Magnetism in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>M</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mi>NbS</mml:mi> <mml:mn>2</mml

We present the results of muon-spin relaxation <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mo>(</a:mo> <a:mi>μ</a:mi> <a:mi>SR</a:mi> <a:mo>)</a:mo> </a:mrow> </a:math> measurements of the static and dynamic magnetism of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:msub> <b:mi>M</b:mi> <b:mrow> <b:mn>1</b:mn> <b:mo>/</b:mo> <b:mn>3</b:mn> </b:mrow> </b:msub> <b:msub> <b:mi>NbS</b:mi> <b:mn>2</b:mn> </b:msub> </b:mrow> </b:math> <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mo>(</c:mo> <c:mi>M</c:mi> <c:mo>=</c:mo> <c:mi>Fe</c:mi> <c:mo>,</c:mo> <c:mo> </c:mo> <c:mi mathvariant="normal">V</c:mi> <c:mo>,</c:mo> <c:mo> </c:mo> <c:mi>Mn</c:mi> <c:mo>)</c:mo> </c:mrow> </c:math> , three intercalated transition-metal dichalcogenides. Transitions to long-range magnetic order are observed in all three materials, and local magnetic fields at muon sites are compared to dipole field calculations. Measurements on <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:msub> <e:mi>Fe</e:mi> <e:mrow> <e:mn>1</e:mn> <e:mo>/</e:mo> <e:mn>3</e:mn> </e:mrow> </e:msub> <e:msub> <e:mi>NbS</e:mi> <e:mn>2</e:mn> </e:msub> </e:mrow> </e:math> capture the evolution of two coexisting magnetic phases. In <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:msub> <f:mi mathvariant="normal">V</f:mi> <f:mrow> <f:mn>1</f:mn> <f:mo>/</f:mo> <f:mn>3</f:mn> </f:mrow> </f:msub> <f:msub> <f:mi>NbS</f:mi> <f:mn>2</f:mn> </f:msub> </f:mrow> </f:math> , we observe a peak in the dynamic response at 9 K, coincident with previous reports of a possible low-temperature phase transition. The observation of high-frequency muon precession in <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:msub> <h:mi>Mn</h:mi> <h:mrow> <h:mn>1</h:mn> <h:mo>/</h:mo> <h:mn>3</h:mn> </h:mrow> </h:msub> <h:msub> <h:mi>NbS</h:mi> <h:mn>2</h:mn> </h:msub> </h:mrow> </h:math> suggests the existence of an additional muon site that implies a difference in the electronic energy landscape compared to the other materials in the series. Taken together, this demonstrates that the change in intercalant species drives significant variations in magnetism, highlighting the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:msub> <i:mi>M</i:mi> <i:mrow> <i:mn>1</i:mn> <i:mo>/</i:mo> <i:mn>3</i:mn> </i:mrow> </i:msub> <i:msub> <i:mi>NbS</i:mi> <i:mn>2</i:mn> </i:msub> </i:mrow> </i:math> series as an ideal group of materials for investigating a wide range of magnetic phenomena.