  In ferroelectric materials, an applied electric field has been shown to
change the phonon dispersion relation sufficiently to alter the lattice thermal
conductivity, opening the theoretical possibility that a heat gradient could
drive a polarization flux, and technologically, also opening a new avenue
toward all solid-state heat switching. In this report, we confirm
experimentally the validity of the theory originally developed for Pb(Zr,Ti)O_3
(PZT) on the ferroelectric relaxor 0.66Pb[Mg_(1/3)Nb_(2/3)]O_3-0.33PbTiO_3
(PMN-33PT). In the theory, the relative change in sound velocity and thermal
conductivity with applied electric field relates to the piezoelectric
coefficients (d_33 and d_31) and the Gr\"uneisen parameter ({\gamma}). The
theory predicts that in PMN-33PT the effect should be an order of magnitude
larger, and of opposite sign as in PZT; this is confirmed here. The effect is
measured on samples that undergo multiple field sweep cycles and pass through 2
phase transitions. The thermal conductivity changes are closely linked to
variations in the piezoelectric coefficients. A null experiment on paraelectric
SrTiO_3 confirms the link between ferroelectricity and phonon spectrum changes.
Changes in heat conduction as large as 10% can be achieved over large
temperature ranges, opening a possibility for practical heat switches based on
phonon spectrum changes.
