Effects of correlations and temperature on the electronic structures and related physical properties of FeSi and CoSi: a comprehensive study

Abstract

Here, we report detailed investigations of the temperature dependent (100–800 K) electronic structures of FeSi and CoSi by using a DFT+DMFT method where self-consistently calculated values of U and J are used. The calculated spectral functions are found to provide fairly good representation for the experimentally observed photoemission spectra for both the compounds. For FeSi, the density of states (DOS) closer to the Fermi level are found to increase with the increase in temperature up to 450 K and then they decrease, whereas, for CoSi DOS continuously decrease with an increase in temperature. The electronic states of FeSi are greatly influenced by electronic correlations while they are moderately influenced in CoSi. From momentum resolved spectral functions, the excitations have shown enhanced broadening with temperature rise in FeSi whereas an opposite behavior is observed in CoSi. In FeSi, the maximum effect of temperature on the lifetime of quasiparticles states is observed where it first decreases to 400 K and then increases, and finally becomes almost infinite at 800 K. The temperature dependent behavior of DOS and quasiparticle lifetime help us in understanding the experimentally observed electrical resistivity and Seebeck coefficient for these compounds. The calculated effective magnetic moment for Fe (∼2.5 , which is closer to the experimental value) is temperature independent. The electronic structures of these compounds are showing the existence of mixed configurations with and for FeSi and CoSi, respectively. Average electrons in the d orbitals are found as ∼6.5 and ∼7.7 for FeSi and CoSi, respectively, with charge fluctuations 0.9 are obtained for both materials. This suggests that both the compounds are lying in the intermediate coupling regime of electronic correlations.

Electronic Structure of B20 (FeSi-Type) Transition-Metal Monosilicides

“…There were also attempts to take into account local electron–electron correlations using the Hubbard model in static (LDA+U) or dynamical mean-field theory (DMFT) approaches. Required values of parameters U and J , describing on-site Coulomb and the exchange interactions of d -electrons can be taken from a comparison with the experiment [85] or obtained from GW [86] or constrained DFT [87] calculations. In general, these values vary in the literature in quite a broad range.…”

“…[86] with U= 5.0 eV and J= 0.7 eV, and for FeSi and CoSi in Ref. [87] with U= 4.4 eV and J= 0.82 eV. Our calculations in the framework of the simplified rotationally invariant LDA+U approach [89] gave a band gap of ϵg = 0.16 eV for Ueff=1 eV and 0.76 eV for Ueff= 4.3 eV, thus not leading to improved ϵg values compared to the GGA approximation.…”

“…On the other hand, dynamic electron correlations in Refs. [85,86,87] predicted a decrease of the band gap to approximately 0.05 eV at low temperatures. In agreement with the experiment, these calculations showed further decrease of the band gap with the rise of temperature.…”

“…Interesting results concerning the broadening of the dispersion lines due to the finite lifetime of coherent states connected with on-site correlations were obtained in Ref. [87]. In the case of FeSi, the degree of incoherence increases with temperature, and the band gap decreases from 100 to 500 K, and then increases above 500 to 800 K. In contrast to FeSi, the degree of band-state incoherence in CoSi is small, in the range of ±0.3 eV near the Fermi level, and decreases with the temperature [87].…”

“…[87]. In the case of FeSi, the degree of incoherence increases with temperature, and the band gap decreases from 100 to 500 K, and then increases above 500 to 800 K. In contrast to FeSi, the degree of band-state incoherence in CoSi is small, in the range of ±0.3 eV near the Fermi level, and decreases with the temperature [87]. Thus, for CoSi, DFT seems to give quite accurate results.…”