class of centrosymmetric structures*

RMn₆Sn₆ compounds, where R is a rare earth element, are a recent addition to 3D systems with a kagome net of magnetic elements, where the Mn atoms form the kagome net in the basal plane of a hexagonal lattice.  More interestingly, these compounds form a wide variety of magnetic structures due to various competing energy scales, including the interlayer nearest and next-nearest exchange interactions that can be tuned with external perturbations, such as magnetic field or doping. In this talk I will discuss magnetic structures of two compounds, YMn₆Sn₆ and TbMn₆Sn₆. The former orders antiferromagnetically at 345 K and quickly transitions into an incommensurate spiral below 333 K. For a magnetic field applied in the ab-plane, a series of competing phases, namely, a distorted spiral (DS), transverse conical spiral (TCS) and fan-like (FL) phases are stabilized before polarizing into the forced ferromagnetic (FF) state. In this field orientation, this compound shows an enigmatic topological Hall effect (THE) near room temperature within the TCS phase, which we attribute to the scalar spin chirality generated by a novel fluctuations-driven mechanism. TbMn₆Sn₆ orders ferrimagnetically with ferromagnetic Mn spins arranged antiparallel to the Tb spins at about 423 K. This compound features a highly unusual magnetic reorientation transition about 100 K below the Curie point, whereby all spins in the system, remaining collinear, rotate by 90 degrees, and also shows an unusual temperature dependence of the anomalous Hall conductivity. Both these effects find quantitative explanation in the fact that Mn and Tb, by virtue of the Mermin-Wagner theorem, have very different spin dynamics, with Tb spins experiencing much more rapid fluctuations.