Berry phase effects in antiferromagnets and Kramers-Weyl semimetals

Abstract

This doctoral dissertation deals with transport phenomena associated with the Berry phase effect. This dissertation consists of part I and part II. In part I, we investigate the Berry phase effect contribution to the spin-orbit torque in an antiferromagnet. In part II, we examine the Berry-phase-induced helical anomaly in a system with a single Weyl node. We identify the effective helicity responsible for the helical anomaly, and investigate the effective helicity-related charge and spin transport phenomena. The detailed abstract is as follows.

Part I: Berry phase effect contribution to the spin-orbit torque in an antiferromagnet Discovery that an electrical current applied to an antiferromagnet can generate spin-orbit torque through the spin-orbit coupling of an antiferromagnet opens an alternative path towards electrically controlled spintronics devices. For example, it has been theoretically and experimentally shown that antiferromagnets can be electrically switchable and antiferromagnetic domain wall motion generated by the spin-orbit torque may exhibit more superb functionalities than ferromagnetic counterparts do. Therefore, to materialized antiferromagnet-based device applications, it is desired to understand general properties of spin-orbit torque in antiferromagnet clearly. Here we extend the scope of previous theoretical studies and demonstrate important roles of the Berry phase.

Previous theoretical calculations of the spin-orbit torque has been limited to ideal antiferromagnets where local spins are perfectly parallel to each other so that anti-unitary symmetries are preserved. Quite often, however, spin configurations deviate from the perfect collinearity and the anti-unitary symmetries are broken. For instance, the Dzyaloshinskii-Moriya interaction due to broken inversion symmetry produces a spin canting that breaks the anti-unitary symmetries. Moreover even in antiferromagnets with collinear spin configurations in equilibrium, spin configurations become noncollinear during their magnetization dynamics and the anti-unitary symmetries are broken.

In part I, we allow the noncollinearity and investigate intrinsic spin-orbit torque originating from the Berry curvature in two types of antiferromagnets, layered and bipartite antiferromagnets. We calculate the Berry phase contribution to the nonequilibrium spin densities, which act as an effective field of the intrinsic spin-orbit torque, by the Kubo formula. The Berry phase contribution is compared for the two cases, one with the antiunitary symmetry and the other with the broken antiunitary symmetry due to the noncollinearity. We find that in clean antiferromagnets, even a weak symmetry breaking can significantly modify properties of spin-orbit torque. Considering that the spin noncollinearity becomes bigger as the magnetization dynamics becomes faster even in antiferromagnets with collinear spin configurations in equilibrium, this implies that spin-orbit torque during fast magnetization dynamics may be quite different from those obtained in earlier studies for collinear magnetization configurations.

Part II: Berry-phase-induced Helical anomaly and charge/spin transports in a three-dimensional system with a single Weyl node Symmetries and related conservation laws of classical theories may be broken and violated in quantum counterparts of the classical theories. This phenomenon is called an anomaly. In a three-dimensional massless Weyl fermion, whose left-handed and right-handed fermions can be exist separately, the charge conservation holds, in classical level, for the left-handed fermions and right-handed fermions separately, but such separate conservation, which is called chiral charge conservation, may be violated in quantum level although the total charge conservation still holds when the left-handed and right-handed fermions are combined. Such violation of the chiral charge is called axial or chiral anomaly. The strength of the chiral charge conservation violation depends on electromagnetic field configurations. It has been demonstrated both theoretically and experimentally that relativistic fermions such as Weyl fermions can emerge as low energy excitations of condensed matter systems. One of materials in which massless fermion appears is a Weyl semimetal. Here, previous studies have shown that the chiral anomaly gives rise to negative longitudinal magnetoresistance, planar Hall effect, and non-ohmic behavior.

In Weyl semimetals, energy bands with linear dispersion cross each other near the Fermi energy. Such crossing points are called Weyl nodes and always exist in pairs with each pair consisting of positive and negative chirality Weyl nodes. In a three-dimensional noncentrosymmetric nonmagnetic chiral crystal with spin-orbit coupling, however, Weyl nodes are located in time-reversal invariant momenta and Weyl nodes that form a pair may be located at different energies. To distinguish this type of Weyl fermions from conventional Weyl fermions, where Weyl nodes that form a pair share the same energy, they are called Kramers-Weyl fermions. If only one of the Weyl nodes is near the Fermi energy and the other Weyl node is far away from the Fermi energy, the system can behave as if there is only one Weyl node that is not paired. In this system with a single Weyl node, the conventional chiral anomaly in context of particle physics does not exist. Nevertheless, when the external electromagnetic fields are applied to the system, in the vicinity of the Weyl node, the charge conservation corresponding to each Fermi surface can be still violated. That is, an anomaly remains in this system.

In part II, we consider three-dimensional system with the single Weyl node. Then, we discuss an anomaly expressed in terms of effective helicity that is the projection of the electron spin onto the direction of the group velocity. We define this kind of anomaly as helical anomaly. Also, we investigate the effective helicity-related charge and spin transport phenomena in the presence of the external electromagnetic fields. The negative longitudinal magnetoresistance that arises from the helical anomaly is calculated. Furthermore, for the first time, we find the anomaly-related nonlinear Hall effect. Finally, a spin current related to the effective helicity is studied. For some material parameters, the spin current can be sizable, which may be utilized in spintronic devices.