mammos_analysis.kuzmin#

Postprocessing functions for micromagnetic property estimation.

Functions

kuzmin_formula(Ms_0, T_c, s, T)

Compute spontaneous magnetization at temperature T using Kuz'min formula.

kuzmin_properties(Ms, T[, Tc, Ms_0, K1_0])

Evaluate intrinsic micromagnetic properties using Kuz’min model.

Classes

KuzminResult(Ms, A, Tc, s[, K1])

Result of Kuz'min magnetic properties estimation.
class mammos_analysis.kuzmin.KuzminResult(Ms, A, Tc, s, K1=None)[source]#

Result of Kuz’min magnetic properties estimation.

Parameters:
A: Callable[[Real | Quantity], Entity]#

Callable returning temperature-dependent exchange stiffness.

K1: Callable[[Real | Quantity], Entity] | None = None#

Callable returning temperature-dependent uniaxial anisotropy.

Ms: Callable[[Real | Quantity], Entity]#

Callable returning temperature-dependent spontaneous magnetization.

Tc: Entity#

Curie temperature.

plot(T=None)[source]#

Create a plot for Ms, A, and K1 as a function of temperature.

Parameters:

T (mammos_entity.Entity | astropy.units.Quantity | numpy.ndarray | None)

Return type:

matplotlib.axes.Axes

s: Quantity#

Kuzmin parameter.

mammos_analysis.kuzmin.kuzmin_formula(Ms_0, T_c, s, T)[source]#

Compute spontaneous magnetization at temperature T using Kuz’min formula.

The formula approximate spontaneous magnetization \(M_s(T)\) for \(0 < T < T_c\) as

\[\begin{split}M_s(T) = M_0 \left[ 1 - s \left( \frac{T}{T_c} \right)^{3/2} \\ - (1-s) \left( \frac{T}{T_c} \right)^{5/2} \right]^{1/3}\end{split}\]

where \(M_0\) is the saturation magnetization, \(T_c\) is the Curie temperature, and \(s\) is an adjustable parameter.

Kuz’min, M.D., Skokov, K.P., Diop, L.B. et al. Exchange stiffness of ferromagnets. Eur. Phys. J. Plus 135, 301 (2020). https://doi.org/10.1140/epjp/s13360-020-00294-y

Parameters:

  • Ms_0 – Spontaneous magnetization at 0 K.

  • T_c – Curie temperature.

  • s – Kuzmin exponent parameter.

  • T – Temperature(s) for evaluation.

Returns:

Spontaneous magnetization at temperature T as an array.

mammos_analysis.kuzmin.kuzmin_properties(Ms, T, Tc=None, Ms_0=None, K1_0=None)[source]#

Evaluate intrinsic micromagnetic properties using Kuz’min model.

Computes Ms, A, and K1 as function of temperature by fitting the Kuz’min equation to Ms vs T. The attributes Ms, A and K1 in the returned object can be called to get values at arbitrary temperatures.

K1 is only available in the output data if the value of the zero-temperature uniaxial anisotropy constant K1_0 has been passed.

If Ms_0 is None, the first value in the Ms series is taken as the zero temperature magnetization Ms_0 only if the first entry of the T series is zero; otherwise, a ValueError is raised.

If Tc is None, it will be treated as an optimization variable and estimated during the fitting process via least squares.

Parameters:

  • Ms (Entity) – Spontaneous magnetization data points as a me.Entity.

  • T (Entity) – Temperature data points as a me.Entity.

  • K1_0 (Entity | None) – Magnetocrystalline anisotropy at 0 K as a me.Entity.

  • Tc (Entity | None) – Curie temperature.

  • Ms_0 (Entity | None) – Spontaneous magnetization at T=0.

Returns:

KuzminResult with temperature-dependent Ms, A, K1 (optional), Curie temperature (optional), and exponent.

Raises:

  • ValueError – Value of Ms at zero temperature is not given.

  • ValueError – If K1_0 has incorrect unit.

Return type:

KuzminResult