Helical spin structure

Fig. 12. Magnetic phase diagrams for Gd-5c and Tb-5e alloys. PM = paramagnet HELIX = helical spin structure SG = spin glass (from Sarkissian and Coles 1976).

Fig. 14.2. A schematic representation of a helical spin structure for the example of a hexagonal lattice. The spins in a plane are parallel, but the direction rotates from plane to plane (Martin, 1967).

The first and second terms here represent the exchange contribution to the free energy. The third term is the energy of the helical spin structure written down in the form proposed by Herpin and Meriel (1961) and Enz (1960), where i and ri2 are the exchange parameters... 

The parameter 77 characterizes the effect of the elastic stresses on the helical spin structure and has the form... 

Fig. 5. Illustration of a helical spin structure. Ordering in each plane is ferromagnetic but the moment direction from plane to plane changes through a constant turn angle W resulting in overall antiferromagnetic behavior (after Taylor ).

Fig. 6. Illustration of metamagnetic behavior via destruction of ideal helical spin structure by an applied field (after Taylor ).

Though in this paper we have used the relativistic KKR wave functions ets betsis functions, the present approach may be easUy realized within any existing method for calculating the electron states. This will allow the electronic properties of materials with complex magnetic structure to be readily calculated without loss of accuracy. The present technique, being most eflicient for the SDW-type systems, can be also used for helical magnetic structures. In the latter case, however, the spin-polarizing part of potential (18) should be appropriately re-defined. 

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). 

Dysprosium. Large axial anisotropy confines the moments on Dy to the basal plane. Between Jn = 178 K and 7c = 85K, a helical AFM spin structure is present. The helix angle decreases with lower temperature. At 7c, an orthorhombic distortion of the hep lattice occurs and the transition into the FM state is of first order. The spins all have the same magnitude and all point along the orthorhombic a axis, so this is a simple FM structure. 

Erbium. The easy direction in Er is the c-axis, and below the second-order Neel transition (Tn = 85 K), the moments order in a longitudinal sine-wave structure. As the temperature is lowered the sine squares up. Aroimd Tb = 52 K, a basal plane component begins to order, leading to a helical AFM structure. Finally, at 7c = 20K a first-order transition into a steep cone (opening angle 30 ) FM spin structure takes place. Several (first-order) spin-slip transitions occur in the helical AFM phase. 

Many years ago, in 1959, to account for the magnetic structure in the ordered state, a helical screw-type structure was proposed by Yoshimori [124], who suggested a spin structure in which the manganese spins screwed along the c-axis with a pitch of 7c/2 (Figure 19.6b). In this way, the magnetic unit cell would be enlarged by a factor of seven in the c-direction with respect to the chemical unit cell. To stabilize this phase. 

These angles were determined in turn from distances between backbone carbonyl spins, measured with the DQ filtered dipolar recoupling with a windowless sequence experiment, and by determination of the mutual orientation of chemical shift anisotropy tensors of carbonyl spins on adjacent peptide planes, obtained from the DQ CP MAS spectrum. It was found that peptides composed of periodic sequences of leucines and lysines were bound along the length of the peptide sequence and displayed a tight a-helical secondary structure on the gold nanoparticles. 

Lee (1964) and Landry (1967) considered the pressure influence on the turn angle

helical antiferromagnetic spin structure in the framework of the model proposed by Herpin and Meriel (1961) and F.nz (1960). The free energy of the crystal was assumed to be ... 

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