Impact of strong electronic correlations on altermagnets: the case of NiS2

TL;DR

This work addresses how strong electronic correlations modify altermagnetic order in a metallic altermagnet, NiS2, near a pressure-driven metal-insulator transition. Using a comparative framework of DFT, DFT+U, and DFT+DMFT, it disentangles static versus dynamic correlation effects and reveals that static correlations largely boost the local Ni moment and AM spin splitting, while dynamic correlations renormalize bandwidth through a momentum- and orbital-weight dependent quasiparticle renormalization $1/Z_{ u}(oldsymbol{k})$, producing a highly nonuniform, band- and energy-dependent spin splitting $Δ_{ ext{AM}}^{ u}(oldsymbol{k})$. Dynamic correlations also generate pronounced spin-resolved lifetime asymmetry $Δ_{ au}(oldsymbol{k}) = τ_{ ext{up}}(oldsymbol{k}) - τ_{ ext{dn}}(oldsymbol{k})$, amplified by Hund's coupling–driven particle-hole asymmetry and kink/shoulder features in the self-energy. Overall, NiS2 serves as a versatile platform to explore the coexistence and competition of Mott and Hund physics with altermagnetic order, with implications for spintronics where one spin channel can remain more coherent than the other.

Abstract

One of the distinguishing features of an altermagnet is that its spin-up and spin-down bands display a nodal momentum-dependent splitting even in the absence of spin-orbit coupling. While this property has been investigated in many weakly-correlated altermagnetic materials, the impact of strong electron-electron interactions on the spin-dependent electronic structure has remained little explored, particularly in metals. Here, we propose NiS2 as a prototypical strongly correlated metallic altermagnet. While at ambient pressure this compound is an altermagnetic Mott insulator, it undergoes a pressure-driven metal-insulator transition (MIT) while maintaining its altermagnetic ordered phase. By systematically comparing DFT, DFT+U, and DFT+DMFT calculations on the metallic altermagnetic phase near the MIT, we disentangle how strong static and dynamic correlations modify the electronic structure. Specifically, the spin splitting of the bands is modified not only through the enhancement of the local magnetic moment caused by static correlations, but also by the momentum-dependent bandwidth renormalization caused by dynamic correlations. Moreover, dynamic electronic correlations cause a pronounced lifetime asymmetry between the spin-up and spin-down quasiparticles, an effect that is amplified by the particle-hole asymmetry promoted by Hund's correlations. Our results not only shed light on the rich landscape of correlation effects in metallic altermagnets, but also establishes NiS2 as a platform to investigate the interplay between Mott and Hund physics and altermagnetic order.

Figures (8)

• Figure 1: (a) Schematic pressure ($P$) - temperature ($T$) phase diagram of NiS$_{2}$. friedemann2016large Open circle indicates the $P,\,T$ values at which the DMFT calculations are performed. (b) Crystal structure of the pyrite NiS$_{2}$. (c) Example of a symmetry relation between two representative Ni atoms with opposite spins The symbol $\left[ C_2 \parallel M_y t \right]$ indicates that the system is invariant under a combination of a two-fold rotation in spin space and a non-symmorphic glide $M_y t$ in real space, with $t= (0, 1/2, 1/2)$ (d) The non-collinear magnetic structure realized experimentally in NiS$_{2}$ and (e) the corresponding approximate collinear structure.
• Figure 2: (a) Non-relativistic DFT band structure for the collinear altermagnetic phase of metallic NiS$_{2}$ at $P=4.3$ GPa. Grey lines are spin-degenerate band dispersions. (b-c) Brillouin zone and high-symmetry $k$-points (b) with spin-degenerate nodal planes and (c) with non-zero spin-splitting at the $k_z=0$ ($k_z=1/2$, $k$-points in parenthesis) planes. Red and blue colors highlight the alternating sign of the splitting between spin-up and spin-down bands.
• Figure 3: (a) Projected density of states (PDOS) of Ni $e_g$ and $t_{2g}$ orbitals. The labels are the same as in Fig. \ref{['fig:1']}(d). (b) Total momentum-resolved spectral function $A(k,\omega)$ and (c) spin-resolved spectral function defined as $\Delta A \equiv A_{\mathrm{up}}(k,\omega) - A_{\mathrm{dn}}(k,\omega)$ along the momentum-space paths R$_1$-$\Gamma$ (left column), M$_1$-$\Gamma$ (middle), and X$_3$-R$_1$ (right). The Brillouin zone notation is the same as in Fig. \ref{['fig:2']}(b).
• Figure 4: Comparison between (a)-(d) DFT, (b)-(e) DFT+$U$, and (c)-(f) DFT+DMFT effective band structures along the X$_3$-R$_1$ (upper panel) and M$_1$-$\Gamma$ (lower panel) paths. The arrows highlight the AM spin-splitting of selected pairs of bands. The yellow shading gives the spectral weight of the S-$p$ orbitals.
• Figure 5: (a)-(d) DFT+DMFT band structures, with the corresponding quasiparticle lifetime marked by colored circles along the (a) $\Gamma$-R$_1$ and (b)-(d) X$_3$-R$_1$ paths. (e)-(h) Altermagnetic spin-splitting, $\Delta_{\mathrm{AM}}\left(\mathbf{k}\right)\equiv \varepsilon_{\mathrm{up}}\left(\mathbf{k}\right) - \varepsilon_{\mathrm{dn}}\left(\mathbf{k}\right)$, along the (e) $\Gamma$-R$_1$ and (f)-(h) X$_3$-R$_1$ paths. (i)-(l) Difference in the lifetimes between "up" and "dn" quasiparticles, $\Delta_\tau\left(\mathbf{k}\right)\equiv \tau_{\mathrm{up}}\left(\mathbf{k}\right)- \tau_{\mathrm{dn}}\left(\mathbf{k}\right)$ and (m)-(p) lifetime $\tau$ as a function of momentum $\mathbf{k}$ along the (m) $\Gamma$-R$_1$ and (n)-(p) $X_3$-R$_1$ paths.