Spin-Orbit Coupling in Single-Layer Ferrimagnets: Direct Observation of Spin-Orbit Torques and Chiral Spin Textures

Sachin Krishnia, Eloi Haltz, Léo Berges, Lucia Aballe, Michael Foerster, Laura Bocher, Raphaël Weil, André Thiaville, João Sampaio, and Alexandra Mougin

Phys. Rev. Applied 16, 024040 – Published 24 August 2021

Abstract

We demonstrate that the effects of spin-orbit coupling and inversion asymmetry exist in a single $Gd − Fe − Co$ ferrimagnetic layer, even without a heavy-metal interface. We use electric transport measurements to quantify the spin-orbit torques. We measure the Dzyaloshinskii-Moriya interaction using the Brillouin light-scattering measurement technique, and we observe the resulting chiral magnetic textures using x-ray photoemission electron microscopy. We attribute these effects to a composition variation along the thickness that we observe by scanning transmission electron microscopy. We show that these effects can be optimized by varying the $Gd − Fe − Co$ thickness or in combination with interfacial effects.

Received 15 July 2020
Revised 25 July 2021
Accepted 3 August 2021

DOI:https://doi.org/10.1103/PhysRevApplied.16.024040

Physics Subject Headings (PhySH)

Domain walls Dzyaloshinskii-Moriya interaction Ferrimagnetism Spin current Spin texture

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Sachin Krishnia ^1,*,‡, Eloi Haltz ^1,‡, Léo Berges ¹, Lucia Aballe ², Michael Foerster², Laura Bocher ¹, Raphaël Weil ¹, André Thiaville ¹, João Sampaio ^1,†, and Alexandra Mougin ¹

¹Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
²Alba Synchrotron Light Facility, CELLS, Barcelona E-08290, Spain

^*sachinbudana@gmail.com
^†joao.sampaio@universite-paris-saclay.fr
^‡S. Krishnia and E. Haltz contributed equally to this work.

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Vol. 16, Iss. 2 — August 2021

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Images

Figure 1
(a) Net magnetization (M_s) versus temperature measured using superconducting quantum interference device (SQUID) magnetometry. (b) Anisotropy field (H_k) in blue and coercive field (H_c) in red as a function of temperature, which diverge at T_M. Normalized R_AHE vs perpendicular magnetic field at (c) T = 270 K < T_M and (d) T = 280 K > T_M. Arrows represent the direction and relative magnitude of $Gd$ (black) and $Fe − Co$ (red) magnetic moments.
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Figure 2
Illustration of harmonic Hall measurements in (a) longitudinal and (b) transverse geometries to obtain H_DL and H_FL. H and I_ac are the applied magnetic field and ac current, respectively. (c) H_DL/J (with J estimated in the $Gd − Fe − Co$ layer) and (d) H_FL/J vs temperature. Purple (khaki) points correspond to an up (down) saturated state. Diagrams represent the direction and magnitude of $Gd$ (black) and $Fe − Co$ (red) magnetic moments. Dotted lines are guides to the eye. Estimated Oersted field $(\sim 1 mT/TA m^{- 2})$ due to I_ac is shown by a line. (e) Spin Hall angle (θ_SH) and (f) Rashba parameter (α_RP) vs temperature.
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Figure 3
(a) Schematic of the XMCD PEEM experiment, showing the magnetization profile of up-down and down-up left-handed Néel DWs and the x-ray beam with grazing incidence (16°) and perpendicular to the DW length. (b) Calculated normalized XMCD PEEM intensity profile for DWs in (a), taking into account the finite microscope resolution (r; blue curves). Gray curve is the profile of Bloch DWs. (c) Multidomain XMCD PEEM images at the $Gd$ M_4,5 edge (1178.7 eV). Green arrow shows the direction of the x-ray beam. Dark (bright) contrast corresponds to a down (up) magnetic domain. Analyzed DWs are in the vicinity of a region of lowered anisotropy induced by long exposure to x-rays (with small domains; in the bottom). (d) Intensity profiles (black lines) averaged over yellow regions in (c). Thick yellow line is a fit using the theoretical profile, as shown in (a), with r = 60 nm, which is measured on dust particles in the image.
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Figure 4
(a) BLS spectrum of ${Si O}_{x} / Gd − Fe − Co / Al$ obtained with a laser wavelength of 532 nm at 293 K under an in-plane magnetic field, µ₀H_ex= 0.52 T, and at beam incidence angle (θ) of 60° (corresponding to |k_SW| = 20.46 µm⁻¹). Yellow lines are Lorentzian fits. Inset shows measurement geometry. DMI-induced frequency shifts (Δf) of nonreciprocal SWs vs wave-vector magnitudes |k_SW| for (b) $Al$ -covered (red) and (c) $Pt$ -covered (blue) films. Thick lines are linear fits. Both samples are measured at T < T_M.
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Figure 5
(a) DMI values measured by BLS as a function of $Gd − Fe − Co$ thickness [in $Gd − Fe − Co$ (t nm)/ $Al$ (5 nm)] (b) Spin Hall angle as a function of temperature for 5 nm $Gd − Fe − Co / Al$ (red) and 8 nm $Gd − Fe − Co / Al$ samples (blue).
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Figure 6
(a) HAADF and (b) BF STEM images of the ${Si O}_{x} / Gd − Fe − Co / Al$ cross section. (c) HAADF intensity map of the probed area with corresponding elemental maps extracted at (d) $Gd$ M_4,5, (e) $Fe$ L_2,3, and (f) $Co$ L_2,3 edges. (g) Superimposed “false-color” map of $Gd$ (red), $Fe$ (blue), and $Co$ (green). (h) Laterally integrated line profiles over a length of 12 nm of $Gd$ M_4,5 (red), $Co$ L_2,3(green), $Fe$ L_2,3 (blue), and $Al$ K (orange) intensities along the film thickness.
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