Giant reversible electrocaloric effect in monolayer group-IV monochalcogenides

Monolayer electrocaloric (EC) materials have emerged as promising candidates to achieve economic and green solid-state refrigeration, especially in micro- or nanoscale chip cooling in the post-Moore law period. In this paper, we trained a machine-learning-based deep potential (DP) model of monolayer group-IV monochalcogenides $\mathit{MX}\mathrm{s}$ ($M$ = Ge, Sn; $X$ = S, Se) with a database from first-principles calculations, which incorporates the accuracy of ab initio molecular dynamics and efficiency of classical method. The DP model was further applied to study the EC effect (ECE) in monolayer $\mathit{MX}\mathrm{s}$ by simulating the temperature-driven phase transitions and electric polarization dynamics under different external electric fields. The results indicate $\mathit{MX}\mathrm{s}$ featuring giant reversible isothermal entropy change (\ensuremath{\Delta}$S$) and adiabatic temperature change (\ensuremath{\Delta}$T$) near their order-disorder phase transition. Particularly, for $E$ = 100 MV/m, |\ensuremath{\Delta}$S$| = 68 J/(kg K) and |\ensuremath{\Delta}$T$| = 75 K are obtained for GeS, which individually rival the state-of-the-art ECE figures of merit, surpassing most other ferroelectric materials, particularly the two-dimensional (2D) CuInPS and strained $\mathrm{SrTi}{\mathrm{O}}_{3}$ films. Furthermore, electric field shifts of the order of 10 MV/m yield huge reversible EC strengths of \ensuremath{\Delta}$S$/\ensuremath{\Delta}$E$ = 5.4 $\mathrm{J}\phantom{\rule{0.16em}{0ex}}\mathrm{m}\phantom{\rule{0.16em}{0ex}}\mathrm{k}{\mathrm{g}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\mathrm{M}{\mathrm{V}}^{\ensuremath{-}1}$ and \ensuremath{\Delta}$T$/\ensuremath{\Delta}$E$ = 6 $\mathrm{K}\phantom{\rule{0.16em}{0ex}}\mathrm{m}\phantom{\rule{0.16em}{0ex}}\mathrm{M}{\mathrm{V}}^{\ensuremath{-}1}$. The origin of the giant ECE in $\mathit{MX}\mathrm{s}$ was explained through macroscopic thermodynamic ratios, phenomenological Landau theory, and microscopic phonon vibration analysis. Interestingly, the entropy change can be approximated to be proportional to the square of the polarization change ($\mathrm{\ensuremath{\Delta}}{P}^{2}$), and the application of electric field shifts the low-frequency phonons to the higher-frequency range, with the $M$ atom contributing more to the entropy change than the $X$ atom. In this paper, we provide important insights for exploration and design of 2D EC materials in future practical applications.