Session L19: Invited Session: Spin Liquids with Disorder

The spin liquid ground state of the $S=1/2$ Heisenberg model on the kagome lattice

Condensed matter physicists have long sought a realistic two-dimensional (2D) magnetic system whose ground state is a {\it spin liquid}---a zero temperature state in which quantum fluctuations have melted away any form of magnetic order. The nearest-neighbor $S=1/2$ Heisenberg model on the kagome lattice has seemed an ideal candidate, but in recent years some approximate numerical approaches to it have yielded instead a valence bond crystal. We have used the density matrix renormalization group to perform very accurate simulations on numerous cylinders with circumferences up to 12 lattice spacings, finding instead of the valence bond crystal a spin liquid, gapped in both the singlet and triplet sectors, with substantially lower energy. [Simeng Yan, David A. Huse, and Steven R. White, {\sl Science} 332, 1173 (2011). {\it Cover article}] Our results, through a combination of very low energy, short correlation lengths and corresponding small finite size effects, a new rigorous energy bound, and consistent behavior on many cylinders, provide strong evidence that the 2D ground state of this model is a gapped spin liquid. One key feature of this spin liquid is that the predominant valence bond resonances occur on eight site loops rather than the shortest six site loops. The eight site loops allow a greater fraction of the bonds in the lattice to resonate. Our recent studies including a next nearest neighbor interaction $J_2$ reveal that the $J_2=0$ point is near the edge of a substantial spin liquid phase centered near $J_2=0.05-0.1$.   

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.   

Disorder in a quantum spin liquid: the Kitaev honeycomb model with vacancies

We address the effects of disorder in the Kitaev honeycomb model, focussing on the interplay of disorder and strong interactions in a quantum spin liquid. It is shown that nonmagnetic impurities bind a quantum of the emergent gauge flux. We find the formation of a local moment, which leads to a local magnetic response near the impurity which is parametrically larger than in the bulk. The magnetic response of a pair of impurities can be parametrically larger than that of an isolated one, and can in particular dominate the magnetic response of the system. The role of such impurities as diagnostic of the spin liquid state are emphasized -- most remarkably, they provide a direct signature of the emergent gauge field.   

Hole doping in frustrated spinels, ZnCr$_{2}$O$_{4}$ and MgCr$_{2}$O$_{4}$, and their two dimensional analogue SCGO, SrCr$_{8}$Ga$_{4}$O$_{19}$

Recent experiments on the complex geometrically frustrated magnet, $\beta $-CaCr$_{2}$O$_{4}$, clearly illustrate the divergent effect of hole and static doping on the magnetic properties [1]. Given the complex parent state of $\beta $-CaCr$_{2}$O$_{4}$ this is not an ideal system for studying perturbations to the magnetic interactions. However, the onset of ferromagnetic fluctuations and ferrimagnetic ordering in $\beta $-Ca$_{1-y}$Cr$_{2}$O$_{4}$ suggests that other hole doped Cr$^{3+/4+}$ systems may be of interest. The extreme sensitivity in the balance of competing magnetic interactions in geometrically frustrated magnets is illustrated clearly in Cr$^{3+}$ spinels, ACr$_{2}$O$_{4}$. Antiferromagnetic (AFM) ordering in ACr$_{2}$O$_{4}$ occurs at a spin-Peierls transition. Both the low temperature magnetic and structural regimes are found to be highly sensitive to the A cation. In the case of ZnCr$_{2}$O$_{4}$ we find that very fine control of the reaction conditions is necessary to make stoichiometric ZnCr$_{2}$O$_{4}$, rather than hole doped Zn$_{1+x}$Cr$_{2-x}$O$_{4}$ (x $\le $ 0.04). From analysis of magnetic measurements, specific heat and neutron diffraction we have probed the nature of the transitions at $T_{N}$ [2]. How hole doping effects the low temperature properties and the role of the $d^{2}$ Cr$^{4+}$ cations on the isotropic $d^{3}$ Cr$^{3+}$ magnetic lattice will be discussed. Our results on the more robust MgCr$_{2}$O$_{4}$ spinel will also be presented. A 2D analogue of the 3D pyrochlore magnetic lattice in the ACr$_{2}$O$_{4}$ spinels is found in SCGO, SrCr$_{8}$Ga$_{4}$O$_{19}$. In hole doped SCGO, SrCr$_{8}$M$_{x}$Ga$_{4-x}$O$_{19}$ (M = Zn, Mg, Cu), a larger fraction of the Cr$^{3+}$ can be oxidized. Hole doping is found to have a significant effect on the magnetic fluctuations, how this depends on the nature of the dopant cation will be addressed [3]. \\[4pt] [1] S. E. Dutton, C. L. Broholm, and R. J. Cava, Journal of Solid State Chemistry \textbf{183}, 1798 (2010). \\[0pt] [2] S. E. Dutton\textit{ et al.}, Physical Review B \textbf{83}, 064407 (2011). \\[0pt] [3] S. E. Dutton\textit{ et al.}, Journal of Physics-Condensed Matter \textbf{23}, 386001 (2011).   

Impurity Effects in Highly Frustrated Diamond-Lattice Antiferromagnets

We consider the effects of local impurities in highly frustrated diamond lattice antiferromagnets, which exhibit large but non-extensive ground state degeneracies. Such models are appropriate to many A-site magnetic spinels. We argue very generally that sufficiently dilute impurities induce an {\sl ordered} magnetic ground state, and provide a mechanism of degeneracy breaking. The states which are selected can be determined by a ``swiss cheese model'' analysis, which we demonstrate numerically for a particular impurity model in this case. Moreover, we present criteria for estimating the stability of the resulting ordered phase to a competing frozen (spin glass) one. The results may explain the contrasting finding of frozen and ordered ground states in CoAl$_2$O$_4$ and MnSc$_2$S$_4$, respectively.