Domain wall dynamics of ferrimagnets influenced by spin current near the angular momentum compensation temperature

V. V. Yurlov, K. A. Zvezdin, P. N. Skirdkov, and A. K. Zvezdin

Phys. Rev. B 103, 134442 – Published 29 April 2021

Abstract

We report on a theoretical study of the spin current excited dynamics of domain walls (DWs) in ferrimagnets in the vicinity of the angular momentum compensation point. For a two-sublattice ferrimagnet effective Lagrangian and nonlinear dynamic equations are derived taking into account both the spin torques and the external magnetic field. The dynamics of the DW is calculated before and after the Walker breakdown for any direction of the spin current polarization. It is shown that for the in-plane polarization of the spin current, the DW mobility reaches a maximum near the temperature of the angular momentum compensation. On the contrary, for the out-of-plane spin polarization, the spin current with densities below the Walker breakdown does not excite DW dynamics. After overcoming the Walker breakdown, the domain wall velocity increases linearly with increasing current density. In this configuration of spin current polarization, the possibility of a gigahertz oscillation dynamics of the quasiantiferromagnetic vector under the action of a dampinglike torque at the angular momentum compensation point is demonstrated. Possible structures for experimental demonstration of the considered effects are discussed.

Received 22 October 2020
Revised 4 February 2021
Accepted 13 April 2021

DOI:https://doi.org/10.1103/PhysRevB.103.134442

Physics Subject Headings (PhySH)

Domain walls Ferrimagnetism

Ferrimagnets

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

V. V. Yurlov¹, K. A. Zvezdin ^2,3,*, P. N. Skirdkov ^2,3, and A. K. Zvezdin²

¹Moscow Institute of Physics and Technology, Institutskiy Pereulok 9, 141700 Dolgoprudny, Russia
²Prokhorov General Physics Institute of the Russian Academy of Sciences, Vavilova 38, 119991 Moscow, Russia
³New Spintronic Technologies, Russian Quantum Center, Bolshoy Bulvar 30, Building 1, 121205 Moscow, Russia

^*zvezdin.ka@phystech.edu

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Issue

Vol. 103, Iss. 13 — 1 April 2021

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Images

Figure 1
Schematic of the considered FiMs with a single domain wall; $σ$ is the polarization vector of the spin current, $l$ is thickness of the sample, and $θ$ and $φ$ are the polar and azimuthal angles of the quasiantiferromagnetic vector $L$ .
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Figure 2
(a) Average DW velocity in Walker and post-Walker regimes as a function of the electrical current density $J$ . (b) Absolute value of the azimuthal angle $φ$ in Walker and post-Walker regimes as a function of the electrical current density $J$ . Blue, green, yellow, red, and black curves correspond to the temperatures $T = 270$ K, $T = 280$ K, $T = 290$ K, $T = T_{A}$ , and $T = 350$ K respectively; the black arrows indicate the transition in the post-Walker regime. All curves are plotted for the in-plane spin current polarization.
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Figure 3
(a) Dependence of the DW velocity on temperature at different current densities. (b) Dependence of the DW velocity on electrical current density at different temperatures. (c) Precession rate as a function of temperature at different current densities. All curves are plotted for the out-of-plane spin current polarization.
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Figure 4
$J - T$ diagram which describes the ranges of steady and nonsteady motions of the DW. The green curve shows the temperature dependence of the critical current $J^{*}$ ; the ranges above ( $J > J^{*}$ ) and below ( $J < J^{*}$ ) the green curve correspond to nonstationary (post-Walker) and stationary (Walker) modes of the DW, respectively. Insets show the time dependence of DW displacement in the nonstationary range for point A ( $T = 320$ K and $J = 2 \times 10^{7}$ A/ ${cm}^{2}$ ) and the stationary range for point B ( $T = 280$ K and $J = 0.3 \times 10^{7}$ A/ ${cm}^{2}$ ) of the diagram. All curves are plotted for the out-of-plane spin current polarization.
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Figure 5
Average DW velocity in the stationary and nonstationary modes as a function of the electrical current density $J$ . Blue, green, and red curves correspond to temperatures $T = 290$ K, $T = T_{A}$ , and $T = 330$ K, respectively; $J_{1, 2}^{*}$ are critical current densities which correspond to $T = 290$ K and $T = 330$ K, respectively. All curves are plotted for the out-of-plane spin current polarization.
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Figure 6
Examples of (a) the MTJ base and (b) and (c) spin Hall based structures, which can be used to observe reported DW motion and oscillation regimes in a FIM film or nanostripe. (b) corresponds to the perpendicular direction of spin current polarization $σ$ , and (c) corresponds to the planar direction.
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