# Spin Torque Standard Problem

The script implements a standard problem inlcuding spin transfer torque as proposed by Najafi et al. A square shaped sample with the material parameters of permalloy is relaxed in a vortex state. Then a spin polarized current is applied which results in an exitation of the vortex.

## Code

from magnum import * # Define a world made of permalloy world = World( RectangularMesh((100, 100, 1), (1e-9, 1e-9, 10e-9)), Body("all", Material.Py(xi=0.05,P=1.0, alpha=0.1))) # Initialize Simulation: Set the magnetization to a predefined state # with a vortex and relax solver = create_solver(world, [StrayField, ExchangeField], log=True) solver.state.M = vortex.magnetizationFunction( core_x=50e-9, core_y=50e-9, polarization=1, core_radius=10e-9) solver.state.alpha = 0.3 solver.relax() # save relaxed state for the next step mag = solver.state.M # Continue the simulation with the relaxed state and apply # a DC current solver = create_solver(world, [StrayField, ExchangeField, SpinTorque, AlternatingCurrent], log=True) solver.state.M = mag solver.state.j_offs = (1e12, 0, 0) # Create step handler that finds and saves the position of the # vortex as well odt = DataTableLog("sp5v02.odt") odt.addColumn( ("Vx", "Vortexcore X-pos.", "m"), ("Vy", "Vortexcore Y-pos.", "m"), lambda s: vortex.findCore(solver, 50e-9, 50e-9, "all")) vtkh = VTKStorage("./", "M") # Add the step handlers solver.addStepHandler(odt, condition.EveryNthStep(100)) solver.addStepHandler(vtkh, condition.EveryNthStep(1000)) # Simulate for 10 ns solver.solve(condition.Time(10e-9))

## Results

As described in the paper of Najafi et al. the equilibrium position of the vortex core changes due to the direct spin-polarized current. Since the current is switched on instantaniously the vortex core performs a damped gyration around the new equilibrium position.

*The time evolution of the magnetization rendered with ParaView*

*The contents of the odt file plotted with gnuplot*

## References

- M. Najafi et al., Proposal for a Standard Problem for Micromagnetic Simulations Including Spin-Transfer Torque. Journal of Applied Physics, 105, 113914-[11pp].
- Official site for the Standard Problem