Topological phase diagrams of in-plane field polarized Kitaev magnets

While the existence of a magnetic field induced quantum spin liquid in Kitaev magnets remains under debate, its topological properties often extend to proximal phases where they can lead to unusual behaviors of both fundamental and applied interests. Subjecting a generic nearest neighbor spin model of Kitaev magnets to a sufficiently strong in-plane magnetic field, we study the resulting polarized phase and the associated magnon excitations. In contrast to the case of an out-of-plane magnetic field where the magnon band topology is enforced by a three-fold symmetry, we find that it is possible for topologically trivial and nontrivial parameter regimes to coexist under in-plane magnetic fields. We map out the topological phase diagrams of the magnon bands, revealing a rich pattern of variation of the Chern number over the parameter space and the field angle. We further compute the magnon thermal Hall conductivity as a weighted summation of Berry curvatures, and discuss experimental implications of our results to planar thermal Hall effects in Kitaev magnets.Comment: 8+7 pages, 5+1 figures, 1+0 tabl

Symmetry fractionalization in the gauge mean-field theory of quantum spin ice

Symmetry fractionalization is a ubiquitous feature of topologically ordered states that can be used to classify different symmetry-enriched topological phases and reveal some of their unique experimental signatures. Despite its vast popularity, there is currently no available framework to study symmetry fractionalization of quantum spin ice (QSI) -- a $U(1)$ quantum spin liquid (QSL) on the pyrochlore lattice supporting emergent photons -- within the most widely used theoretical framework to describe it, gauge mean-field theory (GMFT). In this work, we provide an extension of GMFT that allows for the classification of space-time symmetry fractionalization. The construction classifies all GMFT Ans\"atze that yield physical wavefunctions invariant under given symmetries and a specific low-energy gauge structure. As an application of the framework, we first show that the only two Ans\"atze with emergent $U(1)$ gauge fields that respect all space-group symmetries are the well-known 0- and $\pi$-flux states. We then showcase how the framework may describe QSLs beyond the currently known ones by classifying chiral $U(1)$ QSI. We find two new states described by $\pi/2$- and $3\pi/2$-fluxes of the emergent gauge field threading the hexagonal plaquettes of the pyrochlore lattice. We finally discuss how the different ways translation symmetries fractionalize for all these states lead to unique experimentally relevant signatures and compute their respective inelastic neutron scattering cross-section to illustrate the argument.Comment: 12+10 pages, 4+1 figure

Emergence of a nematic paramagnet via quantum order-by-disorder and pseudo-Goldstone modes in Kitaev magnets

The appearance of nontrivial phases in Kitaev materials exposed to an external magnetic field has recently been a subject of intensive studies. Here, we elucidate the relation between the field-induced ground states of the classical and quantum spin models proposed for such materials, by using the infinite density matrix renormalization group (iDMRG) and the linear spin wave theory (LSWT). We consider the $K \Gamma \Gamma'$ model, where $\Gamma$ and $\Gamma'$ are off-diagonal spin exchanges on top of the dominant Kitaev interaction $K$. Focusing on the magnetic field along the $[111]$ direction, we explain the origin of the nematic paramagnet, which breaks the lattice-rotational symmetry and exists in an extended window of magnetic field, in the quantum model. This phenomenon can be understood as the effect of quantum order-by-disorder in the frustrated ferromagnet with a continuous manifold of degenerate ground states discovered in the corresponding classical model. We compute the dynamical spin structure factors using a matrix operator based time evolution and compare them with the predictions from LSWT. We, thus, provide predictions for future inelastic neutron scattering experiments on Kitaev materials in an external magnetic field along the $[111]$ direction. In particular, the nematic paramagnet exhibits a characteristic pseudo-Goldstone mode which results from the lifting of a continuous degeneracy via quantum fluctuations.Comment: 14 pages, 9 figur

Emergence of nematic paramagnet via quantum order-by-disorder and pseudo-Goldstone modes in Kitaev magnets

The appearance of nontrivial phases in Kitaev materials exposed to an external magnetic field has recently been a subject of intensive studies. Here, we elucidate the relation between the field-induced ground states of the classical and quantum spin models proposed for such materials, by using the infinite density matrix renormalization group (iDMRG) and the linear spin wave theory (LSWT). We consider the KΓΓ′ model, where Γ and Γ′ are off-diagonal spin exchanges on top of the dominant Kitaev interaction K. Focusing on the magnetic field along the [111] direction, we explain the origin of the nematic paramagnet, which breaks the lattice-rotational symmetry and exists in an extended window of magnetic field, in the quantum model. This phenomenon can be understood as the effect of quantum order-by-disorder in the frustrated ferromagnet with a continuous manifold of degenerate ground states discovered in the corresponding classical model. We compute the dynamical spin structure factors using a matrix operator based time evolution and compare them with the predictions from LSWT. We, thus, provide predictions for future inelastic neutron scattering experiments on Kitaev materials in an external magnetic field along the [111] direction. In particular, the nematic paramagnet exhibits a characteristic pseudo-Goldstone mode, which results from the lifting of a continuous degeneracy via quantum fluctuations

Ferromagnetic Kitaev interaction and the origin of large magnetic anisotropy in α\alpha-RuCl3_3

$\alpha$-RuCl$_3$ is drawing much attention as a promising candidate Kitaev quantum spin liquid. However, despite intensive research efforts, controversy remains about the form of the basic interactions governing the physics of this material. Even the sign of the Kitaev interaction (the bond-dependent anisotropic interaction responsible for Kitaev physics) is still under debate, with conflicting results from theoretical and experimental studies. The significance of the symmetric off-diagonal exchange interaction (referred to as the $\Gamma$ term) is another contentious question. Here, we present resonant elastic x-ray scattering data that provides unambiguous experimental constraints to the two leading terms in the magnetic interaction Hamiltonian. We show that the Kitaev interaction ($K$) is ferromagnetic, and that the $\Gamma$ term is antiferromagnetic and comparable in size to the Kitaev interaction. Our findings also provide a natural explanation for the large anisotropy of the magnetic susceptibility in $\alpha$-RuCl$_3$ as arising from the large $\Gamma$ term. We therefore provide a crucial foundation for understanding the interactions underpinning the exotic magnetic behaviours observed in $\alpha$-RuCl$_3$.Comment: 5 pages, two-column, 3 figure