Theoretical study of ferroelectric KNO$_3$

We present a detailed study of the structural behavior and polarization reversal mechanism in phase III of KNO$_3$, an unusual ferroelectric material in which the nitrate groups rotate during polarization reversal. This work extends a preliminary study presented as an example in our earlier paper on the mapping of the energy ($E$) versus polarization ($P$) in insulators.\footnote{O.~Di\'eguez and D.~Vanderbilt, Phys.\ Rev.\ Lett.\ {\bf 96}, 056401 (2006).} Here we analyze in detail a two-parameter model in which the energy of the system is written as a low-order expansion in the polarization and in the nitrate group orientation. Apart from confirming that this model reproduces very well the first-principles results for KNO$_3$ presented in Ref.~[1], we construct its parameter-space phase diagram, and in particular we describe regions of parameter space in which the $E(P)$ curves have an unusual triple-well structure. We also present first-principles calculations of KNO$_3$ under pressure, finding that as the material is compressed its $E(P)$ curves change character, going from having continuous to having discontinuous first derivatives at zero polarization.