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arXiv:1511.05193 · Physical Review Letters

Condensing Magnons in a Degenerate Ferromagnetic Spinor Bose Gas

Fang Fang, Ryan Olf, Shun Wu, Holger Kadau, Dan Stamper-Kurn

Published Mar 1, 2016• 25 citations
arXivHTMLPDF

Abstract

We observe the quasicondensation of magnon excitations within an F=1 ^{87}Rb spinor Bose-Einstein condensed gas. Magnons are pumped into a ferromagnetically ordered gas, allowed to equilibrate to a nondegenerate distribution, and then cooled evaporatively at near-constant net longitudinal magnetization, whereupon they condense. The critical magnon number, spatial distribution, and momentum distribution indicate that magnons condense in a potential that is uniform within the volume of the ferromagnetic condensate. The macroscopic transverse magnetization produced by the degenerate magnon gas remains inhomogeneous within the ∼10 s equilibration time accessed in our experiment, and includes signatures of Mermin-Ho spin textures that appear as phase singularities in the magnon quasicondensate wave function.

DOI
10.1103/physrevlett.116.095301

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We observe the quasicondensation of magnon excitations within an F=1 ^{87}Rb spinor Bose-Einstein condensed gas. Magnons are pumped into a ferromagnetically ordered gas, allowed to equilibrate to a nondegenerate distribution, and then cooled evaporatively at near-constant net longitudinal magnetization, whereupon they condense. The critical magnon number, spatial distribution, and momentum distribution indicate that magnons condense in a potential that is uniform within the volume of the ferromagnetic condensate. The macroscopic transverse magnetization produced by the degenerate magnon gas remains inhomogeneous within the ∼10 s equilibration time accessed in our experiment, and includes signatures of Mermin-Ho spin textures that appear as phase singularities in the magnon quasicondensate wave function.
We investigate the long-term dynamics of spin textures prepared by cooling unmagnetized spinor gases of F=1F=1F=1 87{}^{87}87Rb to quantum degeneracy, observing domain coarsening and a strong dependence of the equilibration dynamics on the quadratic Zeeman shift qqq. For small values of ∣q∣|q|∣q∣, the textures arrive at a configuration independent of the initial spin-state composition, characterized by large length-scale spin domains and the establishment of easy-axis (negative qqq) or easy-plane (positive qqq) magnetic anisotropy. For larger ∣q∣|q|∣q∣, equilibration is delayed as the spin-state composition of the degenerate spinor gas remains close to its initial value. These observations support the mean-field equilibrium phase diagram predicted for a ferromagnetic spinor Bose-Einstein condensate and also illustrate that equilibration is achieved under a narrow range of experimental settings, making the F=1F=1F=1 87{}^{87}87Rb gas more suitable for studies of nonequilibrium quantum dynamics.
We measure the dispersion relation, gap, and magnetic moment of a magnon in the ferromagnetic F = 1 spinor Bose-Einstein condensate of (87)Rb. From the dispersion relation we measure an average effective mass 1.033(2)(stat)(10)(sys) times the atomic mass, as determined by interfering standing and running coherent magnon waves within the dense and trapped condensed gas. The measured mass is higher than theoretical predictions of mean-field and beyond-mean-field Beliaev theory for a bulk spinor Bose gas with s-wave contact interactions. We observe a magnon energy gap of h × 2.5(1)(stat)(2)(sys) Hz, which is consistent with the predicted effect of magnetic dipole-dipole interactions. These dipolar interactions may also account for the high magnon mass. The effective magnetic moment of -1.04(2)(stat)(8)(sys) times the atomic magnetic moment is consistent with mean-field theory.
A quantised spin wave – magnon – in magnetic films can undergo Bose-Einstein condensation (BEC) into two energetically degenerate lowest-energy quantum states with nonzero wave vectors ±k BEC . This corresponds to two interfering condensates forming spontaneously in momentum space. Brillouin Light Scattering studies for a microwavepumped film with submicrometer spatial resolution experimentally confirm the existence of the two wavefunctions and show that their interference results in a nonuniform ground state of the condensate with the density oscillating in space. Moreover, fork dislocations in the density fringes provide direct experimental evidence for the formation of pinned half-quantum vortices in the magnon condensate. The measured amplitude of the density oscillation implies the formation of a nonsymmetric state that corresponds to nonequal occupation of two energy minima. We discuss the experimental findings and consider the theory of magnon condensates, which includes, to leading order, the contribution from the noncondensed magnons. The effect of the noncondensed magnon cloud is to increase the contrast of the asymmetric state and to bring about the experimental measurements. Introduction Magnons are quasiparticles corresponding to quantised spin waves that describe the collective motion of spins [1]. In recent years, it has become possible to realise a BEC of magnons in two remarkably different systems: in superfluid phases of an isotope of helium – Helium-3 at ultralow temperatures [2, 3] and in ferrimagnetic insulators [4, 5, 6, 7]. In the normal, noncondensed state, these magnetic materials exhibit a magnetically ordered state with a gas of magnons whose phases are not correlated. However, once condensation occurs, spins develop phase coherence resulting in a common global frequency and phase of precession. At room temperature, ferrimagnetic insulators, such as yttrium-iron garnet (YIG) films, together with a combination of an in-plane magnetic field and microwave radiation, are required for the magnon condensation [4, 5, 6, 7]. Therefore, in analogy with exciton– polariton condensates, this provides yet another example of a BEC of quasiparticle excitations in a solid-state system. Experimental Realisation of a Bose-Einstein Condensate of Magnons in an Epitaxial YIG-film A room-temperature Bose-Einstein condensate of magnons was created in an epitaxial YIG-film using an experimental setup shown in Fig. 25.1a, which, in general, is similar to that used in our previous studies [4, 5]. Given that magnons are quasiparticle excitations, their number is not conserved and, therefore, the chemical potential is zero.
We report on experimental observation of Bose-Einstein condensation (BEC)-like behavior of quantized electron spin waves (magnons) in a dense gas of spin-polarized atomic hydrogen. The magnons are trapped and controlled with inhomogeneous magnetic fields and described by a Schrödinger-like wave equation, in analogy to the BEC experiments with neutral atoms. We have observed the appearance of a sharp feature in the ESR spectrum displaced from the normal spin wave spectrum. We believe that this observation corresponds to a sudden growth of the ground-state population of the magnons and emergence of their spontaneous coherence for hydrogen gas densities exceeding a critical value, dependent on the trapping potential. We interpret the results as a BEC of nonequilibrium magnons which were formed by applying the rf power.
The formation of a Bose—Einstein condensate of magnons in a perpendicularly magnetized iron yttrium garnet film under radio-frequency pumping in a stripline has been studied experimentally. The characteristics of the nonlinear magnetic resonance and spatial distribution of the Bose—Einstein condensate of magnons in the gradient of a magnetic field have been analyzed. In these experiments, the system of bosonic magnons behaves in much the same way as the Bose—Einstein condensate of magnons in antiferromagnetic superfluid 3 He-B, which was previously studied in detail. The Bose—Einstein condensate of magnons forms a coherently precessing state having the properties of magnon superfluidity. Its stability is determined by the repulsion potential between excited magnons, which compensates the inhomogeneity of the magnetic field.
The Mermin-Ho and Anderson-Toulouse coreless vortices are demonstrated to be thermodynamically stable in ferromagnetic F = 1 spinor Bose-Einstein condensates under rotation. We have carried out extensive calculations of the Gross-Pitaevskii equations by assuming uniform density along the z axis and comparing the energies of other competing non-axis-symmetric or singular vortices. The phase diagram is thereby established in a plane of the rotation drive vs the total magnetization. Their stability is also checked by calculating collective modes based on the Bogoliubov equations.