δ-(Zn,Cr)S(111)表面上的Dzyaloshinsky-Moriya作用:第一性原理计算

根据密度泛函理论的第一性原理计算了具有非中心反演对称的异质结δ-(Zn,Cr)S(111)体系的原子结构和电子结构.Cr原子之间通过第一层S原子传递磁性相互作用.结合广义布洛赫条件,又进一步计算了反方向的自旋螺旋能量与波矢的色散关系E(q)与E(-q).E(q)与E(-q)能量之差反映了δ-(Zn,Cr)S(111)的S层与Cr层之间空间反演对称性破缺引起的DMI的大小.通过海森伯相互作用(HBI)模型与Dzyaloshinsky-Moriya作用(DMI)模型拟合第一性原理计算值,得到了Cr原子间各近邻的HBI参数J_1-J_4与DMI参数d-_1,d_2.在δ-(Zn,Cr)S(111)中,Cr原子间的耦合为M型反铁磁.DMI参数d_1为-0.53 meV,为顺时针手性DMI,在δ-(Zn,Cr)S(111)界面上有可能会产生斯格明子.本文计算表明,磁性和非磁性半导体界面有可能存在DMI,为理论研究和磁存储技术的进步开拓一个新的方向.

Dzyaloshinsky-Moriya interaction in δ-(Zn,Cr)S(111) surface: First principle calculations

According to density functional theory calculations, we elucidate the atomic and electronic structure of δ-(Zn, Cr)S(111) surface. The magnetic interaction between Cr atoms is via S atoms close to the Cr layer. This interaction is shown by the analysis of spin charge contour plot and partial density of states (DOS) of each atom. The DOSs of other S atoms are non magnetic and have no magnetic exchange with the Cr layer. E(q) and E(-q) are the dispersions between energy E and wave vector q of spin spiral in the opposite directions. They are calculated with generalized Bloch equations and all the magnetic moments of Cr atoms are arranged in the plane perpendicular to the δ-(Zn, Cr)S(111) film. The differences between E(q) and E(-q) are caused by the interface of δ-(Zn, Cr)S(111), where the symmetry of space perpendicular to the film is broken. Effective Heisenberg exchange interaction (HBI) and Dzyaloshinsky-Moriya interaction (DMI) parameters between different neighbors (J_i and d_i) are derived by well fitting the ab initio spin spiral dispersion E(q) to HBI with DMI model and E(q)-E(-q) to DMI model, respectively. The J₂ plays a major role with a large negative value of -9.04 meV. The J₁ is about 2/5 of J₂, and J₃ is about 1/4 of J₂ with positive value. The DMI d₁ is -0.53 meV, and d₂ is 0.07 meV. With these HBI parameters, E(0) is the largest one at which δ-(Zn, Cr)S(111) has no ferromagnetic interface. The E(q) has its lowest energy with the q at M=b₁/2 in the first Brillouin zone. Hence, δ-(Zn, Cr)S(111) is an M-type antiferromagnetic (AFM) material. In this type of AFM configuration, magnetic moments of Cr atom in a line along b₂ are parallel to each other, and antiparallel to the magnetic moments in adjacent lines. The E(q) at K=b₁/2+ b₂/2 is almost as large as that at Γ point. The value of DMI parameter d₁ is about 1/5 of that on Co/Pt3 interface and 1/2 of Co/graphene. However, it is a negative number, which shows the clockwise chirality. The δ-(Zn, Cr)S(111) interface has obvious DMI, and skyrmion may be formed at this transition-metal/semiconductor (TM/S) interface. It is a good option to search for DMI in different kinds of TM/S heterojunctions. The material that combines the advantage of heterojunction, and DMI may have new magnetic phenomenon, which is usefulfor the magnetic storage. This paper enriches the research on DMI.