Magnetization easy axis

Figure 1.4 Plot of the lowest hyperfine split pseudo-doublet for field applied along the easy magnetization axis of Na9Ho(W5018)2 t)H20. Grey dotted lines are obtained in the assumption of purely axial symmetry while black continuous lines result after inclusion...

Let us proceed to the derivation of the pertinent Fokker-Planck equation. The probability density W(e,n,t) of various orientations of the magnetic moment and the easy magnetization axis of a ferroparticle must satisfy the conservation law... 

As can be seen from Fig. 2, hydrogenation induces easy plane anisotropy in TbFeeCosTiH. The [100] direction becomes easy magnetization axis and critical fields are not observed in the field dependences of the magnetization for TbFe6Co5TiH. 

Hq is the amplitude of the external uniform magnetic field (the polarizing field), K > 0 is the constant of the effective magnetic anisotropy, and n is a unit vector along the easy magnetization axis. The fact that h is not necessarily parallel to n means that the axial symmetry characteristic of uniaxial anisotropy will be broken. Thus Eq. (80) becomes... 

Powder free to orient by an applied magnetic field (simulating single-crystal measurement along the easy magnetization axis a single-crystal is not available). 

Due to the in-plane surface anisotropy [23] the easy magnetization axis in thin iron films is the in-plane [110] direction being the hard magnetization axis of bulk Fe, switching at a critical thickness to the one of bulk crystals, i.e. the [001] direction. For cobalt films the anisotropy causes the easy magnetization axis to lie in-plane in contrast to bulk-hcp Co with its easy axis perpendicular to the basal plane. Thick rare earth metal films exhibit an easy axis within the surface plane. The shape anisotropy may also change the easy magnetization axis. 

At r = 30 K the fllms with three or four iron monolayers are magnetized perpendicularly to the film surface, while the magnetization of thicker and thinner films lays in the film plane. Epitaxial iron film on Cu( 1,000) substrate has the face-centered structure up to 15 monolayers thickness, while the bulk samples have body-centered structure. The Curie temperature for the films containing three and five monolayers is equal to 390 K, which possibly corresponds to 7). of face-centered bulk iron, while for monolayer Tc = 230 K [68]. The saturation magnetization decreases linearly with temperature near 7),. At room temperature, three and five monolayers films have no magnetization, but at 7 = 30 K, the hysteresis loops have been observed with coercive fields 350 and 650 Oe respectively. The direction of the easy magnetization axis is perpendicular to the film plane. There was no hysteresis even at low temperatures in a monolayer film. 

Fig. 4.22. The ratio of ordering temperatures with and without an applied field Tn(B)/7n(0) as a function of the applied field B for KjFeFj. The points A are for B applied along the easy magnetic axis and the points O and are for B applied along hard magnetic axes. (Boersma et al., 1982.)...

A different conclusion was drawn from the results of a magnetometric measurement on the single crystal of GdMn2Ge2. The magnetization curve at 4.2 K (see fig. 7) shows that the easy magnetization axis is along the c-axis direction (Shigeoka 1984). 

FIGURE 117 The magnetization and inverse magnetic susceptibility of UGe2. Left inset represents the orthorhombic unit cell right inset depicts a typical hysteresis loop at 4.5 K measured along the easy magnetization axis (Saxena et al., 2000). 

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