Insights into the orbital magnetism of noncollinear magnetic systems

Abstract

The orbital magnetic moment is usually associated with the relativistic spin-orbit interaction, but recently it has been shown that noncollinear magnetic structures can also be its driving force. This is important not only for magnetic skyrmions, but also for other noncollinear structures, either bulk-like or at the nanoscale, with consequences regarding their experimental detection. In this work we present a minimal model that contains the effects of both the relativistic spin-orbit interaction and of magnetic noncollinearity on the orbital magnetism. A hierarchy of models is discussed in a step-by-step fashion, highlighting the role of time-reversal symmetry breaking for translational and spin and orbital angular motions. Couplings of spin-orbit and orbit-orbit type are identified as arising from the magnetic noncollinearity. We recover the atomic contribution to the orbital magnetic moment, and a nonlocal one due to the presence of circulating bound currents, exploring different balances between the kinetic energy, the spin exchange interaction, and the relativistic spin-orbit interaction. The connection to the scalar spin chirality is examined. The orbital magnetism driven by magnetic noncollinearity is mostly unexplored, and the presented model contributes to laying its groundwork.1 arXiv:1707.04518v1 [cond-mat.mes-hall]

Topological–chiral magnetic interactions driven by emergent orbital magnetism

“…Acting as an effective magnetic field, the complex spin topology of chiral systems thereby allows for ground-state currents of specific rotational sense that manifest in spontaneous orbital properties of the electrons. This microscopic mechanism induces a topological orbital moment (TOM) that stems from the scalar spin chirality without any reference to relativistic origins, as predicted for several situations ranging from non-collinear 3Q-states to large-scale skyrmions [20][21][22][23][24][25] . In the limit of vanishing effective magnetic field, i.e., in a situation of small spin chirality, the spontaneous TOM is directly proportional to B eff with the proportionality factor given by the topological orbital susceptibility of the system 25 .…”

“…The 3D magnetization textures of 2D skyrmions gives rise to a scalar spin chirality, a driving force behind a plethora of macroscopic phenomena. Examples are the topological Hall effect 18,19 or a finite topological orbital moment (TOM) [20][21][22][23][24][25] , which can both serve as experimental fingerprints of skyrmions. Texture-induced contributions to these macroscopic phenomena were also predicted in frustrated magnets 26,27 , where they originate from the non-trivial spin topology associated with the real-space configuration of magnetic moments S i as reflected by the scalar spin chirality χ ijk = S i · (S j × S k ).…”

Generalization of the Landau–Lifshitz–Gilbert equation by multi-body contributions to Gilbert damping for non-collinear magnets

“…n α i j n β ki e i • (e j × e k ) . The scalar spin chirality directly relates to the topological orbital moment [35][36][37] and therefore the physical origin of those dependencies lies in the topological orbital moment. Even though these terms might not be the most important ones in our model, for specific noncollinear configurations or for some realistic elements with a large topological orbital moment, e.g.…”

Impurity-induced orbital magnetization in a Rashba electron gas

“…with S i being the spin magnetic moment direction at site i 28,29 . Indeed, non-collinear spin textures can be viewed as a gauge field that couples the spin and orbital degrees of freedom30,31 , mimicking the effects of the SO interaction.…”