Magnetism canted spins

Defects in ferrimagnetic structures often lead to noncollinear (canted) spin structures. For example, a diamagnetic substitution or a cation vacancy can result in magnetic frustration which leads to spin-canting such that a spin may form an angle 6c with the collinear spins in the sample [80, 81]. Similarly, the reduced number of neighbor ions at the surface can also lead to spin-canting [80-83]. 

Fig. 7.9. Schematic representation of the orientation of magnetic moments in ordered materials (a) ferromagnetics (b) antiferromagnetics (c) ferrimagnetics (d) canted spin materials.

Magnetization studies on single crystal spheres with fields in the [110], [111], and [100] directions indicate that the NNS state at 1.4 K can be easily modified into a canted spin state, Fukuma et al. [21]. 

If the direction of the spins is not uniform in space, we are dealing with noncollinear magnetism. Noncollinear spin structures appear, e.g., as canted or helical spin configurations in rare-earth compounds, as helical spin-density waves, or as domain walls in fer-romagnets. To describe these, one requires a formulation of SDFT in which the spin magnetization is not a scalar, as above, but a three-component vector m(r). Different proposals for extending SDFT to this situation are available. 

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