An unlikely route to low lattice thermal conductivity: small atoms in a simple layered structure

In the design of materials with low lattice thermal conductivity, compounds with high density, low speed of sound, and complexity at either the atomic, nano- or microstructural level are preferred. The layered compound Mg$_3$Sb$_2$ defies these prevailing paradigms, exhibiting lattice thermal conductivity comparable to PbTe and Bi$_2$Te$_3$, despite its low density and simple structure. The excellent thermoelectric performance ($zT$ $\sim$ 1.5) in $n$-type Mg$_3$Sb$_2$ has thus far been attributed to its multi-valley conduction band, while its anomalous thermal properties have been largely overlooked. To explain the origin of the low lattice thermal conductivity of Mg$_3$Sb$_2$, we have used both experimental methods and ab initio phonon calculations to investigate trends in the elasticity, thermal expansion and anharmonicity of $A$Mg$_2Pn_2$ Zintl compounds with $A$ = Mg, Ca, Yb, and $Pn$ = Sb and Bi. Phonon calculations within the quasi-harmonic approximation reveal large mode Gr\"uneisen parameters in Mg$_3$Sb$_2$ compared with isostructural compounds, in particular in transverse acoustic modes involving shearing of adjacent anionic layers. Measurements of the elastic moduli and sound velocity as a function of temperature using resonant ultrasound spectroscopy provide a window into the softening of the acoustic branches at high temperature, confirming their exceptionally high anharmonicity. We attribute the anomalous thermal behavior of Mg$_3$Sb$_2$ to the diminutive size of Mg, which may be too small for the octahedrally-coordinated site, leading to weak, unstable interlayer Mg-Sb bonding. This suggests more broadly that soft shear modes resulting from undersized cations provide a potential route to achieving low lattice thermal conductivity low-density, earth-abundant materials.