Magnetometry¶

The magnetometry subpackage computes stray magnetic fields above a 2-D magnetic sample using the Biot-Savart law, and evaluates the resulting ODMR frequency shifts across a scan.

`SpinDefectSim.magnetometry.geometry`¶

Sample geometry classes define the spatial domain of a 2-D magnetic sample.

`SampleGeometry` (abstract)¶

from SpinDefectSim.magnetometry.geometry import SampleGeometry

Abstract base class. All concrete geometries derive from this.

Abstract interface¶

Member	Description
`boundary_vertices` (property)	CCW-ordered polygon vertices, shape `(N_verts, 2)`, in metres
`make_grid(n_pts)`	Return `(xx, yy)` meshgrid, each `(n_pts, n_pts)`

Concrete methods¶

`edge_current_segments`¶

def edge_current_segments(M_at_vertices: np.ndarray) -> tuple

Decompose the sample boundary into wire segments carrying edge currents proportional to the local magnetization.

Parameters:

Name	Type	Description
`M_at_vertices`	`np.ndarray (N_verts,)`	Magnetization magnitude at each boundary vertex (A)

Returns: (seg_start, seg_end, seg_current) — each (N_seg, 2), (N_seg, 2), (N_seg,) in SI

`sample_M_at_vertices`¶

def sample_M_at_vertices(
    magnetization: np.ndarray,
    *,
    xx: Optional[np.ndarray] = None,
    yy: Optional[np.ndarray] = None,
) -> np.ndarray

Interpolate a 2-D magnetization grid onto the boundary vertices.

Returns: np.ndarray shape (N_verts,) in A

`bulk_current_density`¶

def bulk_current_density(
    M_grid: np.ndarray,
    xx: np.ndarray,
    yy: np.ndarray,
) -> tuple[np.ndarray, np.ndarray]

Compute the bulk sheet current density K = ∇ × M_z at each grid point using finite differences.

Returns: (Kx, Ky) — each shape (ny, nx) in A/m

`interior_mask`¶

def interior_mask(xx: np.ndarray, yy: np.ndarray) -> np.ndarray

Boolean mask that is True inside the polygon and False outside.

`PolygonGeometry`¶

from SpinDefectSim.magnetometry.geometry import PolygonGeometry

Arbitrary closed polygon sample.

Constructor¶

PolygonGeometry(
    vertices: np.ndarray,
    n_boundary_pts: int = 0,
)

Parameters:

Name	Type	Description
`vertices`	`np.ndarray (N, 2)`	Polygon vertices in CCW order (m)
`n_boundary_pts`	`int`	If > 0, linearly interpolate to this many boundary points

`SquareGeometry`¶

from SpinDefectSim.magnetometry.geometry import SquareGeometry

Axis-aligned square sample.

Constructor¶

SquareGeometry(
    side: float,
    center: tuple = (0, 0),
    n_boundary_pts: int = 200,
)

Parameters:

Name	Type	Description
`side`	`float`	Side length (m)
`center`	`(float, float)`	Centre position (m)
`n_boundary_pts`	`int`	Number of boundary discretisation points

Example:

geom = SquareGeometry(side=2e-6, center=(0, 0))
xx, yy = geom.make_grid(n_pts=100)

`DiskGeometry`¶

from SpinDefectSim.magnetometry.geometry import DiskGeometry

Circular disk sample (approximated as a regular N-gon).

Constructor¶

DiskGeometry(
    radius: float,
    center: tuple = (0, 0),
    n_sides: int = 128,
)

Parameters:

Name	Type	Description
`radius`	`float`	Disk radius (m)
`center`	`(float, float)`	Centre position (m)
`n_sides`	`int`	Number of polygon sides (angular resolution)

Example:

geom = DiskGeometry(radius=1e-6)
xx, yy = geom.make_grid(n_pts=80)
mask = geom.interior_mask(xx, yy)

`SpinDefectSim.magnetometry.bfield`¶

Low-level Biot-Savart functions.

`B_from_wire_segment`¶

from SpinDefectSim.magnetometry.bfield import B_from_wire_segment

def B_from_wire_segment(
    r_start: np.ndarray,
    r_end: np.ndarray,
    current_A: float,
    r_obs_xyz: np.ndarray,
    *,
    r_min: float = 1e-15,
) -> np.ndarray

Analytic Biot-Savart result for a finite straight wire segment carrying a steady current.

Parameters:

Name	Type	Description
`r_start`	`np.ndarray (2,) or (3,)`	Start of the wire (m)
`r_end`	`np.ndarray (2,) or (3,)`	End of the wire (m)
`current_A`	`float`	Current (A)
`r_obs_xyz`	`np.ndarray (3,)`	Observation point (m)
`r_min`	`float`	Regulariser to avoid 1/r singularity (m)

Returns: np.ndarray shape (3,) in T

`B_from_edge_segments`¶

from SpinDefectSim.magnetometry.bfield import B_from_edge_segments

def B_from_edge_segments(
    seg_start: np.ndarray,
    seg_end: np.ndarray,
    seg_current: np.ndarray,
    r_obs_xyz: np.ndarray,
    *,
    r_min: float = 1e-15,
) -> np.ndarray

Vectorised Biot-Savart sum over all boundary wire segments (edge currents from magnetization).

Parameters:

Name	Type	Description
`seg_start`	`np.ndarray (N_seg, 2-3)`	Segment start points (m)
`seg_end`	`np.ndarray (N_seg, 2-3)`	Segment end points (m)
`seg_current`	`np.ndarray (N_seg,)`	Segment currents (A)
`r_obs_xyz`	`np.ndarray (3,)`	Observation point (m)

Returns: np.ndarray shape (3,) in T

`B_from_bulk_current_density`¶

from SpinDefectSim.magnetometry.bfield import B_from_bulk_current_density

def B_from_bulk_current_density(
    xx: np.ndarray,
    yy: np.ndarray,
    Kx: np.ndarray,
    Ky: np.ndarray,
    r_obs_xyz: np.ndarray,
    *,
    mask: Optional[np.ndarray] = None,
    r_min: float = 1e-15,
) -> np.ndarray

Compute the B-field contribution from a 2-D sheet current density K(r) = (Kx, Ky) A/m.

Parameters:

Name	Type	Description
`xx, yy`	`np.ndarray (ny, nx)`	Coordinate meshgrids (m)
`Kx, Ky`	`np.ndarray (ny, nx)`	Sheet current density components (A/m)
`r_obs_xyz`	`np.ndarray (3,)`	Observation point (m)
`mask`	`np.ndarray (ny, nx) bool \\| None`	Only include grid points where mask is True

Returns: np.ndarray shape (3,) in T

`B_from_magnetization_grid`¶

from SpinDefectSim.magnetometry.bfield import B_from_magnetization_grid

def B_from_magnetization_grid(
    geom: SampleGeometry,
    M_grid: np.ndarray,
    r_obs_xyz: np.ndarray,
    *,
    n_pts: int = 100,
    include_bulk: bool = True,
    include_edge: bool = True,
    erode_bulk_boundary: bool = False,
    r_min: float = 1e-15,
) -> np.ndarray

Total B-field from a 2-D out-of-plane magnetization M_z distribution, combining edge and bulk current contributions.

Parameters:

Name	Type	Description
`geom`	`SampleGeometry`	Sample geometry
`M_grid`	`np.ndarray (ny, nx)`	M_z grid (A, or equivalently surface current equivalent)
`r_obs_xyz`	`np.ndarray (3,)`	Observation point (m)
`n_pts`	`int`	Grid resolution for bulk integration
`include_bulk`	`bool`	Include ∇×M bulk term
`include_edge`	`bool`	Include boundary edge term
`erode_bulk_boundary`	`bool`	Exclude the outermost grid row from bulk to reduce double-counting at the edge

Returns: np.ndarray shape (3,) in T

`SpinDefectSim.magnetometry.magnetometry`¶

`MagnetometryExperiment`¶

from SpinDefectSim.magnetometry.magnetometry import MagnetometryExperiment

Computes stray B-field maps and ODMR observables above a 2-D magnetic sample.

Inherits: PhysicalParams

Constructor¶

MagnetometryExperiment(
    geometry: SampleGeometry,
    magnetization: Union[np.ndarray, Callable[[float, float], float]],
    defaults: Optional[Defaults] = None,
    *,
    z_defect: Optional[float] = None,
    n_pts: int = 100,
    include_bulk: bool = True,
    include_edge: bool = True,
    bias_B_T: Optional[np.ndarray] = None,
)

Parameters:

Name	Type	Description
`geometry`	`SampleGeometry`	Sample geometry object
`magnetization`	`np.ndarray (ny, nx) \\| Callable`	M_z grid (A) or callable `(x, y) → float`
`defaults`	`Defaults \\| None`	Global defaults
`z_defect`	`float \\| None`	Defect height above sample surface (m)
`n_pts`	`int`	Grid resolution for Biot-Savart integration
`include_bulk`	`bool`	Include bulk ∇×M contribution
`include_edge`	`bool`	Include edge current contribution
`bias_B_T`	`np.ndarray (3,) \\| None`	Uniform bias B-field (T) applied to all defects

`B_field`¶

def B_field(
    x_obs: float,
    y_obs: float,
    z_obs: Optional[float] = None,
) -> np.ndarray

Stray B-field at a single point.

Returns: np.ndarray shape (3,) in T

`transition_frequencies`¶

def transition_frequencies(
    x_obs: float,
    y_obs: float,
    z_obs: Optional[float] = None,
) -> np.ndarray

ODMR transition frequencies at a single point.

Returns: np.ndarray shape (2,) in Hz

`B_field_map`¶

def B_field_map(
    x_obs: np.ndarray,
    y_obs: np.ndarray,
    z_obs: Optional[float] = None,
) -> np.ndarray

Stray B-field on a 2-D scan grid.

Parameters:

Name	Type	Description
`x_obs`	`np.ndarray`	1-D x coordinates (m)
`y_obs`	`np.ndarray`	1-D y coordinates (m)
`z_obs`	`float \\| None`	z height (m)

Returns: np.ndarray shape (Ny, Nx, 3) in T

`B_z_map`¶

def B_z_map(
    x_obs: np.ndarray,
    y_obs: np.ndarray,
    z_obs: Optional[float] = None,
) -> np.ndarray

Bz component on a 2-D scan grid.

Returns: np.ndarray shape (Ny, Nx) in T

`transition_frequency_map`¶

def transition_frequency_map(
    x_obs: np.ndarray,
    y_obs: np.ndarray,
    z_obs: Optional[float] = None,
) -> np.ndarray

ODMR transition frequencies on a 2-D scan grid.

Returns: np.ndarray shape (Ny, Nx, 2) in Hz

`odmr_spectrum`¶

def odmr_spectrum(
    f_axis: np.ndarray,
    x_obs: float,
    y_obs: float,
    z_obs: Optional[float] = None,
    *,
    linewidth_Hz: Optional[float] = None,
    contrast: Optional[float] = None,
) -> np.ndarray

CW ODMR PL spectrum at a single point.

Parameters:

Name	Type	Description
`f_axis`	`np.ndarray`	MW frequency axis (Hz)
`x_obs, y_obs`	`float`	Observation point (m)
`linewidth_Hz`	`float \\| None`	Lorentzian FWHM; uses `defaults` if `None`
`contrast`	`float \\| None`	ODMR contrast; uses `defaults` if `None`

Returns: np.ndarray normalised PL, same shape as f_axis

`frequency_shift_map`¶

def frequency_shift_map(
    x_obs: np.ndarray,
    y_obs: np.ndarray,
    z_obs: Optional[float] = None,
    *,
    reference_xy: tuple = (1e6, 1e6),
    which: int = 0,
) -> np.ndarray

Map of ODMR frequency shift Δf(x, y) = f(x, y) − f(reference), useful for imaging relative magnetic contrast.

Parameters:

Name	Type	Description
`x_obs, y_obs`	`np.ndarray`	1-D coordinate arrays (m)
`reference_xy`	`(float, float)`	Reference position (far from the sample)
`which`	`int`	Which transition to plot: `0` (lower) or `1` (upper)

Returns: np.ndarray shape (Ny, Nx) in Hz

Example:

import numpy as np
from SpinDefectSim.magnetometry.geometry import SquareGeometry
from SpinDefectSim.magnetometry.magnetometry import MagnetometryExperiment

# 2-µm square sample with uniform magnetization
geom = SquareGeometry(side=2e-6)
xx, yy = geom.make_grid(100)
M = np.ones_like(xx) * 1e-3   # 1 mA equivalent

exp = MagnetometryExperiment(geom, M, z_defect=50e-9)

# Scan from −3 µm to +3 µm
x = np.linspace(-3e-6, 3e-6, 60)
y = np.linspace(-3e-6, 3e-6, 60)

Bz = exp.B_z_map(x, y)           # (60, 60) array in T
dfreq = exp.frequency_shift_map(x, y)  # (60, 60) array in Hz

Magnetometry¶

SpinDefectSim.magnetometry.geometry¶

SampleGeometry (abstract)¶

Abstract interface¶

Concrete methods¶

edge_current_segments¶

sample_M_at_vertices¶

bulk_current_density¶

interior_mask¶

PolygonGeometry¶

Constructor¶

SquareGeometry¶

Constructor¶

DiskGeometry¶

Constructor¶

SpinDefectSim.magnetometry.bfield¶

B_from_wire_segment¶

B_from_edge_segments¶

B_from_bulk_current_density¶

B_from_magnetization_grid¶

SpinDefectSim.magnetometry.magnetometry¶

MagnetometryExperiment¶

Constructor¶

B_field¶

transition_frequencies¶

B_field_map¶

B_z_map¶

transition_frequency_map¶

odmr_spectrum¶

frequency_shift_map¶

`SpinDefectSim.magnetometry.geometry`¶

`SampleGeometry` (abstract)¶

`edge_current_segments`¶

`sample_M_at_vertices`¶

`bulk_current_density`¶

`interior_mask`¶

`PolygonGeometry`¶

`SquareGeometry`¶

`DiskGeometry`¶

`SpinDefectSim.magnetometry.bfield`¶

`B_from_wire_segment`¶

`B_from_edge_segments`¶

`B_from_bulk_current_density`¶

`B_from_magnetization_grid`¶

`SpinDefectSim.magnetometry.magnetometry`¶

`MagnetometryExperiment`¶

`B_field`¶

`transition_frequencies`¶

`B_field_map`¶

`B_z_map`¶

`transition_frequency_map`¶

`odmr_spectrum`¶

`frequency_shift_map`¶