Full magnetoelectric response from first-principles

Abstract

I will describe a first-principles scheme for calculating the zero-temperature linear magnetoelectric coefficient of an insulating crystal, taking into account not only the spin but also the orbital character of both the lattice-mediated and electronic (frozen-ion) responses. This completes the programme initiated in Refs. [1,2], where methods were introduced for determining the spin-lattice and spin-electronic magnetoelectric couplings. In the present scheme the frozen-ion response is extracted as the linear change in magnetization under a small but finite homogeneous electric field, which is added to the Kohn-Sham Hamiltonian via a Berry-phase term [3]. While the spin-magnetization response can be easily computed from the induced spin density integrated over the unit cell, a careful treatment of the orbital magnetization of Bloch electrons in a finite electric field again requires a Berry-phase-type expression[4]. The methodology is used to determine the full magnetoelectric response of Cr2O3, and the quantized “Chern-Simons” orbital-electronic response in the prototypical topological insulator Bi2Se3 [5]. [1] J. Íñiguez, Phys. Rev. Lett. 101, 117201 (2008). [2] E. Bousquet, N. A. Spaldin, and K. T. Delaney, Phys. Rev. Lett. 106, 107202 (2011). [3] I. Souza, J. Íñiguez, and D. Vanderbilt, Phys. Rev. Lett. 89, 117602 (2002). [4] A. Malashevich, I. Souza, S. Coh, and D. Vanderbilt, New J. Phys. 12, 053032 (2010). [5] S. Coh, D. Vanderbilt, A. Malashevich, and I. Souza, Phys. Rev. B 83, 085108 (2011).