Ferromagnetism of Cu-doped anatase TiO₂: the first-principles calculation study

Abstract

The electronic structures and magnetic properties of Cu-doped anatase TiO2 have been investigated by first-principles calculations based on the density functional theory (DFT). Calculation results indicated that one Cu-substituted Ti (Cu@Ti) defect can introduce a total magnetic moment of 1 μB, which mainly distributed on the doped Cu atom and six neighboring oxygen atoms. In accordance with the group theory, the fivefold Cu-3d energy level splits into one threefold t2g orbital and one twofold eg orbital under the octahedral crystal field formed by the six neighboring oxygen atoms. The asymmetric electron occupation of the eg orbital generates a magnetic moment. The magnetic coupling between such two Cu@Ti defects is ferromagnetic, and the ferromagnetic energy advantage is 149 meV compared with the antiferromagnetic one. The larger energy difference means that the ferromagnetic coupling between the Cu@Ti defects is stable even at room temperature. The origin of ferromagnetism can be explained using the double-exchange model.

High anisotropic magnetoresistance, perfect spin-filtering effect, and negative differential resistance effect of Cr-doped anatase phase TiO2

“…We use SGGA + U and choose 10 × 10 × 5 k-point meshes in the geometry optimizations. We set U = 3 eV cause previous studies have shown that is sufficient for transition metal-doped anatase [44][45][46]. The force is less than 0.02 e V/Å −1 on each atom, and the calculation will be terminated till the energy is less than 10 -5 eV.…”

The Role of Concentration, Site, and O Vacancy on Magnetic and Optical Properties of Cu‐Doped Anatase TiO2

“…[ 20 ] Previous studies have proposed that the ferromagnetism in Cu‐doped originates from the double‐exchange interaction between Cu ions. [ 21 ]…”

“…[20] Previous studies have proposed that the ferromagnetism in Cu-doped TiO 2 originates from the double-exchange interaction between Cu ions. [21] The exchange interactions between Cu ions are restricted by the radius of the Cu 3d electrons and diminish as the distance between two Cu ions increases. [19] We investigated the exchange interactions between Cu ions at various distances by computing the energy differences in different supercells, as shown in Figure S2, Supporting Information.…”

“…[ 20 ] Pan et al proposed that the underlying cause of ferromagnetism in Cu‐doped can be explained using the double‐exchange model. [ 21 ] Zheng et al demonstrated that the creation of BMPs, proposed to be oxygen defects at the interface between adjacent grains, is the most important factor for activating ferromagnetism in Cu‐doped films. [ 22 ] Experimental studies have shown that doping concentration and site, as well as the presence of V o , play crucial roles in the ferromagnetism of , supporting the BMPs model.…”

“…[20] Pan et al proposed that the underlying cause of ferromagnetism in Cu-doped TiO 2 can be explained using the doubleexchange model. [21] Zheng et al demonstrated that the creation of…”