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Bulletin of the American Physical Society

Magnetic domain dynamics in an insulating quantum ferromagnet

Christopher R. Tang, D. M. Silevitch, Jian Xu, Karin A. Dahmen, T. F. Rosenbaum

Published Mar 2, 2020• 0 citations
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The hydrodynamic equation of a spinor Bose-Einstein condensate (BEC) gives a simple description of spin dynamics in the condensate. We introduce the hydrodynamic equation of a ferromagnetic BEC with dissipation originating from the energy dissipation of the condensate. The dissipative hydrodynamic equation has the same form as an extended Landau-Lifshitz-Gilbert (LLG) equation, which describes the magnetization dynamics of conducting ferromagnets in which localized magnetization interacts with spin-polarized currents. Employing the dissipative hydrodynamic equation, we demonstrate the magnetic domain pattern dynamics of a ferromagnetic BEC in the presence and absence of a current of particles, and discuss the effects of the current on domain pattern formation. We also discuss the characteristic lengths of domain patterns that have domain walls with and without finite magnetization.
In zero magnetic field the ground-state manifold of a ferromagnetic spin-1 condensate is SO(3) and exhibits Z_{2} vortices as topological defects. We investigate the phase-ordering dynamics of this system after being quenched into this ferromagnetic phase from a zero-temperature unmagnetized phase. Following the quench, we observe the ordering of both magnetic and gauge domains. We find that these domains grow diffusively, i.e., with domain size L(t)∼t^{1/2}, and exhibit dynamic scale invariance. The coarsening dynamics progresses as Z_{2} vortices annihilate; however, we find that at finite energy a number of these vortices persist in small clumps without influencing magnetic or gauge order. We consider the influence of a small nonzero magnetic field, which reduces the ground-state symmetry, and show that this sets a critical length scale such that when the domains reach this size the system dynamically transitions in order parameter and scaling behavior from an isotropic to an anisotropic ferromagnetic superfluid.
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.