First-principles and model simulation of all-optical spin reversal

G. P. Zhang, Z. Babyak, Y. Xue, Y. H. Bai, and Thomas F. George

Phys. Rev. B 96, 134407 – Published 4 October 2017

Abstract

All-optical spin switching is a potential trailblazer for information storage and communication at an unprecedented fast rate free of magnetic fields. However, the current wisdom is largely based on semiempirical models of effective magnetic fields and heat pulses, so it is difficult to provide high-speed design protocols for actual devices. Here, we carry out a massively parallel first-principles and model calculation for 13 spin systems and magnetic layers, free of any effective field, to establish a simpler and alternative paradigm of laser-induced ultrafast spin reversal and to point out a path to a full-integrated photospintronic device. It is the interplay of the optical selection rule and sublattice spin orderings that underlines seemingly irreconcilable helicity-dependent and -independent switchings. Using realistic experimental parameters, we predict that strong ferrimagnets, in particular, Laves phase C15 rare-earth alloys, meet the telecommunication energy requirement of 10 fJ, thus allowing a cost-effective subpicosecond laser to switch spin in the gigahertz region.

Received 1 May 2017
Revised 5 September 2017

DOI:https://doi.org/10.1103/PhysRevB.96.134407

Physics Subject Headings (PhySH)

Antiferromagnetism Ferrimagnetism Ferromagnetism Magnetism Magnetization switching Magneto-optical effect Spin-orbit coupling

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

G. P. Zhang, Z. Babyak, and Y. Xue

Department of Physics, Indiana State University, Terre Haute, Indiana 47809, USA

Y. H. Bai

Office of Information Technology, Indiana State University, Terre Haute, Indiana 47809, USA

Thomas F. George

Office of the Chancellor and Center for Nanoscience, Department of Chemistry and Biochemistry, and Department of Physics and Astronomy, University of Missouri–St. Louis, St. Louis, Missouri 63121, USA

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Issue

Vol. 96, Iss. 13 — 1 October 2017

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Images

Figure 1
Selection rule for all-optical spin switching. The light helicity determines the direction of the spin-orbit torque $τ$ . Left: For a single spin, right-circularly polarized light $σ^{+}$ rotates the spin from out of the page into the page. Right: $σ^{-}$ light does the opposite. Bottom: For a system with two sublattices $a$ and $b, σ^{-}$ and $σ^{+}$ switch different sets of spins. $σ^{+}$ switches a spin from up to down, while $σ^{-}$ switches a spin from down to up.
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Figure 2
First-principles simulation of helicity-dependent spin moment change $Δ M_{z}$ for (a) fcc Ni, (b) and (c) a Ni free-standing monolayer, (d) an Fe monolayer, (e) hcp Gd, and (f) fct CoPt. $Δ M_{z}^{σ^{\pm}} = M_{z}^{σ^{\pm}} - (M_{z}^{σ^{+}} + M_{z}^{σ^{-}}) / 2$ . Here, $M_{z}^{σ^{+ / -}}$ is the spin moment under $σ^{+ / -}$ excitation. Laser parameters are as follows. (a) Duration $τ = 60$ fs, photon energy $ℏ ω = 2.0 eV$ , and vector potential amplitude $A_{0} = 0.0099 V fs / Å$ . (b) $τ = 48$ fs, $ℏ ω = 1.6 eV$ , and $A_{0} = 0.0030 V fs / Å$ . (c) $τ = 48$ fs, $ℏ ω = 1.55 eV$ , and $A_{0} = 0.030 V fs / Å$ . (d) $τ = 48$ fs, $ℏ ω = 2.0 eV$ , and $A_{0} = 0.030 V fs / Å$ . (e) Solid line: $τ = 48$ fs, $ℏ ω = 1.6 eV$ , and $A_{0} = 0.030 V fs / Å$ ; dashed line: $τ = 48$ fs, $ℏ ω = 1.55 eV$ , and $A_{0} = 0.030 V fs / Å$ . (f) Solid line: $τ = 48$ fs, $ℏ ω = 1.6 eV$ , and $A_{0} = 0.030 V fs / Å$ ; dashed line: $τ = 48$ fs, $ℏ ω = 1.55 eV$ , and $A_{0} = 0.030 V fs / Å$ .
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Figure 3
Dependence of the final spin angular momentum on the laser field amplitude $E_{0}$ under right- and left-circularly polarized light in a (a) ferromagnet, (b) weak ferrimagnet, and (c) strong ferrimagnet. $τ = 240$ fs. The open circles denote the results with $σ^{+}$ , and the open squares denote those with $σ^{-}$ . The optimal amplitudes for $σ^{+}$ ( $σ^{-}$ ) reduce from (a) 0.0056 0.0024) $V / Å$ to (b) 0.0023 (0.0012) $V / Å$ to (c) 0.00015 (0.0002) $V / Å$ .
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Figure 4
(a) Laser-induced spin-orbit torque $τ_{soc}$ as a function of time for $σ^{+}$ (solid line) and $σ^{-}$ (dashed line) pulses; $τ = 160$ fs. (b) Same as (a), but $τ = 240$ fs. (c) Final average spin at sublattice $a$ as a function of the initial spin on sublattice lattice $b$ . $Δ S_{z}$ is the sublattice spin magnitude difference. (d) Final average spin at sublattice $b$ as a function of the initial spin on sublattice lattice $b$ .
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Figure 5
(a) Snapshot of spins at the center of a strong ferrimagnet before (gold arrows) and 2 ps after (red arrows) $σ^{-}$ excitation. A partial reversal is observed. The torus arrow shows which spins the laser initially switches. (b) Snapshot of spins at the center of the slab before (gold arrows) and 2 ps after (red arrows) $σ^{+}$ excitation. A nearly complete reversal is found. The torus arrow shows which spins the laser initially switches.
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Figure 6
Top left: Phase diagram of AOS. Switchings in the FM (orange triangle) and weak FIM (light yellow triangle) are always helicity dependent. Helicity-independent switching (dark yellow triangle) occurs in a narrow region when the sublattice spins approach the antiferromagnetic limit. Top right: The envisioned photospintronic device is based on a strong ferrimagnet which allows the laser to store and switch spins rapidly. Bottom: Magnetic spin moment for eight Laves phase C15 rare-earth-transition-metal ferrimagnets. The spin moment at the Fe site is almost constant, but that at the $R$ site peaks at ${GdFe}_{2}$ and decreases along the series. Around ${ErFe}_{2}$ , there is an optimal strong ferrimagnetic configuration (dashed box) where an ideal spin reversal may appear. The dashed line is at $0 μ_{B}$ .
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