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arXiv:2008.08175 · Physical Review Research

Dark-soliton-like magnetic domain walls in a two-dimensional ferromagnetic superfluid

Xiaoquan Yu, P. B. Blakie

Published Apr 14, 2021• 19 citations
arXivHTMLPDF

Abstract

We report a stable magnetic domain wall in a uniform ferromagnetic spin-1 condensate, characterized by the magnetization having a dark soliton profile with nonvanishing superfluid density.We find exact stationary solutions for a particular ratio of interaction parameters with and without magnetic fields, and develop an accurate analytic solution applicable to the whole ferromagnetic phase.In the absence of magnetic fields, this domain wall relates various distinct solitary excitations in binary condensates through SO(3) spin rotations, which otherwise are unconnected.Remarkably, studying the dynamics of a quasi-two-dimensional (quasi-2D) system we show that standing wave excitations of the domain wall oscillate without decay, being stable against the snake instability.The domain wall is dynamically unstable to modes that cause the magnetization to grow perpendicularly while leaving the domain wall unchanged.Real-time dynamics in the presence of white noise reveals that this "spin twist" instability does not destroy the topological structure of the magnetic domain wall.

DOI
10.1103/physrevresearch.3.023043

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We report a stable magnetic domain wall in a uniform ferromagnetic spin-1 condensate, characterized by the magnetization having a dark soliton profile with nonvanishing superfluid density.We find exact stationary solutions for a particular ratio of interaction parameters with and without magnetic fields, and develop an accurate analytic solution applicable to the whole ferromagnetic phase.In the absence of magnetic fields, this domain wall relates various distinct solitary excitations in binary condensates through SO(3) spin rotations, which otherwise are unconnected.Remarkably, studying the dynamics of a quasi-two-dimensional (quasi-2D) system we show that standing wave excitations of the domain wall oscillate without decay, being stable against the snake instability.The domain wall is dynamically unstable to modes that cause the magnetization to grow perpendicularly while leaving the domain wall unchanged.Real-time dynamics in the presence of white noise reveals that this "spin twist" instability does not destroy the topological structure of the magnetic domain wall.
Exact solutions of magnetic field-driven propagating topological solitons are found in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates, manifesting themselves as dark-soliton-like magnetic domain walls. Such solitons have two types: a low energy solution with positive inertial mass and a higher energy solution with negative inertial mass. Both types become identical at the maximum speed, a new speed bound that is different from speed limits set by the elementary excitations. The physical mass, which accounts for the number density dip, is negative for both types. In a finite one-dimensional system subject to a linear potential, the soliton undergoes oscillations, and transitions between the two types occurring at the maximum speed.
We investigate magnetic solitons in an immiscible binary Bose-Einstein condensate (BEC), where the intraspecies interactions are slightly weaker than the interspecies interactions. While their density and phase profiles are analogous to dark-bright solitons, other characteristic properties such as maximum velocities, widths, total density depletions, and in-trap oscillations are different. In the low-velocity regime, a magnetic soliton reduces to a traveling pair of magnetic domain walls. Collisional behaviors of the solitons are also briefly discussed. We further demonstrate that these solitonic states can be realized in a quasi-one-dimensional spin-1 ferromagnetic BEC with a weak spin interaction, e.g., a 87Rb^{87}\mathrm{Rb}87Rb BEC.
Abstract We numerically investigate the collision dynamics of a dark soliton with a domain wall in an immiscible, two-component Bose-Einstein condensate confined in a quasi-two-dimensional harmonic trap. The role of the inter-species interaction strength δ=g12/g11\delta = g_{12}/g_{11}δ=g12​/g11​ and the soliton's initial displacement Δx\Delta_xΔx​ is investigated thoroughly. Our results reveal a clear bifurcation into two distinct dynamical regimes: a penetrationregimepenetration regimepenetrationregime, where the soliton decays into vortex pairs that cross the interface, and a non−penetrationregimenon-penetration regimenon−penetrationregime, where the soliton's energy is dissipated at the interface through sound emission and vortex annihilation. We present a phase diagram that maps these outcomes across the (δ,Δx)(\delta, \Delta_x)(δ,Δx​) parameter space. Furthermore, within the non-penetration regime, we identify a complex excited state characterized by the combination of component breakup in one component and vortex formation in the other. This work provides the systematic study of dark soliton-domain wall interactions in a 2D phase-separated binary BEC, offering new insights into interfacial dynamics and non-equilibrium transport in multi-component quantum fluids.
Compared with a scalar Bose-Einstein condensate (BEC), a spinor BEC supports richer phenomena because of its internal spin degrees of freedom, including topological solitons such as domain walls or skyrmions. Here, we theoretically reveal three distinct axisymmetric soliton structures formed as a circular domain wall in a spin-1 BEC, connected within fixed winding numbers. We refer to these structures as the broken-axisymmetry (BA)-skin, antiferromagnetic (AF)-skin and normal-core phases. Their occurrence is controlled by the two dimensionless parameters in the absence of linear Zeeman coefficient p=0p=0p=0: q/μq/μq/μ, the ratio of the quadratic Zeeman coefficient to the chemical potential, and cs/cnc_s/c_ncs​/cn​, the ratio of spin interaction to the density interaction. The BA-skin and AF-skin phases exhibit local easy-plane magnetic order and local easy-plane spin-nematic order, respectively, while the normal-core phase is similar to a doubly quantized vortex analogous to that of a scalar BEC with a density depletion at the center. We obtain semi-analytical estimates of selected transition boundaries separating these phases by analyzing the Bogoliubov-de Gennes equation and also numerically confirm them by solving the Gross-Pitaevskii equation. We estimate the skyrmion radius using a hydrostatic approximation and compare the result with numerical solutions. We envision our results on skyrmions in a spin-1 BEC can trigger further investigation on novel soliton structures in a magnetic superfluid.
Spinful superfluids of ultracold atoms are ideal for investigating the intrinsic properties of spin current and texture because they are realized in an isolated, nondissipative system free from impurities, dislocations, and thermal fluctuations. This study theoretically reveals the impact of spin current on a magnetic domain wall in spinful superfluids. An exact wall solution is obtained in the ferromagnetic phase of a spin-1 Bose-Einstein condensate with easy-axis anisotropy at zero temperature. The bosonic-quasiparticle mechanics analytically show that the spin current along the wall becomes unstable if the velocity exceeds the critical spin-current velocities, leading to complicated situations because of the competition between transverse magnons and ripplons. Our direct numerical simulation reveals that this system has a mechanism to generate an eccentric fractional skyrmion, which has a fractional topological charge, but its texture is not similar to that of a meron. This mechanism is in contrast to the generation of conventional skyrmions in easy-axis magnets. The theoretical findings can be examined in the same situation as in a recent experiment on ultracold atoms. In terms of the universality of spontaneous symmetry breaking, unexplored similar phenomena are expected in different physical systems with the same broken symmetry.