Magnetic skyrmion

In this example, we demostrate how to get a skyrmion using MicroMagnetic.jl. We use the parameters given in PRL 111 067203 (2013).

Used parameters in the simulation

Parameter	Value
Lattice constant	$a = 0.5$ nm
Spin length	$S = 1$
Magnetic moment	$μ_{s} = 2 μ_{B}$
Excahnge constant	$J = 50 k_{B}$
DMI	$D / J = 0.5$
External field	$H μ_{s} / J = 0.2$

We define a function to specify the problem.

julia

using MicroMagnetic
using CairoMakie

function m0_fun(i, j, k, dx, dy, dz)
    r2 = (i - 25)^2 + (j - 25)^2
    if r2 < 10^2
        return (0.01, 0, -1)
    end
    return (0, 0, 1)
end


function relax_system()
    mesh = CubicMesh(; nx=50, ny=50, nz=1, pbc="xy")

    #We create a simulation with 'SD' driver
    sim = Sim(mesh; driver="SD", name="skx")

    set_mu_s(sim, mu_s_1) # set mu_s of the system

    #Initialize the system using the `m0_fun` function
    init_m0(sim, m0_fun)

    J = 50 * k_B
    add_exch(sim, J; name="exch")
    add_dmi(sim, 0.5 * J; name="dmi")

    Hz = 0.2 * J / mu_s_1
    add_zeeman(sim, (0, 0, Hz)) # the unit of Hz is Tesla

    #Relax the system
    relax(sim; max_steps=2000, stopping_dmdt=0.01)

    #Save the magnetization to vtk file
    save_vtk(sim, "skx"; fields=["exch", "dmi"])

    return sim
end

sim = relax_system();

[ Info: AtomisticSim has been created.
[ Info: Bulk DMI for CubicMesh has been added!
[ Info: Static Zeeman has been added.
[ Info: Running Driver : MicroMagnetic.SD{Float64}.
[ Info: max_dmdt is less than stopping_dmdt=0.01 @steps=39, Done!

After obtain the skyrmion, we use the following script to plot the skyrmion

julia

plot_m(sim)

Magnetic skyrmion ​

Magnetic skyrmion