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We present a systematic investigation of the effect of H, B, C, and Ninterstitials on the electronic, lattice and magnetic properties ofLa(Fe,Si)$_{13}$ using density functional theory. The parent LaSiFe$_{12}$alloy has a shallow, double-well free energy function that is the basis ofitinerant metamagnetism. On increasing the dopant concentration, the resultinglattice expansion causes an initial increase in magnetisation for allinterstitials that is only maintained at higher levels of doping in the case ofhydrogen. Strong s-p band hybridisation occurs at high B,C and Nconcentrations. We thus find that the electronic effects of hydrogen doping aremuch less pronounced than those of other interstitials, and result in thedouble-well structure of the free energy function being least sensitive to theamount of hydrogen. This microscopic picture accounts for the vanishing firstorder nature of the transition by B,C, and N dopants as observedexperimentally. We use our calculated electronic density of states forLaSiFe$_{12}$ and the hydrogenated alloy to infer changes in magneto-elasticcoupling and in phonon entropy on heating through $T_C$ by calculating thefermionic entropy due to the itinerant electrons. Lastly, we predict theelectron thermopower in a spin-mixing, high temperature limit and compare ourfindings to recent literature data.

Electronic structure, metamagnetism and thermopower of LaSiFe$_{12}$ and interstitially doped LaSiFe$_{12}$