Theory of the Knight shift near the points of Fermi surface with changing topology

We propose a theory of the Knight shift for a group of states near the symmetry points of the Brillouin zone, taking into account correctly the magnetization of the state lk, where l is the band number. Using the Green’s function we obtain an equation which makes it possible to calculate directly the quantity ΔH/H for states described by the kp Hamiltonian matrix. This Hamiltonian takes into account the interaction of the electron magnetic moment with the nuclear spin. The general Knight shift is written in the form of a sum of the spin and orbital contributions Ks and Korb. As an example we consider a two-band model. The kp expansion of the Hamiltonian is obtained by the method of invariants for the corresponding points of the Brillouin zone for the body centered cubic, face centered cubic, and hexagonal close-packed lattices, and it is shown that Ks contains a term linearly proportional to the Fourier component of the lattice potential due to transitions between bands.

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