Fig. 3
Driving and resulting edge current. a The two-dimensional kagome lattice ferromagnet is driven by an electromagnetic field perpendicular to the kagome plane. To observe the driven Hall effect (DHE), the field is applied with a linear gradient along y, which leads to a temperature difference along x. Colour gradient from blue to red indicates increasing temperature. b The current as function of time. The shades of blue from dark to bright correspond to \({\cal{E}} = \{ 3,4,5,6\} \times 10^{ - 4}J\), respectively. The straight line is the theoretical prediction for the steady-state value (10). From the equation of motion one can estimate the time to reach the steady state to be of order \(t_{{\mathrm{eq}}}\sim {\cal{E}}^{ - 1}{\mathrm{log}}({\cal{E}}/\eta )\). c The steady-state particle current plotted against the drive strength \({\cal{E}}\). The solid lines correspond to the theoretical formula Eq. (10), whereas the dots are calculated numerically. In {blue, yellow, red, turquoise} we show (γ,η) = {(1, 0.1), (100, 0.1), (50, 1), (10, 10)} × 10−5J. We see that Eq. (10) agrees well with the numerically calculated steady-state current. The yellow, red, and turquoise curves have kinks at \(2{\cal{E}} = \gamma\), which mark the onset of instability. The clear deviation occurs once bulk modes become unstable, in which case our approximations break down and system ceases to remain close to the ground state. All unspecified parameters are as in Fig 1., except for W = 15
