. By doing so, first order The resulting magnetic phase diagram of LiZn 2 Mo 3 O 8 is shown in figure 2d. Near room temperature, the system is paramagnetic and the spins thermally randomize. Cooling below the condensation temperature (T ~ 96 K), two-thirds of the spins form a condensed valence bond state. The remaining one-third spins are still paramagnetic and interacting antiferromagnetically until lower temperatures, at which point they lose entropy in a yet-to-be determined manner.

Recently measurements on various spin–1/2 quantum magnets such as H3LiIr2O6, LiZn2Mo3O8, ZnCu3(OH)6Cl2 and 1T-TaS2—all described by magnetic frustration and quenched disorder but with no other common relation—nevertheless showed apparently universal scaling features at low temperature. In particular the heat capacity C[H, T] in temperature T and magnetic field H exhibits T/H data collapse reminiscent of scaling near a critical point. Here we propose a theory for this scaling collapse based on an emergent random-singlet regime extended to include spin-orbit coupling and antisymmetric Dzyaloshinskii-Moriya (DM) interactions. We derive the scaling C[H, T]/T ~ H−γFq[T/H] with Fq[x] = xq at small x, with q ∈ {0, 1, 2} an integer exponent whose value depends on spatial symmetries. The agreement with experiments indicates that a fraction of spins form random valence bonds and that these are surrounded by a quantum paramagnetic phase. We also discuss distinct scaling for magnetization with a q-dependent subdominant term enforced by Maxwell’s relations.

Inelastic neutron scattering at low temperatures T≤30  K from a powder of LiZn2Mo3O8 demonstrates this triangular-lattice antiferromagnet hosts collective magnetic excitations from spin-1/2 Mo3O13 molecules. Apparently gapless (Δ<0.2  meV) and extending at least up to 2.5 meV, the low-energy magnetic scattering cross section is surprisingly broad in momentum space and involves one-third of the spins present above 100 K. The data are compatible with the presence of valence bonds involving nearest-neighbor and next-nearest-neighbor spins forming a disordered or dynamic state.

When the bonds of a quantum magnet are modulated with a periodic pattern, exotic quantum ground states may emerge. Newly synthesized crystalline barlowite (Cu 4 (OH) 6 FBr) and Zn-substituted barlowite demonstrate the delicate interplay between singlet states and spin order on the spin-1 2 kagome lattice. Our new variant of barlowite maintains hexagonal symmetry at low temperatures with an arrangement of distorted and undistorted kagome triangles, for which numerical simulations predict a pinwheel valence bond crystal (VBC) state instead of a quantum spin liquid (QSL). The presence of interlayer spins eventually leads to novel pinwheel q=0 magnetic order. Partially Zn-substituted barlowite (Cu 3.44 Zn 0.56 (OH) 6 FBr) has an ideal kagome lattice and shows QSL behavior, demonstrating the robustness of the QSL against local impurities. This system is a unique playground displaying QSL, VBC, and spin order, furthering our understanding of these highly competitive quantum states.Identifying the ground state for interacting quantum spins on the kagome lattice is an important unresolved question in condensed matter physics owing to the great difficulty in selecting amongst competing states that are very close in energy. Antiferromagnetic (AF) spins on this lattice are highly frustrated, and for spin-1 2 the ground state does not achieve magnetic order and is believed to be a quantum spin liquid (QSL). (1-9) The QSL is an unusual magnetic ground state, characterized by long-range quantum entanglement of the spins with the absence of long-range magnetic order. (10-13) The recent identification of herbertsmithite (Cu 3 Zn(OH) 6 Cl 2 ) (14-17) as a leading candidate QSL material has ignited intense interest in further understanding similar kagome materials.Often, real kagome materials have interactions that relieve the frustration and drive the moments to magnetically order. (18,19) In contrast, for the ideal S = 1 2 kagome Heisen-

T.M. (2014) 'Local magnetismand spin correlations in the geometrically frustrated cluster magnet LiZn2Mo3O8.', Physical review B., 89 (6). 064407.Further information on publisher's website:http://dx.doi.org/10.1103/PhysRevB.89.064407Publisher's copyright statement:Reprinted with permission from the American Physical Society: J. P. Sheckelton, F. R. Foronda, LiDong Pan, C. Moir, R. D. McDonald, T. Lancaster, P. J. Baker, N. P. Armitage, T. Imai, S. J. Blundell, and T. M. McQueen, Physical Review B, 89, 064407, 2014. c 2014 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modi ed, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society. Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

Combining multiple fast image acquisitions to mitigate scan noise and drift artifacts has proven essential for picometer precision, quantitative analysis of atomic resolution scanning transmission electron microscopy (STEM) data. For very low signal-to-noise ratio (SNR) image stacks - frequently required for undistorted imaging at liquid nitrogen temperatures - image registration is particularly delicate, and standard approaches may either fail, or produce subtly specious reconstructed lattice images. We present an approach which effectively registers and averages image stacks which are challenging due to their low-SNR and propensity for unit cell misalignments. Registering all possible image pairs in a multi-image stack leads to significant information surplus. In combination with a simple physical picture of stage drift, this enables identification of incorrect image registrations, and determination of the optimal image shifts from the complete set of relative shifts. We demonstrate the effectiveness of our approach on experimental, cryogenic STEM datasets, highlighting subtle artifacts endemic to low-SNR lattice images and how they can be avoided. High-SNR average images with information transfer out to 0.72 Å are achieved at 300 kV and with the sample cooled to near liquid nitrogen temperature.

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Insulating Nb 3 Cl 8 is a layered chloride consisting of two-dimensional triangular layers of S e f f = 1/2 Nb 3 Cl 13 clusters at room temperature. Magnetic susceptibility measurement show a sharp, hysteretic drop to a temperature independent value below T = 90 K. Specific heat measurements show that the transition is first order, with ∆S ≈ 5 J · K −1 · mol f .u. −1 , and a low temperature T-linear contribution originating from defect spins. Neutron and X-ray diffraction show a lowering of symmetry from trigonal P3m1 to monoclinic C2/m symmetry, with a change in layer stacking from -AB-AB-to -AB ′ -BC ′ -CA ′ -and no observed magnetic order. This lowering of symmetry and rearrangement of successive layers evades geometric magnetic frustration to form a singlet ground state. It is the lowest temperature at which a change in stacking sequence is known to occur in a Van-der-Waals solid, occurs in the absence of orbital degeneracies, and suggests that designer 2-D heterostructures may be able to undergo similar phase transitions.