Electronic band structure, phonon dispersion, and magnetic triple-q state in GdGaI

TL;DR

This work investigates the magnetic van der Waals material GdGaI by combining first-principles calculations with a Wannier-based tight-binding model and a Kondo-lattice framework. It reports a stable crystal structure with no phonon instabilities and identifies near-$E_F$ bands dominated by Gd $5d$ and Ga $4p$ orbitals, forming a semimetal. By coupling these itinerant electrons to localized Gd $4f$ spins and imposing a triple-$\bm{q}$ all-out order, the authors show a $d$-$d$ hybridization gap opens in the reduced Brillouin zone, with parallel top/bottom layer spins energetically favored, consistent with ARPES features. RKKY analysis, incorporating interband Coulomb interactions via RPA, suggests enhanced spin susceptibility at $\bm{q}_{M}$, providing a mechanism for stabilizing the triple-$\bm{q}$ localized-spin order and highlighting the role of Coulomb interactions near the Fermi level in driving magnetic order in GdGaI.

Abstract

We theoretically investigate the physical properties of the magnetic van der Waals material GdGaI. Using first-principles calculations, we compute the phonon dispersion of GdGaI and show no imaginary phonons, suggesting that phonon-driven phase transitions are unlikely to occur in GdGaI. Our band calculation reveals that the electronic bands near the Fermi energy are composed of Gd 5d and Ga 4p orbitals. We construct a tight-binding model that incorporates the Gd 5d and Ga 4p orbitals to investigate the magnetic structure. We introduce Kondo coupling between electrons in Gd 5d orbitals and localized spins in Gd 4f orbitals and present the modified band structure when localized spins form a magnetic order characterized by three q vectors that connect the valence and conduction bands. We discuss the origin of the spin order based on the Ruderman-Kittel-Kasuya-Yosida mechanism and suggest that Coulomb interactions acting on electrons near the Fermi level can contribute to the ordering of localized spins.

Figures (13)

• Figure 1: (a) Side view of the crystal structure of GdGaI visualized by VESTA VESTA. Red, navy, and purple balls represent Gd, Ga, and I atoms, respectively. (b) GdGa$_3$I$_3$ octahedron. (c) Top view of the Gd and Ga sites.
• Figure 2: (a) Schematic figure of the BZ. (b) Phonon dispersion and (c) electronic band structure obtained with the HSE hybrid functional. The horizontal line in (c) represents the Fermi energy $E_F$.
• Figure 3: Electronic band dispersions with colored weights: (a) Gd $5d$, (b) Ga $4p$, (c) I $5p$, and (d) Ga $4s$ orbitals, respectively.
• Figure 4: (a) Band structure of the 16-orbital $d$-$p$ model obtained by Wannierization (orange dotted lines), where the modeled band structure is superposed on the first-principles band structure using the HSE hybrid functional (gray lines). (b) Electronic bands colored by the orbital components in the $d$-$p$ model. Red and blue indicate the Gd $5d$ and Ga $4p$ orbitals, respectively.
• Figure 5: (a) All-out structure of localized spins. Red balls represent Gd atoms. Arrows represent localized spins on Gd $4f$ orbitals. (b) BZ and three $\bm{q}$ vectors that connect the $\Gamma$ and M points. (c) Band structure with the all-out spin structure in (a), where the electronic bands for $J_{\rm K}=0.4$ eV are plotted in the reduced BZ [shadowed area in (b)]. (d) Band structure along the $\Gamma$--M line in the original BZ, where color indicates the weight of the $\bm{q}=\bm{0}$ component.