Structure, disorder, and magnetism in Herbertsmithite, a kagom\'{e} Heisenberg antiferromagnet

Geometric frustration of magnetic ordering on triangle-based lattices is thought to be one avenue to inducing macroscopic quantum states in electron systems. Due to the triangular arrangement of ions, it is impossible to satisfy all nearest-neighbor interactions simultaneously. This ``frustration'' suppresses classical magnetic long-range order and is thought to be capable of resulting in novel quantum states such as various resonating-valence-bond or ``spin-liquid'' ground states for a two-dimensional (2D) S = 1/2 antiferromagnet. However, ``structurally perfect'' frustrated materials are rare; frequently, materials undergo a structural distortion at low temperature, relieving the magnetic frustration and giving rise to a classical ground state. In this talk, I will present recent structural and property studies of the 2D candidate spin-liquid material ``ZnCu$_3$(OH)$_6$Cl$_2$.'' Using X-ray scattering differences at elemental absorption edges and an improved analysis technique, I will show that there is no Zn occupation of the intralayer Cu sites within the kagom\'{e} layer, as previously reported; however there is Cu present on the Zn intersite, leading to a real structural formula of (Zn$_{0.85}$Cu$_{0.15}$)Cu$_3$(OH)$_6$Cl$_2$. Combined with recent pulsed high field magnetic measurements, the lack of Zn mixing onto the kagom\'{e} lattice sites lends support to the idea that the electronic ground state in ``ZnCu$_3$(OH)$_6$Cl$_2$'' and its relatives is non-trivial.