Self-energies in itinerant magnets: A focus on Fe and Ni

We present a detailed study of local and nonlocal correlations in the electronic structure of elemental transition metals carried out by means of the quasiparticle self-consistent GW ($\mathrm{QS}\mathit{GW}$) and dynamical mean field theory (DMFT). Recent high resolution ARPES and Haas-van Alphen data of two typical transition metal systems (Fe and Ni) are used as a case study. (i) We find that the properties of Fe are very well described by $\mathrm{QS}\mathit{GW}$. Agreement with cyclotron and very clean ARPES measurements is excellent, provided that final-state scattering is taken into account. This establishes the exceptional reliability of $\mathrm{QS}\mathit{GW}$ also in metallic systems. (ii) Nonetheless $\mathrm{QS}\mathit{GW}$ alone is not able to provide an adequate description of the Ni ARPES data due to strong local spin fluctuations. We surmount this deficiency by combining nonlocal charge fluctuations in $\mathrm{QS}\mathit{GW}$ with local spin fluctuations in DMFT. (iii) Finally we show that the dynamics of the local fluctuations are actually not crucial. The addition of an external static field can lead to similarly good results if nonlocal correlations are included through $\mathrm{QS}\mathit{GW}$.

Figure 1

Left: $\mathrm{QS}\mathit{GW}$ band structure of Fe (solid lines), LSDA (gray dashed), $k$-point averaged $\mathrm{QS}\mathit{GW}$ (black dotted, see text), ARPES spectra [1] (diamonds), and inverse photoemission spectra [11] (squares). Right: Fermi surface. Symbols denote FS crossings reported in Ref. [1]. Red and green depict majority and minority $d$ character, respectively.

Figure 2

(a) The $\mathrm{\Gamma }-\mathsf{H}$ line of Fig. 1 in high resolution. Labels correspond to traditional assignments of Fermi surface pockets [1, 9]. (b) Dashed line is $\mathrm{QS}\mathit{GW}$ spectral function $A(k,\omega )$ for various points on the $\mathrm{\Gamma }-\mathsf{H}$ line, with $\mathsf{k}=0$ and $\mathsf{k}=1$ denoting $\mathrm{\Gamma }$ and $\mathsf{H}$. Solid line is $A\left(\omega \right)$ modified according to Eq. (1). (c) The analog of ($b$) at $k=0.77\times \mathsf{H}$ where the ${\mathsf{II}}_{\mathrm{M}}$ band crosses $E_F$. $E_{\mathrm{QP}}$ indicates the $\mathrm{QS}\mathit{GW}$ QP level, and $E_{\mathrm{ARPES}}$ the experimental ARPES peak at $0.77\mathsf{H}$. (d). dispersion in the $\mathrm{QS}\mathit{GW} {\mathsf{II}}_{\mathrm{M}}$ band on a line ${\mathbf{k}}_{\perp }+[0,0,0.77\mathsf{H}]$ normal to the film surface.

Figure 3

(a): $d$ bandwidth (top panel) and exchange splitting $\mathrm{\Delta }{E}_x$ (bottom panel) in the $3d$ elemental metals. (b): Magnetic moment of several compounds

Figure 4

(left) Band structure of Ni in $\mathrm{QS}\mathit{GW}$ (solid lines) and LDA (dotted) and ARPES data [23] (the circle at $-1.3$ eV was taken from Ref. [27]). Red arrows highlight the discrepancy in the exchange splitting $\mathrm{\Delta }{E}_x$ at near L and X. (right) $\mathrm{QS}\mathit{GW}$+LSDMFT bands (solid) and $\mathrm{QS}\mathit{GW}$+$B^{\mathrm{eff}}$ (dashed). (inset) $\mathrm{\Delta }{E}_x$ at L as a function of $M$ obtained by adding an external magnetic field to the $\mathrm{QS}\mathit{GW}$ or LSDA potential (see text).