Numerical solution of spin eigenvalues and eigenvectors for the analysis of the allowed and forbidden electron spin resonance transitions in mixed crystals of ammonium chloride–manganese(II) chloride dihydrate

Abstract

Eigenvalues and eigenvectors for a truncated spin Hamiltonian for NH₄Cl:Mn²⁺,ℋ=gβH·S +b₂⁰[S_z²-1/3S(S+ 1)], have been evaluated by numerical matrix diagonalisation and second-order perturbation theory and compared to the 35 GHz e.s.r. transitions. The accuracy of the eigenvalues is limited by omission of cross-product off-diagonal matrix elements of the form 〈|⅛(⁵⁵A)b₂⁰ sin 2θ(S_zS₊)(l₊S_–)|〉 where ⁵⁵A is the ⁵⁵mn hyperfine splitting. On the minor magnetic axes with θ= 90° the numerical solution and perturbation theory yield eigenvalues accurate to within 10² in 10⁴ gauss, and eigenvectors of the experimental order of magnitude. At low magnetic fields and intermediate angles the accuracy is reduced, and forbidden hyperfine lines appear.