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Physical review. B, Condensed matter

Magnetic-field-induced supercurrents in He3 — A and He3 — A1

Paul Muzikar

Published Oct 1, 1980• 4 citations
Publisher

Abstract

This paper discusses how a spatially inhomogeneous magnetic field can induce super spin currents in $^{3}\mathrm{He}$---$A$ and super number currents in $^{3}\mathrm{He}$---${A}_{1}$. These are analogous to previously discussed currents induced in $^{3}\mathrm{He}$---$A$ by an inhomogeneous scalar potential, which are related to the existence of an intrinsic angular momentum. The sign of the ${A}_{1}$ current depends upon which spin population is superfluid.

DOI
10.1103/physrevb.22.3200

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This paper discusses how a spatially inhomogeneous magnetic field can induce super spin currents in 3He^{3}\mathrm{He}3He---AAA and super number currents in 3He^{3}\mathrm{He}3He---A1{A}_{1}A1​. These are analogous to previously discussed currents induced in 3He^{3}\mathrm{He}3He---AAA by an inhomogeneous scalar potential, which are related to the existence of an intrinsic angular momentum. The sign of the A1{A}_{1}A1​ current depends upon which spin population is superfluid.
It is shown here that superfluids (such as 3He^{3}\mathrm{He}3He-AAA and Bose-condensed spin-polarized hydrogen) whose order parameters transform like an angular momentum eigenstate $|j, m\ensuremath{\ne}0〉$ will have similar superfluidity---similar Josephson and vorticity equations. In particular, if spin-polarized hydrogen condenses into the bbb state as currently believed, it will not have a stable superflow. Nonuniform magnetic fields can also induce in it a persistent current similar to that of 3He^{3}\mathrm{He}3He-AAA.
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.
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)
The magnitude, sign, and momentum dependence of the effective interaction between He3{\mathrm{He}}^{3}He3 atoms in superfluid He4{\mathrm{He}}^{4}He4 are derived from the experimental data. Calculations of the Fermi-liquid parameters for the normal state of He3{\mathrm{He}}^{3}He3 in solution yield results in agreement with experiment; the temperature for a superfluid transition associated with the He3{\mathrm{He}}^{3}He3 is estimated to be \ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ \ifmmode^\circ\else\textdegree\fi{}K.
In the article by Shevchenko and A. S. Rukin, Pis'ma v Zh. Eksp. Teor. Fiz. 90, 46 (2009), it has been found that quantized vortices in superfluid systems acquire a charge in a magnetic field. A compensating charge with the opposite sign on a surface of the system can be at a macroscopic distance apart from the charge of the vortex. It is shown that as a result the total energy of the vortex charge and the compensating charge can be negative in the presence of an inhomogeneous electric field, normal to a homogeneous magnetic field. The conditions under which this leads to the spontaneous emergence of quantized vortices in the system are found. A possibility to observe the effect in He II, Bose gases of alkali metals and systems with spatially indirect excitons is discussed.
In the superfluid 3 He A-phase, the edge mass current which accompanies surface Andreev bound states flows due to topological features. We discuss the relation between the angular momentum by the edge mass current and the macroscopic intrinsic angular momentum L = N ℏ/2 by the Cooper pairs with aligned angular momenta, based on the quasi-classical theory. At the low temperature limit, half of the edge mass current from the bound state is canceled by that from the continuum state. Then, the magnitude of the total angular momentum is L = N ℏ/2 which corresponds to the macroscopic intrinsic angular momentum of N particles. The net angular momentum decreases monotonously toward zero at the transition temperature. However, that is larger than the macroscopic intrinsic angular momentum expected from the same behavior of the superfluid density in middle temperatures.