Antiferromagnetic insulators (AFIs) were proposed as channels for dissipationless spin-superfluid transport: a spin accumulation applied across a metal|AFI|metal heterostructure drives a phase gradient of the Néel order parameter, carrying spin as a supercurrent. The originating theory (Takei, Halperin, Yacoby, and Tserkovnyak, 2014) is restricted to the low-temperature, condensate-dominated regime and identifies as open the extension to finite temperature, where the thermal magnon cloud contributes appreciably and a two-fluid theory is required, together with experimental determination of the antiferromagnet|metal spin-mixing conductances and low-temperature bulk damping and anisotropy parameters on which the quantitative device predictions depend. Later work built fragments of this program (a two-fluid theory for ferromagnet-like insulators, a Landau–Khalatnikov-style theory with Boltzmann-derived dissipation for ferro- and antiferromagnets, viscous magnon hydrodynamics in collinear AFs) and produced nonlocal transport experiments in Cr2O3, hematite, and CrCl3 whose interpretation — spin superfluidity versus thermal-magnon/spin-Seebeck transport — remains contested. A quantitative, experimentally validated finite-temperature theory of spin transport in AFIs, including condensate–thermal-cloud coupling, realistic dissipation, and interface conductances, remains an open problem.

Background

An antiferromagnetic insulator is a crystal in which magnetic ions on two interpenetrating sublattices carry oppositely oriented magnetic moments, so the net magnetization vanishes while the staggered order is described by a unit vector called the Néel vector. The elementary spin excitations of such a magnet are magnons (quantized spin waves). In an easy-plane antiferromagnet — where the energy is minimized when the Néel vector lies in a particular crystallographic plane — the azimuthal angle of the Néel vector in that plane is an approximate U(1) Goldstone mode, and a gradient of this angle carries a spin angular-momentum current, called a spin supercurrent, in close analogy with mass flow in a superfluid; this phenomenon is referred to as spin superfluidity. In a metal with strong spin–orbit coupling, a charge current can generate a transverse spin accumulation via the spin Hall effect, and its inverse allows spin flow to be converted back into a measurable voltage, so that a metal|AFI|metal structure with two platinum contacts can inject and detect spin through the insulator without charge current flowing in it. The efficiency of spin transfer at such a magnetic-insulator|metal interface is quantified by the spin-mixing conductance, a boundary parameter measurable via spin pumping, while relaxation of the magnetic order in the bulk is parametrized by a Gilbert damping constant (often extracted from antiferromagnetic-resonance linewidths) and in-plane magnetic anisotropy sets a pinning strength that a supercurrent must exceed. The proposal of Takei, Halperin, Yacoby, and Tserkovnyak (Phys. Rev. B 90, 094408 (2014)) showed, using Landau–Lifshitz dynamics (the standard continuum equations of motion for magnetization) and magneto-circuit theory, that a spin bias applied across a compensated AFI drives spin-superfluid transport whose crossover length, critical currents, and detectable nonlocal drag signal are fixed by the spin-mixing conductance, the bulk damping, and the anisotropy, and it estimated device-relevant numbers for the nearly isotropic cubic antiferromagnets RbMnF3 and KNiF3. That theory is deliberately restricted to temperatures well below the Néel temperature (the ordering temperature below which antiferromagnetic order exists), where transport is mediated essentially by the condensate; at elevated temperatures a population of thermal magnons (the normal, incoherent spin excitations) contributes, and the paper states that a theory of finite-temperature spin transport in antiferromagnets has two-fluid character — condensate plus thermal cloud — for which the two-fluid hydrodynamics of Landau and Khalatnikov for superfluid 4He should supply the long-wavelength, collision-dominated description. Subsequent literature developed parts of this picture: a two-fluid theory of thermal and condensed magnons exists for easy-plane magnetic insulators in the regime of a magnetic-field-tuned magnon Bose–Einstein condensate, i.e. a coherently and macroscopically occupied magnon mode (Flebus et al., 2016); Sonin (2019) constructed a Landau–Khalatnikov-style two-fluid theory of superfluid spin transport in ferro- and antiferromagnets with dissipation coefficients computed from a Boltzmann equation for magnons scattered by defects; Tatara and Ortiz Pauyac (2019) formulated a finite-temperature theory of spin transport through an antiferromagnetic insulator in terms of magnon correlation functions and a temperature-dependent damping, which reaches high-temperature regimes but describes thermal-magnon diffusion and contains no condensate component; magnon-viscous hydrodynamics for collinear antiferromagnets was formulated recently (2025); and nonlocal spin-transport experiments on Cr2O3, hematite (α-Fe2O3), and CrCl3 have explored the temperature and field dependence of long-distance signals, with a live controversy over whether the observed signals arise from superfluid spin transport or from the spin Seebeck effect (spin flow driven by a heat current) and related thermal-magnon diffusion.

Problem Statement

Construct and validate a quantitative finite-temperature theory of spin transport through easy-plane antiferromagnetic insulators in metal|AFI|metal heterostructures, and obtain the interface and bulk parameters it requires. Specifically: (1) develop the two-fluid description of antiferromagnetic spin transport in which the magnon condensate (carrying the spin supercurrent, described by a phase gradient of the Néel order parameter) and the thermal cloud of incoherent magnons are treated as coupled components with realistic dissipation — transport coefficients derived microscopically rather than from a single Gilbert damping parameter — valid in the collision-dominated long-wavelength regime; (2) obtain from this theory the temperature dependence of the nonlocal transport signals (spin current, drag coefficient, and crossover from coherent, weakly decaying transport to diffusive thermal-magnon transport), the behavior at elevated temperatures up to and approaching the Néel temperature, and the thresholds (critical spin currents set by anisotropy pinning) as functions of temperature; (3) obtain the antiferromagnet|metal spin-mixing conductance for representative compensated antiferromagnetic interfaces, including its dependence on interfacial disorder, materials, and preparation, together with the low-temperature bulk damping and anisotropy parameters of candidate antiferromagnetic insulators, so that the theory's device-relevant predictions (transport crossover lengths, critical currents) become quantitative; and (4) resolve the mechanistic ambiguity in existing nonlocal measurements by establishing criteria or experiments that distinguish genuine superfluid spin transport from spin-Seebeck/heat-transport and thermal-magnon diffusion signals. The single scientific objective uniting these items is to extend the theory of superfluid spin transport in antiferromagnetic insulators from the low-temperature, condensate-dominated regime, where it is established, to the experimentally relevant finite-temperature regime, with a predictive, parameter-calibrated theory whose signatures can be tested in nonlocal spin-transport experiments.

These four items are components of this single objective rather than independent alternatives to it: items (1) and (2) supply the two-fluid theory and its temperature-dependent predictions, and items (3) and (4) supply the interface and bulk parameters and the discriminating criteria that make those predictions quantitative and experimentally testable. The theory must reduce to the established low-temperature, condensate-dominated theory as a limiting case and account for the temperature and field dependence of the existing nonlocal measurements.

References

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