Proximity effects in graphene on monolayers of transition-metal phosphorus trichalcogenides <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>M</mml:mi><mml:mi mathvariant="normal">P</mml:mi><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>M</mml:mi><mml:mo>:</mml:mo><mml:mi>Mn</mml:mi><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:mi>Fe</mml:mi><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:mi>Ni</mml:mi><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:mi>Co</mml:mi><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:mi>and</mml:mi><mml:mo> </mml:mo><mml:mi>X</mml:mi><mml:mo>:</mml:mo><mml:mo> </mml:mo><mml:mi mathvariant="normal">S</mml:mi><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:mi>Se</mml:mi><mml:mo>)</mml:mo></mml:math>

Abstract

We investigate the electronic band structure of graphene on a series of two-dimensional magnetic transition-metal phosphorus trichalcogenide monolayers, ${M\text{P}X}_{3}$ with $M={\mathrm{Mn},\mathrm{Fe},\mathrm{Ni},\mathrm{Co}}$ and $X={\mathrm{S},\mathrm{Se}}$, with first-principles calculations. A symmetry-based model Hamiltonian is employed to extract orbital parameters and sublattice resolved proximity-induced exchange couplings (${\ensuremath{\lambda}}_{\text{ex}}^{\text{A}}$ and ${\ensuremath{\lambda}}_{\text{ex}}^{\text{B}}$) from the low-energy Dirac bands of the proximitized graphene. Depending on the magnetic phase of the ${M\text{P}X}_{3}$ layer (ferromagnetic and three antiferromagnetic ones), completely different Dirac dispersions can be realized with exchange splittings ranging from 0 to 10 meV. Remarkably, not only the magnitude of the exchange couplings depends on the magnetic phase, but also the global sign and the type. Important, one can realize uniform $({\ensuremath{\lambda}}_{\text{ex}}^{\text{A}}\ensuremath{\approx}{\ensuremath{\lambda}}_{\text{ex}}^{\text{B}})$ and staggered $({\ensuremath{\lambda}}_{\text{ex}}^{\text{A}}\ensuremath{\approx}\ensuremath{-}{\ensuremath{\lambda}}_{\text{ex}}^{\text{B}})$ exchange couplings in graphene. From selected cases we find that the interlayer distance, as well as a transverse electric field, are efficient tuning knobs for the exchange splittings of the Dirac bands. More specifically, decreasing the interlayer distance by only about 10%, a giant fivefold enhancement of proximity exchange is found, while applying few V/nm of electric field, provides tunability of proximity exchange by tens of percent. We have also studied the dependence on the Hubbard $U$ parameter and find it to be weak. Moreover, we find that the effect of SOC on the proximitized Dirac dispersion is negligible compared to the exchange coupling.

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