Ultrafast Optical Demagnetization manipulates Nanoscale Spin Structure in Domain Walls: Supplementary Information

Transcription

1 Ultrafast Optical Demagnetization manipulates Nanoscale Spin Structure in Domain Walls: Supplementary Information B. Pfau 1, S. Schaffert 1, L. Müller, C. Gutt, A. Al-Shemmary, F. Büttner 1,3,4,5, R. Delaunay 6, S. Düsterer, S. Flewett 1,4, R. Frömter 7, J. Geilhufe 8, E. Guehrs 1, C. M. Günther 1, R. Hawaldar 6, M. Hille 7, N. Jaouen 9, A. Kobs 7, K. Li 6, J. Mohanty 1, H. Redlin, W. F. Schlotter 10, D. Stickler 7, R. Treusch, B. Vodungbo 6,11, M. Kläui 3,4,5, H. P. Oepen 7, J. Lüning 6, G. Grübel, S. Eisebitt 1,8 1 TU Berlin, Institut für Optik und Atomare Physik, 1063 Berlin, Germany Deutsches Elektronen-Synchrotron DESY, 607 Hamburg, Germany 3 Johannes Gutenberg-Universität Mainz, Institut für Physik, Mainz, Germany 4 SwissFEL, Paul Scherrer Institut, 53 Villigen PSI, Switzerland 5 École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland 6 Université Pierre et Marie Curie, Laboratoire de Chimie Physique Matière et Rayonnement CNRS UMR 7614, Paris, France 7 Universität Hamburg, Institut für Angewandte Physik, 0355 Hamburg, Germany 8 Helmholtz-Zentrum Berlin für Materialien und Energie, Berlin, Germany 9 Synchrotron SOLEIL, L Orme des Merisiers, Saint-Aubin, 9119 Gif-sur-Yvette Cedex, France 10 Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, California 9405, USA 11 Laboratoire d Optique Appliquée, ENSTA ParisTech CNRS UMR 7639 École polytechnique, Chemin de la Hunière, Palaiseau, France 1

2 Supplementary figures

3 (a) (f) M/M S M/M S M/M S (b) (c) (d) (e) x position scattering factor scattering factor (g) q x position Supplementary Figure S1: One-dimensional domain model. The left side (a e) shows the real space properties and the right panels (f,g) the corresponding scattering factors in reciprocal space in same color. x and q x are scaled to the lattice parameter. (a) basic lattice, (b) magnetic unit cell, (c) smoothing kernel, (d) convolution of (b) and (c) giving smoothed magnetic profiles, (e) convolution of (a) and (d) yields the complete model structure. (f) The structure factor (blue), form factor (violet) and domain-wall factor (red) of the domain model. (g) Form factor of the smoothed magnetic unit cell (violet) and the resulting scattering factor of the domain arrangement (blue). 3

4 1 0.5 M z /M S slice position (nm) Supplementary Figure S: Result from micromagnetic simulations. Magnetization profile (out-of-plane component M z normalized to the saturation magnetization M S ) at a domain wall for equilibrium domain configuration (blue) and 1 ps after a sudden reduction of the anisotropy and magnetization (green) as obtained from micromagnetic simulations. In the simulation, an equilibrium domain-wall width (from 0.5M z /M S to 0.5M z /M S ) of 6. nm is yielded which in the first picosecond dynamically changes by 1. nm. 4

5 Supplementary discussion The elastic resonant magnetic scattering factor is given by [13 15,31]: F = (ɛ ɛ 1 ) G 0 + i(ɛ ɛ 1 ) m G 1 + (ɛ m)(ɛ 1 m) G, (S1) where ɛ 1 and ɛ denote the polarization vectors of the incident and scattered radiation and m the unit vector of the magnetization direction. G 0, G 1, and G contain the sums of the transition probabilities of the atomic excitation and decay processes involved in the resonant scattering process. G 0 is independent on the magnetization M and thus describes charge scattering, G 1 is first order in M and G is second order in M. The first and the last term can be neglected in our experiment [14,15] and the scattering amplitude is referred to the second term, the XMCD effect. For circularly polarized light the cross-product of the polarization vectors gives ɛ ɛ 1 = ±k with k being the light s propagation direction and the sign depending on the helicity of the incoming x-rays. The magnetic SAXS intensity is determined equally for both helicities by: I(q) = V F exp(iqr) dr = V (k m) G 1 exp(iqr) dr, (S) with the integral ranging over the whole probed volume and G 1 measuring the magnetization magnitude by sensing the spin-polarization of the d-electrons. Identifying the propagation direction with the z-direction, i.e. along the depth of the thin film, and assuming a homogeneous magnetization along that direction, one yields: I(q) A M z (r) exp(iqr) dr, (S3) where A is the probed thin film area and M z the out-of-plane component of the magnetization. In the following the composition of the magnetic scattering factor shall be explained considering a one-dimensional model domain system as presented in Supplementary Fig. S1. In this model the magnetization alternates along the x-axis periodically from M S to +M S representing the magnetic domains (Supplementary Fig. S1e). The width of all domains is equal and the magnetization profile at the domain walls is smoothed. This arrangement can be decomposed into three contributions. Supplementary Fig. S1a: The sequential character is represented by a lattice or comb of delta functions separated by the magnetic correlation length giving the magnetic structure factor in Fourier-space. Supplementary Fig. S1b: The alternating magnetization is resembled by a unit cell consisting of a pair of a down and an up domain. The unit cell s squared Fourier-transform gives already the largest contribution to the magnetic form factor. Due to the special characteristic of that form factor, magnetic scattering is not observed at q = 0 and for all even diffraction orders of the lattice. Supplementary Fig. S1c: The unit cell is additionally modulated by a Gaussian effecting the softening of the domain walls. In Fourier-space this has a similar effect as known from 5

6 the Debye-Waller factor in crystallography: it mainly suppresses higher diffraction orders. This domain-wall factor is the second contribution to the form factor. In the presented model only the height of the structure factor peaks is modulated by the form factor, but not the q x position. In order to explain the observed shift in the q peak values one has to take into account that the domain width is not equal for all domains but has a certain distribution leading to strong broadening of the structure peaks. As shown in Fig. 3d and explained in the main text, the deformation of the broadened structure peak by the dynamic change of the domain-wall factor leads to the shift in the position of the structure factor peak. 6