Topological Magnon Bands and Unconventional Superconductivity in Pyrochlore Iridate Thin Films

Magnon bands in pyrochlore slabs with Heisenberg exchange and anisotropies

The pyrochlore lattice is a versatile venue to probe the properties of magnetically ordered states induced or perturbed by anisotropic terms like the Dzyaloshinskii-Moriya interactions or single-ion anisotropy. Several such ordered states have been investigated recently as precursors of topological magnons and the associated surface states. In parallel, there has been recent progress in growing thin films of magnetic materials with this lattice structure along high symmetry directions of the lattice. In both cases, an account of the magnetic excitations of relevant Hamiltonians for finite slabs is a necessary step in the analysis of the physics of these systems. While the analysis of bulk magnons for these systems is quite common, a direct evaluation of the magnon spectra in the slab geometry, though required, is less frequently encountered. We study here magnon bands in the slab geometry for a class of spin models on the pyrochlore lattice with Heisenberg exchange, Dzyaloshinskii-Moriya interaction and spin-ice anisotropy. For a range of model parameters, for both ferromagnetic and antiferromagnetic exchange, we compute the classical ground states for different slab orientations and determine the spin wave excitations above them. We analyze the ferromagnetic splay phase, the all-in-all-out (AIAO) phase and a coplanar phase and evaluate magnon dispersions for slabs oriented perpendicular to the [111], [100] and [110] directions. For all the phases considered, depending on the slab orientation, magnon band structures can be non-reciprocal and we highlight the differences in the three orientations from this point-of-view. Finally, we present details of the surface localized magnons for all the three slab orientations in the phases we study. For the ferromagnetic splay phase and the AIAO phase we analyze surface states associated with point degeneracies or nodal lines in the bulk spectrum by computing the magnonic Berry curvature and Weyl charges or Chern numbers associated with it.

Topological Superconductivity Mediated by Skyrmionic Magnons

Topological superconductors are associated with the appearance of Majorana bound states, with promising applications in topologically protected quantum computing. In this Letter, we study a system where a skyrmion crystal is interfaced with a normal metal. Through interfacial exchange coupling, spin fluctuations in the skyrmion crystal mediate an effective electron-electron interaction in the normal metal. We study superconductivity within a weak-coupling approach and solve gap equations both close to the critical temperature and at zero temperature. Special features in the effective electron-electron interaction due to the noncolinearity of the magnetic ground state yield topological superconductivity at the interface.

Thermal Hall Effect of Magnons in Collinear Antiferromagnetic Insulators: Signatures of Magnetic and Topological Phase Transitions

We demonstrate theoretically that the thermal Hall effect of magnons in collinear antiferromagnetic insulators is an indicator of magnetic and topological phase transitions in the magnon spectrum. The transversal heat current of magnons caused by a thermal gradient is calculated for an antiferromagnet on a honeycomb lattice. An applied magnetic field drives the system from the antiferromagnetic phase via a spin-flop phase into the field-polarized phase. In addition to these magnetic phase transitions, we find topological phase transitions within the spin-flop phase. Both types of transitions manifest themselves in prominent and distinguishing features in the thermal conductivity, which changes by several orders of magnitude. The variation of temperature provides a tool to discern experimentally the two types of phase transitions. We include numerical results for the van der Waals magnet MnPS_{3}.

Magnetic Weyl Semimetallic Phase in Thin Films of Eu_{2}Ir_{2}O_{7}

The interplay between electronic interactions and strong spin-orbit coupling is expected to create a plethora of fascinating correlated topological states of quantum matter. Of particular interest are magnetic Weyl semimetals originally proposed in the pyrochlore iridates, which are only expected to reveal their topological nature in thin film form. To date, however, direct experimental demonstrations of these exotic phases remain elusive, due to the lack of usable single crystals and the insufficient quality of available films. Here, we report on the discovery of signatures for the long-sought magnetic Weyl semimetallic phase in (111)-oriented Eu_{2}Ir_{2}O_{7} high-quality epitaxial thin films. We observed an intrinsic anomalous Hall effect with colossal coercivity but vanishing net magnetization, which emerges right below the onset of a peculiar magnetic phase with all-in-all-out (AIAO) antiferromagnetic ordering. The anomalous Hall conductivity obtained experimentally is consistent with the theoretical prediction, likely arising from the nonzero Berry curvature emanated by Weyl node pairs near the Fermi level that act as sources and sinks of Berry flux, activated by broken cubic crystal symmetry at the top and bottom terminations of the thin film.

Thermal Hall and Nernst responses in ultrathin magnetic films of pyrochlore lattice

The ultrathin films of pyrochlore lattice along [111] direction provide a fertile ground for exploring topological states in oxide materials, where the electron correlations are strong and magnetically ordered states are favored. As a result of strong interactions, most of states are magnetic insulators with strong Dzyaloshinskii-Moriya and anisotropic spin interactions. We considered three types of heterostructures, a bilayer of triangular-kagome (TK), and two trilayers of triangular-kagome-triangular (TKT) and kagome-triangular-kagome (KTK) thin films. The ground states are magnetically ordered with the low-energy excitations, the magnons, characterized by nontrivial topology. While for TK model the lowest magnon band is trivial, the lowest bands in TKT and KTK model are topological. These features have direct consequences on the thermal Hall conductivity, where we observed that the latter quantity onsets at lower temperature in multilayer models, suggesting that the thermal Hall response can be controlled by engineering lattice-driven magnetic band structure. We also introduce the thermal sublattice Nernst effect in these layers and found the corresponding response is as large as the thermal Hall response.

Topological Magnons with Nodal-Line and Triple-Point Degeneracies: Implications for Thermal Hall Effect in Pyrochlore Iridates

We analyze the magnon excitations in pyrochlore iridates with all-in-all-out (AIAO) antiferromagnetic order, focusing on their topological features. We identify the magnetic point group symmetries that protect the nodal-line band crossings and triple-point degeneracies that dominate the Berry curvature. We find three distinct regimes of magnon band topology, as a function of the ratio of Dzyaloshinskii-Moriya interaction to the antiferromagnetic exchange. We show how the thermal Hall response provides a unique probe of the topological magnon band structure in AIAO systems.

Interacting topological insulators: a review

The discovery of the quantum spin Hall effect and topological insulators more than a decade ago has revolutionized modern condensed matter physics. Today, the field of topological states of matter is one of the most active and fruitful research areas for both experimentalists and theorists. The physics of topological insulators is typically well described by band theory and systems of non-interacting fermions. In contrast, several of the most fascinating effects in condensed matter physics merely exist due to electron-electron interactions, examples include unconventional superconductivity, the Kondo effect, and the Mott-Hubbard transition. The aim of this review article is to give an overview of the manifold directions which emerge when topological bandstructures and correlation physics interfere and compete. These include the study of the stability of topological bandstructures and correlated topological insulators. Interaction-induced topological phases such as the topological Kondo insulator provide another exciting topic. More exotic states of matter such as topological Mott insulator and fractional Chern insulators only exist due to the interplay of topology and strong interactions and do not have any bandstructure analogue. Eventually the relation between topological bandstructures and frustrated quantum magnetism in certain transition metal oxides is emphasized.

Topological Magnon Modes in Patterned Ferrimagnetic Insulator Thin Films

Manipulation of magnons opens an attractive direction in the future energy-efficient information processing devices. Such quasi-particles can transfer and process information free from the troublesome Ohmic loss in conventional electronic devices. Here, we propose to realize topologically protected magnon modes using the interface between the patterned ferrimagnetic insulator thin films of different configurations without the Dzyaloshinskii-Moriya interaction. The interface thus behaves like a perfect waveguide to conduct the magnon modes lying in the band gap. These modes are immune to backscattering even in sharply bent tracks, robust against the disorders, and maintain a high degree of coherence during propagation. We design a magnonic Mach-Zehnder interferometer, which realizes a continuous change of magnon signal with varying external magnetic field or driving frequency. Our results pave a new way for realizing topologically protected magnon waveguide and finally achieving a scalable low-dissipation spintronic devices and even the magnonic integrated circuit.

Topological magnon bands and unconventional thermal Hall effect on the frustrated honeycomb and bilayer triangular lattice

In the conventional ferromagnetic systems, topological magnon bands and thermal Hall effect are due to the Dzyaloshinskii-Moriya interaction (DMI). In principle, however, the DMI is either negligible or it is not allowed by symmetry in some quantum magnets. Therefore, we expect that topological magnon features will not be present in those systems. In addition, quantum magnets on the triangular-lattice are not expected to possess topological features as the DMI or spin-chirality cancels out due to equal and opposite contributions from adjacent triangles. Here, however, we predict that the isomorphic frustrated honeycomb-lattice and bilayer triangular-lattice antiferromagnetic system will exhibit topological magnon bands and topological thermal Hall effect in the absence of an intrinsic DMI. These unconventional topological magnon features are present as a result of magnetic-field-induced non-coplanar spin configurations with nonzero scalar spin chirality. The relevance of the results to realistic bilayer triangular antiferromagnetic materials are discussed.