Numerical renormalization group calculations of the magnetization of Kondo impurities with and without uniaxial anisotropy

Höck M, Schnack J. Numerical renormalization group calculations of the magnetization of Kondo impurities with and without uniaxial anisotropy. Physical Review B. 2013;87(18): 184408.We study a Kondo impurity model with additional uniaxial anisotropy D in a nonzero magnetic field B using the numerical renormalization group (NRG). The ratio g(e)/g(S) of electron and impurity g factor is regarded as a free parameter and, in particular, the special cases of a "local" (g(e) = 0) and "bulk" (g(e) = g(S)) field are considered. For a bulk field, the relationship between the impurity magnetization M and the impurity contribution to the magnetization M-imp is investigated and it is shown that M and M-imp are proportional to each other for fixed coupling strength. Furthermore, we find that the g-factor ratio effectively rescales the magnetic field argument of the zero-temperature impurity magnetization. In case of an impurity with D = 0 and g(e) = g(S), it is demonstrated that at zero temperature M(B), unlike M-imp(B), does not display universal behavior. With additional "easy-axis" anisotropy, the impurity magnetization is "stabilized" at a D-dependent value for k(B)T << gs beta B-B << vertical bar D vertical bar and, for nonzero temperature, is well described by a shifted and rescaled Brillouin function on energy scales that are small compared to vertical bar D vertical bar. In the case of "hard-axis" anisotropy, the magnetization curves can feature steps which are due to field-induced pseudo-spin-1/2 Kondo effects. For large hard-axis anisotropy and a local field, these screening effects are described by an exchange-anisotropic spin-1/2 Kondo model with an additional scattering term that is spin dependent (in contrast to ordinary potential scattering). In accordance with the observed step widths, this effective model predicts a decrease of the Kondo temperature with every further step that occurs upon increasing the field. Our study is motivated by the question as to how the magnetic properties of a deposited magnetic molecule are modified by the interaction with a nonmagnetic metallic surface