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Register a new userMicroscopic approach to orientational order of domain walls
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We develop a fully microscopic, statistical mechanics approach to study phase transitions in Ising systems with competing interactions at different scales. Our aim is to consider orientational and positional order parameters in a unified framework. In this work we consider two dimensional stripe forming systems, where nematic, smectic and crystal phases are possible. We introduce a nematic order parameter in a lattice, which measures orientational order of interfaces. We develop a mean field approach which leads to a free energy which is a function of both the magnetization (density) and the orientational (nematic) order parameters. Self-consistent equations for the order parameters are obtained and the solutions are described for a particular system, the Dipolar Frustrated Ising Ferromagnet. We show that this system has an Ising-nematic phase at low temperatures in the square lattice, where positional order (staggered magnetization) is zero. At lower temperatures a crystal-stripe phase may appear. In the continuum limit the present approach connects to a Ginsburg-Landau theory, which has an isotropic-nematic phase transition with breaking of a continuous symmetry.
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A magnetic helix arises in chiral magnets with a wavelength set by the spin-orbit coupling. We show that the helimagnetic order is a nanoscale analog to liquid crystals, exhibiting topological structures and domain walls that are distinctly different from classical magnets. Using magnetic force microscopy and micromagnetic simulations, we demonstrate that - similar to cholesteric liquid crystals - three fundamental types of domain walls are realized in the helimagnet FeGe. We reveal the micromagnetic wall structure and show that they can carry a finite skyrmion charge, permitting coupling to spin currents and contributions to a topological Hall effect. Our study establishes a new class of magnetic nano-objects with non-trivial topology, opening the door to innovative device concepts based on helimagnetic domain walls.
We introduce a minimal model of solid-forming anisotropic molecules that displays, in thermal equilibrium, surface orientational order without bulk orientational order. The model reproduces the nonequilibrium behavior of recent experiments in that a bulk nonequilibrium structure grown by deposition contains regions of orientational order characteristic of the surface equilibrium. This order is deposited in general in a nonuniform way, because of the emergence of a growth-poisoning mechanism that causes equilibrated surfaces to grow slower than non-equilibrated surfaces. We use evolutionary methods to design oscillatory protocols able to grow nonequilibrium structures with uniform order, demonstrating the potential of protocol design for the fabrication of this class of materials.
Diffusive dynamics in presence of deep energy minima and weak nongradient forces can be coarse-grained into a mesoscopic jump process over the various basins of attraction. Combining standard weak-noise results with a path integral expansion around equilibrium, we show that the emerging transition rates satisfy local detailed balance (LDB). Namely, the log ratio of the transition rates between nearby basins of attractions equals the free-energy variation appearing at equilibrium, supplemented by the work done by the nonconservative forces along the typical transition path. When the mesoscopic dynamics possesses a large-size deterministic limit, it can be further reduced to a jump process over macroscopic states satisfying LDB. The persistence of LDB under coarse graining of weakly nonequilibrium states is a generic consequence of the fact that only dissipative effects matter close to equilibrium.
The effect of a change of noise amplitudes in overdamped diffusive systems is linked to their unperturbed behavior by means of a nonequilibrium fluctuation-response relation. This formula holds also for systems with state-independent nontrivial diffusivity matrices, as we show with an application to an experiment of two trapped and hydrodynamically coupled colloids, one of which is subject to an external random forcing that mimics an effective temperature. The nonequilibrium susceptibility of the energy to a variation of this driving is an example of our formulation, which improves an earlier version, as it does not depend on the time-discretization of the stochastic dynamics. This scheme holds for generic systems with additive noise and can be easily implemented numerically, thanks to matrix operations.
It is well documented that subjecting perpendicular magnetic films which exhibit the interfacial Dzyaloshinskii-Moriya interaction (DMI) to an in-plane magnetic field results in a domain wall (DW) energy, $sigma$, that is highly anisotropic with respect to the orientation of the DW in the film plane, $Theta$. We demonstrate that this anisotropy has a profound impact on the elastic response of the DW as characterized by the surface stiffness, $tilde{sigma}(Theta) = sigma(Theta) + sigma(Theta)$, and evaluate its dependence on the length scale of deformation. The influence of the stiffness on DW mobility in the creep regime is assessed, with analytic and numerical calculations showing trends in $tilde{sigma}$ that better represent experimental measurements of domain wall velocity in magnetic thin films compared to $sigma$ alone. Our treatment provides experimental support for theoretical models of the mobility of anisotropic elastic manifolds and makes progress toward a more complete understanding of magnetic domain wall creep.
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