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QSGW + Spin-Dynamical Mean Field Theory Applied to Ni

Density-Functional theory, while being immensely popular thanks to its simplicity, nevertheless is limited in its reliability. The QuasiParticle Self-Consistent GW approximation, while more demanding than DFT, is vastly more reliable than DFT, or GW theory based on DFT, for calculation of optical properties in weakly correlated systems.

In this Phys Rev paper, the validity of QSGW for two magnetic transition metals are critically examined : Fe and Ni. We show spectacular agreement with a variety of experiments for states near the Fermi level in Fe. QSGW theory is precise enough that we can identify limits to the standard interpretation of Angle Resolved Photoemission measurements.

QSGW bands of Fe

For Ni, QSGW agrees less well because spin fluctuations are missing in GW theory (as they are in Density Functional theory). By constructing a novel form of QSGW+Dynamical Mean Field theory, where the spin-only part of the DMFT self-energy is added to the spin-averaged part of the QSGW self-energy we can include spin fluctuations with a minimum of ambiguity, e.g. in the problem of double-counting. Excellent agreement with Angle Resolved Photoemission measurements is found, and a satisfactory description of the role of spin fluctuations in modifying the magnetic moment obtained.

The left panel of the figure below (taken from the Phys Rev paper) compares the energy band structure of Ni in QSGW (solid lines) and LDA (dotted lines), and ARPES data (symbols). Red arrows highlight the discrepancy in the exchange splitting ∆Ex at near L and X. Right panel: QSGW+DMFT bands (solid) and a simple approximation to it QSGW+Beff (dashed), which adds a constant magnetic field to account for the reduction in magnetic moment M from spin fluctuations. Inset: ∆Ex at L as a function of M obtained by adding an external magnetic field Beff to the QSGW or LSDA potential. For details, refer to the paper.

QSGW and QSGW+DMFT bands of Ni