Spin Fluctuation-Induced Hall Effects in Two-Dimensional Magnets

In this thesis, we consider Hall-type responses mediated by magnetic spin waves invarious 2D magnets. At low temperatures, quasiparticle descriptions called magnons allow for the Hall response due to intrinsic nontrivial topology in momentum space to be characterized through the use of well-established band theory. However, this quasiparticle description is not valid across the temperature range and is limited to the so-called linear spin wave regime. Furthermore, Hall-type responses may be attributed to a real space topology in the underlying magnetic spin texture in which the spin wave travels, a contribution that is not captured in the band theory approach. For these reasons, a universal description of Hall effects mediated by spin waves that is valid at all temperatures has remained elusive. Here, we present our approaches to studying the temperature dependence of the thermal Hall effect and spin Nernst effect in several 2D magnetic systems. In our first approach, we provide a first order" correction to the temperature dependence of the magnon band by introducing a mean-field description of the spin length, which in turn acquires its own temperature dependence. In conjunction with previous results connecting the thermal Hall conductivity to the topological character of the underlying band structure, we use this method to provide a theoretical description for the experimentally-observed temperature dependence of the thermal Hall conductivity in VI3, a layered van der Waals ferromagnet modeled by a chiral 2D honeycomb ferromagnet. In our second approach, we directly simulate the classical dynamics of the 2D magnets via the stochastic Landau-Lifshitz-Gilbert equation to acquire the timedependent dynamical properties which may be connected to the thermal response coefficients through linear response theory. We use this second approach to study the thermal Hall effect in a square lattice chiral ferromagnetic model which yields a topologically trivial magnon band, but exhibits a nontrivial real space topology at elevated temperatures near the critical temperature Tc. We show numerically that even in the paramagnetic phase, transient spin waves may mediate a thermal Hall response through collective scattering off of a dynamic topological spin texture. Lastly, we also use this numerical technique to study the high-temperature spin Nernst effect in a chiral honeycomb antiferromagnet. We show that the spin Nernst effect is especially robust near Tc and persists well into the paramagnetic phase, which we attribute to a novel order parameter for the real space topology called the vector spin chirality.