Coordinates

mrfmsim is flexible in setting up the coordinates for the simulation. Currently, the components that involve coordinates are the grid and the magnet.

As shown in the figure above, the setup is determined by the origin of the magnet (magnet.origin), the origin of the grid (grid.origin), and the tip-sample separation (h). Although only the relative position of the magnet and the grid is important, the convention is to set the face of the grid and the magnet flush with a origin plane — the \(xy\) plane for the left figure and the \(xz\) plane for the right figure.

For example, with the left figure setup,

from mrfmsim.component import Grid, SphereMagnet

grid = Grid(shape=[11, 11, 11], step=[20.0, 20.0, 20.0], origin=[0.0, 0.0, -110])
magnet = SphereMagnet(radius=50.0, mu0_Ms=1800.0, origin=[0.0, 0.0, 50.0])

The grid has a height of 220 nm in \(z\)-direction, and the magnet has a radius of 50 nm. The grid origin is set to be 110 nm below the \(xy\)-plane, and the magnet origin is set to be 50 nm above the \(xy\)-plane. The magnet and the grid are flush, and the tip-sample separation is 0 nm.

With the right figure setup,

from mrfmsim.component import Grid, RectangularMagnet

grid = Grid(shape=[11, 11, 11], step=[20.0, 20.0, 20.0], origin=[0.0, -110, 0.0])
magnet = RectangularMagnet([70, 70, 1500], mu0_Ms=1800.0, origin=[0.0, 750.0, 0.0])

The grid has a width of 220 nm in \(y\)-direction, and the magnet has a height of 1500 nm. The grid origin is set to be 110 nm below left of the \(xz\)-plane, and the magnet origin is set to be 750 nm right to the \(xz\)-plane. The magnet and the grid are flush, and the tip-sample separation is 0 nm.

Note

The magnet calculation assumes the magnet is magnetized in the \(z\)-direction, and the external field is applied in the \(z\)-direction.