Incommensurate magnetic order arising from frustrated interchain interactions in the spin- 12 chain compound AgCuVO4

Quantum spin chains with competing interactions offer a platform where low dimensionality and frustration—both acting to suppress magnetic order—intersect. We studied magnetic ordering in the spin-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mfrac><a:mn>1</a:mn><a:mn>2</a:mn></a:mfrac></a:math> chain compound <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>AgCuVO</b:mi><b:mn>4</b:mn></b:msub></b:math> using muon spin spectroscopy and neutron diffraction. Long-range magnetic order emerges at <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi>T</c:mi><c:mi>N</c:mi></c:msub><c:mo>=</c:mo><c:mn>2.0</c:mn><c:mrow><c:mo>(</c:mo><c:mn>1</c:mn><c:mo>)</c:mo></c:mrow><c:mspace width="0.28em"/><c:mi mathvariant="normal">K</c:mi></c:mrow></c:math>, which is <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mo>∼</f:mo><f:mn>1</f:mn><f:mo>/</f:mo><f:mn>200</f:mn></f:mrow></f:math> of the dominant intrachain coupling <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mi>J</g:mi></g:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mo>∼</h:mo><h:mn>1</h:mn><h:mo>/</h:mo><h:mn>15</h:mn></h:mrow></h:math> of the interchain interactions. The collinear incommensurate amplitude-modulated magnetic structure features a reduced ordered moment of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mn>0.13</i:mn><i:mrow><i:mo>(</i:mo><i:mn>3</i:mn><i:mo>)</i:mo></i:mrow><i:msub><i:mi>µ</i:mi><i:mi mathvariant="normal">B</i:mi></i:msub></i:mrow></i:math>, confined to the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:mi>a</k:mi><k:mi>b</k:mi></k:mrow></k:math> plane and modulated along the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mi>c</l:mi></l:math> axis—perpendicular to the spin chains—indicating frustrated interchain couplings. The low <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>, small moment, and incommensurate order highlight strong frustration, positioning <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"><n:msub><n:mi>AgCuVO</n:mi><n:mn>4</n:mn></n:msub></n:math> as a model system for exploring frustration in quantum spin chains.