Finite-temperature ferroelectric phase transitions from machine-learned force fields

Simulating finite-temperature phase transitions from first principles is computationally challenging. Recently, molecular-dynamics (MD) simulations using machine-learned force fields (MLFFs) have opened a new avenue for finite-temperature calculations with near-first-principles accuracy. Here we use MLFFs, generated using on-the-fly training, to investigate structural phase transitions in four of the most well-studied ferroelectric oxides: <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>BaTiO</a:mi> <a:mn>3</a:mn> </a:msub> <a:mo>,</a:mo> <a:mo> </a:mo> <a:msub> <a:mi>PbTiO</a:mi> <a:mn>3</a:mn> </a:msub> <a:mo>,</a:mo> <a:mo> </a:mo> <a:msub> <a:mi>LiNbO</a:mi> <a:mn>3</a:mn> </a:msub> </a:math> , and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>BiFeO</b:mi> <b:mn>3</b:mn> </b:msub> </b:math> . Only using the 0 K ground-state structure as input for the training, the resulting MLFFs can qualitatively predict all the main structural phases and phase transitions, while the quantitative results are sensitive to the choice of exchange-correlation functional with PBEsol found to be more robust than LDA and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msup> <c:mrow> <c:mi mathvariant="normal">r</c:mi> </c:mrow> <c:mn>2</c:mn> </c:msup> <c:mi>SCAN</c:mi> </c:mrow> </c:math> . MD simulations also reproduce the experimentally observed order-disorder character of Ti displacements in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msub> <e:mi>BaTiO</e:mi> <e:mn>3</e:mn> </e:msub> </e:math> , the abrupt first-order transitions of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:msub> <f:mi>BiFeO</f:mi> <f:mn>3</f:mn> </f:msub> </f:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:msub> <g:mi>PbTiO</g:mi> <g:mn>3</g:mn> </g:msub> </g:math> , and the mixed order-disorder and displacive character of the ferroelectric transition in <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:msub> <h:mi>LiNbO</h:mi> <h:mn>3</h:mn> </h:msub> </h:math> . Finally, we discuss the potential and limitations of using MLFFs for simulating ferroelectric phase transitions.