First-principles studies of spin-orbit and Dzyaloshinskii-Moriya interactions in the {Cu3} single-molecule magnet

J. F. Nossa, M. F. Islam, C. M. Canali, and M. R. Pederson
Phys. Rev. B 85, 085427 – Published 22 February 2012

Abstract

Frustrated triangular molecule magnets such as {Cu3} are characterized by two degenerate S=1/2 ground states with opposite chirality. Recently, it has been proposed theoretically [M. Trif et al., Phys. Rev. Lett. 101, 217201 (2008)] and verified by ab initio calculations [M. F. Islam et al., Phys. Rev. B 82, 155446 (2010)] that an external electric field can efficiently couple these two chiral spin states, even in the absence of spin-orbit interaction (SOI). The SOI is, nevertheless, important since it introduces a splitting in the ground-state manifold via the Dzyaloshinskii-Moriya (DM) interaction. In this paper, we present a theoretical study of the effect of the SOI on the chiral states within spin-density functional theory. We employ a recently introduced Hubbard-model approach to elucidate the connection between the SOI and the Dzyaloshinskii-Moriya interaction. This allows us to express the Dzyaloshinskii-Moriya interaction constant D in terms of the microscopic Hubbard-model parameters, which we calculate from first principles. The small splitting that we find for the {Cu3} chiral state energies (Δ0.02 meV) is consistent with experimental results. The one-band Hubbard-model approach adopted and analyzed here also yields a better estimate of the isotropic exchange constant than the ones obtained by comparing total energies of different spin configurations. The method used here for calculating the DM interaction unmasks its simple fundamental origin, which is the off-diagonal spin-orbit interaction between the generally multireference vacuum state and single-electron excitations out of those states.

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  • Received 13 November 2011

DOI:https://doi.org/10.1103/PhysRevB.85.085427

©2012 American Physical Society

Authors & Affiliations

J. F. Nossa, M. F. Islam, and C. M. Canali

  • School of Computer Science, Physics and Mathematics, Linnaeus University, SE-39182 Kalmar, Sweden

M. R. Pederson

  • US Department of Energy SC22.1, Washington DC 20585-1290

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Issue

Vol. 85, Iss. 8 — 15 February 2012

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