Oleg Tchernyshyov

We describe a geometric phenomenon in which a traveling wave made of degenerate Goldstone modes leaves behind a transformed ground state. In a triangular Heisenberg antiferromagnet, a pulse of circularly polarized spin waves rotates the spins within their plane. An exact solution of the nonlinear equations of motion demonstrates that the accumulated rotation is a geometric phase related to parallel transport of the order parameter. We point out a curious analogy between the motion of the magnetic order parameter and that of a wobbling coin. This phenomenon opens a new route for controlling antiferromagnetic order by spin waves and may extend to other frustrated magnets as well as other physical systems with noncommuting broken-symmetry generators.

In the search for unconventional magnetism, exotic quantum states are characterized by a lack of order and a broad spin excitation continuum approaching zero temperature. We study the two-dimensional triangular-lattice effective spin- 1 2 system CeMgAl ₁₁ O ₁₉ , which shows slight disorder but no magnetic ordering down to 100 millikelvin. Spin-wave analysis in the magnetic-field–polarized state determines the spin Hamiltonian featuring a mixed ferromagnetic-antiferromagnetic nearest-neighbor exchange interaction [ J z = −0.024(5) milli–electron volts, J ⊥ = 0.056(3) milli–electron volts]. This places the system near an exactly solvable point of the spin- 1 2 triangular-lattice XXZ model ( J z = − 1 2 J ⊥ ) with extensive ground-state degeneracy. In zero field, neutron spectroscopy reveals a prominent continuum; we show that this arises from an ensemble average of spin-wave spectra across the degenerate ground-state manifold. This demonstrates that the role of weak quenched disorder can be quantitatively constrained: It inhibits unique ground-state selection and stabilizes a local distribution within the degenerate manifold, yielding continuum-like spectra that necessitate a critical reevaluation of the experimental signatures of exotic quantum states.

Noncollinear antiferromagnets (AFMs) have recently attracted attention in the emerging field of antiferromagnetic spintronics because of their various interesting properties. Because of the noncollinear magnetic order, the localized electron spins on different magnetic sublattices are not conserved even when spin-orbit coupling is neglected, making it difficult to understand the transport of spin angular momentum. Here we study the conserved Noether current due to spin-rotation symmetry of the local spins in noncollinear AFMs. Interestingly, we find that a Hall component of the spin current can be generically created by a longitudinal driving force associated with a propagating spin wave, inherently distinguishing noncollinear AFMs from collinear ones. We coin the corresponding Hall coefficient, an isotropic rank-four tensor, as the Hall (inverse) mass, which generally exists in noncollinear AFMs and their polycrystals. The resulting Hall spin current can be realized by spin pumping in a ferromagnet-noncollinear AFM bilayer structure as we demonstrate numerically, for which we also give the criteria of ideal boundary conditions. Our results shed light on the potential of noncollinear AFMs in manipulating the polarization and flow of spin currents in general spintronic devices.

These lecture notes from the 2023 Summer School ``Principles and applications of symmetry in magnetism’’ introduce the reader to the classical field theory of ferromagnets and antiferromagnets.

We present a nonlinear field theory of a three-sublattice hexagonal antiferromagnet. The order parameter is the spin frame, an orthogonal triplet of vectors related to sublattice magnetizations and spin chirality. The exchange energy, quadratic in spin-frame gradients, has three coupling constants, only two of which manifest themselves in the bulk. As a result, the three spin-wave velocities satisfy a universal relation. Vortices generally have an elliptical shape with the eccentricity determined by the Lamé parameters.

We theoretically investigate the interaction between magnons and a skyrmion-textured domain wall in a two-dimensional antiferromagnet and elucidate the resultant properties of magnon transport. Using supersymmetric quantum mechanics, we solve the scattering problem of magnons on top of the domain wall and obtain the exact solutions of propagating and bound magnon modes. Then, we find their properties of reflection and refraction in the skyrmion-textured domain wall, where magnons experience an emergent magnetic field due to their nontrivial spin texture-induced effective gauge field. Based on the obtained scattering properties of magnons and the domain wall, we show that the thermal transport decreases as the domain wall's chirality increases. Our results suggest that the thermal transport of an antiferromagnet is tunable by modulating the skyrmion charge density of the domain wall, which might be useful for realizing electrically tunable spin caloritronic devices.

This paper gives a pedagogical introduction to the mechanics of ferromagnetic solitons. We start with the dynamics of a single spin and develop all the tools required for the description of the dynamics of solitons in a ferromagnet.