Magnetic tunneling told to ignorants by two ignorants

Magnetic tunneling of a large spin subject to the Hamiltonian H = -DSz2 + BSx2 - g mu(B)H . S is investigated by elementary methods for weak fields H. In zero field (H = 0) the tunnel frequency in the ground state is found to be equal to Ds[1 + (2D/B) + 2 root(1 + D/B)D/B](-s) multiplied by a quantity whose variation with s is slower than exponential. This result coincides with that of path integral methods [16]. For the values of the longitudinal field which allow tunneling, the tunnel frequency w(T) is shown to vanish when H-y = 0 for certain "diabolic" values of g mu(B)H(x)/root B(D + B), in qualitative agreement with experiments by Wernsdorfer and Sessoli. The particular case H-z = 0 was already obtained by Garg by means of path integrals. The diabolic values of g mu(B)H(x)/root B(D + B) are in agreement with numerical results but, as already noticed by Wernsdorfer and Sessoli, they disagree with the experimental ones. This may be an effect of higher order anisotropy terms, which is briefly addressed in the conclusion.