An ab-initio scheme is developed and used to investigate finite-temperature properties of a prototype of the complex rare earth - iron garnets, namely ${Gd}_3{Fe}_5{O}_{12}$ (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${}_{rev}$, at which all magnetic ions revert the direction of their spins. This T${}_{rev}$ critical temperature is well seen via a peak in the specific heat-versus-temperature curve under field and depends on different magnetic field’s magnitude regimes: () for fields up to about 20T, it is field-independent, rather sudden, and coincides with the so-called compensation temperature, T${}_M$~ 286 K, at which the sum of all local magnetic moments is annihilated; (2) for fields larger than 70T, there is no more full cancellation of these local magnetic moments for any temperature and T${}_{rev}$ is also field-independent but now occurring via rotation of the local magnetic moments and at a temperature smaller from the zero-field T${}_M$ by about 100K; and (3) for intermediate fields ranging between 20T and 70T, T$_{rev\thinspace }$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 on all these effects. bf …

中文翻译：

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磁场中稀土铁石榴石的有限温度特性

开发了一个从头算方案，并用于研究复杂稀土-铁石榴石原型的有限温度特性，即 ${Gd}_3{FË}_5{Ø}_{12}$（即，以d为稀土离子）在磁场作用下。发现这种系统在临界温度T下经历了场致跃迁${}_{\mathrm{[R}Ëv}$，所有的磁性离子都将其自旋方向还原。这个T${}_{\mathrm{[R}Ëv}$ 通过磁场下特定热-温度曲线的峰值可以清楚地看到临界温度，并且取决于不同磁场的大小范围：（）对于高达20T的磁场，它与电场无关，相当突然，并且与所谓补偿温度，T${}_{\mathrm{中号}}$〜286 K，所有局部磁矩之和被消除；（2）对于大于70T的磁场，在任何温度和T下都无法完全抵消这些局部磁矩${}_{\mathrm{[R}Ëv}$ 也是与磁场无关的，但现在是通过局部磁矩的旋转并且在比零磁场T小的温度下发生的${}_{\mathrm{中号}}$大约十万；（3）对于介于20T和70T之间的中间磁场，T $ _ {rev \ thinspace} $现在与磁场有关，并且随着磁场的大小而减小，同时还与这些局部磁矩的旋转有关。我们的计算还强调了Gd离子自旋在所有这些效应中的主要作用。bf…