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 $T_{C}$ . We show that higher order exchange coefficients, $J_{3}$ or higher, of Fe $_{3}$ GaTe $_{2}$ are positive whereas those of Fe $_{3}$ GeTe $_{2}$ are negative. As a consequence, total sum of all possible exchange coefficients in Fe $_{3}$ GaTe $_{2}$ are larger than Fe $_{3}$ GeTe $_{2}$ , which accounts for higher $T_{C}$ . To validate these findings, $T_{C}$ 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 $_{2}$ .

Why Fe $_{3}$ GaTe $_{2}$ has higher Curie temperature than Fe $_{3}$ GeTe $_{2}$ ?

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Why Fe $_{3}$ GaTe $_{2}$ has higher Curie temperature than Fe $_{3}$ GeTe $_{2}$ ?

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Why Fe33​GaTe22​ has higher Curie temperature than Fe33​GeTe22​?

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Why Fe33​GaTe22​ has higher Curie temperature than Fe33​GeTe22​?

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Why Fe $_{3}$ GaTe $_{2}$ has higher Curie temperature than Fe $_{3}$ GeTe $_{2}$ ?

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Why Fe $_{3}$ GaTe $_{2}$ has higher Curie temperature than Fe $_{3}$ GeTe $_{2}$ ?

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