Magnetism of iron and nickel from rotationally invariant Hirsch-Fye quantum Monte Carlo calculations

Abstract

We present a rotationally invariant Hirsch-Fye quantum Monte Carlo algorithm in which the spin rotational invariance of Hund's exchange is approximated by averaging over all possible directions of the spin quantization axis. We employ this technique to perform benchmark calculations for the two-and three-band Hubbard models on the infinite-dimensional Bethe lattice. Our results agree quantitatively well with those obtained using the continuous-time quantum Monte Carlo method with rotationally invariant Coulomb interaction. The proposed approach is employed to compute the electronic and magnetic properties of paramagnetic α iron and nickel. The obtained Curie temperatures agree well with experiment. Our results indicate that the magnetic transition temperature is significantly overestimated by using the density-density type of Coulomb interaction.

Momentum space anisotropy of electronic correlations in Fe and Ni: An analysis of magnetic Compton profiles

“…Subsequently this opened the path towards the computation of the phonon spectra across the α-to-γ phase transition and the study of lattice stability in the presence of electronic correlations [46]. Concerning the methodological background, the generalization to a rotational invariant exchange interaction allowed to revisit the magnetic properties of paramagnetic α iron [47] and to establish a reasonably good agreement for the Curie temperature of Fe and Ni [48]. A remarkable difference between Fe on the one side and Ni on the other side lies in the fact that in the latter the majority spin bands are fully occupied, while this is not the case in Fe.…”

Nonlocal correlations in the vicinity of the α−γ phase transition in iron within a DMFT plus spin-fermion model approach

“…To treat the effect of local correlations we apply in the present paper the combination of dynamical mean-field theory (DMFT) 10 with density functional theory (DFT) methods, usually called LDA+DMFT 11 . Previous studies by LDA+DMFT allowed one to obtain the correct values of magnetic moments in α and γ phases [12][13][14][15][16] , the linear behavior of the temperature dependence of the inverse local [13][14][15][16] (α,γ phases) and uniform magnetic 12,17,18 (α phase) susceptibilities, and revealed the non-monotonic temperature dependence of inverse the uniform magnetic susceptibility in the γ phase in a broad temperature range 14 .…”

“…As a result, the description of the magnetization 12 , the temperature of the α-γ transition 19 , and the phonon spectra 20 was provided in units of the calculated Curie temperature. The overestimation of the Curie temperature mainly comes from the DMFT part and is due to using the approximate (density-density) form of the Coulomb interaction 16,17 and neglecting nonlocal correlations in DMFT.…”

“…To solve the former problem, we apply in the present study the spin-rotationally-invariant DMFT approach 17 . Although the nonlocal corrections to DMFT can be taken into account using, e.g., the dynamic vertex approximation 21 , the dual fermion approach 22 , or cluster methods 23 , these approaches are too computationally expensive to be applied to real multiorbital compounds at the moment.…”

LDA+DMFT approach to ordering phenomena and the structural stability of correlated materials

“…We now understand that this is due to the presence of local moments above T C which cannot be treated realistically by conventional band structure techniques. This problem has been overcome by employing the DFT+DMFT approach which allows one to study correlated materials both in to the long-range ordered and paramagnetic state [27,28,43,[132][133][134][135][136]. The DFT+DMFT method naturally accounts for the existence of local moments above T C and has shown to provide a good quantitative description of the properties of α iron.…”