Colloquium : Herbertsmithite and the search for the quantum spin liquid

Abstract

Quantum spin liquids form a novel class of matter where, despite the existence of strong exchange interactions, spins do not order down to the lowest measured temperature. Typically, these occur in lattices that act to frustrate the appearance of magnetism. In two dimensions, the classic example is the kagome lattice composed of corner sharing triangles. There are a variety of minerals whose transition metal ions form such a lattice. Hence, a number of them have been studied, and were then subsequently synthesized in order to obtain more pristine samples. Of particular note was the report in 2005 by Dan Nocera's group of the synthesis of herbertsmithite, composed of a lattice of copper ions sitting on a kagome lattice, which indeed does not order down to the lowest measured temperature despite the existence of a large exchange interaction of 17 meV. Over the past decade, this material has been extensively studied, yielding a number of intriguing surprises that have in turn motivated a resurgence of interest in the theoretical study of the spin 1 2 Heisenberg model on a kagome lattice. In this colloquium article, I will review these developments, and then discuss potential future directions, both experimental and theoretical, as well as the challenge of doping these materials with the hope that this could lead to the discovery of novel topological and superconducting phases.

Tuning of a Kagome Magnet: Insulating Ground State in Ga‐Substituted Cu4(OH)6Cl2

“…The dominant magnetic interaction in herbertsmithite is caused by Cu–O–Cu antiferromagnetic superexchange with an exchange energy of J ≈ 17 meV, but no magnetic long‐range order has been observed down to 50 mK . Therefore, the spin‐liquid ground‐state of this material was investigated in great detail . However, a strong structural drawback of herbertsmithite is the intrinsic Zn‐Cu‐antisite disorder of up to 15% .…”

Nature of optical excitations in the frustrated kagome compound herbertsmithite

“…They are key ingredients of high-T c cuprates and have been widely investigated in the last decades. A recent revival of interest in Cu-based materials was triggered by the discovery of geometrically frustrated cuprates that seem to exhibit spin-liquid properties [7][8][9][10][11][12][13][14][15][16] and may even harbor unconventional superconductivity with higher angular momenta than existing superconductors [17] or further topological phases [18] although synthesis seems to be difficult [19].In this work we investigate the origin of the optical excitations in the spin-liquid candidate Herbertsmithite and concentrate on the following conceptual issue: which measurable properties in correlated systems are strongly affected by correlation effects and which are not? We will show, experimentally and theoretically, that in a single experimental probe, namely optical conductivity, one can simultaneously observe properties dramatically influenced by Coulomb (Mott-Hubbard) correlation effects, and those that are hardly affected at all.…”

Hierarchy of Exchange Interactions in the Triangular-Lattice Spin Liquid YbMgGaO4

“…The magnetic Yb 3þ ions carry effective spin-1=2 moments in a symmetry environment allowing anisotropic exchange interactions [41,47] in the absence of antisymmetric (Dzyaloshinsky-Moriya) terms and magnetic defects, both of which are present in other two-dimensional QSL candidates such as herbertsmithite [56][57][58]. The immediate availability of single crystals [55] uncovered a QSL phenomenology in YbMgGaO 4 characterized by the absence of spin ordering or freezing down to T ¼ 100 mK in muon spin relaxation measurements [59], much lower than the Curie-Weiss temperature θ W ≈ −4 K, and a power-law behavior for the magnetic specific heat at low temperatures [55,60].…”