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In this work, we present a comparative first principles study of mechanicalproperties, electronic structure, phonon dispersion relation, electron-phononcoupling and magnetism in three isostructural superconductors, namely, ThFeAsN,ThCoAsN and ThNiAsN. Experimentally, ThFeAsN and ThNiAsN show superconductingproperties, while ThCoAsN has not been synthesized. Our calculated elasticconstants show that all these systems are mechanically stable. Significantdifferences in the electronic structures of these three compounds in terms ofdensity of states, band structures and Fermi surfaces, are found. Our phononcalculations reveal that all the systems including ThCoAsN, are dynamicallystable. Phonon dispersion relations indicate that the optical modes of all thethree systems are almost the same while there are significant variations in thelow frequency manifold consisting of mixed modes. The electron-phonon couplingconstants and superconducting transition temperatures calculated based on theEliashberg formalism, predict a rather high $T_c$ of 6.4 K for ThCoAsN and alsoa $T_c$ of 3.4 K for ThNiAsN which agrees well with the experimental value of4.3 K. Nevertheless, we find a $T_c$ of 0.05 K for ThFeAsN, which is muchsmaller than the experimental $T_c$ of $\sim$30 K. However, a simple analysisconsidering the amplifying effects of spin density wave order and out-of-planesoft phonon modes suggests that the $T_c$ could be increased considerably to$\sim$10 K. Finally, we also discuss the effect of anion As height on theelectronic structures and study possible magnetic states in these threecompounds.

Electronic structure, lattice dynamics and magnetism of new ThXAsN (X=Fe,Co,Ni) superconductors: A First Principles Study