Coexistence of long-range magnetic order and dynamical magnetism in the V-based kagome metals: A combined thermodynamic and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mi>SR</mml:mi> </mml:mrow> </mml:

V-based kagome metals exhibit a unique lattice geometry that can give rise to exotic electronic and magnetic phenomena, making them an ideal platform to study the interplay of topology and magnetism. We present a combined thermodynamic and 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> investigation of single-crystal <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:msub> <b:mrow> <b:mi>R</b:mi> <b:mi mathvariant="normal">V</b:mi> </b:mrow> <b:mn>6</b:mn> </b:msub> <b:msub> <b:mi>Sn</b:mi> <b:mn>6</b:mn> </b:msub> </b:mrow> </b:math> <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mo>(</d:mo> <d:mi>R</d:mi> <d:mo>=</d:mo> <d:mtext>Tb</d:mtext> <d:mo>,</d:mo> <d:mo> </d:mo> <d:mi>Dy</d:mi> <d:mo>,</d:mo> <d:mo> </d:mo> <d:mi>Ho</d:mi> <d:mo>,</d:mo> <d:mo> </d:mo> <d:mi>Er</d:mi> <d:mo>)</d:mo> </d:mrow> </d:math> compounds, focusing on their low-temperature magnetic behavior. Heat-capacity and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>μ</e:mi> <e:mi>SR</e:mi> </e:mrow> </e:math> measurements reveal distinct magnetic phase transitions below 4 K, confirming the emergence of long-range magnetic order in all compounds studied. The <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mi>μ</f:mi> <f:mi>SR</f:mi> </f:mrow> </f:math> results further indicate persistent spin fluctuations within the magnetically ordered state down to 50 mK, reflected in reduced ordered moments obtained from a hyperfine analysis of the heat-capacity measurements. These findings uncover the coexistence of static and dynamic magnetism in V-based kagome metals and emphasizing the key role of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mn>4</g:mn> <g:mi>f</g:mi> </g:mrow> </g:math> -electron anisotropy in shaping their magnetic ground states. Compared with the Mn-based <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mi>R</h:mi> <h:msub> <h:mi>Mn</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> analogs, our results highlight the unique magnetism arising from the decoupled rare-earth sublattice and its interplay with the nonmagnetic V kagome network.