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Anomalous dynamics of magnetic field-driven propagating magnetic domain walls

Xiaoquan Yu, P. B. Blakie

Published Apr 27, 2021• 1 citation
OpenAlex

Abstract

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.

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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.
Exact propagating topological solitons are found in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates, manifesting themselves as kinks in the transverse magnetization. Propagation is only possible when the symmetry-breaking longitudinal magnetic field is applied. Such solitons have two types: a low energy branch with positive inertial mass and a higher energy branch 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 caused by transitions between the two types occurring at the maximum speed.
We develop an analytical description of static ferrodark solitons, the Z2{\mathbb{Z}}_{2}Z2​ topological defects in the magnetic order, in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates. We find that the type-I ferrodark soliton has a single width while the type-II ferrodark soliton exhibits two characteristic length scales. The proposed Ans\"atze show excellent agreement with numerical results. Spin-singlet amplitudes, nematic tensor densities, and nematic currents of ferrodark solitons are also discussed. The Z2{\mathbb{Z}}_{2}Z2​ topological defects in the mass superfluid order, dark-dark-dark vector solitons, are obtained exactly in the parameter regime where exact ferrodark solitons exist. The dark-dark-dark vector soliton has higher excitation energy than ferrodark solitons.
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.
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.
The recent experimental realization of spin-orbit coupling for ultracold atomic gases opens a new avenue for engineering solitons with internal spatial structures through tuning atomic band dispersions. However, the types of the resulting stripe solitons in a spin-1/2 Bose-Einstein condensate (BEC) have been limited to dark-dark or bright-bright with the same density profiles for different spins. Here we propose that general types of stripe solitons, including magnetic stripe solitons (e.g., dark-bright) and localized stripe waves (neither bright nor dark), could be realized in a spin-1 BEC with widely tunable band dispersions through modulating the coupling between three spin states and the linear momentum of atoms. Surprisingly, a moving magnetic stripe soliton can possess both negative and positive effective masses at different velocities, leading to a zero-mass soliton at certain velocity. Our work showcases the great potential of realizing novel types of solitons through band dispersion engineering, which may provide a new approach for exploring soliton physics in many physical branches.
We study magnetic solitons, solitary waves of spin polarization (i.e., magnetization), in binary Bose-Einstein condensates in the presence of Rabi coupling. We show that the system exhibits two types of magnetic solitons, called $2\ensuremath{\pi}$ and $0\ensuremath{\pi}$ solitons, characterized by a different behavior of the relative phase between the two spin components. $2\ensuremath{\pi}$ solitons exhibit a $2\ensuremath{\pi}$ jump of the relative phase, independent of their velocity, the static domain wall explored by Son and Stephanov being an example of such $2\ensuremath{\pi}$ solitons with vanishing velocity and magnetization. $0\ensuremath{\pi}$ solitons instead do not exhibit any asymptotic jump in the relative phase. Systematic results are provided for both types of solitons in uniform matter. Numerical calculations in the presence of a one-dimensional harmonic trap reveal that a $2\ensuremath{\pi}$ soliton evolves in time into a $0\ensuremath{\pi}$ soliton, and vice versa, oscillating around the center of the trap. Results for the effective mass, the Landau critical velocity, and the role of the transverse confinement are also discussed.