Topological Hall effect in the Shastry-Sutherland lattice

Abstract

We study the classical Heisenberg model on the geometrically frustrated Shastry-Sutherland (SS) lattice with additional Dzyaloshinskii-Moriya (DM) interaction in the presence of an external magnetic field. We show that several noncollinear and noncoplanar magnetic phases, such as the flux, all-in/all-out, 3-in-1-out/3-out-1-in, and canted-flux phases are stabilized over wide ranges of parameters in the presence of the DM interaction. We discuss the role of DM interaction in stabilizing these complex magnetic phases. When coupled to these noncoplanar magnetic phases, itinerant electrons experience a finite Berry phase, which manifests in the form of topological Hall effect, whereby a nonzero transverse conductivity is observed even in the absence of a magnetic field. We study this anomalous magnetotransport by calculating the electron band structure and transverse conductivity for a wide range of parameter values, and demonstrate the existence of topological Hall effect in the SS lattice. We explore the role of the strength of itinerant electron-local moment coupling on electron transport and show that the topological Hall features evolve significantly from strong to intermediate values of the coupling strength, and are accompanied by the appearance of a finite spin Hall conductivity.

Skyrmion-driven topological Hall effect in a Shastry-Sutherland magnet

“…We simulate a finite-sized SSL of dimensions L × L (L = 32, 40, and 48) with periodic boundary con-ditions. Efficient thermalization is ensured by simulated annealing [39][40][41][42] where the simulation is started from a random spin configuration corresponding to high temperature T high ∼ 2J, followed by a reduction of temperature in steps of T = 0.01J until the lowest temperature T low = 0.01J is reached. At each temperature, we use 5 × 10 5 MC sweeps for equilibration, and 5 × 10 5 MC sweeps (in steps of 5000 MC sweeps) for the measurement of physical observable.…”

Spin-hedgehog-derived electromagnetic effects in itinerant magnets

“…In practice, we form a 2N Â 2N matrix of the single-particle Hamiltonian (eqn 4) and diagonalize it using the LAPACK library for linear algebra to find its exact eigenvalues E m and eigenvectors |mi. 49,61 The Hall conductivity as evaluated according to eqn (5) at o = 0 is shown in Fig. 3(a).…”

Atomic scale skyrmions and large topological Hall effect in a breathing-kagome lattice

“…Instead we strive to capture the principal features of the magnetic phase diagram and magnetotransport experiments. We focus on various non-collinear magnetic phases stabilized on this lattice and their effect on the conduction electron motion via a coupled electronspin model [33][34][35][36][37][38] . Our results can be summarized as follows: (i) Competing interactions give rise to a Skyrmions phase in this lattice.…”