A theory of the μSR method is developed for uniaxial anisotropic high-Tc superconductors. Using the London equation for the anisotropic uniaxial superconductor we obtain formulas representing the microscopic field distribution in the form of one dimensional Fourier series. In extreme cases ( a 2 π λ ≪ 1) summing can be done analytically and the field is expressed in terms of Jacobi θ{symbol}-functions in both cases of the rectangular and the triangular vortex lattice. The existence of two logarithmic van Hove singularities is demonstrated for the spectral density of polarization P(t) in experiments with monocrystalline samples in a transverse field for arbitrary orientation. In the two "appropriate" extreme cases of Hext∥c and Hext⊥c there is one singularity only, as it is in the case of isotropic superconductors. Analytical formulas are obtained which makes it possible to determine from the position of this singularity the type and parameters of vortex lattice, such as λab and λc and, respectively, Hc1⊥ and Hc1∥. Convenient expressions for numerical calculations are obtained for arbitrary orientation of the external field, and an algorithm is provided to compute the mean field B, the vortex lattice parameters and the bulk field distribution in an anisotropic superconductor. The Fourier spectrum of polarization based on these calculations can be used to check independently the validity of the high-Tc parameters determination for "appropriate" orientations. It is shown that the location of van Hove singularities is ruled by the distribution of the microscopic field module (Larmor frequency values), while the form of the spectrum strongly depends upon the angular distribution of the field vector. A qualitative discussion of experiments with polycrystalline samples is given. Important information in this case can be obtained from the dependency of the precessing component of polarization and induction B relative to the external field Hext. A qualitative description of the polycrystal Fourier-spectrum is given. Accent is placed on the advantages of longitudinal field experiments. It is difficult to make a quantitative analysis for the polycrystal due to the lack of a reliable theoretical model of the magnetic field behaviour in a bulk sample. © 1990.
