Interplay between electron localization, magnetic order, and Jahn-Teller distortion dictates <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>LiMnO</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> phase stability

The development of manganese (Mn)-rich cathodes for Li-ion batteries promises to alleviate potential supply chain bottlenecks in battery manufacturing. Fundamental challenges in Mn-rich cathodes arise from phenomena such as structural changes due to cooperative Jahn-Teller (JT) distortions of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msup><a:mrow><a:mi>Mn</a:mi></a:mrow><a:mrow><a:mn>3</a:mn><a:mo>+</a:mo></a:mrow></a:msup></a:math> in octahedral environments, Mn migration, and phase transformations to spinel-like order, all of which affect the electrochemical performance. These physically complex phenomena motivate an re-examination of the Li-Mn-O rock-salt space, with a focus on the thermodynamics of the prototypical, <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>LiMnO</b:mi><b:mn>2</b:mn></b:msub></b:math> polymorphs. It is found that the generalized gradient approximation (GGA-PBEsol) and meta-GGA (<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>) density functionals with empirically fitted on-site Hubbard <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>U</e:mi></e:math> corrections yield spurious stable phases for <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msub><f:mi>LiMnO</f:mi><f:mn>2</f:mn></f:msub></f:math>, such as predicting a phase with <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>γ</g:mi><g:mtext>−</g:mtext><g:msub><g:mi>LiFeO</g:mi><g:mn>2</g:mn></g:msub></g:mrow></g:math>-like order (<h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mi>γ</h:mi><h:mtext>−</h:mtext><h:msub><h:mi>LiMnO</h:mi><h:mn>2</h:mn></h:msub></h:mrow></h:math>) to be the ground state instead of the orthorhombic (Pmmn) phase, which is the experimentally known ground state. Accounting for antiferromagnetic order in each structure is shown to have a substantial effect on the total energies and resulting phase stability. By using hybrid-GGA (HSE06) and GGA with self-consistent Hubbard parameters (on-site <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mi>U</i:mi></i:math> and inter-site <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mi>V</j:mi></j:math>) calculated from linear response theory, the experimentally observed <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:msub><k:mi>LiMnO</k:mi><k:mn>2</k:mn></k:msub></k:math> phase stability trends are recovered. The calculated on-site <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mi>U</l:mi></l:math> between Mn-<m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mn>3</m:mn><m:mi>d</m:mi></m:mrow></m:math> states in the experimentally observed orthorhombic, layered, and spinel phases are significantly smaller than <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"><n:mi>U</n:mi></n:math> in <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"><o:mrow><o:mi>γ</o:mi><o:mtext>−</o:mtext><o:msub><o:mi>LiMnO</o:mi><o:mn>2</o:mn></o:msub></o:mrow></o:math> and disordered layered structures, by <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"><p:mrow><p:mn>0.5</p:mn><p:mtext>–</p:mtext><p:mn>0.6</p:mn><p:mspace width="0.16em"/><p:mi>eV</p:mi></p:mrow></p:math> within GGA. The smaller values of <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"><r:mi>U</r:mi></r:math> are shown to be correlated with a collinear ordering of JT distortions, in which all <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"><s:msub><s:mi>e</s:mi><s:mi>g</s:mi></s:msub></s:math> orbitals are oriented in the same direction. This cooperative JT effect can lead to greater electron delocalization from Mn along the <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"><t:msub><t:mi>e</t:mi><t:mi>g</t:mi></t:msub></t:math> states due to increased Mn-O covalency, which contributes to the greater electronic stability compared to the phases with noncollinear JT arrangements. The structures with collinear ordering of JT distortions also generate greater vibrational entropy, which helps stabilize these phases at high temperature. These phases are shown to be strongly insulating with large calculated band gaps <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"><u:mrow><u:mo>&gt;</u:mo><u:mn>3</u:mn><u:mspace width="0.16em"/><u:mi>eV</u:mi></u:mrow></u:math>, which are computed using HSE06 and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML"><w:mrow><w:msub><w:mi>G</w:mi><w:mn>0</w:mn></w:msub><w:msub><w:mi>W</w:mi><w:mn>0</w:mn></w:msub></w:mrow></w:math>.