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Oleg Tchernyshyov

Publications and source records attributed to Oleg Tchernyshyov.

At least 19 recordsLinked to original sources
arXiv2026

Ferromagnetic Bloch Line as a Bead on a String

We present a simple model of a Bloch line in a thin-film ferromagnet with strong easy-axis and intermediate in-plane anisotropies. The meron is represented as a charged, massless particle that slides along the linear domain wall in a background magnetic field- a gyroscopic bead on a string. Its gyroscopic behavior dynamically isolates the wall segments on either side of the meron, motivating the model for a Bloch line as two strings joined at a moving boundary. The meron clamps the wall at this junction, completely reflecting low-amplitude spin waves that propagate along it. Out-of-plane and in-plane magnetic fields and spin-transfer torques then act in two ways: by exerting a force on the Bloch line itself, or by driving the wall as a whole. Predictions of this model are in agreement with numerical simulations.

cond-mat.mes-hall↗
arXiv2026

Geometric Spin Rotation in Triangular Antiferromagnets

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.

cond-mat.str-el↗
arXiv2025

Spontaneous symmetry breaking in the Heisenberg antiferromagnet on a triangular lattice

We present a detailed investigation of an overlooked symmetry structure in non-collinear antiferromagnets that gives rise to an emergent quantum number for magnons. Focusing on the triangular-lattice Heisenberg antiferromagnet, we show that its spin order parameter transforms under an enlarged symmetry group, $\mathrm{SO(3)_L \times SO(2)_R}$, rather than the conventional spin-rotation group $\mathrm{SO(3)}$. Although this larger symmetry is spontaneously broken by the ground state, a residual subgroup survives, leading to conserved Noether charges that, upon quantization, endow magnons with an additional quantum number -- \emph{isospin} -- beyond their energy and momentum. Our results provide a comprehensive framework for understanding symmetry, degeneracy, and quantum numbers in non-collinear magnetic systems, and bridge an unexpected connection between the paradigms of symmetry breaking in non-collinear antiferromagnets and chiral symmetry breaking in particle physics.

cond-mat.str-el↗
arXiv2024

Hall mass and transverse Noether spin currents in noncollinear antiferromagnets

Noncollinear antiferromagnets (AFMs) have recently attracted attention in the emerging field of antiferromagnetic spintronics because of their various interesting properties. Due to 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-4 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 (FM)-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.

cond-mat.mes-hall↗
arXiv2024

Helical edge modes in a triangular Heisenberg antiferromagnet

We investigate the emergence of helical edge modes in a Heisenberg antiferromagnet on a triangular lattice, driven by a topological mechanism similar to that proposed by Dong et al. [Phys. Rev. Lett. 130, 206701 (2023)] for chiral spin waves in ferromagnets. The spin-frame field theory of a three-sublattice antiferromagnet allows for a topological term in the energy that modifies the boundary conditions for certain polarizations of spin waves and gives rise to edge modes. These edge modes are helical: modes with left and right circular polarizations propagate in opposite directions along the boundary in a way reminiscent of the electron edge modes in two-dimensional topological insulators. The field-theoretic arguments are verified in a realistic lattice model of a Heisenberg antiferromagnet with superexchange interactions that exhibits helical edge modes. The strength of the topological term is proportional to the disparity between two inequivalent superexchange paths. These findings suggest potential avenues for realizing magnonic edge states in frustrated antiferromagnets without requiring Dzyaloshinskii-Moriya interactions or nontrivial magnon band topology.

cond-mat.str-el↗
arXiv2024

Spin Excitation Continuum in the Exactly Solvable Triangular-Lattice Spin Liquid CeMgAl11O19

In magnetically ordered insulators, elementary quasiparticles manifest as spin waves - collective motions of localized magnetic moments propagating through the lattice - observed via inelastic neutron scattering. In effective spin-1/2 systems where geometric frustrations suppress static magnetic order, spin excitation continua can emerge, either from degenerate classical spin ground states or from entangled quantum spins characterized by emergent gauge fields and deconfined fractionalized excitations. Comparing the spin Hamiltonian with theoretical models can unveil the microscopic origins of these zero-field spin excitation continua. Here, we use neutron scattering to study spin excitations of the two-dimensional (2D) triangular-lattice effective spin-1/2 antiferromagnet CeMgAl11O19. Analyzing the spin waves in the field-polarized ferromagnetic state, we find that the spin Hamiltonian is close to an exactly solvable 2D triangular-lattice XXZ model, where degenerate 120$^\circ$ ordered ground states - umbrella states - develop in the zero temperature limit. We then find that the observed zero-field spin excitation continuum matches the calculated ensemble of spin waves from the umbrella state manifold, and thus conclude that CeMgAl11O19 is the first example of an exactly solvable spin liquid on a triangular lattice where the spin excitation continuum arises from the ground state degeneracy.

cond-mat.str-el↗
arXiv2023

Spin-frame field theory of a three-sublattice antiferromagnet

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.

cond-mat.str-el↗
arXiv2022

Mechanics of a ferromagnetic domain wall

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.

cond-mat.mes-hall↗
arXiv2022

Magnon dynamics in a Skyrmion-textured domain wall of antiferromagnets

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 its non-trivial 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.

cond-mat.mes-hall↗
arXiv2022

Unified theory of spin and charge in a ferromagnet

We derive a unified theory of spin and charge degrees of freedom in a ferromagnet. The spin-transfer torque and spin electromotive force are examined from the coarse-grained perspective of collective coordinates. The resulting equations of motion reflect a balance of conservative, gyroscopic (Berry-phase), and dissipative forces. We then expand the space of collective coordinates by adding the electric charge. The adiabatic spin-transfer torque and spin emf turn out to be a gyroscopic force; their nonadiabatic counterparts are a dissipative force.

cond-mat.mes-hall↗
arXiv2022

Gyroscopic tensor of a magnetic soliton

The gyroscopic force acting on a ferromagnetic soliton reflects the tendency of spins to precess. Its components increase linearly with (generalized) velocities of the soliton. The proportionality coefficients form the gyroscopic tensor, a generalization of Thiele's gyrovector. Originally introduced as an auxiliary quantity, the gyroscopic tensor turns out to be a mathematical object of fundamental importance with a long history going back to Lagrange. We review the applications of the gyroscopic tensor and its historical roots.

nlin.PS↗
arXiv2022

How a skyrmion can appear both massive and massless

When a magnetic skyrmion is modeled as a point particle, its dynamics depends on the precise definition of the skyrmion center. The guiding-center position, defined as the first moment of the skyrmion density, exhibits Thiele's massless dynamics; position based on the first moment of magnetization component $m_z$ shows Larmor oscillations characteristic of a massive particle. We show that, even with the latter definition, the Larmor oscillations may be absent for certain types of external forces such as adiabatic spin torque. We offer an alternative mechanical model of a skyrmion featuring two coupled massless particles.

cond-mat.mes-hall↗
arXiv2022

Strong Magneto-Elastic Coupling in Mn$_3$X (X = Ge, Sn)

We measure the full elastic tensors of Mn$_3$Ge and Mn$_3$Sn as a function of temperature through their respective antiferromagnetic phase transitions. Large discontinuities in the bulk moduli at the Néel transitions indicate strong magnetoelastic coupling in both compounds. Strikingly, the discontinuities are nearly a factor of 10 larger in Mn$_3$Ge than in Mn$_3$Sn. We use the magnitudes of the discontinuities to calculate the pressure derivatives of the Néel temperature, which are 39 K/GPa 14.3 K/GPa for Mn$_3$Ge and Mn$_3$Sn, respectively. We measured in-plane shear modulus $c_{66}$, which couples strongly to the magnetic order, in magnetic fields up to 18 T and found quantitatively similar behavior in both compounds. Recent measurements have demonstrated strong piezomagnetism in Mn$_3$Sn: our results suggest that Mn$_3$Ge may be an even better candidate for this effect.

cond-mat.str-el↗
arXiv2021

Conserved momenta of ferromagnetic solitons through the prism of differential geometry

The relation between symmetries and conservation laws for solitons in a ferromagnet is complicated by the presence of gyroscopic (precessional) forces, whose description in the Lagrangian framework involves a background gauge field. This makes canonical momenta gauge-dependent and requires a careful application of Noether's theorem. We show that Cartan's theory of differential forms is a natural language for this task. We use it to derive conserved momenta of the Belavin--Polyakov skyrmion, whose symmetries include translation, global spin rotation, and dilation.

cond-mat.mes-hall↗
arXiv2021

Chiral magnetism: a geometric perspective

We discuss a geometric perspective on chiral ferromagnetism. Much like gravity becomes the effect of spacetime curvature in theory of relativity, the Dzyaloshinski-Moriya interaction arises in a Heisenberg model with nontrivial spin parallel transport. The Dzyaloshinskii-Moriya vectors serve as a background SO(3) gauge field. In 2 spatial dimensions, the model is partly solvable when an applied magnetic field matches the gauge curvature. At this special point, solutions to the Bogomolny equation are exact excited states of the model. We construct a variational ground state in the form of a skyrmion crystal and confirm its viability by Monte Carlo simulations. The geometric perspective offers insights into important problems in magnetism, e.g., conservation of spin current in the presence of chiral interactions.

cond-mat.mes-hall↗
arXiv2020

Theory of spin waves in a hexagonal antiferromagnet

We construct a field-theoretic description of spin waves in hexagonal antiferromagnets with three magnetic sublattices and coplanar $120^\circ$ magnetic order. The three Goldstone modes can be separated by point-group symmetry into a singlet $α_{0}$ and a doublet $(β_x,β_y)$. The $α_0$ singlet is described by the standard theory of a free relativistic scalar field. The field theory of the $(β_x,β_y)$ doublet is analogous to the theory of elasticity of a two-dimensional isotropic solid with distinct longitudinal and transverse "speeds of sound". The well-known Heisenberg models on the triangular and kagome lattices with nearest-neighbour exchange turn out to be special cases with accidental degeneracy of the spin-wave velocities. The speeds of sound can be readily calculated for any lattice model. We apply this approach to the compounds of the Mn$_3$X family with stacked kagome layers.

cond-mat.mes-hall↗
arXiv2020

Quantum statistics of vortices from a dual theory of the XY ferromagnet

We extend the well-known mapping between the easy-plane ferromagnet and electrostatics in $d=2$ spatial dimensions to dynamical and quantum phenomena in a $d=2+1$ spacetime. Ferromagnetic vortices behave like quantum particles with an electric charge equal to the vortex number and a magnetic flux equal to the transverse spin of the vortex core. Vortices with half-integer core spin exhibit fermionic statistics.

cond-mat.mes-hall↗