Effective spin-charge transport theory and spin-transfer physics in frustrated magnets within the slave-boson approach

We study the electron dynamics in magnetic conductors with frustrated interactions dominated by isotropic exchange. We present a transport theory for itinerant carriers built upon the (single-band) doped Hubbard model and the slave-boson formalism, which incorporates the spin-exchange with the magnetically frustrated background into the representation of electron operators in a clear and controllable way. We also formulate hydrodynamic equations for the itinerant charge and spin degrees of freedom, whose currents contain new contributions that depend on the spatiotemporal variations of the order parameter of the frustrated magnet, which are described by Yang-Mills fields. Furthermore, we elucidate the transfer of angular momentum from the itinerant charge fluid to the magnet (i.e., the spin-transfer torque) via reciprocity arguments. A detailed microscopic derivation of our effective theory is also provided for one of the simplest models of frustrated magnetism, namely the Heisenberg antiferromagnet on a triangular lattice. Our findings point towards the possibility of previously unanticipated Hall physics in these frustrated platforms.

Figure 1

Main symmetries of frustrated magnets, namely (a) global rotational symmetry and (b) local discrete invariance. Red arrows represent the lattice spins and “$+/-$” denotes the sign of the exchange coupling constant on each lattice bond. ${\mathcal{E}}_{i\left(f\right)}$ stands for the energy of the initial (final) spin configuration. In the case of global rotational symmetry, (relativistic) magnetocrystalline anisotropies lift weakly the degeneracy between the initial and final states. The choice of a square lattice is merely illustrative.

Figure 2

Triangular lattice for the Heisenberg antiferromagnet. The three sublattices are labeled by the numbers 1,2 and 3. The reference ordered state for spins is represented by magenta arrows. Director vectors along the bonds are depicted by turquoise arrows. Golden stars denote the magnetic lattice of the system and the peach rhombus depicts the magnetic unit cell.

Figure 3

Electron hopping processes in the half-filled limit. Circles and stars denote electrons and holes, respectively.