Pressure-induced orbital reordering in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Na</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>CuF</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>

The high-pressure behavior of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi mathvariant="normal">N</a:mi><a:msub><a:mi mathvariant="normal">a</a:mi><a:mn>2</a:mn></a:msub><a:mi>Cu</a:mi><a:msub><a:mi mathvariant="normal">F</a:mi><a:mn>4</a:mn></a:msub></a:mrow></a:math> is explored by powder neutron diffraction and density functional theory (DFT) calculations. A first-order phase transition is observed to take place between 2.4 and 2.9 GPa, involving a reorientation of the Jahn-Teller (JT) long axes of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mo>[</e:mo><e:mrow><e:mi>Cu</e:mi><e:msub><e:mi mathvariant="normal">F</e:mi><e:mn>6</e:mn></e:msub></e:mrow><e:mo>]</e:mo></e:mrow></e:math> octahedra (and therefore the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:msub><g:mi>d</g:mi><g:msup><g:mrow><g:mi>z</g:mi></g:mrow><g:mn>2</g:mn></g:msup></g:msub></g:math> Cu orbitals), in agreement with our DFT calculations which suggest a transition at <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mo>∼</h:mo><h:mn>2.8</h:mn></h:mrow></h:math> GPa. The transition can be described as being between a state of ferro-orbital order and one of A-type antiferro-orbital order, reflecting a shift in the associated electronic instability from being in the zone center to zone boundary of the first Brillouin zone of the parent structure. This change results in a decoupling of magnitude of the associated Jahn-Teller distortion of the Cu-F bond lengths from the lattice strain. This scenario is supported by our observations that the compressibility of the pretransition phase is highly anisotropic, while in the posttransition phase it becomes almost isotropic, and that we observed no further decrease of the magnitude the JT distortion up to 5 GPa, or melting of the orbital ordering in our DFT calculations up to at least 5 GPa.