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The Ce$_2$Fe$_{17}$ intermetallic compound has been studied intensely for several decades; its low-temperature state is reported experimentally either as ferromagnetic or antiferromagnetic by different authors, with a measured ordering temperature ranging within a hundred Kelvin. The existing theoretical investigations overestimate the experimental total magnetic moment of Ce$_2$Fe$_{17}$ by 20-40 % and predict a ferromagnetic ground state. By means of first-principle electronic structure calculations, we show that the total magnetic moment of Ce$_2$Fe$_{17}$ can be reproduced within the Local Density Approximation while functionals based on the Generalized Gradient Approximation fail. Atomistic spin dynamics simulations are shown to capture the change in the magnetic state of Ce$_2$Fe$_{17}$ with temperature, and closely replicate the reported helical structure that appears in some of the experimental investigations.

A new class of rare-earth-free permanent magnets is proposed. The parent compound of this class is Co$_3$Mn$_2$Ge, and its discovery is the result of first principles theory combined with experimental synthesis and characterisation. The theory is based on a high-throughput/data-mining search among materials listed in the ICSD database. From ab-initio theory of the defect free material it is predicted that the saturation magnetization is 1.71 T, the uniaxial magnetocrystalline anisotropy is 1.44 MJ/m$^3$, and the Curie temperature is 700 K. Co$_3$Mn$_2$Ge samples were then synthesized and characterised with respect to structure and magnetism. The crystal structure was found to be the MgZn$_2$-type, with partial disorder of Co and Ge on the crystallographic lattice sites. From magnetization measurements a saturation polarization of 0.86 T at 10 K was detected, together with a uniaxial magnetocrystalline anisotropy constant of 1.18 MJ/m$^3$, and the Curie temperature of $T_{\rm C}$ = 359 K. These magnetic properties make Co$_3$Mn$_2$Ge a very promising material as a rare-earth free permanent magnet, and since we can demonstrate that magnetism depends critically on the amount of disorder of the Co and Ge atoms, a further improvement of the magnetism is possible. From the theoretical works, a substitution of Ge by neighboring elements suggest two other promising materials - Co$_3$Mn$_2$Al and Co$_3$Mn$_2$Ga. We demonstrate here that the class of compounds based on $T_3$Mn$_2$X (T = Co or alloys between Fe and Ni; X=Ge, Al or Ga) in the MgZn$_2$ structure type, form a new class of rare-earth free permanent magnets with very promising performance.

We present an application of a high-throughput search of new rare-earth free permanent magnets focusing on 3d-5d transition metal compounds. The search involved a part of the ICSD database (international crystallographic structural database), together with tailored search criteria and electronic structure calculations of magnetic properties. Our results suggest that it possible to find candidates for rare-earth free permanent magnets using a data-mining/data-filtering approach. The most promising candidates identified here are Pt$_2$FeNi, Pt$_2$FeCu, and W$_2$FeB$_2$. We suggest these materials to be a good platform for further investigations in the search of novel rare-earth free permanent magnets.