Band topology is both constrained and enriched by the presence of symmetry. The importance of anti-unitary symmetries such as time reversal was recognized early on leading to the classification of topological band structures based on the ten-fold way
. Since then, lattice point group and non-symmorphic symmetries have been seen to lead to a vast range of possible topologically nontrivial band structures many of which are realized in materials. In this paper we show that band topology is further enriched in many physically realizable instances where magnetic and lattice degrees of freedom are wholly or partially decoupled. The appropriate symmetry groups to describe general magnetic systems are the spin-space groups. Here we describe cases where spin-space groups are essential to understand the band topology in magnetic materials. We then focus on magnon band topology where the theory of spin-space groups has its simplest realization. We consider magnetic Hamiltonians with various types of coupling including Heisenberg and Kitaev couplings revealing a hierarchy of enhanced magnetic symmetry groups depending on the nature of the lattice and the couplings. We describe, in detail, the associated representation theory and compatibility relations thus characterizing symmetry-enforced constraints on the magnon bands revealing a proliferation of nodal points, lines, planes and volumes.
We study the Kitaev-Heisenberg-$Gamma$-$Gamma$ model that describes the magnetism in strong spin-orbit coupled honeycomb lattice Mott insulators. In strong $[111]$ magnetic fields that bring the system into the fully polarized paramagnetic phase, we
find that the spin wave bands carry nontrivial Chern numbers over large regions of the phase diagram implying the presence of chiral magnon edge states. In contrast to other topological magnon systems, the topological nontriviality of these systems results from the presence of magnon number non-conserving terms in the Hamiltonian. Since the effects of interactions are suppressed by $J/h$, the validity of the single particle picture is tunable making paramagnetic phases particularly suitable for the exploration of this physics. Using time dependent DMRG and interacting spin wave theory, we demonstrate the presence of the chiral edge mode and its evolution with field.
In multiferroic BiFeO$_3$ a cycloidal antiferromagnetic structure is coupled to a large electric polarization at room temperature, giving rise to magnetoelectric functionality that may be exploited in novel multiferroic-based devices. In this paper,
we demonstrate that by substituting samarium for 10% of the bismuth ions the periodicity of the room temperature cycloid is increased, and by cooling below $sim15$ K the magnetic structure tends towards a simple G-type antiferromagnet, which is fully established at 1.5 K. We show that this transition results from $f-d$ exchange coupling, which induces a local anisotropy on the iron magnetic moments that destroys the cycloidal order - a result of general significance regarding the stability of non-collinear magnetic structures in the presence of multiple magnetic sublattices.
Sr$_{3}$ZnIrO$_{6}$ is an effective spin one-half Mott insulating iridate belonging to a family of magnets which includes a number of quasi-one dimensional systems as well as materials exhibiting three dimensional order. Here we present the results o
f an extensive investigation into the magnetism including heat capacity, a.c. susceptibility, muon spin rotation ($mu$SR), neutron diffraction and inelastic neutron scattering on the same sample. It is established that the material exhibits a transition at about $17$ K into a three-dimensional antiferromagnetic structure with propagation vector $boldsymbol{k}=(0,frac{1}{2},1)$ in the hexagonal setting of R$bar{3}$c and non-collinear moments of $0.87$$mu_B$ on Ir$^{4+}$ ions. Further we have observed a well defined powder averaged spin wave spectrum with zone boundary energy of $sim 5$ meV at $5$ K. We stress that a theoretical analysis shows that the observed non-collinear magnetic structure arises from anisotropic inter- and intra- chain exchange which has its origin in significant spin-orbit coupling. The model can satisfactorily explain the observed spin wave excitations.
We consider the possibility that the discrete long-range ordered states of Er2Ti2O7 are selected energetically at the mean field level as an alternative scenario that suggests selection via thermal fluctuations. We show that nearest neighbour exchang
e interactions alone are not sufficient for this purpose, but that anisotropies arising from excited single ion crystal field states in Er2Ti2O7, together with appropriate anisotropic exchange interactions, can produce the required long range order. However, the effect of the single ion anisotropies is rather weak so we expect thermal or quantum fluctuations, in some guise, to be ultimately important in this material. We reproduce recent experimental results for the variation of magnetic Bragg peak intensities as a function of magnetic field.
We study some aspects of a Monte Carlo method invented by Maggs and Rossetto for simulating systems of charged particles. It has the feature that the discretized electric field is updated locally when charges move. Results of simulations of the two d
imensional one-component plasma are presented. Highly accurate results can be obtained very efficiently using this lattice method over a large temperature range. The method differs from global methods in having additional degrees of freedom which leads to the question of how a faster method can result. We argue that efficient sampling depends on charge mobility and find that the mobility is close to maximum for a low rate of independent plaquette updates for intermediate temperatures. We present a simple model to account for this behavior. We also report on the role of uniform electric field sampling using this method.
