Noncollinear Configurations

The A-B interactions are especially weak if the B-site eg orbitals are empty, and noncollincar spin configurations are anticipated if the B-site 3dn ions have n < 3. The common occurrence of noncollinear configurations is evident from Table XVI, where the saturation magnetizations of several spinels containing V4+ and Cr3+ are found to be incompatible with N el ordering. That the ratio JbhSbb/Ja b a... 

Such noncollinear magnetism appears, e.g., as canted or helical spin configurations in rare-earth compounds, or as domain walls in ferromagnets. 

In other more complex cases, the spins can take on a configuration that is not well approximated as a perturbed collinear configuration and such is the case for the spiral or helimagnetic ordering depicted in Figure 1. Noncollinear configurations are also observed in the family of so-called geometrically frustrated materials to be discussed later. 

Fig. 116. Field dependence of the magnetization in hexagonal PiGa2 compound along the [120] direction at 5 K (Ball et al. 1993c, Ball 1993). The circles are experimental the solid line is calculated by the PF model for the Dy,- and Z>9o-domains (see references). Several noncollinear configurations for the magnetic moments are also shown. Inset initial moment configurations of the domains with respect to the applied field for the calculations.

Fig. 2.5. Relative arrangement of three interacting atoms a, noncollinear configuration and b, collinear configuration.

Since a molecule or a quantum dot can emit no more than one photon per excitation, the optimum source for ultrafast fluorescence microscopy has a high repetition rate (10 -10 Hz) and a pulse energy sufficient to pump an excitation NOPA (noncollinear optical parametric amplifier) and to drive the Kerr or up-conversion gate. The current configuration of the Rutgers microscope relies on a cryogenically cooled Ti sapphire regenerative amplifier which produces 50 gJ... 

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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