We studied the magnetism of Mn(II)-doped anatase TiO₂ (a-TiO₂) with and without oxygen vacancy (V_O) by Heyd-Scuseria-Ernzerhof hybrid functional method. Introduction of Mn(II) dopants causes the nonmagnetic a-TiO₂ to have a magnetic moment, which is in direct proportion to the limited doped concentrations. The type of preferential magnetic coupling in Ti_1-δMn(II)_δO₂ depends upon the Mn-Mn distance. Introduction of ${\text{V}}_{\text{O}}^{\text{+}}$ increases the local magnetic moment in Ti_1-δMn(II)_δO₂, and the antiferromagnetism of the system is further enhanced. In contrast, the local magnetic moment of Ti_1-δMn(II)_δO₂ with ${\text{V}}_{\text{O}}^{\text{2+}}$ does not change, but the ferromagnetic coupling becomes more stable.

我们通过Heyd-Scuseria-Ernzerhof混合功能方法研究了Mn（II）掺杂的锐钛矿型TiO ₂（a -TiO ₂）的磁性，该氧有无氧空位（V _O）。Mn（II）掺杂剂的引入使非磁性a -TiO ₂具有磁矩，该磁矩与有限的掺杂浓度成正比。以Ti类型优先磁耦合的_1-δ的Mn（II）_δ Ò ₂取决于锰锰距离。介绍${\text{V}}_{\text{Ø}}^{\text{+}}$增加的Ti局部磁矩_1-δ的Mn（II）_δ Ò ₂，和该系统的反铁磁性进一步提高。与此相反，Ti中的局部磁矩_1-δ的Mn（II）_δ Ò ₂与${\text{V}}_{\text{Ø}}^{\text{2+}}$ 不变，但铁磁耦合变得更稳定。