Stability Frontiers in the <i>AM</i>₆<i>X</i>₆ Kagome Metals: The <i>Ln</i>Nb₆Sn₆ (<i>Ln</i>:Ce–Lu,Y) Family and Density-Wave Transition in LuNb₆Sn₆

The kagome motif is a versatile platform for condensed matter physics, hosting rich interactions between magnetic, electronic, and structural degrees of freedom. In recent years, the discovery of a charge density wave (CDW) in the AV₃Sb₅ superconductors and structurally-derived bond density waves (BDW) in FeGe and ScV₆Sn₆ have stoked the search for new kagome platforms broadly exhibiting density wave (DW) transitions. In this work, we evaluate the known <i>AM</i>₆<i>X</i>₆ chemistries and construct a stability diagram that summarizes the structural relationships among the >125 member family. Subsequently, we introduce our discovery of the broader <i>Ln</i>Nb₆Sn₆ (<i>Ln</i>:Ce-Nd,Sm,Gd-Tm,Lu,Y) family of kagome metals and an analogous DW transition in LuNb₆Sn₆. Our X-ray scattering measurements clearly indicate a (1/3, 1/3, 1/3) ordering wave vector (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msqrt><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msqrt><mml:mo>×</mml:mo><mml:msqrt><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msqrt><mml:mo>×</mml:mo><mml:mn>3</mml:mn></mml:math> superlattice) and diffuse scattering on half-integer <i>L</i>-planes. Our analysis of the structural data supports the "rattling mode" DW model proposed for ScV₆Sn₆ and paints a detailed picture of the steric interactions between the rare-earth filler element and the host Nb-Sn kagome scaffolding. We also provide a broad survey of the magnetic properties within the HfFe₆Ge₆-type <i>Ln</i>Nb₆Sn₆ members, revealing a number of complex antiferromagnetic and metamagnetic transitions throughout the family. This work integrates our new <i>Ln</i>Nb₆Sn₆ series of compounds into the broader <i>AM</i>₆<i>X</i>₆ family, providing new material platforms and forging a new route forward at the frontier of kagome metal research.