Our research interests are centered on topological transport phenomena, topological solitons, and topological phases in condensed matter systems, which are of fundamental interest and of practical importance as will be explained below. Ordered quantum materials are particularly attractive systems to study since they can support a variety of topological solitons such as domain walls, vortices, and skyrmions and provide diverse platforms such as ferromagnets, antiferromagnets, and superconductors where topological phases can be found. Now is an especially exciting time to study charge, spin, and heat transport in various quantum materials due to the recent rapid developments of experimental techniques in spintronics for observing and controlling spin degrees of freedom in addition to existing techniques for controlling charge and heat degrees of freedom.

Dynamics of solitons

Topological magnetic solitons can exhibit interesting dynamics, often associated with their topological characteristics, as macroscopic manifestations of the spin Berry phase. For example, a skyrmion in a two-dimensional magnet experiences a Berry-phase-induced Magnus force, which is proportional to its winding number and the spin density of the magnet. By exploiting the Magnus force on a skyrmion, we showed that a ferrimagnetic skyrmion can exhibit snake-like trajectories along the line of vanishing spin density, analogous to the snake orbits of electrons in a nonuniform magnetic field. These can be utilized as self-focusing racetracks for skyrmions, paving the way for skyrmion-based memory devices which have been touted in spintronics. For further details, please see our PRB Rapid paper (Editors' Suggestion): [Phys. Rev. B 95, 140404(R) (2017)].

In addition, the interactions of topological solitons with other degrees of freedom can host interesting physics as well as useful applications. One example would be our work on mechanical actuation of magnetic domain-wall motion via a phononic torque and force. The underlying mechanism for the phononic torque has an interesting analogy with optics. A domain wall is birefringent for transverse acoustic waves and can thus act as a wave plate that alters the circular polarization---and thus the angular momentum---of phonons traveling through it. This change of the phonons' angular momentum applies a torque on the domain wall. This work shows that elastic waves can provide an efficient means to drive solitons, particularly in magnetic insulators, the control of which has been challenging due to the lack of charge degrees of freedom. For further details, please see our PRL paper:[Phys. Rev. Lett. 117, 237201 (2016)].

Spin transport

Topological solitons can play important and interesting roles in charge and spin transport in matter. One well-known example would be vortices in superconductors, which disturb the charge supercurrent and can destroy the long-range superconducting order. Motivated by this example, we studied the effects of magnetic vortices on spin transport in easy-plane spin chains. Easy-plane magnets with U(1) spin-rotational symmetry are known to support superfluid-like transport of spins, which is associated with spontaneous U(1) symmetry breaking of the ground states. Intrinsic resistances in such spin superfluids arise via processes called phase slips, which manifest in the form of magnetic vortices in Euclidean spacetime in one-dimensional cases. In our study of quantum phase slips in antiferromagnetic spin-s chains with easy-plane anisotropy, we showed that integer-s chains exhibit 2π phase slips like ones in conventional superconductors, but half-odd-integer-s chains exhibit exotic 4π phase slips. We found that, for half-odd-integer spin chains, 2π phase slips are completely suppressed via the same topological mechanism that prohibits the gap generation in isotropic spin chains. Using spintronic techniques, we proposed an experiment that can support the theoretical prediction. This work exemplifies a new research area exploring quantum magnetism with spin-transport measurements, which can complement traditional probes such as neutron scattering. For further details, please see our PRL paper: [Phys. Rev. Lett. 116, 127201 (2016)].

In addition, we have shown that a magnetic domain wall can serve as a reprogrammable conduit for spin superfluids [Phys. Rev. Lett. 119, 047202 (2017)]. Here is the animation showing how the spin supercurrent flows through a domain wall.

Topological phases

We have a keen interest in topological phases of spin systems, not only for their intriguing mathematical structures but also for their practical capabilities such as dissipationless spin transport. For example, we demonstrated that bosonic topological phases can be realized in a Heisenberg ferromagnet with a spin-orbit coupling on the honeycomb lattice. At sufficiently low temperatures, where the magnet is ordered, the effective Hamiltonian for magnons is shown to be equivalent to the Haldane model for electrons, which is an archetype of Chern insulators characterized by chiral edge modes. At high temperatures, where the magnet is thermally disordered, the mean-field spinon band is shown to form a bosonic counterpart of the Kane-Mele model for a topological insulator. This work may trigger the search for topological phases in disordered magnets in addition to ordered ones, which forms a new research area and, for this reason, has been published in PRL.

As another example, we showed that antiferromagnets can become magnonic topological insulators with helical edge modes when they are subjected to a sufficiently strong electric- field-gradient, which exerts an effective magnetic field on magnons via the Aharonov-Casher (AC) effect and makes them form Landau levels. For further details, please see our PRB paper: [Phys. Rev. B 96, 224414 (2017)]. This work exemplifies an emerging field of antiferromagnet-based topological phases, which we will continue to work on in the future.

Soliton-based metamaterials

Moving beyond understanding materials already existing in nature, there are ongoing theoretical and experimental efforts in creating artificial composite materials with useful functionalities, which are referred to as metamaterials. Since they can form exotic phases similar to natural materials and those phases can be manipulated on the level of elementary units called metaatoms, they provide an exciting venue to look for controllable topological phases. In particular, topological magnetic solitons can serve as a unique set of metaatoms with gyroscopic characteristics that are derived from constituent spins. Motivated by this idea, we considered a metamaterial composed of magnetic vortex disks on a honeycomb lattice, and found that the collective gyrotropic dynamics of vortex cores exhibit a topologically protected chiral edge mode. Furthermore, the chirality of the edge mode is determined by the polarity of vortices, which can be controlled easily by standard techniques in spintronics. This work opens a new field of soliton-based metamaterials. For further details, please see our PRL paper: [Phys. Rev. Lett. 119, 077204 (2017)].