Ab initio study of the ferroelectric transition in cubic Pb3GeTe4

In the substitutionally disordered narrow-gap semiconductor Pb1-xGexTe, a finite-temperature cubic-to-rhombohedral transition appears above a critical concentration x approximate to 0.005. As a first step towards a first-principles investigation of this transition in the disordered system, a (hypothetical) ordered cubic Pb3GeTe4 supercell is studied. First-principles density-functional calculations of total energies and linear-response functions are performed using the conjugate-gradients method with ab initio pseudopotentials and a plane-wave basis set. Unstable modes in Pb3GeTe4 are found, dominated by off-centering of the Ge ions coupled with displacements of their neighboring Te ions. A model Hamiltonian for this system is constructed using the lattice Wannier function formalism. The parameters for this Hamiltonian are determined from first principles. The equilibrium thermodynamics of the model system is studied via Metropolis Monte Carlo simulations. The calculated transition temperature, T-c, is approximately 620 K for the cubic Pb3GeTe4 model, compared to the experimental value of T-c approximate to 350 K for disordered Pb0.75Ge0.25Te. Generalization of this analysis to the disordered Pb1-xGexTe system is discussed.