Easy magnetisation direction

Here, Ms is the saturation magnetisation. Notice, that apparently, the stress transfer from the kapton substrate to the deposited film was ignored (compare eq. (IS) with eq. (1 Id)). A consistent result was obtained by determining the anisotropy from the hysteresis loops measured in the hard and easy magnetisation directions, using a vibrating sample magnetometer. 

Magnetic and magnetostrictive properties of the RC02 compounds Curie temperature (Tq), saturation magnetic magnetization (A/j), easy magnetisation direction (EMD), A,oo and A,u at 4.2 K... 

For thin films with a perpendicular anisotropy (easy axis normal to the film plane), Huang et al. (199S) determined magnetostriction (As) and anisotropy (Iff) values, by using the so-called initial-susceptibility method. An ac magnetic field was applied in the film direction, and the induced magnetisation component in the field direction was measured. These authors deduced K and As from the x 1 vs. o plots, using ... 

For the rotation of the magnetisation out of the easy axis into the field direction, the magnetostriction is related to the magnetisation as (Chikazumi 1964) ... 

Fig. 4.35. Magnetisation in a Co single crystal with the applied field parallel and perpendicular to the c-axis, which is the easy direction. (Adapted from Kaya, 1928.)...

In addition to domain wall bowing and displacement, there are two other magnetisation mechanisms spin rotation and spin waves. In the former, Fig. 4.44, magnetic moments within domains are simply rotated out of their easy direction by the external field. This mechanism occurs for virtually any magnitude of field the rotational permeability is a linear function of the field it is reversible and is typically small. It is discussed in Section 4.5.1. 

Fig. 4.53. Magnetisation behaviour of a single-domain particle assuming rotation-only mechanism (a) applied field at 90° from the easy direction (b) field collinear to the easy direction (Stoner Wohlfarth, 1948).

At very high frequencies, domain walls are unable to follow the field and the only remaining magnetisation mechanism is spin rotation within domains. This mechanism eventually also shows a dispersion, which always takes the form of a resonance. Spins are subjected to the anisotropy field, representing spin-lattice coupling as an external field is applied (out of the spins easy direction), spins experience a torque. However, the response of spins is not instantaneous spins precess around the field direction for a certain time (the relaxation time, r) before adopting the new orientation. Fig. 4.62. The frequency of this precession is given by the Larmor frequency ... 

Directional order results in a strong induced anisotropy (and an easy axis) in the field direction this leads to large 180° domains separated by highly mobile domain walls parallel to this axis. Induced anisotropy values in the range. 100-400 J/m have been observed in Ni-Fe alloys (Ferguson, 1958). The application of a field parallel to the induced anisotropy axis results in extremely soft behaviour (Fig. 6.9(c)) saturation is reached for small fields, as a result of domain wall mobility. If the field is instead applied in a transverse direction, completely different behaviour is observed. Fig. 6.9(d). Since domain wall displacement has no net effect on the magnetisation in the field direction (domain walls are 180° Bloch walls, oriented in a direction perpendicular to the field), magnetisation proceeds mainly by spin rotation (see Section 4.5.1). The hysteresis loop in Fig. 6.9(a) was obtained after heat treatment at T > 7 (7 for this composition is around 900 K), and therefore corresponds simply to the stress-free state. 

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