Field-induced spin dynamics in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>i</mml:mi></mml:math>-MAX Tb compound

We report a comprehensive study of spin dynamics in the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mrow><a:mo>(</a:mo><a:msub><a:mi>Mo</a:mi><a:mrow><a:mn>2</a:mn><a:mo>/</a:mo><a:mn>3</a:mn></a:mrow></a:msub><a:msub><a:mi>Tb</a:mi><a:mrow><a:mn>1</a:mn><a:mo>/</a:mo><a:mn>3</a:mn></a:mrow></a:msub><a:mo>)</a:mo></a:mrow><a:mn>2</a:mn></a:msub><a:mi>AlC</a:mi></a:mrow><a:mo> </a:mo><a:mi>i</a:mi></a:math>-MAX compound using ac susceptibility measurements across a range of magnetic fields. Unique behaviors were observed, including spin dynamics in the kHz range between <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msub><b:mi>μ</b:mi><b:mn>0</b:mn></b:msub><b:mi>H</b:mi><b:mo>≈</b:mo><b:mn>0.2</b:mn><b:mi>T</b:mi><b:mo>−</b:mo><b:mn>6</b:mn><b:mi>T</b:mi></b:mrow></b:math>, indicating a nontrivial superparamagnetic state, suggesting that the compound acts as a transitional system within the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>i</c:mi></c:math>-MAX family, bridging stable spin-dynamic materials and fluctuation-dominated ones. Field- and frequency-dependent magnetic phase transitions, coupled with relaxation behaviors, reveal complex interactions between spin density waves and superparamagnetic components. These findings, corroborated by <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>μ</d:mi><d:mi>SR</d:mi></d:mrow></d:math> studies, deepen our understanding of magnetic phase diagrams and field-induced phenomena in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>i</e:mi></e:math>-MAX systems, laying the groundwork for further exploration of their unique properties and applications.