Sublattice Ferrimagnetism in Quasifreestanding Graphene

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Sublattice Ferrimagnetism in Quasifreestanding Graphene

Artem G. Rybkin, Artem V. Tarasov, Anna A. Rybkina, Dmitry Yu. Usachov, Anatoly E. Petukhov, Alexander V. Eryzhenkov, Dmitrii A. Pudikov, Alevtina A. Gogina, Ilya I. Klimovskikh, Giovanni Di Santo, Luca Petaccia, Andrei Varykhalov, and Alexander M. Shikin

Phys. Rev. Lett. 129, 226401 – Published 22 November 2022

Abstract

We show that graphene can be magnetized by coupling to a ferromagnetic Co film through a Au monolayer. The presence of dislocation loops under graphene leads to a ferrimagnetic ordering of moments in the two C sublattices. It is shown that the band gap of $\sim 80 meV$ in the $\bar{K}$ point has a magnetic nature and exists for ferrimagnetic ordering. Interplay between Rashba and exchange couplings is evidenced by spin splitting asymmetry in spin-ARPES measurements and fully supported by DFT calculation of a ( $9 \times 9$ ) unit cell. Owing to sign-opposite Berry curvatures for $\bar{K}$ and ${\bar{K}}^{'}$ valleys, the synthesized system is promising for the realization of a circular dichroism Hall effect.

Received 28 December 2021
Revised 17 August 2022
Accepted 14 October 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.226401

Physics Subject Headings (PhySH)

Dirac fermions Disclinations & dislocations Ferrimagnetism Rashba coupling Spin-orbit coupling Surface reconstruction

Graphene Solid-solid interfaces Ultrathin films

Band structure methods Density functional theory Hubbard model Low-energy electron diffraction Photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Artem G. Rybkin ^1,*, Artem V. Tarasov ¹, Anna A. Rybkina ¹, Dmitry Yu. Usachov ¹, Anatoly E. Petukhov ¹, Alexander V. Eryzhenkov ¹, Dmitrii A. Pudikov ¹, Alevtina A. Gogina ¹, Ilya I. Klimovskikh ^2,1, Giovanni Di Santo ³, Luca Petaccia ³, Andrei Varykhalov ⁴, and Alexander M. Shikin ¹

¹St. Petersburg State University, 198504 St. Petersburg, Russia
²Center for Advanced Mesoscience and Nanotechnology, Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia
³Elettra Sincrotrone Trieste, Strada Statale 14 km 163.5, 34149 Trieste, Italy
⁴Helmholtz-Zentrum Berlin für Materialien und Energie, Elektronenspeicherring BESSY II, Albert-Einstein-Str. 15, D-12489 Berlin, Germany

^*artem.rybkin@spbu.ru

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Issue

Vol. 129, Iss. 22 — 23 November 2022

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Images

Figure 1
(a) ARPES intensity map for the $π$ band, including the enlarged map (c) and its second derivative with respect to energy (d). Solid red line shows the result of momentum distribution curves fitting with Lorentzian peak function. (b) LEED pattern of the epitaxial $\sim (9 \times 9)$ graphene superlattice formed on the $Au / Co (0001)$ interface. (e) Spin-ARPES spectra (with the spin polarizations on the right side) of $Gr / Au / Co (0001) / W (110)$ system measured at $k_{1}$ , $k_{2}$ , and $k_{3}$ momenta in (a) and for opposite magnetization directions obtained by 180° sample rotation. The photon energy is 21.2 eV.
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Figure 2
Relaxed unit cell of $Gr / Au / Co$ structure with dislocation loop: top view (a), side view (b), and isometric view of Au-Co dislocation loop under graphene (c). The dislocation loop is marked by a dotted line in panel (c) and on the inserted STM image. Sizes of the arrows are proportional to atomic magnetic moment values on gold and carbon atoms. The arrows indicating the maximum magnetic moments in two opposite directions for graphene and Au-Co dislocation loop are included in the legends. The direction of Co layer magnetization points to the right. The unit cell drawings are produced by VESTA software [48].
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Figure 3
(a) The unfolded ( $9 \times 9$ ) band structure of Gr/Au/Co around the opposite ${\bar{K}}^{'}$ and $\bar{K}$ points. The symbol size and color represent the Bloch spectral weight for $S_{y}$ spin component. (b) The unfolded ( $9 \times 9$ ) graphene band structure of $Gr / Au / Co$ without dislocation loop. Spectral weights were used for the ARPES simulation in which the bands were broadened using a Lorentzian function with a half width of 0.02 eV. Cobalt layer was magnetized in-plane perpendicular to the $\bar{Γ} \bar{K} ({\bar{K}}^{'})$ direction in both calculations. $M_{Gr} ↑$ and $M_{Co} ↓$ denote the magnetization directions of graphene and cobalt layers, respectively.
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Figure 4
The band structures calculated around the $\bar{K}$ ( ${\bar{K}}^{'}$ ) points using a model Hamiltonian for different graphene magnetizations and without spin-orbit interaction: AFM (a), FIM (b), and FM (c). Panel (d) shows the FIM case with Rashba interaction to fit the DFT and experimental data. (e) Schematic illustration of circular dichroism Hall effect with left-handed ( $σ_{-}$ ) and right-handed ( $σ_{+}$ ) light polarizations. The maxima on the Hall conductivity curve are observed due to the inclusion of new interband transitions with increasing the photon energy. A square line shape with $Δ E / ℏ ω = 10 %$ was set for the model curve of power spectral density.
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