Multiscale study of magnetism at the nanoscale: highlighting spin-orbit induced phenomena

Abstract: Traditional Heisenberg spin-models including on-site magnetic anisotropies and magnetic dipole-dipole interactions have proved insufficient in case of magnetic objects at the nanoscale. Beside the inter-site magnetic anisotropies that have crucial importance for the finite temperature magnetism of bulk magnets, the role of the Dzyaloshinskii-Moriya (DM) interaction gets largely enhanced in reduced dimension. Well-known examples are the magnetic pattern formation [1] and the homochirality of domain walls [2] in ultrathin films.
Multiple scattering theory provides a traightforward tool to calculate spin-interactions in metals within the framework of relativistic electron theory. I briefly discuss two different methods to accomplish this task. Related to the relativistic torque method, I mainly focus on the calculation of spin-wave spectra [3] by showing that the chiral degeneracy of the magnon spectrum can be lifted due to the presence of DM interactions [4]. I discuss the symmetry conditions under which such a chiral asymmetry occurs. Calculations for an Fe monolayer on W(110) will be presented, emphasizing the possibility to directly measure the DM interactions in ultrathin films.
A recently developed Spin Cluster Expansion technique as based on the relativistic Disordered Local Moment picture will also be introduced [5]. Our results on Mn/W(001) are clearly consistent with the spin-spiral formation reported recently in the literature [6]. Moreover, I shall highlight a potential evaluation of higher order spin-interactions within this method. In this context, effects of biquadratic coupling will be demonstrated in ultrathin Fe/Ir(001) films.

[1] M. Bode et al., Nature 447, 190 (2007)
[2] M. Heide et al., Phys. Rev. B 78, 140403(R) (2008)
[3] L. Udvardi et al., Phys. Rev. B 78, 140403(R) (2003)
[4] L. Udvardi and L. Szunyogh, Phys. Rev. Lett. 102, 207204 (2009)
[5] L. Szunyogh et al., Phys. Rev. B 83, 024401 (2011)
[6] B. Ferriani et al., Phys. Rev. Lett. 102, 019901 (2009)