Antiferromagnetic magnon pseudospin: Dynamics and diffusive transport

Akashdeep Kamra, Tobias Wimmer, Hans Huebl, and Matthias Althammer

Phys. Rev. B 102, 174445 – Published 30 November 2020

Abstract

We formulate a theoretical description of antiferromagnetic magnons and their transport in terms of an associated pseudospin. The need and strength of this formulation emerges from the antiferromagnetic eigenmodes being formed from superpositions of spin-up and -down magnons, depending on the material anisotropies. Consequently, a description analogous to that of spin- $\frac{1}{2}$ electrons is demonstrated while accounting for the bosonic nature of the antiferromagnetic eigenmodes. Introducing the concepts of a pseudospin chemical potential together with a pseudofield and relating magnon spin to pseudospin allows a consistent description of diffusive spin transport in antiferromagnetic insulators with any given anisotropies and interactions. Employing the formalism developed, we elucidate the general features of recent nonlocal spin transport experiments in antiferromagnetic insulators hosting magnons with different polarizations. The pseudospin formalism developed herein is valid for any pair of coupled bosons and is likely to be useful in other systems comprising interacting bosonic modes.

Received 9 October 2020
Revised 10 November 2020
Accepted 10 November 2020

DOI:https://doi.org/10.1103/PhysRevB.102.174445

Physics Subject Headings (PhySH)

Magnons Spin accumulation Spin current Spin diffusion Spin waves

Antiferromagnets

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Akashdeep Kamra ^1,*, Tobias Wimmer ^2,3, Hans Huebl ^2,3,4, and Matthias Althammer^2,3

¹Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
²Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
³Physik-Department, Technische Universität München, 85748 Garching, Germany
⁴Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany

^*akashdeep.kamra@ntnu.no

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Issue

Vol. 102, Iss. 17 — 1 November 2020

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Images

Figure 1
Schematic depiction of the two antiferromagnetic eigenmodes. The pseudofield vector [see Eq. (19)] depicted as a blue arrow intersects the Bloch sphere with unit radius at red and green points. These respectively represent the lower- and higher-energy magnonic eigenmodes [see Eq. (14)]. As discussed in the text, the depicted sphere is in the creation operator space.
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Figure 2
Schematic depiction of AFI eigenmodes for pseudofield $ω$ directed along (a) $\hat{z}$ , (b) $\hat{x}$ , and (c) $\hat{y}$ . In the quantum picture, the eigenmodes are expressed as superpositions of the natural Bloch sphere basis, the spin-up and -down magnons. In the Landau-Lifshitz description, the eigenmodes correspond to (a) circular precession or (b), (c) linear oscillations of the two sublattice magnetizations.
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Figure 3
Schematic depicting the precession of pseudospin chemical potential vector about a pseudofield directed along $\hat{x}$ . The analogous transmutation between the antiferromagnetic magnonic modes is also shown. The arrow of time goes from left to right.
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Figure 4
Device schematic for nonlocal magnon spin transport experiments. A $z$ -polarized magnon spin and pseudospin currents are injected into and detected from the antiferromagnetic insulator (AFI) using two spatial separated heavy metal (HM) electrodes.
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Figure 5
Oscillating magnon spin chemical potential [Eq. (51)]vs (a) distance from the injector electrode and (b) normalized pseudofield magnitude. The $z$ component of the pseudospin chemical potential vector corresponds to the magnonic spin accumulation detected in a typical nonlocal magnon spin transport setup. In (a), we plot the appropriately normalized oscillating contribution to it $μ_{osc}$ [Eq. (51)] as a function of the distance $z$ , normalized by the spin diffusion length $l_{s}$ , from the injector electrode for various values of the normalized pseudofield magnitude $β$ [Eq. (55)]. A sign reversal in the spin accumulation, resulting from pseudospin precession about the pseudofield, occurs for $β ≳ 1$ and can be seen in the curve corresponding to $β = 10$ . In (b), we plot a normalized magnon spin accumulation $μ_{osc}$ [Eq. (51)] detected at an electrode a distance $d$ from the injector as a function of the pseudofield magnitude. Several oscillations can be seen for distances $d$ significantly larger than the spin diffusion length. The absolute value of $μ_{osc}$ , however, diminishes with $d$ making it harder to detect multiple oscillations in experiments.
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