We identify a quasi-two-dimensional (quasi-2D) phonon mode in the layered-perovskite ${\mathrm{Ca}}_3{\mathrm{Ti}}_2{\mathrm{O}}_7$, which exhibits an acoustic branch with quadratic dispersion. Using first-principles methods, we show this mode exhibits atomic displacements perpendicular to the layered $[{\mathrm{CaTiO}}_3{]}_2$ blocks comprising the structure and a negative Grüneisen parameter. Owing to these quasi-2D structural and dynamical features, we find that the mode can be utilized to realize unusual membrane effects, including a tunable negative thermal expansion (NTE) and a rare pressure-independent thermal softening of the bulk modulus. Detailed microscopic analysis shows that the NTE relies on strong intralayer Ti—O covalent bonding and weaker interlayer interactions, which is in contrast to conventional NTE mechanisms for perovskites, such as rigid-unit modes, structural transitions, and electronic or magnetic ordering. The general application of the quasi-2D lattice dynamics opens exciting avenues for the control of lattice dynamical and thermodynamic responses of other complex layered compounds through rational chemical substitution, as we show in $A_3{\mathrm{Zr}}_2{\mathrm{O}}_7$ ($A=\mathrm{Ca}$, Sr), and by heterostructuring.

• Received 6 March 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.115901