Near room temperature magnetoelectric response and tunable magnetic anisotropy in the two-dimensional magnet 1T-CrTe2

TL;DR

This work addresses the challenge of achieving room-temperature operable, tunable magnetism in two-dimensional magnets by focusing on 1T-CrTe2. Using ab initio DFT combined with tight-binding/perturbation analyses and Monte Carlo simulations, the authors map how strain, a perpendicular electric field, and electronic correlations (U) modulate magnetocrystalline anisotropy and exchange interactions in monolayer and AA-stacked bilayer CrTe2, and they quantify the resulting magnetoelectric response. They find ferromagnetic intralayer order in the monolayer and antiferromagnetic interlayer order in the bilayer, with magnetocrystalline anisotropy that can be switched between in-plane and out-of-plane by tuning U, strain, and layer spacing; Tc values near or above room temperature emerge under favorable conditions. The work highlights a practical route to gate-controlled spin states and magnetoelectric devices in a robust, tunable 2D magnet and provides a microscopic orbital-level explanation for the exchange interactions via t2g–t2g and t2g–eg pathways.

Abstract

Magnets with controllable magnetization and high critical temperature are essential for practical spintronics devices, among which the two-dimensional 1T-CrTe2 stands out because of its high experimental critical temperature up to about 300K down to the single layer limit. By using ab initio density functional theory, we investigate the magnetic properties of monolayer and bilayer 1T-CrTe2 and demonstrate that the magnetic properties, such as the magnetocrystalline anisotropy, critical Curie temperature and magnetizations, can be influenced by strain or electric fields.

Figures (5)

• Figure 1: (a) Coordination structure and hexagonal Brillouin zone (BZ) of 1T-$\mathrm{CrTe}_{2}$. Blue and pink spheres represent Cr and Te atoms, respectively. (b) Schematic top view of the rectangular bilayer (BL) 1T-$\mathrm{CrTe}_{2}$ unit cell used for magnetic phases. The corresponding hexagonal unit cell is shown as a gray rhombus. (c) and (e) Orbital-projected band structures of monolayer 1T-$\mathrm{CrTe}_{2}$ for Cr $d$ orbitals and Te $p$ orbitals, respectively. Colored circles indicate the orbital contributions from Cr and Te atoms, where the color denotes orbital character and the circle radius is proportional to the orbital weight. (d) and (f) Orbital-projected band structures of bilayer 1T-$\mathrm{CrTe}_{2}$ for $p$ orbitals of interface Te atoms and outer Te atoms, respectively.
• Figure 2: (a) Orbital-resolved hopping parameters for $p$ and $d$ orbitals in monolayer 1T-$\mathrm{CrTe}_{2}$. The green and purple rectangles represent $p$- and $d$-orbital hopping interactions between Te and Cr atoms, denoted as $t$-Te–Cr and $b$-Te–Cr, respectively. To clearly visualize the relative magnitudes of the hopping interactions, parameters close to zero are shown in white. (b) Hopping terms of $d$ orbitals between adjacent Cr atoms ($\mathrm{Cr}_{1}^{3+}$ and $\mathrm{Cr}_{2}^{3+}$). (c) Effective $d$-orbital hopping terms between adjacent $\mathrm{Cr}_{1}^{3+}$ and $\mathrm{Cr}_{2}^{3+}$ atoms, classified into $t_{2g}$ and $e_{g}$ symmetries. (d) Schematic illustration of the evolution of electronic states along two Cr–Te–Cr superexchange (SE) pathways, showing the ferromagnetic (FM) alignment of intralayer $\mathrm{Cr}^{3+}$ cations.
• Figure 3: (a) Orbital-resolved hopping parameters for $p$ and $d$ orbitals in bilayer 1T-$\mathrm{CrTe}_{2}$. The atomic indices are indicated in Figs. \ref{['Manuscript:fig:hopping']}(c). To clearly visualize the magnitudes of the hopping interactions, parameters close to zero are shown in white. The green and purple rectangles represent $p$- and $d$-orbital hopping interactions between top (t) and bottom (b) Te atoms and Cr atoms, denoted as $t$-Te and $b$-Te, respectively. (b) Schematic illustration of the evolution of electronic states along the Cr–Te–Te–Cr super-superexchange (SSE) pathway, showing the antiferromagnetic (AFM) alignment of interlayer $\mathrm{Cr}^{3+}$ cations. (c) Maximally localized Wannier functions (MLWFs) of interface Te $p_{z}$ orbitals in bilayer 1T-$\mathrm{CrTe}_{2}$. $l_{2}$, $l_{3}$, and $l_{4}$ denote the exchange interaction paths between atoms, corresponding to Fig. \ref{['Manuscript:fig:hopping']}(b). (d) Transformation of $2\times 2$ hopping-term blocks into an effective hopping matrix using degenerate-state perturbation theory. (e) Effective hopping terms between top-layer and bottom-layer Cr atoms, classified into $t_{2g}$ and $e_{g}$ symmetries. Here, T and B denote the top and bottom layers, respectively. (f) Explicit effective hopping terms between top-layer and bottom-layer Cr atoms.
• Figure 4: Magnetic anisotropy energy (MAE) in bilayer (BL) 1T-$\mathrm{CrTe}_{2}$ under different electronic correlations ($U$), interlayer distances and in-plane strains. (a–c) Spherical plots of the ground-state energies for $U = 2$, $3$, and $4$ eV, respectively. Darker colors and larger radial distances correspond to higher MAE values. The spin orientation $\mathbf{\hat{s}}(\theta,\varphi)$ is indicated by a red arrow, where $\theta$ and $\varphi$ denote the azimuthal and polar angles, respectively. (d) MAE along the $xz$ plane as a function of on-site electron–electron interaction $U$ (0–5 eV). The red dotted line corresponds to the monolayer, and the blue dotted line corresponds to the bilayer 1T-$\mathrm{CrTe}_{2}$. (e) Ground-state energies of four different magnetic states as a function of interlayer Cr–Cr distance, with the lowest energy set as the reference. (f) MAE along the $xz$ plane versus interlayer Cr–Cr distance in bilayer 1T-$\mathrm{CrTe}_{2}$. (g) MAE as a function of in-plane strain ($-4\%$ to $+4\%$) in bilayer 1T-$\mathrm{CrTe}_{2}$ where spins are rotated in the $xz$ plane.
• Figure 5: (a) Temperature dependence of the heat capacity in monolayer (ML) and bilayer (BL) 1T-$\mathrm{CrTe_{2}}$ considering only out-of-plane anisotropy (polar angle $\varphi = 90^{\circ}$, azimuthal angle $\theta$ variable). The definition follows Eq. (\ref{['Manuscript:maeo']}), where $E_{xy}$ and $E_{z}$ denote the in-plane and out-of-plane anisotropy energies, respectively. (b) Temperature dependence of the heat capacity in ML and BL 1T-$\mathrm{CrTe_{2}}$ considering only in-plane anisotropy (azimuthal angle $\theta = 90^{\circ}$, polar angle $\varphi$ variable). The definition follows Eq. (\ref{['Manuscript:maei']}), where $E_{x}$ and $E_{y}$ correspond to the anisotropy energies along the in-plane $x$ and $y$ directions, respectively. (c) Magnetoelectric response of bilayer 1T-$\mathrm{CrTe_{2}}$ obtained from mean-field theory and (d) numerical Monte Carlo simulations. (Inset of (c)) Schematic side view of a polarized bilayer 1T-$\mathrm{CrTe_{2}}$ in the AFM phase, illustrating the magnetoelectric response induced by an applied vertical electric field ($-3$ to $+3$ V/nm).