Quantum-kinetic theory of spin-transfer torque and magnon-assisted transport in nanoscale magnetic junctions

Scott A. Bender, Rembert A. Duine, and Yaroslav Tserkovnyak

Phys. Rev. B 99, 024434 – Published 29 January 2019

Abstract

We theoretically investigate the role of spin fluctuations in charge transport through a magnetic junction. Motivated by recent experiments that measure a nonlinear dependence of the current on electrical bias, we develop a systematic understanding of the interplay of charge and spin dynamics in nanoscale magnetic junctions. Our model captures two distinct features arising from these fluctuations: magnon-assisted transport and the effect of spin-transfer torque on the magnetoconductance. The latter stems from magnetic misalignment in the junction induced by spin-current fluctuations. As the temperature is lowered, inelastic quantum scattering takes over thermal fluctuations, exhibiting signatures that make it readily distinguishable from magnon-assisted transport.

Received 2 August 2018
Revised 2 November 2018

DOI:https://doi.org/10.1103/PhysRevB.99.024434

Physics Subject Headings (PhySH)

Magnons Spin torque Spin transfer torque Spintronics

Magnetic tunnel junctions Nanostructures

Green's function methods Holstein-Primakoff method Landau-Lifshitz model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Scott A. Bender¹, Rembert A. Duine^1,2, and Yaroslav Tserkovnyak³

¹Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, Netherlands
²Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
³Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 99, Iss. 2 — 1 January 2019

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Top left: magnon-assisted transport. Electrons excite or destroy magnons as they move across a heterostructure. Bottom left: spin-transfer torque (STT) alteration of the magnetoresistance. The STT alters fluctuations of the spin $S$ , affecting $〈 S 〉$ and thereby the magnetoconductance $G_{m}$ . Right: MTJ schematic. The magnetic island does not hold charge, but the island spin $S$ , which is allowed to fluctuate, gives rise to spin-dependent hopping between the left and right leads.
Reuse & Permissions
Figure 2
Left: steady-state magnon number $N_{s}$ , Eq. (14), versus bias $V$ for $T / ℏ Ω = 0$ (blue) to 10 (red) in units of 1 for the antiparallel MTJ configuration with $α_{p} / α_{e} = 25$ . The symmetry between positive and negative $V$ is broken by the left-lead polarization $P_{L} = 0.2$ . Employing the parametrization from the discussion below Eq. (11) and taking $P = P_{L}$ , one has $Δ (G_{ϕ} / G_{0}) = (G_{m} / G_{0}) = P^{2} / (1 + P^{2})$ . At high temperatures, the STT gives rise to a monotonically increasing magnon occupation number, while at low temperatures, a minimum near zero bias is formed. Right: electron/hole pairs giving rise to spin and charge transport at zero temperature.
Reuse & Permissions
Figure 3
Plot of the ratio of $r = G_{STT}^{'} / G_{MAT}^{'}$ as a function of bias $V$ and temperature $T$ , demonstrating the relative importance of STT to MAT in the nonlinear charge transport features. MAT dominates over STT at low temperatures and biases. Blue (red) contours correspond to MAT (STT) dominating, i.e., to $r < 1$ ( $r > 1$ ) in steps of $1 / 2$ . The black solid lines correspond to $N_{0} = \tilde{N}$ . At temperatures above this line, $N_{0} > \tilde{N}$ , and classical STT-driven thermal fluctuations dominate the response $G_{STT}$ ; below, $\tilde{N} > N_{0}$ , and inelastic-scattering dominates. The parameters are the same as in Fig. 2, so $S / S_{c} = 25$ . Left and right insets: $r$ for $S / S_{c} = 250$ and $S / S_{c} = 2.5$ , respectively, with the same axis scale as the main panel. For $S < S_{c}, r$ no longer depends on $S$ ; for $S ≫ S_{c}$ , MAT dominates over STT for a larger range of temperatures and biases, reflecting the decreased importance of fluctuations of $S$ .
Reuse & Permissions
Figure 4
Low-temperature resistance $R$ versus bias for parallel (P) and antiparallel (AP) configurations, respectively corresponding to $η = \pm 1$ , as well as $P_{L} = G_{m} = 0$ (left lead unpolarized). Shown are temperatures ranging from $T / ℏ Ω = 0$ (blue) to 2 (red) in steps of $1 / 4$ . MAT dominates at temperatures $T ≪ ℏ Ω$ and $e | V | ≲ ℏ Ω$ but vanishes as the temperature is raised. Inset: high-temperature $R$ versus bias for the parallel configuration for temperatures ranging from $T / ℏ Ω = 0$ (blue) to 8 (red) in steps of $1 / 2$ . At $T = 0$ , the resistance exhibits a maximum around zero bias, reflecting MAT. At $T / ℏ Ω \sim 1$ the resistance exhibits a minimum near zero bias, stemming from quantum STT. As $T$ is further increased, classical STT dominates, and $R$ no longer shows local extrema near zero bias. All unspecified parameters are the same as in Fig. 2. We find that the MAT-induced resistance plateau survives at $P_{L} = G_{m} = 0$ , as only one magnetic component is required to inelastically scatter electrons.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics