16
Ò. Iglesias and H. Kachkachi
1.3 Results
In the following sections we shall present a sample of our previous results on finitesize, boundary, shape and surface effects. We first present results for model NMs
with a simple cubic lattice, spherical and cubic shapes. Next, we discuss the results
for more specific situations with antiferromagnetic couplings and core/shell configurations.
1.3.1 Finite-Size Effects
1.3.1.1 Switching Field
For many-spin NMs of variable size, but which still exhibit a collinear spin configuration, the hysteresis loop can be scaled with that rendered by the macrospin
Stoner-Wohlfarth model, even in the general case of a field applied at an arbitrary
angle with respect to the core easy axis.
The effect of finite-size on the hysteretic properties of NMs have been investigated
by many authors, see [36, 37, 47] and references therein.
In Fig. 1.9 we plot on the left the coercive field of a spherical NM and on the
right the Stoner-Wohlfarth astroid. We see that the results for a many-spin NM with
physical parameters within the range of the OSP model scale with those of the StonerWohlfarth model. The scaling constant is the ratio of the number of core spins to
Fig. 1.9 Left: coercive field versus the linear size of a spherical NM. Right: Switching field of a
spherical NM with ks/j 0.01, for different values of the surface-to-volume ratio N st = N s /N .
Calculations performed using the Landau-Lifshitz equation. Source Reprinted with permission from
[37]. Copyright (2020), AIP Publishing LLC
Ò. Iglesias and H. Kachkachi
1.3 Results
In the following sections we shall present a sample of our previous results on finitesize, boundary, shape and surface effects. We first present results for model NMs
with a simple cubic lattice, spherical and cubic shapes. Next, we discuss the results
for more specific situations with antiferromagnetic couplings and core/shell configurations.
1.3.1 Finite-Size Effects
1.3.1.1 Switching Field
For many-spin NMs of variable size, but which still exhibit a collinear spin configuration, the hysteresis loop can be scaled with that rendered by the macrospin
Stoner-Wohlfarth model, even in the general case of a field applied at an arbitrary
angle with respect to the core easy axis.
The effect of finite-size on the hysteretic properties of NMs have been investigated
by many authors, see [36, 37, 47] and references therein.
In Fig. 1.9 we plot on the left the coercive field of a spherical NM and on the
right the Stoner-Wohlfarth astroid. We see that the results for a many-spin NM with
physical parameters within the range of the OSP model scale with those of the StonerWohlfarth model. The scaling constant is the ratio of the number of core spins to
Fig. 1.9 Left: coercive field versus the linear size of a spherical NM. Right: Switching field of a
spherical NM with ks/j 0.01, for different values of the surface-to-volume ratio N st = N s /N .
Calculations performed using the Landau-Lifshitz equation. Source Reprinted with permission from
[37]. Copyright (2020), AIP Publishing LLC