Theory of Orbital Magnetization in Solids

Abstract

In this review article, we survey the relatively new theory of orbital magnetization in solids-often referred to as the "modern theory of orbital magnetization"-and its applications. Surprisingly, while the calculation of the orbital magnetization in finite systems such as atoms and molecules is straight forward, in extended systems or solids it has long eluded calculations owing to the fact that the position operator is ill-defined in such a context. Approaches that overcome this problem were first developed in 2005 and in the first part of this review we present the main ideas reaching from a Wannier function approach to semi-classical and finite-temperature formalisms. In the second part, we describe practical aspects of calculating the orbital magnetization, such as taking k-space derivatives, a formalism for pseudopotentials, a single k-point derivation, a Wannier interpolation scheme, and DFT specific aspects. We then show results of recent calculations on Fe, Co, and Ni. In the last part of this review, we focus on direct applications of the orbital magnetization. In particular, we will review how properties such as the nuclear magnetic resonance shielding tensor and the electron paramagnetic resonance g-tensor can elegantly be calculated in terms of a derivative of the orbital magnetization.

Higher-dimensional Wannier Interpolation for the Modern Theory of the Dzyaloshinskii–Moriya Interaction: Application to Co-based Trilayers

“…23,24,27) The antidamping spin-orbit torques are ascribed to the non-trivial geometry of the mixed phase space of k andm in terms of the so-called mixed Berry curvature Ωm k i j of all occupied states: 23)…”

Insights into the orbital magnetism of noncollinear magnetic systems

“…In general such a separation is also possible, as established by the modern theory of orbital magnetization. 45,46 They give access to two aspects of the persistent (bound) current flowing around the trimer: whether it swirls locally around each atomic site (the local orbital moment), and whether there is a net current circulating around the trimer (the nonlocal orbital moment). Our previous work in Ref.…”

Topological superconductivity in an ultrathin, magnetically-doped topological insulator proximity coupled to a conventional superconductor

“…Previous work considering the effects of magnetic dopants on the surface physics of TRI TI indicates that the addition of magnetically ordered impurities allows for the development of a net ferromagnetic order, [31][32][33] and thus a uniform magnetization can provide a simple but accurate picture of the TI with magnetic dopants. Within this work, we ignore any orbital effects as those resulting from magnetic dopants are negligible 34 .…”