. B. Topical Rev., J. Phys. Condens. Matter 15, R193-R232 (23)
1/23 J in ter (µev/atom) 2 1 Ni 7 Cu 9 Co 2 /Cu(1) T=55K - 332K T=294K 8 v=2.8 1cm/s F v =2.8 1 cm/s T 5/2 T 3/2 2 4 6 8 T 3/2 F 7 J inter (µev/atom) 15 1 5 (Fe 2 V 5 ) 5 T=15K - 252K, T C =35K 5/2 (T/T C) 6 v F=5.3 1 cm/s 3/2 (T/T C ).2.4.6.8 3/2 (T/T ) C
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12/23 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)
See yesterdays talk by Talat Rahman 13/23 Freie Universität Berlin UC Irvine 26.-28. May 21
14/23 Manipulation of surface MAE, K S by adsorbed molecules, metal cap and surfactant growth constant K V KNi cubic K (µev/atom) 2 25 2 15 1 5-5 -1-15 d(ml) 1 7 5 2 M 2 t=.75 Ni vacuum Ni + Cu cap Ni + O surfactant -2.5.1 1/d (1/ML) Ni/Cu(1) J. Lindner et al. Surf. Sci. Lett. 523, L65 (23).15.2 Ni/vacuum Ni/Cu Ni/CO (van Dijken et al.) Ni/H 2 Ni/O K i = K i V S K + 2 i d Interface (van Dijken et al.) (surfactant) K S ( ev/atom) -17-59 -81-7 -17 d C (ML) 1.8 7.6 7.3 6.8 4.9 Changes of K S shift the spin reorientation transition d C K. B. Handbook of Magnetism and Advanced Magnetic Materials, Vol. 3 Ed. Kronmüller and Parkin, 27 John Wiley & Sons, Ltd.
15/23 Results of ab initio calculations R. Q. Wu & coworkers Phys. Rev. Lett. 92, 14722 (24) 4 MAE along X axis MAE (µev / atom) 3 2 1 O/Ni /O n Cu /Ni 5 n MAE (mev) 2 1 O/Ni clean Ni X -1.2.4.6.8.1.12 1/d (1/ML) clean Ni n Ni n slabs, n = 9, 11, 13: clean, Ni n Cu 5 superlattice, and c(2x2) O/Ni n on each side O-induced surface state seen in the vicinity of X-point is responsible for change in MAE
16/23 Spin Dynamics: Damping and Scattering Landau-Lifshitz-Gilbert equation(1935) dm dt m H eff m dm dt Gilbert damping M =const. M spirals on a sphere into z- axis Bloch-Bloembergen Equation (1956) dm dt dm z dt x, y ( m H 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.
17/23 Gilbert damping versus magnon-magnon scattering. In nanoscale magnetism path 2 has been discussed very very little. Mostly an effective damping (path 1) is modeled/fitted. Path 3: magnon-phonon scattering, see Bovensiepen PRL 28
18/23 FMR Linewidth - Damping Landau-Lifshitz-Gilbert-Equation 2-magnon-scattering 1 M t = _ (M H G M 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 (k ) k > c k < FMR c Gilbert-damping ~ k Gil H ( ) = G 2 M S H 2Mag ( ) = arcsin 2 2 1/2 +( /2) ] - /2 2 2 1/2 +( /2) ] + /2 = (2K2-4 M S), =( B/h)g K - uniaxial anisotropy constant 2 M - saturation magnetization Which (FMR)-publication has checked (disproved) quantitatively this analytical function? S
19/23 Gilbert damping contribution: linear in frequency two-magnon excitations (thin films): non-linear frequency dependence H 2 magnon with ( ) arcsin 2 ( / 2) 2 ( / 2) / 2 / 2 Meff R. Arias et al., PRB 6, 7395 (1999) 2 2 K. Lenz et al., PRB 73, 144424 (26) 2 H H H (Oe) 1 H * H 2-magnon H inhom H Gilbert + H inhom inhomogeneous broadening 2 4 6 8 /2 (GHz)
2/23 HPP(Oe) 4 2 8 4 15 Oe! 4 8 5 1 15 2 f (GHz) two-magnon scattering observed in Fe/V superlattices J. Lindner et al., PRB 68, 612 (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 G H (koe) (1 8 s -1 ) (1 8 s -1 ) (1-3 ) (Oe) Fe 4 V 2 ; H [1].27 5..26 1.26 Fe 4 V 4 ; H [1].139 26.1.45 2.59 Fe 4 V 2 ; H [11].15 27.9.22 1.6 Fe 4 V 4 ; H [11].45 8.4.77 4.44 Fe 4 V 4 ; H [1].76 4.38 5.8 G isotropic dissipation and anisotropic spin wave scattering
21/23 Angular- and frequency-dependent FMR on Fe 3 Si binary Heusler structures epitaxially grown on MgO(1) d = 4nm Kh. Zakeri et al. PRB 76,14416 (27) PRB 8, 5991 (29) Angular dependence at 9 and 24 GHz (26 53) 1 7 sec -1, anisotropic G 5 1 7 sec -1, isotropic A phenomenological effective Gilbert damping parameter gives very little insight into the microscopic relaxation and scattering.
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Doug, we wish you all the best! Freie Universität Berlin UC Irvine 26.-28. May 21 23/23
24/23 Magnetism of ultrathin Ferromagnets: Theory and Experiment Klaus Baberschke Institut für Experimentalphysik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany Ultrathin films of few atomic layers thickness only, are a new type of designer materials. They have no counterpart in bulk magnetism; they offer the opportunity to study new fundamental aspects of magnetism: The critical temperature Tc changes as function of the thickness from Tcbulk to zero. Modification of the n.n. distance by few hundreds of Å may change the magnetic part of the free energy by orders of magnitude. In multilayer ferromagnetic- and antiferromagnetic-coupling can be manipulated via the spacer thickness. The unusual static properties as well as dynamic characteristics (magnons) are investigated by theory and experiment. Recent specific example will be discussed1,2. This field of low dimensional magnetism demonstrates the very successful collaboration between theory and experiment, and gives some insight for the fundamental understanding of magnetism. 1 D. L. Mills and S. M. Rezende in Spin dynamics in confined magnetic structures II Topics in Applied Physics vol. 87, p.27 Springer 23 2 K. Baberschke in Handbook of magnetism and advanced magnetic materials vol. 3, p.1617 John Wiley & Sons 27 ^ UCI 28.5.21