Easy axis rotation

As the appHed field is reduced, the iaductioa does aot retrace curve 1 but foUows curve 2 as the domaias at first merely rotate back to the aearest local easy axis directioa. The value of B at i/ = 0 is the remanent iaductioa. At H = which is the coercive-field strength of coercive force or... 

Rotating single-crystal measurements also permitted the extraction of the orientation of the magnetic tensor in the molecular reference frame and the experimental easy axis was found to coincide with the idealized tetragonal axis of the coordination dodecahedron of Dy. Crystal field calculations assuming idealized tetragonal symmetry permitted the reproduction of magnetic susceptibility data for gz = 19.9 and gxy 0 [121]. More elaborated calculations such as ab initio post Hartree-Fock CASSCF confirmed this simple analysis [119]. 

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) ... 

At a field H at which the particle is saturated perpendicular to the easy axis (a = 90), Hs = 2K/ fi0 Ms. This field can be defined as the anisotropy field Hk. Applying a field in opposite direction in the easy axis, a completely reversible change of M, by pure rotation, occurs without hysteresis. On the contrary, if a field is applied antiparallel to the anisotropy axis the particle switches irreversibly (no rotation) only after applying a field greater than... 

If a 0, we have the noninertial response. This is treated by Shliomis and Stepanov [9], who were able to factorize the joint distribution of the dipole and easy axis orientations in the Fokker Planck equation into the product of the two separate distributions. Thus as far as the internal relaxation process is concerned, the axially symmetric treatment of Brown [50] applies. Hence no intrinsic coupling between the transverse and longitudinal modes exists that is, the eigenvalues of the longitudinal relaxation process are independent of a. The distribution function of the easy axis orientations n is simply that of a free Brownian rotator excluding inertial effects. 

In NMR we have control over both the phase of the pulses and the receiver phase. The effect of changing the phase of a pulse is easy to visualise in the usual rotating frame. So, for example, a 90° pulse about the x-axis rotates... 

Fig. 3 Top Transmission spectrum recorded at 1.77 K on a single crystals mosaic of Mni2Ac with the crystallographic c-axis (easy axis) parallel to the radiation propagation direction, using parallel polarizer and analyzer. Bottom Frequency dependence of the Faraday rotation, derived from the transmission spectrum. Adapted from [84]...

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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