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

Abstract

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 g S μ B B |D| and, for nonzero temperature, is well described by a shifted and rescaled Brillouin function on energy scales that are small compared to |D|. 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.

Ground state of the impurity Anderson model revisited: A projector operator solution

“…This agrees with the expected behavior of the Kondo problem indicative of a screened impurity spin. On the other hand, for larger fields, we obtain the characteristic slow asymptotic approach to the value of saturation which also agrees with the well‐known logarithmic corrections .…”

Tailoring the Magnetism of Co Atoms on Graphene through Substrate Hybridization

“…Multiplet calculations show excellent agreement with the value of m L =m SþD at normal incidence obtained from the sum rules, but overestimate m SþD and m L by 25%-30%. We attribute this to the fraction of Co atoms whose magnetic moments are Kondo screened, thus, giving little or no dichroic contribution [58]. Assuming full screening of the magnetic moment, we corrected for the Kondo species and obtained the m SþD and m L values of the majority population, which agrees very well with those deduced from the multiplet calculations, see Table I.…”

Control of single-spin magnetic anisotropy by exchange coupling

“…Tuning magnetic anisotropy normally can be done via structural 10,13 or mechanical 15 means, though electrical control of anisotropy through the addition and subtraction of discrete units of charge on a molecule has been observed 16 . The interplay between magnetic anisotropy and Kondo screening at the atomic and molecular scale has also recently received theoretical and experimental attention 15,[17][18][19] .…”