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Frustrated out-of-plane Dzyaloshinskii-Moriya interaction and the onset of atomic-scale 3$q$ magnetic textures in 2D Fe$_{3}$GeXTe (X = Te, Se, S) monolayers

Caglayan Rabia, Desplat Louise, Nikolaev Sergey, Ibrahim Fatima, Li Jing, Mogulkoc Yesim, Mogulkoc Aybey, Chshiev Mairbek

Abstract

We theoretically study the effect of in- and out-of-plane Dzyaloshinskii-Moriya interaction (DMI) on the magnetic ground states of two-dimensional (2D) Fe$_3$GeXTe (X=Te, Se, S) monolayers, where X=Se, S correspond to antisymmetric Janus structures with nonvanishing in-plane DMI. We perform atomistic spin simulations with the extended Heisenberg Hamiltonian parametrized by first principles calculations. While we find that the base DMI in all systems is too weak to stabilize noncollinear states, we show how the frustrated out-of-plane DMI tends to favor atomic-scale $3q$ magnetic textures at the edge of the Brillouin zone. Owing to the ability to tune the DMI in 2D magnets via applied strain or electric field, we study the evolution of the systems' ground state with increasing DMI amplitude. We find that nonplanar $3q$ states are favored under scaling factors as low as 3, while larger DMI tends to stabilize states reminiscent of nanoskyrmion lattices at the atomic-scale.

Frustrated out-of-plane Dzyaloshinskii-Moriya interaction and the onset of atomic-scale 3$q$ magnetic textures in 2D Fe$_{3}$GeXTe (X = Te, Se, S) monolayers

Abstract

We theoretically study the effect of in- and out-of-plane Dzyaloshinskii-Moriya interaction (DMI) on the magnetic ground states of two-dimensional (2D) FeGeXTe (X=Te, Se, S) monolayers, where X=Se, S correspond to antisymmetric Janus structures with nonvanishing in-plane DMI. We perform atomistic spin simulations with the extended Heisenberg Hamiltonian parametrized by first principles calculations. While we find that the base DMI in all systems is too weak to stabilize noncollinear states, we show how the frustrated out-of-plane DMI tends to favor atomic-scale magnetic textures at the edge of the Brillouin zone. Owing to the ability to tune the DMI in 2D magnets via applied strain or electric field, we study the evolution of the systems' ground state with increasing DMI amplitude. We find that nonplanar states are favored under scaling factors as low as 3, while larger DMI tends to stabilize states reminiscent of nanoskyrmion lattices at the atomic-scale.

Paper Structure

This paper contains 19 sections, 3 equations, 13 figures, 3 tables.

Table of Contents

  1. Introduction
  2. First principles calculations
  3. Heisenberg Hamiltonian model
  4. Isotropic Exchange
  5. DMI
  6. First neighbors interlayer:
  7. First neighbors intralayer:
  8. Dispersion of $1q$ spin spirals
  9. Out-of-plane spirals
  10. In-plane spirals
  11. Emergence of a $3q$ DMI ground state
  12. FGT$_2$
  13. Janus monolayers
  14. "Nanoskyrmion" lattice
  15. DMI energy
  16. ...and 4 more sections

Figures (13)

  • Figure 1: Schematic representation of the atomic structure of Fe${_3}$GeXTe (X = S, Se, Te) monolayers, showing the distinct Fe, Ge, and chalcogen layers.
  • Figure 2: (a)–(c) Electrostatic potential energy distributions for (a) FGT$_2$, (b) FGTSe, and (c) FGTS monolayers. Panels (d)–(f) show the corresponding charge density differences.
  • Figure 3: Isotropic exchange constant as a function of neighbor distance $R_{ij}$ in the three systems up to a distance of 12 Å, where (a--c) correspond to interlayer exchange, and (d--f) correspond to intralayer exchange. Exchange is given in meV per Fe atom, where $J_{ij}>0 (<0)$ indicates (anti)ferromagnetic coupling.
  • Figure 4: Anatomy of the DMI in (a, d, g) FGT$_2$, (b, e, h) FGTSe, and (c, f, i) FGTS. (a--c) show the interlayer DMI in the first unit cell, while (d--i) show the intralayer DMI between neighboring sites separated by one lattice constant. All components of the DMI vectors are plotted in (a--f), while in (g--i), purely the in-plane components are shown, and scaled up for readability. The DMI vectors are colored according to their polar angle in the XY plane. The solid orange arrows indicate the direction of the bonds, and point away from the central atom. The solid grey semicircles in (g--i) indicates the in-plane chirality of the DM vectors. Note that for readability, the scaling applied to the DMI vectors is consistent within each subfigure, but not between different subfigures. In (g), we also show the in-plane Bravais vectors in real space, $\hat{\bf a}_1$ and $\hat{\bf a}_2$.
  • Figure 5: Amplitude of the in-plane DMI components as a function of neighbor distance in the three systems up to a distance of 12 Å, where (a--c) correspond to interlayer DMI, and (d--f) correspond to intralayer DMI. The DMI amplitude is given is meV per Fe atom, where $D^\parallel_{ij}>0 (<0)$ indicates counterclockwise (clockwise) chirality of the in-plane DM vectors.
  • ...and 8 more figures