  We theoretically investigate the effect of transverse magnetic anisotropy on
spin-flip assisted tunneling through atomic spin chains. Using a
phenomenological approach and first-order perturbation theory, we analytically
calculate the inelastic tunneling current, differential conductance and atomic
spin transition rates. We predict the appearance of additional steps in the
differential conductance and a pronounced increase in the spin-flip transition
rate which at low voltages scale quadratically with the ratio of the transverse
anisotropy energy and the sum of the longitudinal anisotropy energy and the
exchange energy. Our results provide intuitive quantitative insight in the role
played by transverse anisotropy in inelastic tunneling spectroscopy of atomic
chains and can be observed under realistic experimental conditions.
