Magnetic structure of polar <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>G</mml:mi> </mml:math> -type charge- and orbital-ordered Hg-manganite quadruple perovskites

The magnetic structure of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>Hg</a:mi> <a:mrow> <a:mn>0.7</a:mn> </a:mrow> </a:msub> <a:msub> <a:mi>Na</a:mi> <a:mrow> <a:mn>0.3</a:mn> </a:mrow> </a:msub> <a:msub> <a:mi>Mn</a:mi> <a:mn>3</a:mn> </a:msub> <a:msub> <a:mi>Mn</a:mi> <a:mn>4</a:mn> </a:msub> <a:msub> <a:mi mathvariant="normal">O</a:mi> <a:mn>12</a:mn> </a:msub> </a:mrow> </a:math> , a quadruple manganite perovskite that exhibits a unique <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>G</c:mi> </c:math> -type charge- and orbital-ordered state distinct to other <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:msup> <d:mi>A</d:mi> <d:mrow> <d:mn>2</d:mn> <d:mo>+</d:mo> </d:mrow> </d:msup> <d:msub> <d:mi>Mn</d:mi> <d:mn>3</d:mn> </d:msub> <d:msub> <d:mi>Mn</d:mi> <d:mn>4</d:mn> </d:msub> <d:msub> <d:mi mathvariant="normal">O</d:mi> <d:mn>12</d:mn> </d:msub> </d:mrow> </d:math> equivalents <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mo>(</f:mo> <f:mi>A</f:mi> <f:mo>=</f:mo> <f:mrow> <f:mi>Ca</f:mi> <f:mo>,</f:mo> <f:mi>Sr</f:mi> <f:mo>,</f:mo> <f:mi>Cd</f:mi> <f:mo>,</f:mo> <f:mi>Pb</f:mi> </f:mrow> <f:mo>)</f:mo> </f:mrow> </f:math> , has been solved using powder neutron diffraction and symmetry-motivated analysis. A <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mi>G</g:mi> </g:math> -type-like antiferromagnetic (AFM) ordering of Mn on the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:msup> <h:mi>A</h:mi> <h:mo>′</h:mo> </h:msup> </h:math> sites and a ‘‘up-up–down-down’’ AFM moment configuration of Mn spins on the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mi>B</i:mi> </i:math> sites is found to occur. The mechanism for the onset and stabilization of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mi>B</j:mi> </j:math> -site up-up–down-down AFM order is explored in terms of coupling between structural and magnetic distortions. The results presented here provide evidence of the exotic charge, orbital, electronic, and magnetic orderings that quadruple manganite perovskites demonstrate, and further highlighting the distinct chemistry that <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:msup> <k:mrow> <k:mi>Hg</k:mi> </k:mrow> <k:mrow> <k:mn>2</k:mn> <k:mo>+</k:mo> </k:mrow> </k:msup> </k:math> plays in stabilizing novel states compared to other divalent <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mi>A</l:mi> </l:math> -site cation equivalents.