"Ferroelectric instabilities and self-consistent mechanism for the isotopic substitution in KDP"

S. KOVAL; J. KOHANOFF; R. L. MIGONI; E. TOSATTI

Williamsburg, Virginia, USA

Conferencia; Fundamental Physics of Ferroelectrics 2003, Williamsburg, USA; 2003

We performed {\it ab initio} calculations to study ferroelectric instabilities and isotope effectsin the H-bonded ferroelectric KH$_2$PO$_4$ (KDP).The paraelectric (PE) phase is unstable with respect to a collective H ordering in the H-bridges, even keeping the K and P atomic positionsfixed at their mean values of that phase. We demonstrate that the source of the ferroelectric (FE) instabilityis the hydrogen off-centering.This ordering, perpendicular tothe tetragonal axis $c$, produces an electronic charge redistributionwithin the PO$_4$ tetrahedral units, which polarize along $c$. Additionaldisplacements of the P and K atoms reinforce the polarization.Cluster distortions following the H off-centered relaxation pattern in a mean-field PE phase, lead to instabilities which are significant onlywhen the heavy ions P and K are also allowed to relax.The accurate description of the energetics achievedfrom first-principles, also allow us to conduct a firststudy of the nuclear quantum effects over the effective{\it ab initio} potentials and of the changesproduced by isotopic substitution.Above certain cluster size, which is much smaller for DKDP, quantum mechanicalcalculations for the effective cluster mass yield energy levels below theintervalley barrier of the double-well cluster potential energy. Thus,cluster tunneling is allowed for distortions including heavy ions relaxations, with effective masses much larger than thetotal involved H or D mass. This explains the H double occupancyobserved experimentally in the PE phase, and is also in agreementwith the P-atom multi-site distribution detected experimentally in DKDP.Mass changes due to deuteration at fixed structuralparameters cannot account for the huge isotope effect.However, the main effect of deuteration is a depletionof the proton probability density at the O-H-O center,which in turn weakens the proton-mediated covalency in the bridge.A lattice expansion follows then, which is coupled self-consistentlywith the proton off-centering. This self-consistent mechanism is illustrated with a non-linear modeldeduced from the {\it ab initio} calculations, and allows usto explain the huge isotope effect observed and the importanceof geometrical effects proved by high-pressure experiments.