Structure, Spin Correlations, and Magnetism of the S = 1/2 Square-Lattice Antiferromagnet Sr2CuTe1-xWxO6 (0 ≤ x ≤ 1).

Quantum spin liquids are highly entangled magnetic states with exotic properties. The S = 1/2 square-lattice Heisenberg model is one of the foundational models in frustrated magnetism with a predicted, but never observed, quantum spin liquid state. Isostructural double perovskites Sr2CuTeO6 and Sr2CuWO6 are physical realizations of this model but have distinctly different types of magnetic order and interactions due to a d10/d0 effect. Long-range magnetic order is suppressed in the solid solution Sr2CuTe1-xWxO6 in a wide region of x = 0.05-0.6, where the ground state has been proposed to be a disorder-induced spin liquid. Here, we present a comprehensive neutron scattering study of this system. We show using polarized neutron scattering that the spin liquid-like x = 0.2 and x = 0.5 samples have distinctly different local spin correlations, which suggests that they have different ground states. Low-temperature neutron diffraction measurements of the magnetically ordered W-rich samples reveal magnetic phase separation, which suggests that the previously ignored interlayer coupling between the square planes plays a role in the suppression of magnetic order at x ≈ 0.6. These results highlight the complex magnetism of Sr2CuTe1-xWxO6 and hint at a new quantum critical point between 0.2 < x < 0.4.

Spinteract: a program to refine magnetic interactions to diffuse scattering data.

Magnetic diffuse scattering-the broad magnetic scattering features observed in neutron-diffraction data above a material's magnetic ordering temperature-provides a rich source of information about the material's magnetic Hamiltonian. However, this information has often remained under-utilised due to a lack of available computer software that can fit values of magnetic interaction parameters to such data. Here, an open-source computer program, Spinteract, is presented, which enables straightforward refinement of magnetic interaction parameters to powder and single-crystal magnetic diffuse scattering data. The theory and implementation of this approach are summarised. Examples are presented of refinements to published experimental diffuse-scattering data sets for the canonical antiferromagnet MnO and the highly-frustrated classical spin liquid Gd3Ga5O12. Guidelines for data collection and refinement are outlined, and possible developments of the approach are discussed.

Line-Graph Approach to Spiral Spin Liquids.

Competition among exchange interactions is able to induce novel spin correlations on a bipartite lattice without geometrical frustration. A prototype example is the spiral spin liquid, which is a correlated paramagnetic state characterized by subdimensional degenerate propagation vectors. Here, using spectral graph theory, we show that spiral spin liquids on a bipartite lattice can be approximated by a further-neighbor model on the corresponding line-graph lattice that is nonbipartite, thus broadening the space of candidate materials that may support the spiral spin liquid phases. As illustrations, we examine neutron scattering experiments performed on two spinel compounds, ZnCr_{2}Se_{4} and CuInCr_{4}Se_{8}, to demonstrate the feasibility of this new approach and expose its possible limitations in experimental realizations.

Magnetic Interactions of the Centrosymmetric Skyrmion Material Gd_{2}PdSi_{3}.

The experimental realization of magnetic skyrmion crystals in centrosymmetric materials has been driven by theoretical understanding of how a delicate balance of anisotropy and frustration can stabilize topological spin structures in applied magnetic fields. Recently, the centrosymmetric material Gd_{2}PdSi_{3} was shown to host a field-induced skyrmion crystal, but the skyrmion stabilization mechanism remains unclear. Here, we employ neutron-scattering measurements on an isotopically enriched polycrystalline Gd_{2}PdSi_{3} sample to quantify the interactions that drive skyrmion formation. Our analysis reveals spatially extended interactions in triangular planes, and large ferromagnetic interplanar magnetic interactions that are modulated by the Pd/Si superstructure. The skyrmion crystal emerges from a zero-field helical magnetic order with magnetic moments perpendicular to the magnetic propagation vector, indicating that the magnetic dipolar interaction plays a significant role. Our experimental results establish an interaction space that can promote skyrmion formation, facilitating identification and design of centrosymmetric skyrmion materials.

Geometric Frustration on the Trillium Lattice in a Magnetic Metal-Organic Framework.

In the dense metal-organic framework Na[Mn(HCOO)_{3}], Mn^{2+} ions (S=5/2) occupy the nodes of a "trillium" net. We show that the system is strongly magnetically frustrated: the Néel transition is suppressed well below the characteristic magnetic interaction strength; short-range magnetic order persists far above the Néel temperature; and the magnetic susceptibility exhibits a pseudo-plateau at 1/3-saturation magnetization. A simple model of nearest-neighbor Heisenberg antiferromagnetic and dipolar interactions accounts quantitatively for all observations, including an unusual 2-k magnetic ground state. We show that the relative strength of dipolar interactions is crucial to selecting this particular ground state. Geometric frustration within the classical spin liquid regime gives rise to a large magnetocaloric response at low applied fields that is degraded in powder samples as a consequence of the anisotropy of dipolar interactions.

Sample Dependence of Magnetism in the Next-Generation Cathode Material LiNi0.8Mn0.1Co0.1O2.

We present a structural and magnetic study of two batches of polycrystalline LiNi0.8Mn0.1Co0.1O2 (commonly known as Li NMC 811), a Ni-rich Li ion battery cathode material, using elemental analysis, X-ray and neutron diffraction, magnetometry, and polarized neutron scattering measurements. We find that the samples, labeled S1 and S2, have the composition Li1-xNi0.9+x-yMnyCo0.1O2, with x = 0.025(2), y = 0.120(2) for S1 and x = 0.002(2), y = 0.094(2) for S2, corresponding to different concentrations of magnetic ions and excess Ni2+ in the Li+ layers. Both samples show a peak in the zero-field-cooled (ZFC) dc susceptibility at 8.0(2) K, but the temperature at which the ZFC and FC (field-cooled) curves deviate is substantially different: 64(2) K for S1 and 122(2) K for S2. The ac susceptibility measurements show that the transition for S1 shifts with frequency whereas no such shift is observed for S2 within the resolution of our measurements. Our results demonstrate the sample dependence of magnetic properties in Li NMC 811, consistent with previous reports on the parent material LiNiO2. We further establish that a combination of experimental techniques is necessary to accurately determine the chemical composition of next-generation battery materials with multiple cations.

Cluster Frustration in the Breathing Pyrochlore Magnet LiGaCr_{4}S_{8}.

We present a comprehensive neutron scattering study of the breathing pyrochlore magnet LiGaCr_{4}S_{8}. We observe an unconventional magnetic excitation spectrum with a separation of high- and low-energy spin dynamics in the correlated paramagnetic regime above a spin-freezing transition at 12(2) K. By fitting to magnetic diffuse-scattering data, we parametrize the spin Hamiltonian. We find that interactions are ferromagnetic within the large and small tetrahedra of the breathing pyrochlore lattice, but antiferromagnetic further-neighbor interactions are also essential to explain our data, in qualitative agreement with density-functional-theory predictions [Ghosh et al., npj Quantum Mater. 4, 63 (2019)2397-464810.1038/s41535-019-0202-z]. We explain the origin of geometrical frustration in LiGaCr_{4}S_{8} in terms of net antiferromagnetic coupling between emergent tetrahedral spin clusters that occupy a face-centered-cubic lattice. Our results provide insight into the emergence of frustration in the presence of strong further-neighbor couplings, and a blueprint for the determination of magnetic interactions in classical spin liquids.

Strengthening the Magnetic Interactions in Pseudobinary First-Row Transition Metal Thiocyanates, M(NCS)2.

Understanding the effect of chemical composition on the strength of magnetic interactions is key to the design of magnets with high operating temperatures. The magnetic divalent first-row transition metal (TM) thiocyanates are a class of chemically simple layered molecular frameworks. Here, we report two new members of the family, manganese(II) thiocyanate, Mn(NCS)2, and iron(II) thiocyanate, Fe(NCS)2. Using magnetic susceptibility measurements on these materials and on cobalt(II) thiocyanate and nickel(II) thiocyanate, Co(NCS)2 and Ni(NCS)2, respectively, we identify significantly stronger net antiferromagnetic interactions between the earlier TM ions-a decrease in the Weiss constant, θ, from 29 K for Ni(NCS)2 to -115 K for Mn(NCS)2-a consequence of more diffuse 3d orbitals, increased orbital overlap, and increasing numbers of unpaired t2g electrons. We elucidate the magnetic structures of these materials: Mn(NCS)2, Fe(NCS)2, and Co(NCS)2 order into the same antiferromagnetic commensurate ground state, while Ni(NCS)2 adopts a ground state structure consisting of ferromagnetically ordered layers stacked antiferromagnetically. We show that significantly stronger exchange interactions can be realized in these thiocyanate frameworks by using earlier TMs.

Quantum Versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho3Mg2Sb3O14.

A promising route to realize entangled magnetic states combines geometrical frustration with quantum-tunneling effects. Spin-ice materials are canonical examples of frustration, and Ising spins in a transverse magnetic field are the simplest many-body model of quantum tunneling. Here, we show that the tripod-kagome lattice material Ho3Mg2Sb3O14 unites an icelike magnetic degeneracy with quantum-tunneling terms generated by an intrinsic splitting of the Ho3+ ground-state doublet, which is further coupled to a nuclear spin bath. Using neutron scattering and thermodynamic experiments, we observe a symmetry-breaking transition at T*≈0.32K to a remarkable state with three peculiarities: a concurrent recovery of magnetic entropy associated with the strongly coupled electronic and nuclear degrees of freedom; a fragmentation of the spin into periodic and icelike components; and persistent inelastic magnetic excitations down to T≈0.12K. These observations deviate from expectations of classical spin fragmentation on a kagome lattice, but can be understood within a model of dipolar kagome ice under a homogeneous transverse magnetic field, which we survey with exact diagonalization on small clusters and mean-field calculations. In Ho3Mg2Sb3O14, hyperfine interactions dramatically alter the single-ion and collective properties, and suppress possible quantum correlations, rendering the fragmentation with predominantly single-ion quantum fluctuations. Our results highlight the crucial role played by hyperfine interactions in frustrated quantum magnets and motivate further investigations of the role of quantum fluctuations on partially ordered magnetic states.

Scattering Signatures of Bond-Dependent Magnetic Interactions.

Bond-dependent magnetic interactions can generate exotic phases such as Kitaev spin-liquid states. Experimentally determining the values of bond-dependent interactions is a challenging but crucial problem. Here, I show that each symmetry-allowed nearest-neighbor interaction on triangular and honeycomb lattices has a distinct signature in paramagnetic neutron-diffraction data, and that such data contain sufficient information to determine the spin Hamiltonian unambiguously via unconstrained fits. Moreover, I show that bond-dependent interactions can often be extracted from powder-averaged data. These results facilitate experimental determination of spin Hamiltonians for materials that do not show conventional magnetic ordering.

Ultrafast calculation of diffuse scattering from atomistic models.

Diffuse scattering is a rich source of information about disorder in crystalline materials, which can be modelled using atomistic techniques such as Monte Carlo and molecular dynamics simulations. Modern X-ray and neutron scattering instruments can rapidly measure large volumes of diffuse-scattering data. Unfortunately, current algorithms for atomistic diffuse-scattering calculations are too slow to model large data sets completely, because the fast Fourier transform (FFT) algorithm has long been considered unsuitable for such calculations [Butler & Welberry (1992). J. Appl. Cryst. 25, 391-399]. Here, a new approach is presented for ultrafast calculation of atomistic diffuse-scattering patterns. It is shown that the FFT can actually be used to perform such calculations rapidly, and that a fast method based on sampling theory can be used to reduce high-frequency noise in the calculations. These algorithms are benchmarked using realistic examples of compositional, magnetic and displacive disorder. They accelerate the calculations by a factor of at least 102, making refinement of atomistic models to large diffuse-scattering volumes practical.

Spin correlations in the dipolar pyrochlore antiferromagnet Gd2Sn2O7.

We investigate spin correlations in the dipolar Heisenberg antiferromagnet Gd2Sn2O7 using polarised neutron-scattering measurements in the correlated paramagnetic regime. Using Monte Carlo methods, we show that our data are sensitive to weak further-neighbour exchange interactions of magnitude ∼0.5% of the nearest-neighbour interaction, and are compatible with either antiferromagnetic next-nearest-neighbour interactions, or ferromagnetic third-neighbour interactions that connect spins across hexagonal loops. Calculations of the magnetic scattering intensity reveal rods of diffuse scattering along [1 1 1] reciprocal-space directions, which we explain in terms of strong antiferromagnetic correlations parallel to the set of [Formula: see text] directions that connect a given spin with its nearest neighbours. Finally, we demonstrate that the spin correlations in Gd2Sn2O7 are highly anisotropic, and correlations parallel to third-neighbour separations are particularly sensitive to critical fluctuations associated with incipient long-range order.

Orbital Dimer Model for the Spin-Glass State in Y_{2}Mo_{2}O_{7}.

The formation of a spin glass generally requires that magnetic exchange interactions are both frustrated and disordered. Consequently, the origin of spin-glass behavior in Y_{2}Mo_{2}O_{7}-in which magnetic Mo^{4+} ions occupy a frustrated pyrochlore lattice with minimal compositional disorder-has been a longstanding question. Here, we use neutron and x-ray pair-distribution function (PDF) analysis to develop a disorder model that resolves apparent incompatibilities between previously reported PDF, extended x-ray-absorption fine structure spectroscopy, and NMR studies, and provides a new and physical explanation of the exchange disorder responsible for spin-glass formation. We show that Mo^{4+} ions displace according to a local "two-in-two-out" rule on each Mo_{4} tetrahedron, driven by orbital dimerization of Jahn-Teller active Mo^{4+} ions. Long-range orbital order is prevented by the macroscopic degeneracy of dimer coverings permitted by the pyrochlore lattice. Cooperative O^{2-} displacements yield a distribution of Mo-O-Mo angles, which in turn introduces disorder into magnetic interactions. Our study demonstrates experimentally how frustration of atomic displacements can assume the role of compositional disorder in driving a spin-glass transition.

Emergent order in the kagome Ising magnet Dy3Mg2Sb3O14.

The Ising model-in which degrees of freedom (spins) are binary valued (up/down)-is a cornerstone of statistical physics that shows rich behaviour when spins occupy a highly frustrated lattice such as kagome. Here we show that the layered Ising magnet Dy3Mg2Sb3O14 hosts an emergent order predicted theoretically for individual kagome layers of in-plane Ising spins. Neutron-scattering and bulk thermomagnetic measurements reveal a phase transition at ∼0.3 K from a disordered spin-ice-like regime to an emergent charge ordered state, in which emergent magnetic charge degrees of freedom exhibit three-dimensional order while spins remain partially disordered. Monte Carlo simulations show that an interplay of inter-layer interactions, spin canting and chemical disorder stabilizes this state. Our results establish Dy3Mg2Sb3O14 as a tuneable system to study interacting emergent charges arising from kagome Ising frustration.

Encoding complexity within supramolecular analogues of frustrated magnets.

The solid phases of gold(I) and/or silver(I) cyanides are supramolecular assemblies of inorganic polymer chains in which the key structural degrees of freedom-namely, the relative vertical shifts of neighbouring chains-are mathematically equivalent to the phase angles of rotating planar ('XY') spins. Here, we show how the supramolecular interactions between chains can be tuned to mimic different magnetic interactions. In this way, the structures of gold(I) and/or silver(I) cyanides reflect the phase behaviour of triangular XY magnets. Complex magnetic states predicted for this family of magnets-including collective spin-vortices of relevance to data storage applications-are realized in the structural chemistry of these cyanide polymers. Our results demonstrate how chemically simple inorganic materials can behave as structural analogues of otherwise inaccessible 'toy' spin models and also how the theoretical understanding of those models allows control over collective ('emergent') phenomena in supramolecular systems.

Hidden order in spin-liquid Gd3Ga5O12.

Frustrated magnetic materials are promising candidates for new states of matter because lattice geometry suppresses conventional magnetic dipole order, potentially allowing "hidden" order to emerge in its place. A model of a hidden-order state at the atomic scale is difficult to deduce because microscopic probes are not directly sensitive to hidden order. Here, we develop such a model of the spin-liquid state in the canonical frustrated magnet gadolinium gallium garnet (Gd3Ga5O12). We show that this state exhibits a long-range hidden order in which multipoles are formed from 10-spin loops. The order is a consequence of the interplay between antiferromagnetic spin correlations and local magnetic anisotropy, which allows it to be indirectly observed in neutron-scattering experiments.

SPINVERT: a program for refinement of paramagnetic diffuse scattering data.

We present a program (spinvert; http://spinvert.chem.ox.ac.uk) for refinement of magnetic diffuse scattering data for frustrated magnets, spin liquids, spin glasses, and other magnetically disordered materials. The approach uses reverse Monte Carlo refinement to fit a large configuration of spins to experimental powder neutron diffraction data. Despite fitting to spherically averaged data, this approach allows the recovery of the three-dimensional magnetic diffuse scattering pattern and the spin-pair correlation function. We illustrate the use of the spinvert program with two case studies. First, we use simulated powder data for the canonical antiferromagnetic Heisenberg model on the kagome lattice to discuss the sensitivity of spinvert refinement to both pairwise and higher-order spin correlations. The effect of limited experimental data on the results is also considered. Second, we re-analyse published experimental data on the frustrated system Y0.5Ca0.5BaCo4O7. The results from spinvert refinement indicate similarities between Y0.5Ca0.5BaCo4O7 and its parent compound YBaCo4O7, which were overlooked in previous analyses using powder data.

Emergent frustration in co-doped ß-Mn.

We investigate low-temperature spin correlations in the metallic frustrated magnet ß-Mn1-xCox. Single-crystal polarized-neutron scattering experiments reveal the persistence of highly structured magnetic diffuse scattering and the absence of periodic magnetic order to T=0.05 K. We employ reverse Monte Carlo refinements and mean-field theory calculations to construct an effective Hamiltonian which accounts for the magnetic scattering. The interactions we identify describe an emergent spin structure which mimics the triangular lattice antiferromagnet, one of the canonical models of frustrated magnetism.

Empirical magnetic structure solution of frustrated spin systems.

Frustrated magnetism plays a central role in the phenomenology of exotic quantum states. However, since the magnetic structures of frustrated systems are often aperiodic, there has been the problem that they cannot be determined by using traditional crystallographic techniques. Here we show that the magnetic component of powder neutron scattering data is actually sufficiently information-rich to drive magnetic structure solution for frustrated systems, including spin ices, spin liquids, and molecular magnets. Our methodology employs ab initio reverse Monte Carlo refinement, making informed use of an additional constraint that minimizes variance in local spin environments. The atomistic spin configurations obtained in this way not only reflect a magnetic structure "solution" but also reproduce the full three-dimensional magnetic scattering pattern.