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Physical Review Letters

Persistent spin precession in B3 in the regime of vanishing quasiparticle density

Yu. M. Bunkov, S. N. Fisher, A. M. Guénault, G. R. Pickett

Published Nov 23, 1992• 80 citations
Publisher

Abstract

We describe the observation of an extremely long-lived induction decay signal of the precession of the magnetization in superfluid $^{3}\mathit{B}$. This is probably the first evidence of the formation of a coherent quantum magnetic state with deflected magnetization. This state can be excited at a frequency of 1 MHz at temperatures of about 0.1${\mathit{T}}_{\mathit{c}}$ and has been observed to persist for periods up to 25 s. The properties are entirely distinct from those of the well-known long-lived induction decay signal arising from a homogeneously precessing domain.

DOI
10.1103/physrevlett.69.3092

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We describe the observation of an extremely long-lived induction decay signal of the precession of the magnetization in superfluid 3B^{3}\mathit{B}3B. This is probably the first evidence of the formation of a coherent quantum magnetic state with deflected magnetization. This state can be excited at a frequency of 1 MHz at temperatures of about 0.1Tc{\mathit{T}}_{\mathit{c}}Tc​ and has been observed to persist for periods up to 25 s. The properties are entirely distinct from those of the well-known long-lived induction decay signal arising from a homogeneously precessing domain.
The B phase of superfluid 3{}^{3}3He can support regions of extremely long-lived coherent spin precession at ultralow temperatures, known as persistent precessing domains (PPD). The domains have been described in terms of a Bose-Einstein condensate of magnons and in terms of Q balls in field theory. The domains form in a magnetic field minimum along the vertical axis of a cylindrical cell. When far from the ends of the cell, the PPD lifetime grows exponentially on decreasing temperature. When the PPD is close to the horizontal end wall of the cell, an extra surface dissipation mechanism dominates at low temperatures. We present measurements of the PPD generated at various locations in the cell over a broad range of temperatures below 0.3 TC{T}_{C}TC​. We compare the measured properties with theoretical expectations for spin-wave modes. We present model calculations of different dissipation mechanisms and we compare these to the measured lifetimes.
States with a coherent precession of magnetization such as a homogeneously precessing domain or a persistently precessing domain created in the superfluid 3{}^{3}3He-BBB represent the macroscopic examples of the Bose-Einstein condensates of magnons. Once the magnons form one of these states, this many-magnon coherent quantum state is described by a ``single-magnon wave function'' (or an order parameter). A suitable external perturbation may cause the condensate to oscillate around the state of coherent precession, which demonstrates a collective rigidity of the condensate against scattering a single magnon out of it. The states corresponding to a free coherent precession of magnetization are degenerate in the phase of precession, so there exist oscillations around such states with a gapless dispersion relation, known as the Goldstone modes. Here, we present both experimental and theoretical results of the study of the spin density oscillations superposed on a homogeneously precessing domain in superfluid 3{}^{3}3He-BBB in the presence of a high-frequency excitation field Brf{B}_{\text{rf}}Brf​. We show that the presence of this field lifts the degeneracy of the precessing state with respect to the phase of precession, that is, it violates the symmetry of the magnon condensate, and former Goldstone modes become non-Goldstone ones, as they acquire the energy gap in their spectrum.
Bose-Einstein condensation (BEC) is a quantum phenomenon of formation of a collective quantum state in which a macroscopic number of particles occupy the lowest energy state and thus is governed by a single wavefunction. Here we highlight the BEC in a magnetic subsystem--the BEC of magnons, elementary magnetic excitations. The magnon BEC is manifested as the spontaneously emerging state of the precessing spins, in which all spins precess with the same frequency and phase even in an inhomogeneous magnetic field. The coherent spin precession was observed first in superfluid (3)He-B and this domain was called the homogeneously precessing domain (HPD). The main feature of the HPD is the induction decay signal, which ranges over many orders of magnitude longer than is prescribed by the inhomogeneity of magnetic field. This means that spins precess not with a local Larmor frequency, but coherently with a common frequency and phase. This BEC can also be created and stabilized by continuous NMR pumping. In this case the NMR frequency plays the role of a magnon chemical potential, which determines the density of the magnon condensate. The interference between two condensates has also been demonstrated. It was shown that HPD exhibits all the properties of spin superfluidity. The main property is the existence of a spin supercurrent. This spin supercurrent flows separately from the mass current. Transfer of magnetization by the spin supercurrent by a distance of more than 1 cm has been observed. Also related phenomena have been observed: the spin current Josephson effect; the phase-slip processes at the critical current; and the spin current vortex--a topological defect which is the analog of a quantized vortex in superfluids and of an Abrikosov vortex in superconductors; and so on. It is important to mention that the spin supercurrent is a magnetic phenomenon, which is not directly related to the mass superfluidity of (3)He: it is the consequence of a specific antiferromagnetic ordering in superfluid (3)He. Several different states of coherent precession have been observed in (3)He-B: the homogeneously precessing domain (HPD); a persistent signal formed by Q-balls at very low temperatures; coherent precession with fractional magnetization; and two new modes of coherent precession in compressed aerogel. In compressed aerogel the coherent precession has been also found in (3)He-A. We demonstrate that the coherent precession of magnetization is a true BEC of magnons, with the magnon interaction term in the Gross-Pitaevskii equation being provided by spin-orbit coupling which is different for different states of the magnon BEC.
We report experimental realization of a quantum time quasicrystal and its transformation to a quantum time crystal. We study Bose-Einstein condensation of magnons, associated with coherent spin precession, created in a flexible trap in superfluid ^{3}He-B. Under a periodic drive with an oscillating magnetic field, the coherent spin precession is stabilized at a frequency smaller than that of the drive, demonstrating spontaneous breaking of discrete time translation symmetry. The induced precession frequency is incommensurate with the drive, and hence, the obtained state is a time quasicrystal. When the drive is turned off, the self-sustained coherent precession lives a macroscopically long time, now representing a time crystal with broken symmetry with respect to continuous time translations. Additionally, the magnon condensate manifests spin superfluidity, justifying calling the obtained state a time supersolid or a time supercrystal.
Helium stays in liquid form down to absolute zero temperature. Since the effects of quantum mechanics become particularly evident at low temperatures, helium is an ideal system for experimental studies of macroscopic quantum phenomena. One of the most remarkable of these is the transition into zero-viscosity superfluid phase. In case of fermionic helium-3 isotope, this transition occurs at temperatures below 0.003 K. In the low-temperature B phase of superfluid helium-3, the transport of both mass and magnetization occur without losses. The spin superfluidity gives rise to spontaneous coherent long-living precession of magnetization observed in nuclear magnetic resonance (NMR) experiments. The coherent precession can be described in terms of spin-wave excitations, or in the language of Bose-Einstein condensation (BEC) of magnon quasiparticles. In this dissertation, we trap these quasiparticle condensates at selected locations in the superfluid order parameter texture, using both textural and magnetic energies for confinement. The sample is cooled to ultra-low temperatures in rotating adiabatic demagnetization refrigerator. Careful characterization of the creation and the decay of the trapped magnon BEC reveals nonhydrodynamic spin diffusion as the main temperature-dependent source of relaxation. Using this property, we suggest magnon-BEC-based microkelvin thermometry in helium-3 systems. Both the relaxation rate and the precession frequency of magnetization are sensitive to changes in the properties of the surrounding superfluid at the lowest temperatures and clearly more informative than conventional NMR techniques which freeze to a temperature-independent state. Here we have used the magnon BECs to detect quantized vortices, gravity waves on the free surface of superfluid, and long-living textural defects related to the creation and the annihilation of phase boundaries. We have also found enhanced zero-temperature relaxation of magnon BEC due to free surface. We propose that it originates from the bound quasiparticle states at the surface which supposedly have Majorana nature following from the topology of helium-3. Owing to diverse properties, superfluid helium-3 serves as an experimentally accessible model system for phenomena elsewhere in physics. We have found self-trapping of magnons towards a box-like confinement potential via coupling with the order parameter which resembles the Q-ball in quantum field theories. We have also observed the interplay between three low-energy spin-wave modes, one of which acquires mass due to spin-orbit interaction and becomes similar to the light Higgs particle considered in extensions of Standard Model.
The conventional magnon Bose-Einstein condensation (BEC of magnons with k = 0) is a coherent state of excited magnons described by a common wave function. It was observed first in antiferromagnetic superfluid states of 3He. Here we report on the discovery of a very similar magnon BEC in ferrimagnetic film at room temperature. The experiments were performed in Yttrium Iron Garnet (YIG) films at a magnetic field oriented perpendicular to the film. The high-density quasiequilibrium state of excited magnon was formed by methods of pulse and/or Continuous Waves (CW) magnetic resonance. We have observed a Long Lived Induction Decay Signals (LLIDS), well known as a signature of spin superfluidity. We demonstrate that the BEC state may maintain permanently by continuous replenishment of magnons with a small radiofrequency (RF) field. Our finding opens the way for development of potential supermagnonic applications at an ambient conditions.