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Physical Review Letters

Investigation of spin supercurrents in B3

A. S. Borovik‐Romanov, Yu. M. Bunkov, Vladimir V. Dmitriev, Yu. M. Mukharsky, Dmitri A. Sergatskov

Published Apr 3, 1989• 126 citations
Publisher

Abstract

Magnetic supercurrents are observed in superfluid $^{3}\mathit{B}$. These supercurrents transport the longitudinal magnetization from one experimental cell to another through a narrow channel, driven by gradients of the order parameter. In both cells NMR is induced by separate signal generators at the same frequency. The supercurrent arises if a phase difference of the magnetization precession is established across the narrow channel. A critical spin supercurrent is measured at which precession phase slippage takes place. Experimental values of the critical spin supercurrent are in agreement with theoretical predictions.

DOI
10.1103/physrevlett.62.1631

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Magnetic supercurrents are observed in superfluid 3B^{3}\mathit{B}3B. These supercurrents transport the longitudinal magnetization from one experimental cell to another through a narrow channel, driven by gradients of the order parameter. In both cells NMR is induced by separate signal generators at the same frequency. The supercurrent arises if a phase difference of the magnetization precession is established across the narrow channel. A critical spin supercurrent is measured at which precession phase slippage takes place. Experimental values of the critical spin supercurrent are in agreement with theoretical predictions.
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The spin superfluidity -- superfluidity in the magnetic subsystem of a condensed matter -- is manifested as the spontaneous phase-coherent precession of spins first discovered in 1984 in ^3He-B. This superfluid current of spins -- spin supercurrent -- is one more representative of superfluid currents known or discussed in other systems, such as the superfluid current of mass and atoms in superfluid ^4He; superfluid current of electric charge in superconductors; superfluid current of hypercharge in Standard Model of particle physics; superfluid baryonic current and current of chiral charge in quark matter; etc. Spin superfluidity can be described in terms of the Bose condensation of spin waves -- magnons. We discuss different states of magnon superfluidity with different types of spin-orbit coupling: in bulk ^3He-B; magnetically traped "Q-balls" at very low temperatures; in ^3He-A and ^3He-B immerged in deformed aerogel; etc. Some effects in normal ^3He can also be treated as a magnetic BEC of fermi liquid. A very similar phenomena can be observed also in a magnetic systems with dinamical frequensy shift, like MnC03. We will discuss the main experimental signatures of magnons superfluidity: (i) spin supercurrent, which transports the magnetization on a macroscopic distance more than 1 cm long; (ii) spin current Josephson effect which shows interference between two condensates; (iii) spin current vortex -- a topological defect which is an analog of a quantized vortex in superfluids, of an Abrikosov vortex in superconductors, and cosmic strings in relativistic theories; (iv) Goldstone modes related to the broken U(1) symmetry -- phonons in the spin-superfluid magnon gas; etc. For recent review see Yu. M. Bunkov and G. E. Volovik J. Phys. Cond. Matter. 22, 164210 (2010)
We show that spinor Bose gases subject to a quadratic Zeeman effect exhibit coexisting superfluidity and spin superfluidity, and study the interplay between these two distinct types of superfluidity. To illustrate that the basic principles governing these two types of superfluidity are the same, we describe the magnetization and particle-density dynamics in a single hydrodynamic framework. In this description spin and mass supercurrents are driven by their respective chemical potential gradients. As an application, we propose an experimentally accessible stationary state, where the two types of supercurrents counterflow and cancel each other, thus resulting in no mass transport. Furthermore, we propose a straightforward setup to probe spin superfluidity by measuring the in-plane magnetization angle of the whole cloud of atoms. We verify the robustness of these findings by evaluating the four-magnon collision time, and find that the time scale for coherent (superfluid) dynamics is separated from that of the slower incoherent dynamics by one order of magnitude. Comparing the atom and magnon kinetics reveals that while the former can be hydrodynamic, the latter is typically collisionless under most experimental conditions. This implies that, while our zero-temperature hydrodynamic equations are a valid description of spin transport in Bose gases, a hydrodynamic description that treats both mass and spin transport at finite temperatures may not be readily feasible.
The spin superfluidity -- superfluidity in the magnetic subsystem of a condensed matter - is manifested as the spontaneous phase-coherent precession of spins first discovered in 1984 in 3He-B. This superfluid current of spins - spin supercurrent - is one more representative of superfluid currents known or discussed in other systems, such as the superfluid current of mass and atoms in superfluid 4He; superfluid current of electric charge in superconductors; superfluid current of hypercharge in Standard Model of particle physics; superfluid baryonic current and current of chiral charge in quark matter; etc. Spin superfluidity can be described in terms of the Bose condensation of spin waves - magnons. We discuss different phases of magnon superfluidity, including those in magnetic trap; and signatures of magnons superfluidity: (i) spin supercurrent, which transports the magnetization on a macroscopic distance more than 1 cm long; (ii) spin current Josephson effect which shows interference between two condensates; (iii) spin current vortex - a topological defect which is an analog of a quantized vortex in superfluids, of an Abrikosov vortex in superconductors, and cosmic strings in relativistic theories; (iv) Goldstone modes related to the broken U(1) symmetry - phonons in the spin-superfluid magnon gas; etc. We also touch the topic of spin supercurrent in general including spin Hall and intrinsic quantum spin Hall effects.
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.
In transverse NMR at high rf excitation, it is possible to separate a 3B^{3}\mathit{B}3B sample into two magnetic domains. In one domain the spins are precessing coherently with a large tilting angle in relation to the polarizing magnetic field while in the other they are stationary and oriented parallel to the field. We have studied the two-domain system during vortex-free rotation and found that the boundary region between the precessing and static domains is sensitive to superfluid counterflow, flowing parallel to the boundary. The volume of the precessing domain decreases and the NMR absorption, associated with spin diffusion across the boundary, increases. The shift of the domain boundary is analyzed in terms of the competition between the kinetic energy of counterflow and the gradient in the Zeeman energy. From the shift we obtain the superfluid density anisotropy, induced by the magnetic field. A calculation in the weak-coupling approximation explains only half of the measured ansiotropy at low pressures. At high pressures the discrepancy is smaller.