Role of exchange splitting and ligand-field splitting in tuning the magnetic anisotropy of an individual iridium atom on TaS2 substrate

Abstract

In this work, using first-principle calculation we investigate the magnetic anisotropy (MA) of single-atom iridium (Ir) on TaS 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 spin-conservation term and spin-flip term. The spin-conservation term is generated by spin-orbit coupling (SOC) interaction on d xy /d x2-y2 orbitals and is contributed to the out-of-plane MA. The spin-flip term is caused by SOC interaction on 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 enhance the exchange splitting and reduce the ligand field splitting, resulting in the enhancement of the in-plane MA from d xy /d x2-y2 orbitals and the reduction of the out-of-plane MA from d xz /d yz and p x /p y orbitals, and hence leading to the change of the strength and direction of the total MA. Our study provides a way for tuning the MA of single-atoms magnet on 2D transition metal dichalcogenides substrate by control of the exchange splitting and the ligand field splitting.

Magnetic anisotropy and ferroelectric-driven magnetic phase transition in monolayer Cr2Ge2Te6

“…Here, E MCA is determined by the total energy change as the magnetization rotates from in-plane to out-of-plane direction with respect to ML-CGT layer; that is E MCA = E SOC‖ − E SOC⊥ .where L and S are the orbital and spin angular momentum, respectively, and V ( r ) is the spherical part of the effective potential within the PAW sphere. 62 According to second-order perturbation theory, 63 the MCA can be further expressed as: 64,65 Δ E −− = E −− ( x ) − E −− ( z )Δ E ± = E ± ( x ) − E ± ( z )where ξ is the SOC constant, u and o are the energy levels of the unoccupied states and the occupied states, + and − are majority- and minority-spin states, respectively. Table 1 lists the corresponding matrix element differences for Te-p orbitals, (including |〈o − | L̂ z |u − 〉| 2 − |〈o − | L̂ x |u − 〉| 2 and |〈o + | L̂ z |u − 〉| 2 − |〈o + | L̂ x |u − 〉| 2 ), while the corresponding matrix element differences of Cr-d orbital are illustrated in Table SII †.…”

Large perpendicular magnetic anisotropy of transition metal dimers driven by polarization switching of a two-dimensional ferroelectric In2Se3 substrate

“…The nonzero L z and L x matrix elements are 31 In terms of eqn ( 1) and ( 2 is the exchange splitting, which is the energy difference between the spin-minority state and the spinmajority state. 32 A large exchange splitting will reduce the absolute value of the negative MAE from the spin-flip term for the d xy /d x 2 Ày 2 and d xz /d yz orbitals, and hence increase the total MAE. When the absolute value of the positive part of MAE becomes larger than that of the negative part of MAE, the MA easy axis turns into the out-of-plane direction.…”

Giant unilateral electric-field control of magnetic anisotropy in MgO/Rh2CoSb heterojunctions

“…The MAE was calculated based on the total energy difference when the magnetization directions are in the xy plane ([100]) and the z axis ([001]), MAE = E ‖ − E ⊥ . The atomically- and orbital-resolved MAE were obtained from the difference of SOC energies, 45–48 . Here, , where V ( r ) is the spherical part of the effective potential within the PAW sphere.…”