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arXiv 2006.06309cond-mat.mtrl-sci
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Mn掺杂普通CdTe和拓扑HgTe半导体的动量分辨自旋分裂

Momentum-resolved spin splitting in Mn-doped trivial CdTe and topological HgTe semiconductors

Carmine Autieri, Cezary Śliwa, Rajibul Islam, Giuseppe Cuono, Tomasz Dietl

摘要:

局域自旋和能带或拓扑态之间的交换耦合解释了巨磁输运和磁光效应,并决定了磁性绝缘体和半导体中的自旋-自旋相互作用。然而,即使在典型的稀磁半导体中,如Cd $_{1-x}$ Mn $_x$ Te和Hg $_{1-x}$ Mn $_x$ Te,这种耦合与波矢的演化也不清楚。一系列的实验已经证明,在布里渊区的L点处的Cd $_{1-x}$ Mn $_x$ Te和Zn $_{1-x}$ Mn $_x$ Te的磁光光谱的交换诱导分裂与现有的理论相矛盾,与其在区中心处的值相比,小了一个数量级以上,并且可以显示出意想不到的有效Landé因子的迹象。这些发现的起源,我们阐明定量相结合:(i)相对论第一性原理密度泛函计算,(ii)紧束缚的方法,仔细考虑k-依赖的潜在和动力学sp-d交换相互作用;(iii)用于$E_1$和$E_1$ + $Δ_1$光学跃迁的磁性圆二色性(MCD)理论,在这里开发的包络函数$kp$形式主义内的布里渊区的L点的锌晶体。这种方法的组合导致的结论是,在布里渊区的边界处的MCD的物理学受到特定化合物中的两种相对论效应的强度的强烈影响:(i)质量-速度项,其控制在L点处的导带到Mn离子的上哈伯德带的距离,因此,导带和价带中交换分裂的相对大小和符号;(ii)自旋-动量锁定-- 轨道耦合,其根据特定L谷相对于磁化方向的取向来减少交换分裂。

英文摘要:

Exchange coupling between localized spins and band or topological states accounts for giant magnetotransport and magnetooptical effects as well as determines spin-spin interactions in magnetic insulators and semiconductors. However, even in archetypical dilute magnetic semiconductors such as Cd$_{1-x}$Mn$_x$Te and Hg$_{1-x}$Mn$_x$Te the evolution of this coupling with the wave vector is not understood. A series of experiments have demonstrated that exchange-induced splitting of magnetooptical spectra of Cd$_{1-x}$Mn$_x$Te and Zn$_{1-x}$Mn$_x$Te at the L points of the Brillouin zone is, in contradiction to the existing theories, more than one order of magnitude smaller compared to its value at the zone center and can show an unexpected sign of the effective Landé factors. The origin of these findings we elucidate quantitatively by combining: (i) relativistic first-principles density functional calculations; (ii) a tight-binding approach that takes carefully into account k-dependence of the potential and kinetic sp-d exchange interactions; (iii) a theory of magnetic circular dichroism (MCD) for $E_1$ and $E_1$ + $Δ_1$ optical transitions, developed here within the envelope function $kp$ formalism for the L point of the Brillouin zone in zinc-blende crystals. This combination of methods leads to the conclusion that the physics of MCD at the boundary of the Brillouin zone is strongly affected by the strength of two relativistic effects in particular compounds: (i) the mass-velocity term that controls the distance of the conduction band at the L point to the upper Hubbard band of Mn ions and, thus, a relative magnitude and sign of the exchange splittings in the conduction and valence bands; (ii) the spin-momentum locking by spin-orbit coupling that reduces exchange splitting depending on the orientation of particular L valleys with respect to the magnetization direction.

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