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 $\text{5}d$ orbitals and localized spins in Gd $\text{4}f$ orbitals and present the modified band structure when localized spins form a magnetic order characterized by three $\mathit{q}$ 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.

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• Electronic structure
• Magnetism
• Phonons
• Strongly correlated systems
• Triangular lattice
• First-principles calculations
• Kondo lattice model
• Tight-binding model