Thermal Physics of RFe₄P₁₂ (R = La, Ce, and Pr) Filled Skutterudites

Phosphide skutterudites attracted much attention in the 2000s due to their potential application as thermoelectrical materials, but also for exhibiting interesting phenomena depending on the filler of its icosahedral cages: superconducting LaFe₄P₁₂ below 4.2 K, insulating CeFe₄P₁₂, antiferromagnetic PrFe₄P₁₂ below 6.4 K, and ferromagnetic NdFe₄P₁₂ below 1.9 K [1]. Experimental and theoretical investigations have sought insight into their unusual lattice dynamics, electronic structure with strongly correlated electrons, and thermoelectric performance [2-5]. However, most first-principles modeling has been performed at fixed temperatures - primarily considering the 0-K equilibrium structure, and there has yet to be a comprehensive and systematic computational study of the effect of temperature on these material properties. In this work, we report a comparative lattice-dynamics study of the temperature dependence of the properties of RFe₄P₁₂ (R = La, Ce, and Pr), focusing mainly on phonon frequencies, thermal displacements, and electronic band structure. Calculations were performed within the quasiharmonic approximation using GGA for the exchange-correlation energy [6]. The results are compared against experimental data and other calculations, adding insight to the ongoing debate on the filled skutterudites and the role of filler-cage dynamics in the figure of merit ZT, which provides clear directions toward designing more efficient P-based skutterudites for thermoelectric applications.<br/><br/>[1] M. S. Torikachvili et al. Low-temperature properties of rare-earth and actinide iron phosphide compounds MFe₄P₁₂ (M = La, Pr, Nd, and Th). Phys. Rev B 36, 8660 (1987). 10.1103/PhysRevB.36.8660<br/><br/>[2] H. Sato et al. Anomalous transport properties of RFe₄P₁₂ (R = La, Ce, Pr, and Nd). Phys. Rev B 62, 15125 (2000). 10.1103/PhysRevB.62.15125<br/><br/>[3] M. Mizumaki et al. Rare Earth Dependence of Einstein Temperatures in Filled Skutterudite Compounds REFe₄P₁₂ (RE = La, Ce, Pr, Nd, and Sm). JPSJ 80, 074603 (2011). 10.1143/JPSJ.80.074603<br/><br/>[4] M. Ameri et al. First-principles investigation on structural, elastic, electronic and thermodynamic properties of filled skutterudite PrFe₄P₁₂ compound for thermoelectric applications. Mol Simul 40, 15 (2014). 10.1080/08927022.2013.854898<br/><br/>[5] E. Flage-Larsen et al. Bond analysis of phosphorus skutterudites: Elongated lanthanum electron buildup in LaFe₄P₁₂. Comput. Mater. Sci. 47, 3 (2010). 10.1016/j.commatsci.2009.10.018<br/><br/>[6] A. Togo and I. Tanaka. First principles phonon calculations in materials science. Scr. Mater. 108, 1359-6462 (2015). 10.1016/j.scriptamat.2015.07.021