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PGI-1 Talk: Prof. Dr. Laszlo Szunyogh

Weak ferromagnetism in hexagonal Mn3Z (Z=Sn, Ge, Ga) alloys

26 Sep 2019 11:30
PGI lecture hall

Budapest University of Technology and Economics, Hungary


In their hexagonal phase the Mn3Z (Z=Sn, Ge, Ga) compounds exhibit a triangular spin structure with weak ferromagnetic distortion that has widely been studied both experimentally and theoretically. The weak ferromagnetism of Mn3Sn was explained in the original paper of Tomiyoshi and Yamaguchi using a simple effective spin model containing isotropic exchange interactions, Dzyaloshinsky-Moriya interactions and magnetic anisotropy. Later on Sandratskii and Kübler discussed in particular the orbital polarization effects on the weak ferromagnetism of Mn3Sn in terms of self-consistent ab initio calculations.

We revisit the weak ferromagnetism of the Mn3Z alloys using a combination of ab initio and spin model calculations. Using the point-group symmetry of the systems we set up a model for the three Mn sublattices including the relativistic terms of the Heisenberg Hamiltonian. The parameters of this model are obtained from ab initio calculations relying on a spin-cluster expansion. Based on a group-theoretical analysis we show that there are two degenerate ground states, WFx and WFy, being the mixture of the G5 and FM states. The analytical forms of the mixing coefficients imply that the weak ferromagnetic states will only form if the anisotropy parameters distinguish between the x and y spin directions. We recover this result from analytical expressions for the energy within the classical spin model.

We also perform self-consistent relativistic local density functional calculations in order to investigate the weak ferromagnetic states in a more involved way. In agreement with the seminal work for Mn3Sn by Sandratskii and Kübler, our results highlighted the significance of the orbital moments in the weak ferromagnetism of the Mn3Z alloys. A key observation from our calculations is that, as opposed to the spin moments, the orbital moments almost strictly follow the decomposition according to irreducible representations as predicted by group theory.

As far as the spin moments of the Mn atoms and the weak ferromagnetic moments are concerned, we find a good agreement with the experiments for all the three alloys. By switching on the spin-orbit coupling at different sites selectively we discuss the role of the SOC on the formation of weak ferromagnetic moments and recover the peculiar cancellation of orbital moments for Mn3Sn reported in Ref., while we also find an argument for the opposite weak ferromagnetic distortion as compared to Mn3Ge and Mn3Ga. In terms of constrained density functional calculations we establish that the induced spin moment of Ga plays an important role in the formation of the weak ferromagnetic moment in Mn3Ga and also it is one of the reasons for the observed large asymmetry of the net moment concerning the WFx and WFy states.


Dr. Manuel dos Santos Dias
Phone: +49 2461 61-5956
Fax: +49 2461 61-2850