Hard magnet material exploration

Introduction

• In this notebook we explore hard magnet properties such as Hc as function of material and temperature.

• For more in-depth explanations we recommend starting with the hard magnet tutorial.

Requirements:

• Software: mammos, esys-escript

• Basic understanding of mammos-units and mammos-entity

%config InlineBackend.figure_format = "retina"

import math
import time

import mammos_analysis
import mammos_dft
import mammos_mumag
import mammos_spindynamics
import mammos_units as u
import matplotlib.pyplot as plt
import numpy as np
from matplotlib import colormaps

# Allow convenient conversions between A/m and T
u.set_enabled_equivalencies(u.magnetic_flux_field());

Select material

Change the index in the first line of the following cell to select one of the available materials:

index = 1  # select desired material

match index:
    case 1:
        material = "Co2Fe2H4"
        H_max = (5 * u.T).to("A/m")
    case 2:
        material = "Fe16N2"
        H_max = (1.2 * u.T).to("A/m")
    case 3:
        material = "Nd2Fe14B"
        H_max = (7 * u.T).to("A/m")

material

'Co2Fe2H4'

Load data from DFT and spindynamics databases

results_dft = mammos_dft.db.get_micromagnetic_properties(material)

results_spindynamics = mammos_spindynamics.db.get_spontaneous_magnetization(material)

Calculate micromagnetic intrinsic properties using Kuz’min formula

results_kuzmin = mammos_analysis.kuzmin_properties(
    T=results_spindynamics.T,
    Ms=results_spindynamics.Ms,
    K1_0=results_dft.K1_0,
)

results_kuzmin.plot();

ax = results_kuzmin.Ms.plot(label="Kuzmin fit")
results_spindynamics.plot(ax=ax, label="Spin dynamics");

Compute Hc(T)

T = np.linspace(0, results_kuzmin.Tc * 1.1, 7)

simulations = []
start_time = time.time()
for temperature in T:
    print(f"Running simulation for T={temperature:.0f}, {int(time.time() - start_time)} seconds")
    results_hysteresis = mammos_mumag.hysteresis.run(
        mesh_filepath=mammos_mumag.mesh.CUBE_20_nm,
        Ms=results_kuzmin.Ms(temperature),
        A=results_kuzmin.A(temperature),
        K1=results_kuzmin.K1(temperature),
        hstart=H_max,
        hfinal=-H_max,
        hnsteps=30,
    )
    simulations.append(results_hysteresis)

Running simulation for T=0 K, 0 seconds
Running simulation for T=195 K, 44 seconds
Running simulation for T=389 K, 103 seconds
Running simulation for T=584 K, 166 seconds
Running simulation for T=778 K, 223 seconds
Running simulation for T=973 K, 265 seconds
Running simulation for T=1168 K, 316 seconds

We can now use mammos_analysis.hysteresis as shown before to extract Hc for all simulations and visualize Hc(T):

Hcs = []
for res in simulations:
    cf = mammos_analysis.hysteresis.extract_coercive_field(H=res.H, M=res.M).value
    if np.isnan(cf):  # Above Tc
        cf = 0
    Hcs.append(cf)

plt.plot(T, Hcs, linestyle="-", marker="o")
plt.xlabel("Temperature [K]")
plt.ylabel("Coercitivity Hc External [A / m]");

We can also show the hysteresis loops of all simulations:

colors = colormaps["plasma"].colors[:: math.ceil(256 / len(T))]

fix, ax = plt.subplots()
for temperature, sim, color in zip(T, simulations, colors, strict=False):
    if np.isnan(sim.M).all():  # no Ms above Tc
        continue
    sim.plot(ax=ax, label=f"{temperature:.0f}", color=color, duplicate_change_color=False)
ax.legend(loc="lower right");