Noncollinear and noncoplanar magnetic orders lead to unusual electronic structures and transport properties. We here investigate two types of multiple-Q magnetically ordered states and a topological phase transition between them in two dimensions. One is a coplanar but noncollinear double-Q state on a square lattice, which is a semimetal accommodating massless Dirac electrons. The other is a noncoplanar triple-Q state on a triangular lattice, which is a Chern insulator showing the quantum anomalous Hall effect. We discuss the peculiar electronic structures in these two multiple-Q states in a unified way on the basis of the Kondo lattice model, which suggests a quantum phase transition between the two states in a continuous change of lattice geometry between the square and triangular lattices. We systematically examine the possibility of such a transition by using the mean-field approximation for the ground state of the periodic Anderson model. After clarifying the parameter region in which the double-Q (triple-Q) state is stabilized on the square (triangular) lattice, we show that a continuous topological phase transition indeed takes place between the double-Q Dirac semimetal and the triple-Q Chern insulator on the square-to-triangular lattice. The nature of the transition is discussed by the topologically-protected edge states as well as the bulk magnetic and electronic properties. The results indicate that unusual critical phenomena may occur at finite temperature related with multiple-Q chiral spin-liquid states.
Field-tunable toroidal moment and anomalous Hall effect in noncollinear antiferromagnetic Weyl semimetal Co1/3TaS2
将磁性与能带拓扑结构相结合，提供了各种新颖的相位，这在其他方面是不可能的。其中，非共线金属反铁磁体因其不同的磁基态而具有丰富的拓扑物理性质。然而，由于缺乏合适的材料，特别是三角晶格反铁磁体，只有很少的实验研究。在这里，我们报告，金属三角形反铁磁体Co 1/3 TaS 2表现出大量的异常霍尔效应（AHE）有关的非共线磁序。我们的第一性原理计算发现，沙漏外尔费米子从非对称对称触发AHE。我们进一步表明，AHE在Co 1/3 TaS 2的特点是由环向力矩，一个涡旋状的多极分量，产生的手征晶格和几何挫折的组合。最后，不寻常的磁场可调性的环矩把Co 1/3 TaS 2作为一个罕见的例子，非共线金属反铁磁体充满有趣的磁性和拓扑性质。
Spin structure and dynamics of the topological semimetal Co$_{3}$Sn$_{2-x}$In$_{x}$S$_{2}$
反常霍尔效应（AHE），通常在铁磁（FM）金属中观察到，具有破缺的时间反转对称性，取决于电子和磁性。在Co $_{3}$ Sn $_{2-x}$ In $_{x}$ S $_{2}$中，一个巨大的AHE被归因于与FM Weyl半金属相相关的Berry曲率，但最近的研究报告了复杂的磁性。我们使用中子散射来确定自旋动力学和结构作为$x$的函数，并提供了微观理解的AHE和磁性的相互作用。自旋间隙和刚度表明从外尔费米子的贡献与AHE一致。磁结构从$x$ = 0时的$c$轴铁磁性演变为倾斜反铁磁（AFM）结构，其具有减小的$c$轴矩和在$x$ = 0.12时的面内AFM阶，以及在$x$ = 0.3时进一步减小的$c$轴FM矩。由于非共线自旋可以在真实空间中诱导非零的Berry曲率作为虚拟磁场，我们的结果揭示了另一个AHE贡献，建立了磁性对运输的影响。
First-principles study on cubic pyrochlore iridates Y2Ir2O7 and Pr2Ir2O7
基于非共线局域自旋密度近似（LSDA），对烧绿石铱酸盐Y $_2$ Ir $_2$ O $_7$和Pr $_2$ Ir $_2$ O $_7$进行了完全相对论第一性原理电子结构计算.在LSDA+ $U$方案中，全进全出反铁磁（AF）有序由在位库仑排斥$U>U_c$稳定，其中Y $_2$、Ir $_2$ O $_7$和Pr $_2$、Ir $_2$ O $_7$的$U_c\sim1.1$分别为$U_c\sim1.1$ ~eV和1.3~eV.随着$U$的进一步增加，有和没有Weyl点的AF半金属以及拓扑平凡的AF绝缘体相继出现。对于$U=1.3$ ~eV，Y $_2$ Ir $_2$ O $_7$是拓扑平凡的窄隙AF绝缘体，具有有序的局部磁矩$\sim0.5μ_B$ /Ir，而Pr $_2$ Ir $_2$ O $_7$几乎是顺磁性半金属，电子和空穴浓度为$0.016$ /Ir，与实验总体一致。随着描述IrO $_6$八面体三角压缩的氧位置参数$x$的减小，Pr $_2$ Ir $_2$ O $_7$被驱动通过仅具有隔离费米点$Γ_8^+$的非费米液体半金属，显示二次带接触，到$Z_2$拓扑绝缘体。
Anomalous Hall Response Induced by Correlated Disorder in the Breathing Kagome Lattice Mn$_{3}$Sn
Oak Ridge National Laboratory（橡树岭国家实验室）；The Pennsylvania State University（宾夕法尼亚州立大学）；Weizmann Institute of Science（魏茨曼科学研究所）；Brigham Young University（杨百翰大学）；Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；Brookhaven National Laboratory（布鲁克海文国家实验室）
