Built-in electric field control of magnetic coupling in van der Waals semiconductors

Electrical control of magnetism in a two-dimensional (2D) semiconductor is of great interest for emerging nanoscale low-dissipation spintronic devices. Here, we propose a general approach of tuning magnetic coupling and anisotropy of a van der Waals (vdW) 2D magnetic semiconductor via a built-in electric field generated by the adsorption of superatomic ions. Using first-principles calculations, we predict a significant enhancement of ferromagnetic coupling and a great change of magnetic anisotropy in 2D semiconductors when they are sandwiched between superatomic cations and anions. The magnetic coupling is directly affected by the built-in electric field, which lifts the energy levels of mediated ligands' orbitals and enhances the superexchange interactions. These findings will be of interest for ionic gating controlled ferromagnets and magnetoelectronics based on vdW 2D semiconductors.

Figure 1

(a) A magnetic cluster including two nearest-neighbor magnetic sites in a ${\mathrm{CrI}}_3$-like material. Orange and blue balls represent nonmagnetic ligand ions (e.g., I) and magnetic ions (e.g., Cr), respectively. (b) Schematic diagram of the double-orbital model. α and β orbitals are spin-polarized orbitals of magnetic ions. γ orbitals are fully occupied orbitals of nonmagnetic ions. (c) The exchange energy $\left(E_{\mathrm{ex}}=E_{\mathrm{AFM}}-E_{\mathrm{FM}}\right)$ as a function of the on-site energy level split of the two nonmagnetic orbitals (${\mathrm{\Delta }}_{\mathrm{p}}$) when the hopping strength $t_1>t_2$. (d) The individual influences of the raising of ${\gamma }_{II}$ orbital and the lowering of ${\gamma }_I$ orbital on the $E_{\mathrm{ex}}.t_1$ and $t_2$ are set to 0.7 and 0.3 eV, respectively. The crystal field splitting (${\mathrm{\Delta }}_c$), exchange field $\left(U\right)$, initial on-site energy of γ orbitals ($E_{\mathrm{p}}$), and direct hopping strength between α and β orbitals ($t_{\mathrm{d}}$) are set to 2, 4, 0.2 (the on-site energies of ${\alpha }_1$ and ${\beta }_1$ orbitals are set to zero), and 0.05 eV, respectively.

Figure 2

(a) Schematic diagram of inducing a splitting of $p$ orbitals through a built-in electric field formed by the adsorption of superatomic ions. (b) A possible approach to realize the sandwich structure built by a vdW 2D semiconductor and superatomic ions via the ionic liquid gating. The vdW 2D FM semiconductor (e.g., ${\mathrm{CrI}}_3$) is placed in the middle. By applying a positive gate voltage across the ionic liquid containing $\mathrm{N}{{\mathrm{H}}_4}^{+}$ (e.g., ${\mathrm{NH}}_4\mathrm{Cl}$), the $\mathrm{N}{{\mathrm{H}}_4}^{+}$ will adsorb on the left side of ${\mathrm{CrI}}_3$ layer. On the contrary, a negative gate voltage applied across the ionic liquid (e.g., $\left[EM\mathrm{I}M\right]\left[\mathrm{B}{\left(\mathrm{CN}\right)}_4\right]$) will make the $\mathrm{B}{{\left(\mathrm{CN}\right)}_4}^{–}$ adsorb on the right side of ${\mathrm{CrI}}_3$ layer. (c) Planar average charge difference and electrostatic potential of ${\mathrm{CrI}}_3$ monolayer under an external out-of-plane electric field (left panel) and under a built-in electric field generated by the adsorbed superatomic ions $[\mathrm{B}{{\left(\mathrm{CN}\right)}_4}^{–}$ and $\mathrm{N}{{\mathrm{H}}_4}^{+}]$ (right panel). Insets: the side view of ${\mathrm{CrI}}_3$ monolayer and $\mathrm{B}{\left(\mathrm{CN}\right)}_4/{\mathrm{Cr}}_2{\mathrm{I}}_6/\mathrm{N}{\mathrm{H}}_4$. Light blue, orange, brown, green, dark blue, gray, and cyan balls represent Cr, I/Te, N, C, N, H, and Ge atoms, respectively.

Figure 3

Spin-resolved band structure and projected density of states (DOS) of (a) pristine ${\mathrm{CrI}}_3$ monolayer and (b) $\mathrm{B}{\left(\mathrm{CN}\right)}_4/{\mathrm{Cr}}_2{\mathrm{I}}_6/\mathrm{N}{\mathrm{H}}_4$. Green and orange profiles represent spin-up and spin-down bands, respectively. (c) The exchange energies ($E_{\mathrm{ex}}=E_{\mathrm{AFM}}-E_{\mathrm{FM}}$) for different magnetic semiconductor monolayers before (blue cylinders) and after (orange cylinders) adsorbing $\mathrm{B}{{\left(\mathrm{CN}\right)}_4}^{–}$ and $\mathrm{N}{{\mathrm{H}}_4}^{+}$ on their two sides. Positive and negative values represent ferromagnetic and antiferromagnetic couplings, respectively. (d) Magnetic moment per metal atom and specific heat ($C_{\mathrm{v}}$) as function of temperature for pristine ${\mathrm{CrI}}_3$ monolayer, $\mathrm{B}{\left(\mathrm{CN}\right)}_4/{\mathrm{Cr}}_2{\mathrm{I}}_6/\mathrm{N}{\mathrm{H}}_4, \mathrm{B}{\left(\mathrm{CN}\right)}_4/{\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6/{\mathrm{NH}}_4$ and $\mathrm{B}{\left(\mathrm{CN}\right)}_4/{\mathrm{Mn}}_4{\mathrm{S}}_8/{\mathrm{NH}}_4$.