Cycloidal structure

In a second paper (43) y Werner reiterated his belief that the cycloid structure of Liebermann s theory (21) does not explain the peculiar properties of lakes, as it only affords the metal an opportunity of combining with the organic body by means of its primary valencies. 

Figure 3.4 Examples of magnetic structures. In all cases the orientation of the lattice is similar, except in the second view of (b), where the point of view is nearly along a. (a) Sinusoidal structure with propagation vector k = (0,, 0) and Sk = (0,0,w). (b) Helical, or spiral, structure with propagation vector k = (0,(5,0) and Sk = (w/,0,w). (c) Cycloidal structure with propagation vector k = (0,, 0) and Sk = (0,u,ui).

Fig. 29. The calculated arrangement of moments in the r , = cycloidal structure of Er in zero field (i) in the fl - c plane and (ii) in the h - c plane. The figure is drawn to emphasize the fact that the moments are not confined to the a - c plane, but instead wobble about this plane. Scaling a to c 1 1, and 6 to c 10 1. The numerical labels refer to moments in successive planes along the c axis. (From Jehan et al. 1994.)...

Simple artificial examples of sinusoidal, helical and cycloid magnetic structures are given in Figure 3.4. In Figure 3.5 there is a real example of the incommensurate conical structure of DyMugGcg propagation vector ki = (0,0,0) and k2 = (0,0,5) at the interior of Brillouin Zone. 

Fig. 42. Structural and magnetic phase diagram tor the Co Ni MnGe system. Tu is the temperature of the first-order structural transition, the Neel temperature, Tc the Curie temperature. Structures SS, simple spiral CS, cycloidal spiral FS ferromagnetic spiral (Zach et al. 1984, Niziol et al. 1982).

If the canting is not the same for each magnetic cation but varies in a regular way, then a number of commensurate or incommensurate spin structures can arise, including helical, helicoidal, cycloidal and sinusoidal. The helicoidal and sinusoidal ordering patterns are illustrated by the magnetic structure of TbMnOj (Section 7.10). 

Figure 7.19 TbMnO (a) crystal structure (b) schematic depiction of the incommensurate sinusoidal spin ordering on Tb lying on (iOO) and (200) below approximately 42 K (c and d) schematic depiction of the cycloidal spin geometry of Mn projected onto (100) and (200)...

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