Magnetic hopfion

In this example, we demostrate how to get a magnetic hopfion using MicroMagnetic.jl. We use the parameters given in PRL 124, 127204 (2020).

using MicroMagnetic
using CairoMakie

mesh = CubicMesh(nx=64, ny=64, nz=32, dx=1e-9, dy=1e-9, dz=1e-9, pbc="xyz")

function relax_system()

    sim = Sim(mesh; driver="SD", name="hopfion")

    set_mu_s(sim, 1)

    hopf = hopfion(R=20e-9, p=1, q=1)
    init_m0(sim, hopf)

    J1 = 1
    add_exch(sim, J1; name="exch", J2=-0.164, J3=0, J4=-0.082)

    relax(sim; max_steps=50000, stopping_dmdt=1e-3, using_time_factor=false)

    MicroMagnetic.save_vtk_points(sim, "hopfion")

    return sim
end

relax_system (generic function with 1 method)

Recall the function relax_system to obtain the hopfion.

sim = relax_system()

[ Info: AtomisticSim has been created.
[ Info: Exchange has been added.
[ Info: Running Driver : MicroMagnetic.SD{Float64}.
[ Info: max_dmdt is less than stopping_dmdt=0.001 @steps=850, Done!

After obtain the hopfion, we plot the hopfion

plot_m(sim, k=16)