High-pressure and magnetism in the quasi-one-dimensional solid solution <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Ca</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mtext>−</mml:mtext> <mml:mi>x</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mi>Na</mml:mi> <mml:mi>x</mml:mi> </mml:msub> <mml:msub> <mml:mi>Cr</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi mathvariant="normal">O</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:mrow> </mml:math> : A multimodal neutron, muon, and x-ray study

We investigate the pressure-dependent magnetism of the quasi-one-dimensional solid solution <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>Ca</a:mi> <a:mrow> <a:mn>1</a:mn> <a:mtext>−</a:mtext> <a:mi>x</a:mi> </a:mrow> </a:msub> <a:msub> <a:mi>Na</a:mi> <a:mi>x</a:mi> </a:msub> <a:msub> <a:mi>Cr</a:mi> <a:mn>2</a:mn> </a:msub> <a:msub> <a:mi mathvariant="normal">O</a:mi> <a:mn>4</a:mn> </a:msub> </a:mrow> </a:math> using neutron diffraction, Cr K-edge x-ray absorption spectroscopy, and muon spin rotation/relaxation. Na substitution is known to increase oxygen-ligand hole density (partial <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msup> <c:mrow> <c:mi>Cr</c:mi> </c:mrow> <c:mrow> <c:mn>3</c:mn> <c:mo>+</c:mo> </c:mrow> </c:msup> </c:math> to <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msup> <d:mrow> <d:mi>Cr</d:mi> </d:mrow> <d:mrow> <d:mn>4</d:mn> <d:mo>+</d:mo> </d:mrow> </d:msup> </d:math> character) and to drive the evolution from incommensurate order in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:msub> <e:mi>CaCr</e:mi> <e:mn>2</e:mn> </e:msub> <e:msub> <e:mi mathvariant="normal">O</e:mi> <e:mn>4</e:mn> </e:msub> </e:mrow> </e:math> to commensurate antiferromagnetism in <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:msub> <g:mi>NaCr</g:mi> <g:mn>2</g:mn> </g:msub> <g:msub> <g:mi mathvariant="normal">O</g:mi> <g:mn>4</g:mn> </g:msub> </g:mrow> </g:math> , suggesting a complex interplay between charge doping and structural changes. Here we apply hydrostatic pressure to tune the lattice without altering the nominal hole count, thereby separating compression effects from ligand-hole physics. For <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:mi>x</i:mi> <i:mo>=</i:mo> <i:mn>0</i:mn> </i:mrow> </i:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mrow> <j:mi>x</j:mi> <j:mo>=</j:mo> <j:mn>0.5</j:mn> </j:mrow> </j:math> the magnetic transition temperature is essentially pressure independent within our explored range, whereas in <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mrow> <k:msub> <k:mi>NaCr</k:mi> <k:mn>2</k:mn> </k:msub> <k:msub> <k:mi mathvariant="normal">O</k:mi> <k:mn>4</k:mn> </k:msub> </k:mrow> </k:math> long-range order is progressively suppressed with pressure, as seen by a decrease of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>T</m:mi> <m:mi>N</m:mi> </m:msub> </m:math> and of the magnetic Bragg intensity. Over the same pressure range, Cr K-edge x-ray absorption spectroscopy shows no resolvable change in the average Cr valence or coordination, and the refined corner-sharing Cr–O–Cr geometry remains nearly invariant within uncertainty. Extrapolating the pressure dependence of the magnetic order parameter suggests a critical pressure <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:mrow> <n:msub> <n:mi>P</n:mi> <n:mi>c</n:mi> </n:msub> <n:mo>=</n:mo> <n:mn>107</n:mn> <n:mrow> <n:mo>(</n:mo> <n:mn>8</n:mn> <n:mo>)</n:mo> </n:mrow> </n:mrow> </n:math> kbar for complete suppression of long-range order. These results support ligand-hole density as the primary control parameter across <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:mrow> <o:msub> <o:mi>Ca</o:mi> <o:mrow> <o:mn>1</o:mn> <o:mtext>−</o:mtext> <o:mi>x</o:mi> </o:mrow> </o:msub> <o:msub> <o:mi>Na</o:mi> <o:mi>x</o:mi> </o:msub> <o:msub> <o:mi>Cr</o:mi> <o:mn>2</o:mn> </o:msub> <o:msub> <o:mi mathvariant="normal">O</o:mi> <o:mn>4</o:mn> </o:msub> </o:mrow> </o:math> , with pressure acting as a secondary electronic tuning knob that weakens ordering in the Na-rich end member without inducing a new magnetic phase.