Non-Hermitian topology of spontaneous magnon decay

Spontaneous magnon decay is a generic feature of the magnetic excitations of anisotropic magnets and isotropic magnets with non-collinear order. In this paper, we argue that the effect of interactions on one-magnon states can, under many circumstances, be treated in terms of an effective, energy independent, non-Hermitian Hamiltonian for the magnons. In the vicinity of Dirac or Weyl touching points, we show that the spectral function has a characteristic anisotropy arising from topologically protected exceptional points or lines in the non-Hermitian spectrum. Such features can, in principle, be detected using inelastic neutron scattering or other spectroscopic probes. We illustrate this physics through a concrete example: a honeycomb ferromagnet with Dzyaloshinskii-Moriya exchange. We perform interacting spin wave calculations of the structure factor and spectral function of this model, showing good agreement with results from a simple effective non-Hermitian model for the splitting of the Dirac point. Finally, we argue that the zoo of known topological protected magnon band structures may serve as a nearly ideal platform for realizing and exploring non-Hermitian physics in solid-state systems.Comment: 4+epsilon page

Hidden and antiferromagnetic order as a rank-5 superspin in URu2Si2

We propose a candidate for the hidden order in URu2Si2: a rank-5 E type spin density wave between Uranium 5f crystal field doublets breaking time reversal and lattice tetragonal symmetry in a manner consistent with recent torque measurements [R. Okazaki et al, Science 331, 439 (2011)]. We argue that coupling of this order parameter to magnetic probes can be hidden by crystal field effects, while still having significant effects on transport, thermodynamics and magnetic susceptibilities. In a simple tight-binding model for the heavy quasiparticles, we show the connection between the hidden order and antiferromagnetic phases arises since they form different components of this single rank-5 pseudo-spin vector. Using a phenomenological theory, we show the experimental pressure-temperature phase diagram can be qualitatively reproduced by tuning terms which break pseudo-spin rotational symmetry. As a test of our proposal, we predict the presence of small magnetic moments in the basal plane oriented in the [110] direction ordered at the wave-vector (0,0,1).Comment: 5 page

Spin ice thin films: Large-N theory and Monte Carlo simulations

We explore the physics of highly frustrated magnets in confined geometries, focusing on the Coulomb phase of pyrochlore spin ices. As a specific example, we investigate thin films of nearest-neighbor spin ice, using a combination of analytic large-N techniques and Monte Carlo simulations. In the simplest film geometry, with surfaces perpendicular to the [001] crystallographic direction, we observe pinch points in the spin-spin correlations characteristic of a two-dimensional Coulomb phase. We then consider the consequences of crystal symmetry breaking on the surfaces of the film through the inclusion of orphan bonds. We find that when these bonds are ferromagnetic, the Coulomb phase is destroyed by the presence of fluctuating surface magnetic charges, leading to a classical Z_2 spin liquid. Building on this understanding, we discuss other film geometries with surfaces perpendicular to the [110] or the [111] direction. We generically predict the appearance of surface magnetic charges and discuss their implications for the physics of such films, including the possibility of an unusual Z_3 classical spin liquid. Finally, we comment on open questions and promising avenues for future research.Comment: 17 pages, 11 figures. Minor improvements, typos correcte