We predict that a temperature gradient can induce a magnon-mediated spin Hall response in an antiferromagnet with non-trivial magnon Berry curvature. We develop a linear response theory which gives a general condition for a Hall current to be well defined, even when the thermal Hall response is forbidden by symmetry. We apply our theory to a honeycomb lattice antiferromagnet and discuss a role of magnon edge states in a finite geometry.

We predict that a temperature gradient can induce a magnon-mediated intrinsic torque in systems with non-trivial magnon Berry curvature. With the help of a microscopic linear response theory of nonequilibrium magnon-mediated torques and spin currents we identify the interband and intraband components that manifest in ferromagnets with Dzyaloshinskii-Moriya interactions and magnetic textures. To illustrate and assess the importance of such effects, we apply the linear response theory to the magnon-mediated spin Nernst and torque responses in a kagome lattice ferromagnet.

In addition to charge plasmons, a 2D electron system with Rashba-type spin-orbit coupling (SOC) also supports three collective modes in the spin sector: the chiral-spin modes. We study the dispersions of the charge and spin modes and their coupling to each other within a generalized Random Phase Approximation for arbitrarily strong SOC, and both in 2D and 3D systems. In both 2D and 3D, we find that the charge plasmons are coupled to only one of the three chiral-spin modes. This coupling is shown to affect the dispersions of the modes at finite but not at zero wavenumbers. In 3D, the chiral-spin modes are strongly damped by particle-hole excitations and disappear for weak electron-electron interaction. Landau damping of the chiral-spin modes in 3D is directly related to the fact that, in contrast to 2D, there is no gap for particle-hole excitations between spin-split subbands. The gapless continuum is also responsible for Landau damping of the charge plasmon in 3D -a qualitatively new feature of the SOC system. We also discuss the optical conductivity of clean 2D and 3D systems and show that SOC introduces spectral weight at finite frequency in a such way that the sum rule is satisfied. The in-plane tranverse chiral-spin mode shows up as dispersing peak in the optical conductivity at finite number which can can be measured in the presence of diffraction grating. We also discuss possible experimental manifestations of chiral-spin modes in semiconductor quantum wells such InGaAs/AlGaAs and 3D giant Rashba materials of the BiTeI family.

We study electric field and temperature gradient driven magnetoconductivity of a Weyl semimetal system. To analyze the responses, we utilize the kinetic equation with semiclassical equations of motion modified by the Berry curvature and orbital magnetization of the wave-packet. Apart from known positive quadratic magnetoconductivity, we show that due to chiral anomaly, the magnetconductivity can become non-analytic function of the magnetic field, proportional to 3/2 power of the magnetic field at finite temperatures. We also show that time-reversal symmetry breaking tilt of the Dirac cones results in linear magnetoconductivity. This is due to one-dimensional chiral anomaly the tilt is responsible for. PACS numbers:Introduction. Three dimensional Dirac and Weyl semimetals are materials whose band structure has a linearly touching conduction and valence bands, 1-4 the Dirac cones. Dirac semimetal is degenerate in electron's right and left chiralities, while the Weyl semimetal has the two chiralities split in energy or momentum. Inversion or time-reversal symmetries must be broken to obtain the splitting of chiralities in Dirac semimetal.Theoretically, the linear band touching introduces the non-trivial Berry 5 curvature in to the description of the fermion dynamics. The Berry curvature in this case is an effective magnetic field in k− space which is created by a magnetic monopole located at the band touching point. For a review on effects of Berry curvature on electronic properties see Ref. [6].Weyl semimetals with broken time-reversal symmetry are characterized by the anomalous Hall effect.4,7 Due to splitting of the Dirac cones, there are chiral edge states on the physical boundaries of the system.2,4 Apart from that there is the so-called chiral anomaly of the Dirac fermions -non-conservation of particles with a given chirality in presence of magnetic and electric fields.