Role of exchange splitting and ligand-field splitting in tuning the magnetic anisotropy of an individual iridium atom on $\mathrm{Ta}{\mathrm{S}}_2$ substrate

In this work, using first-principles calculation we investigate the magnetic anisotropy (MA) of single-atom iridium (Ir) on $\mathrm{Ta}{\mathrm{S}}_2$ substrate. We find that the strength and direction of MA in the Ir adatom can be tuned by strain. The MA arises from two sources, namely the spin-conservation term and the spin-flip term. The spin-conservation term is mainly generated by spin-orbit coupling (SOC) interaction on the $d_{xy}/d_{x^2\text{−}{y}^2}$ orbitals and is contributed to the out-of-plane MA. The spin-flip term is caused by SOC interaction on the $d_{xz}/d_{yz}$ and $p_x/p_y$ orbitals and is responsible for the in-plane MA. We further find that strain-tuned MA is mainly determined by exchange splitting and ligand-field splitting. Increase of strain will reduce the ligand-field splitting and enhance the exchange splitting, resulting in the enhancement of the out-of-plane MA from $d_{xy}/d_{x^2\text{−}{y}^2}$ orbitals and the reduction of the in-plane MA from $d_{xz}/d_{yz}$ and $p_x/p_y$ orbitals, hence leading to the change of the strength and direction of the total MA. Our study provides a way for tuning the MA of a single-atom magnet on 2D transition metal dichalcogenide substrate by control of the exchange splitting and the ligand-field splitting.

Figure 1

$\mathrm{Ta}{\mathrm{S}}_2$ supercell and three possible configuration of Ir anchored on the basal plane of $\mathrm{Ta}{\mathrm{S}}_2$. (a) $4\times 4$ supercell of $\mathrm{Ta}{\mathrm{S}}_2$. (b) supercell with Ir anchoring on the hollow site. (c) supercell with Ir anchoring on the S atop site. (d) supercell with Ir anchoring on the Ta atop site.

Figure 2

(a) The MAE of Ir adatom as a function of strain in Ir anchored on $\mathrm{Ta}{\mathrm{S}}_2$. (b) Schematic diagram of strain dependence of MAE on Ir adatom.

Figure 3

PDOS of $d$ orbitals of Ir adatom on $\mathrm{Ta}{\mathrm{S}}_2$ with strain −8%, 0% and 8%. (a) (b) (c) are of strain −8%, 0% and 8%, respectively.

Figure 4

(a) Schematic diagram of energy splitting of $d$ orbital under the influence of ligand field and exchange interaction. (b) DOS of $p$ orbital of S atom and DOS of $d$ orbital of Ir adatom for the Ir-anchored $\mathrm{Ta}{\mathrm{S}}_2$. (c), (d) Dependence of strain on the magnetic moment and the difference of orbital moments ($\mathrm{\Delta }{m}_{\mathrm{o}}$).

Figure 5

Orbital-resolved MAE of Ir adatom under strain of −8%, 0%, and 8%. (a)–(c) are of $d$ orbital; (d)–(f) are of $p$ orbital.

Figure 6

MAE as a function of strain for the $d_{xy}/d_{x^2\text{−}{y}^2}$ orbitals, $d_{xz}/d_{yz}$ orbitals and $p_x/p_y$ orbitals. (a) (b) (c) are of $d_{xy}/d_{x^2\text{−}{y}^2}$, $d_{xz}/d_{yz}$ and $p_x/p_y$ orbitals respectively.

Figure 7

PDOS of $p_x/p_y$, $d_{xy}/d_{x^2\text{−}{y}^2}$ and $d_{xz}/d_{yz}$ orbitals of Ir adatom under strain of −8%, 0% and 8%. (a) (b) (c) are of $p_x/p_y$, $d_{xy}/d_{x^2\text{−}{y}^2}$ and $d_{xz}/d_{yz}$ orbitals respectively.