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Register a new userTopological energy bounds for frustrated magnets
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Derek Harland
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Frustrated magnets are known to support two-dimensional topological solitons, called skyrmions. A continuum model for frustrated magnets has recently been shown to support both two-dimensional skyrmions and three-dimensional knotted solitons (hopfions). In this note we derive lower bounds for the energies of these solitons expressed in terms of their topological invariants. The bounds are linear in the degree in the case of skyrmions and scale as the Hopf degree to the power 3/4 in the case of hopfions.
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We exhaustively construct instanton solutions and elucidate their properties in one-dimensional anti-ferromagnetic chiral magnets based on the $O(3)$ nonlinear sigma model description of spin chains with the Dzyaloshinskii-Moriya (DM) interaction. By introducing an easy-axis potential and a staggered magnetic field, we obtain a phase diagram consisting of ground-state phases with two points (or one point) in the easy-axis dominant cases, a helical modulation at a fixed latitude of the sphere, and a tricritical point allowing helical modulations at an arbitrary latitude. We find that instantons (or skyrmions in two-dimensional Euclidean space) appear as composite solitons in different fashions in these phases: temporal domain walls or wall-antiwall pairs (bions) in the easy-axis dominant cases, dislocations (or phase slips) with fractional instanton numbers in the helical state, and isolated instantons and calorons living on the top of the helical modulation at the tricritical point. We also show that the models with DM interaction and an easy-plane potential can be mapped into those without them, providing a useful tool to investigate the model with the DM interaction.
We construct a low-energy effective action for a two-dimensional non-relativistic topological (i.e. gapped) phase of matter in a continuum, which completely describes all of its bulk electrical, thermal, and stress-related properties in the limit of low frequencies, long distances, and zero temperature, without assuming either Lorentz or Galilean invariance. This is done by generalizing Luttingers approach to thermoelectric phenomena, via the introduction of a background vielbein (i.e. gravitational) field and spin connection a la Cartan, in addition to the electromagnetic vector potential, in the action for the microscopic degrees of freedom (the matter fields). Crucially, the geometry of spacetime is allowed to have timelike and spacelike torsion. These background fields make all natural invariances--- under U(1) gauge transformations, translations in both space and time, and spatial rotations---appear locally, and corresponding conserved currents and the stress tensor can be obtained, which obey natural continuity equations. On integrating out the matter fields, we derive the most general form of a local bulk induced action to first order in derivatives of the background fields, from which thermodynamic and transport properties can be obtained. We show that the gapped bulk cannot contribute to low-temperature thermoelectric transport other than the ordinary Hall conductivity; the other thermoelectric effects (if they occur) are thus purely edge effects. The coupling to reduced spacelike torsion is found to be absent in minimally-coupled models, and using a generalized Belinfante stress tensor, the stress response to time-dependent vielbeins (i.e. strains) is the Hall viscosity, which is robust against perturbations and related to the spin current as in earlier work.
We investigate the spin transport across the magnetic phase diagram of a frustrated antiferromagnetic insulator and uncover a drastic modification of the transport regime from spin diffusion to spin superfluidity. Adopting a triangular lattice accounting for both nearest neighbor and next-nearest neighbor exchange interactions with easy-plane anisotropy, we perform atomistic spin simulations on a two-terminal configuration across the full magnetic phase diagram. We found that as long as the ground state magnetic moments remain in-plane, irrespective of whether the magnetic configuration is ferromagnetic, collinear or non-collinear antiferromagnetic, the system exhibits spin superfluid behavior with a device output that is independent on the value of the exchange interactions. When the magnetic frustration is large enough to compete with the easy-plane anisotropy and cant the magnetic moments out of the plane, the spin transport progressively evolves towards the diffusive regime. The robustness of spin superfluidity close to magnetic phase boundaries is investigated and we uncover the possibility for {em proximate} spin superfluidity close to the ferromagnetic transition.
The ground state of frustrated (antiferromagnetic) triangular molecular magnets is characterized by two total-spin $S =1/2$ doublets with opposite chirality. According to a group theory analysis [M. Trif textit{et al.}, Phys. Rev. Lett. textbf{101}, 217201 (2008)] an external electric field can efficiently couple these two chiral spin states, even when the spin-orbit interaction (SOI) is absent. The strength of this coupling, $d$, is determined by an off-diagonal matrix element of the dipole operator, which can be calculated by textit{ab-initio} methods [M. F. Islam textit{et al.}, Phys. Rev. B textbf{82}, 155446 (2010)]. In this work we propose that Coulomb-blockade transport experiments in the cotunneling regime can provide a direct way to determine the spin-electric coupling strength. Indeed, an electric field generates a $d$-dependent splitting of the ground state manifold, which can be detected in the inelastic cotunneling conductance. Our theoretical analysis is supported by master-equation calculations of quantum transport in the cotunneling regime. We employ a Hubbard-model approach to elucidate the relationship between the Hubbard parameters $t$ and $U$, and the spin-electric coupling constant $d$. This allows us to predict the regime in which the coupling constant $d$ can be extracted from experiment.
We theoretically investigate the dynamics of magnetic hedgehogs, which are three-dimensional topological spin textures that exist in common magnets, focusing on their transport properties and connections to spintronics. We show that fictitious magnetic monopoles carried by hedgehog textures obey a topological conservation law, based on which a hydrodynamic theory is developed. We propose a nonlocal transport measurement in the disordered phase, where the conservation of the hedgehog flow results in a nonlocal signal decaying inversely proportional to the distance. The bulk-edge correspondence between hedgehog number and skyrmion number, the fictitious electric charges arising from magnetic dynamics, and the analogy between bound states of hedgehogs in ordered phase and the quark confinement in quantum chromodynamics are also discussed. Our study points to a practical potential in utilizing hedgehog flows for long-range neutral signal propagation or manipulation of skyrmion textures in three-dimensional magnetic materials.
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