Figure 3 : Paramagnetic spin response of nickel at ambient pressure.

From: Local magnetic moments in iron and nickel at ambient and Earth’s core conditions

Figure 3

(a) Temperature dependence of the static local spin susceptibility of nickel in DFT+DMFT, compared to the ‘bubble’ approximation and to the non-interacting one. To show that the characteristic temperature dependence of the non-interacting susceptibility originates from the t2g sector and its van Hove singularity, we also plot the intra-orbital contribution to the full (‘full’), considering the cases where either the five orbital-diagonal terms of are summed (‘’), or only the two eg terms are retained (‘eg only’). This shows the more conventional Pauli spin response of the eg part is in agreement with the fact that the eg DOS is much smoother around EF=0. (b) Inverse susceptibility for the non-interacting and DFT+DMFT case. This illustrates the main peculiarity of nickel, namely that already the non-interacting spin response is characterized by a 1/T law. As explained in the text, this is due to pre-localized moments arising from the vicinity to the van Hove singularity. (c) Electronic band dispersion of nickel on the hexagonal face of the Brillouin zone, close to the L point. The colors indicate the energy of the band relative to the Fermi level, which is located at zero energy. The extended flat region around the shallow maximum at L is responsible for the van Hove singularity. (d) t2g and eg DOS for energies close to EF=0. In the inset, the electronic state dispersion of nickel, close to the W-L-K region and to the top of the band is shown. The distance of the sharp step in the t2g orbitals at E=0.17 eV corresponds to the kink of the non-interacting susceptibility in b at T=2,000 K. (e) for β=4 eV−1 (dashed) and 30 eV−1 (solid). (f) Instantaneous (τ=0) and long-time () values of . From the latter one can clearly see that the moment is eventually screened at temperatures much lower than TC. The comparison with the non-interacting and with the ‘bubble’ results shows also that vertex corrections are important and the DFT+DMFT result cannot be obtained by using ‘dressed’ quasiparticle propagators (see also b).