Topological aspects of antiferromagnets

Abstract

The long fascination that antiferromagnetic materials has exerted on the scientific community over about a century has been entirely renewed recently with the discovery of several unexpected phenomena, including various classes of anomalous spin and charge Hall effects and unconventional magnonic transport, and also homochiral magnetic entities such as skyrmions. With these breakthroughs, antiferromagnets stand out as a rich playground for the investigation of novel topological behavior, and as promising candidate materials for disruptive low-power microelectronic applications. Remarkably, the newly discovered phenomena are all related to the topology of the magnetic, electronic or magnonic ground state of the antiferromagnets. This review exposes how non-trivial topology emerges at different levels in antiferromagnets and explores the novel mechanisms that have been discovered recently. We also discuss how novel classes of quantum magnets could enrich the currently expanding field of antiferromagnetic spintronics and how spin transport can in turn favor a better understanding of exotic quantum excitations.

Theory of perturbatively nonlinear quantum transport I: general formulation and structure of the retarded correlator

“…Both sources of unease can be whisked away by realizing that there is an underlying structure in which several different notions of 'time-reversal' all play an important role. Roughly speaking, from the microscopic point of view, it is clear that the macroscopic, linear constitutive relation represents a perturbative expansion of an expectation value to leading order in the driving field, i.e., J ∝ Ĵ ∝ E. Since the dependence on m arises through the equilibrium Hamiltonian, it is clear that the macroscopic average of the observable itself, which is on the left hand side of the constitutive relation, should be dependent on m, i.e., we should have j i (m) = σ ik (m)E k [25]. At this point we can distinguish between two operations; magnetic-inversion K m that acts by only reversing m, i.e., K m j i (m) = j i (−m) → K m σ ik (m) = σ ik (−m), and full time-reversal T full that acts by reversing not only m, but also the flow of current, i.e., T full j i (m) = −j i (−m) → T full σ ik (m) = −σ ik (−m).…”

“…providing a probe of only the m-dependence. The natural need to separately look at magnetic-inversion and full time-reversal becomes clearly apparent (see also [25] for an elementary account of this). Conversely, for example, the author of [21] asserts that differentiating between time-reversal and magnetic-inversion, the latter referred to as 'magnetic-reversal', leads to "unnecessary complications" and maintains the widespread view that Onsager's reciprocity principal has to be invoked for a consistent discussion.…”

Theory of perturbatively nonlinear quantum transport II: Hilbert space truncation, gauge invariance, and second order transport in a spatially uniform, time-varying electric field

“…A natural question to ask is: how could a non-flat connection on the trivial Hilbert bundle over parameter space with components A i arise? For the purposes of this paper, we look at a standard construction that we adapt from [39], also discussed in [52] for the special case of periodic Bloch states. Suppose we have a state |ψ(t, p) as a local section of a trivial Hilbert bundle π : R × B × H → R × B, where B is the parameter space and R refers to time.…”

Topological phase transition and thermal Hall effect in kagome ferromagnets

“…Physically, the essential concept in topological band theory is the topological invariants linked to the topological protected edge states, when the spin-orbit coupling (SOC) is present and opens a topological nontrivial gap [6,7]. As the band topology is independent of the statistical regularity of (quasi)particles, such ideas can be realized in bosonic systems such as photons [8][9][10][11][12], phonons [13][14][15], and magnons [16][17][18][19][20][21]. Different from electronic charge particles, magnons are electrically neutral bosonic quasiparticles, thus they can propagate over long distances without experiencing a Lorentz force and incuring Joule heating in magnetic insulators.…”