Why Fe 3 GaTe 2 has higher Curie temperature than Fe 3 GeTe 2

Physics of Fe 3 GaTe 2 having higher Curie temperature ( T C ) than Fe 3 GeTe 2 is explored theoretically in the framework of magnetic exchange interactions. Fe 3 GaTe 2 and Fe 3 GeTe 2 are isostructural, with Fe 3 GaTe 2 having one less valence electron and smaller nearest-neighbor exchange coefficients ( J 1 and J 2 ) , challenging the conventional notion that larger J 1 or J 2 leads to a higher T C . Based on the hybridization exchange, we show that higher-order exchange coefficients ( J 3 or higher) are positive for Fe 3 GaTe 2 but negative for Fe 3 GeTe 2 , due to a one-electron difference. As a consequence, total sum of all possible exchange coefficients in Fe 3 GaTe 2 are larger than that for Fe 3 GeTe 2 , which accounts for higher T C . To validate these findings, T C values are computed using both mean-field theory and Monte Carlo simulation. Indeed, higher-order exchange interactions, when properly accounting for the number of neighbors, confirm the higher T C of Fe 3 GaTe 2 .