When most of elementary solid state physics textbooks introduce the energy band or the Fermi surface of electron, they usually ignore the degree of freedom of spin for simplicity. However, considering noncentrosymmetric materials that lack a space inversion symmetry, the spin-degenerate bands split owing to the parity violation. This produces two similar, but different in volume, Fermi surfaces. In such a case, spin orientations depend on the wave vector k due to the antisymmetric spin orbit interaction (ASOI), forming spin texture in k-space.
It is generally difficult to detect this spin texture.

In the noncentrosymmetric metals belonging to a certain point group, the spin degeneracy recovers at the special symmetry points. Carriers can travel from an orbit of one Fermi surface to another orbit of the paired Fermi surface across the degenerate point. Recently, we observed this orbital crossing between doubly split Fermi surfaces via the de Haas-van Alphen (dHvA) effect in a noncentrosymmetric metal.

The dHvA effect is a quantum oscillation of magnetization. The frequency of the oscillation, with respect to inverse magnetic field, is proportional to the extremal cross-sectional area of the Fermi surface. In noncentrosymmetric metals consisting of a pair of split Fermi surfaces, as shown in Fig. 1(a), a composite dHvA oscillation with two close frequencies, e.g. β₁ and β₅ in Fig. 2, is expected to be observed. However, we actually detected one additional oscilation for the field from the [110] to the [100] directions and two more oscillations in the vicinity of the [100] direction between the β₁ and β₅ branches. These extra-oscillations evidence that the orbital crossing takes place at the degenerate points.

We can estimate the intersecting probability from the amplitude of the dHvA oscillation. It is not clear what is the control parameter of the probability. Since the orbital crossing can be accompanied by a spin flip, the spin texture on Fermi surface may play an important role to affect the orbital motion.

See also, AAPPS Bulletin, vol. 29 No. 1
http://aappsbulletin.org/myboard/read.php?Board=focus&id=111

Fig. 1 (a) An example of Fermi surface pair in noncentrosymmetric metal (Yb₄Sb₃). (b) Cross section of the Fermi surface pair in (a) for the magnetic field applied along <100> direction, shown as the pink plane. The orbit for each Fermi surface is colored by green and blue. There are four degenerate points on the cross sections. The arrows indicate the effective local field at each k, corresponding to the spin direction. (c) and (d) Detailed views of the circled part in (b) at an enlarged scale for the cases of inner-to-inner path (c) and of inner-to-outer path (d).

Fig.2 Angular dependence of the dHvA frequency with its amplitude depicted by a contour plot.