An ab initio scheme is developed and used to investigate finite-temperature properties of a prototype of the complex rare-earth iron garnets, namely, $\mathrm{G}{\mathrm{d}}_3\mathrm{F}{\mathrm{e}}_5{\mathrm{O}}_{12}$ (that is, possessing gadolinium as its rare-earth ion), under applied magnetic fields. It is found that such a system undergoes a field-induced transition at a critical temperature, $T_{\mathrm{rev}}$, at which all magnetic ions reverse the direction of their spins. This $T_{\mathrm{rev}}$ critical temperature is well seen via a peak in the specific heat versus temperature curve under field and depends on different magnetic fields’ magnitude regimes: (1) for fields up to about 20 T, it is field independent, rather sudden, and coincides with the so-called compensation temperature, $T_M\sim 286$ K, at which the sum of all local magnetic moments is annihilated; (2) for fields larger than 70 T, there is no more full cancellation of these local magnetic moments for any temperature and $T_{\mathrm{rev}}$ is also field independent but now occurs via rotation of the local magnetic moments and at a temperature smaller than the zero-field $T_M$ by about 100 K; and (3) for intermediate fields ranging between 20 and 70 T, $T_{\mathrm{rev}}$ is now field dependent and decreases with the field's magnitude while also being associated with a rotation of these local magnetic moments. Our calculations also highlight the predominant role of the spins of the Gd ions in all these effects.

• Received 2 June 2020
• Revised 9 September 2020
• Accepted 18 September 2020

DOI:https://doi.org/10.1103/PhysRevB.102.144406