Electronic Crystallization in a Lithium Battery Material: Columnar Ordering of Electrons and Holes in the Spinel<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>LiMn</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

${\mathrm{LiMn}}_{2}{\mathrm{O}}_{4}$ presents a first order structural transition at 290 K that was known to perturb the functioning as cathode in rechargeable Li batteries. We have solved the structure at 230 K and deciphered unambiguously the nature of this phase transition. The analysis of valence bond sums shows that the transition results from a partial charge ordering: two of the five Mn sites correspond to well-defined ${\mathrm{Mn}}^{4+}$ and the other three sites are close to ${\mathrm{Mn}}^{3+}$ ions. Charge ordering is accompanied by simultaneous orbital ordering due to the Jahn-Teller effect in ${\mathrm{Mn}}^{3+}$ ions. The microscopic details obtained from the structure are crucial for understanding the electron hopping persisting below the transition.