Topological magnon in exchange frustration driven incommensurate spin spiral of kagome-lattice <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>YMn</mml:mi><mml:mn>6</mml:mn></mml:msub><mml:msub><mml:mi>Sn</mml:mi>

<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>YMn</a:mi><a:mn>6</a:mn></a:msub><a:msub><a:mi>Sn</a:mi><a:mn>6</a:mn></a:msub></a:mrow></a:math> consists of two types of Mn-based kagome planes stacked along the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>c</b:mi></b:math>-axis having a complex magnetic interaction. We report a spin reconstruction in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi>YMn</c:mi><c:mn>6</c:mn></c:msub><c:msub><c:mi>Sn</c:mi><c:mn>6</c:mn></c:msub></c:mrow></c:math> from ferromagnetic (FM) into a combination of two incommensurate spin spirals (SSs) originating from two different types of Mn kagome planes driven by frustrated magnetic exchanges along the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>c</d:mi></d:math>-axis with the inclusion of the Hubbard <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>U</e:mi></e:math>. The pitch angle and wave vector of the incommensurate SSs are <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mo>∼</f:mo><f:mn>89</f:mn><f:mo>.</f:mo><f:msup><f:mn>3</f:mn><f:mo>∘</f:mo></f:msup></f:mrow></f:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mo>∼</g:mo></g:math> (0 0 0.248), respectively, which are in excellent agreement with the experiment. We employ an effective model Hamiltonian constructed out of exchange interactions to capture the experimentally observed nonequivalent nature of the two incommensurate SSs which also explain the FM-SS crossover due to antiferromagntic spin exchange with correlation. We further report the existence of a topological magnon with spin-orbit coupling in the incommensurate SS phase of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:msub><h:mi>YMn</h:mi><h:mn>6</h:mn></h:msub><h:msub><h:mi>Sn</h:mi><h:mn>6</h:mn></h:msub></h:mrow></h:math> by calculating the topological invariants and Berry curvature profile. The location of the Dirac magnon in the energy landscape at 73 meV matches with another experimental report. We demonstrate the accuracy of our results by highlighting the experimental features in <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:msub><i:mi>YMn</i:mi><i:mn>6</i:mn></i:msub><i:msub><i:mi>Sn</i:mi><i:mn>6</i:mn></i:msub></i:mrow></i:math>. Published by the American Physical Society 2024