Units
MicroMagnetic.jl uses SI units by default in simulations.
Micromagnetic Model
In the Micromagnetic model, all parameters are expressed using SI units. Below is a summary of the physical quantities and their corresponding units.
| Physical Quantity | Units | Example Usage |
|---|---|---|
| Length | m | mesh = FDMesh(dx=1e-9, dy=1e-9, dz=1e-9, nx=10, ny=10, nz=1) |
| Time | s | run_sim(sim; steps=100, dt=1e-11) |
| Saturation Magnetization | A/m | set_Ms(sim, 8.6e5) |
| Exchange Constant | J/m | add_exch(sim, 1.3e-11) |
| DMI Constant | J/m² | add_dmi(sim, 1e-3) |
| Anisotropy Constant | J/m³ | add_anis(sim, 1e5; axis=(0,0,1)) |
| External Magnetic Field | A/m | add_zeeman(sim, (-24.6mT, 4.3mT, 0)) |
| Gyromagnetic Ratio | m/(A·s) | sim.driver.gamma = 2.21e5 |
| Temperature | K | add_thermal_noise(sim, 100.0) |
Atomistic Model
The Atomistic model also use SI units where applicable but often expressed in terms of energy or magnetic moments.
| Physical Quantity | Units | Example Usage |
|---|---|---|
| Length | m | mesh = CubicMesh(dx=1e-9, dy=1e-9, dz=1e-9, nx=10, ny=10, nz=1) |
| Time | s | run_sim(sim; steps=100, dt=1e-11) |
| Magnetic Moment | A·m² | set_mu_s(sim, mu_s_1) |
| Exchange Interaction | J | add_exch(sim, 50 * k_B) |
| DMI Constant | J | add_dmi(sim, 5 * k_B) |
| Anisotropy Energy | J | add_anis(sim, 5 * k_B; axis=(0,0,1)) |
| External Magnetic Field | T | add_zeeman(sim, (0, 0, 0.1)) |
| Gyromagnetic Ratio | rad/(T·s) | sim.driver.gamma = 1.76e11 |
| Temperature | K | add_thermal_noise(sim, 100.0) |
Dimensionless Units
In certain cases, simulations can be simplified using dimensionless units, particularly useful in theoretical studies or scaling analyses.
Example of Dimensionless Setup
| Parameter | Value |
|---|---|
| Lattice Constant | |
| Spin Length | |
| Gyromagnetic Ratio | $ \gamma = 1 $ |
| Magnetic Moment | $ \mu_s = 1 $ |
| Exchange Constant | $ J = 1 $ |
| DMI Strength | $ D/J = 0.09 $ |
| Magnetic Field | $ H_0 = 0.00729 $ |
| Gilbert Damping | $ \alpha = 0.04 $ |
Below is an example of using dimensionless units for setting up a simulation in MicroMagnetic.jl:
julia
using MicroMagnetic
# Define a cubic mesh with normalized lattice units
mesh = CubicMesh(; nx=200, ny=200, nz=1, dx=1, dy=1, dz=1)
# Initialize the simulation with the Landau-Lifshitz-Gilbert (LLG) driver
sim = Sim(mesh; driver="LLG", name="test")
sim.driver.gamma = 1
sim.driver.alpha = 0.04
# Set magnetic moment
set_mu_s(sim, 1)
# Initialize magnetization direction
init_m0(sim, (1, 0.2, 0))
# Add exchange and DMI interactions
add_exch(sim, 1; name="exch")
add_dmi(sim, 0.09; name="dmi")
# Apply a dimensionless external magnetic field
add_zeeman(sim, (0, 0, 0.00729))