Landau theory and giant room-temperature barocaloric effect in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>M</mml:mi><mml:msub><mml:mi mathvariant="normal">F</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> metal trifluorides

The structural phase transitions of $M{\mathrm{F}}_{3}$ ($M$ = Al, Cr, V, Fe, Ti, Sc) metal trifluorides are studied within a simple Landau theory consisting of tilts of rigid $M{\mathrm{F}}_{6}$ octahedra associated with soft antiferrodistortive optic modes that are coupled to long-wavelength strain generating acoustic phonons. We calculate the temperature and pressure dependence of several quantities such as the spontaneous distortions, volume expansion, and shear strains as well as $T\ensuremath{-}P$ phase diagrams. By contrasting our model to experiments we quantify the deviations from mean-field behavior and find that the tilt fluctuations of the $M{\mathrm{F}}_{6}$ octahedra increase with metal cation size. We apply our model to predict giant barocaloric effects in Sc-substituted ${\mathrm{TiF}}_{3}$ of up to about $15\phantom{\rule{0.16em}{0ex}}{\mathrm{J}\phantom{\rule{0.16em}{0ex}}\mathrm{K}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{kg}}^{\ensuremath{-}1}$ for modest hydrostatic compressions of $0.2\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$. The effect extends over a wide temperature range of over $140\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ (including room temperature) due to a large predicted rate, $d{T}_{c}/dP=723\phantom{\rule{0.16em}{0ex}}\mathrm{K}\phantom{\rule{4pt}{0ex}}{\mathrm{GPa}}^{\ensuremath{-}1}$, which exceeds those of typical barocaloric materials. Our results suggest that open lattice frameworks such as the trifluorides are an attractive platform to search for giant barocaloric effects.