(ESICMM-G8 Symposium on Next Generation Permanent Magnets, Tsukuba, 2015)
Theoretical description of the magnetic anisotropy in
transition metal based systems


H. Ebert, J. Minar, J. Braun, and S. Mankovsky

Universität München, Department Chemie, Butenandtstr. 5-13, D-81377 München

Abstract:

  The various sources for the magnetic anisotropy in bulk and low dimensional materials are reviewed and discussed. Emphasize is put on models that allow for a numeric evaluation of the anisotropy energy within the framework of local spin density theory and extensions to this. In the case of rare earth - transition metal compounds the contribution to the anisotropy connected with the f-electron system is often dominating. Usually this is described on the basis of the single ion model. Examples for corresponding calculations for the bulk as well as nano systems will be presented. On the transition metal side the anisotropy is ascribed to the interplay of spin-orbit coupling and spin polarization. As a consequence corresponding ab-initio calculations are quite demanding as they have to deal with both on the same level. Results of such calculations for thin film systems will be presented [1]. Conventionally, the so-called shape anisotropy is attributed to the dipole-dipole interaction and for that reason treated in a classical way. It will be shown that this important contribution to the anisotropy is connected with the Breit interaction, that can be incorporated within ab-initio calculations [2]. Another source for magnetic anisotropy is connected with the anisotropic exchange interaction [3]. An example will be discussed for the strong interconnection of the conventional anisotropy due to spin-orbit coupling and the anisotropic exchange [4]. The anisotropic exchange interaction includes in particular the so-called Dzyaloshinsky-Moriya interaction that gives rise for low dimensional systems to interesting phenomena. As an example results on the formation of skyrmions in magnetic surface layers (see Fig.1) will be presented [5].
FIG. 1. (a) Low-temperature part of B-T phase diagram calculated for FePt/Pt(111); (b)-(g) representative magnetic structures of the phase diagram regions indicated in (a) obtained at B = 0.0 T, T = 3.0 K (b), B = 2.5 T, T = 3.0 K (c), B = 7.5 T, T = 3.0 K (d), B = 12.5 T, T = 3.0 K (e), B = 1.0 T, T = 22.0 K (f), B = 3.5 T, T = 17.0 K (g)
[1] M. Kosuth, V. Popescu, H. Ebert, and G. Bayreuther, Europhys. Lett. 72, 816 (2005).
[2] S. Bornemann, J. Minar, J. Braun, D. Ködderitzsch, and H. Ebert, Solid State Commun. 152, 85 (2012).
[3] H. Ebert and S. Mankovsky, Phys. Rev. B 79, 045209 (2009).
[4] S. Mankovsky, S. Polesya, S. Bornemann, J. Minar, F. Hoffmann, C. H. Back, and H. Ebert, Phys. Rev. B 84, 201201 (2011).
[5] S. Polesya, S. Mankovsky, S. Bornemann, D. Ködderitzsch, J. Minar, and H. Ebert, Phys. Rev. B 89, 184414 (2014).