Layer-by-layer epitaxial thin films of the pyrochlore Tb2Ti2O7.

Layer-by-layer epitaxial growth of the pyrochlore magnet Tb2Ti2O7 on the isostructural substrate Y2Ti2O7 results in high-quality single crystal films of up to 60 nm thickness. Substrate-induced strain is shown to act as a strong and controlled perturbation to the exotic magnetism of Tb2Ti2O7, opening up the general prospect of strain-engineering the diverse magnetic and electrical properties of pyrochlore oxides.

Spin-Glass States Generated in a van der Waals Magnet by Alkali-Ion Intercalation.

Tuning magnetic properties in layered van der Waals (vdW) materials has captured significant attention due to the efficient control of ground states by heterostructuring and external stimuli. Electron doping by electrostatic gating, interfacial charge transfer, and intercalation is particularly effective in manipulating the exchange and spin-orbit properties, resulting in a control of Curie temperature (TC) and magnetic anisotropy. Here, an uncharted role of intercalation is discovered to generate magnetic frustration. As a model study, Na atoms are intercalated into the vdW gaps of pristine Cr2Ge2Te6 (CGT) where generated magnetic frustration leads to emerging spin-glass states coexisting with a ferromagnetic order. A series of dynamic magnetic susceptibility measurements/analysis confirms the formation of magnetic clusters representing slow dynamics with a distribution of relaxation times. The intercalation also modifies other macroscopic physical parameters including the significant enhancement of TC from 66 to 240 K and the switching of magnetic easy-hard axis direction. This study identifies intercalation as a unique route to generate emerging frustrated spin states in simple vdW crystals.

Analytic form of a two-dimensional critical distribution.

This paper explores the possibility of establishing an analytic form of the distribution of the order parameter fluctuations in a two-dimensional critical spin-wave model, or width fluctuations of a two-dimensional Edwards-Wilkinson interface. It is shown that the characteristic function of the distribution can be expressed exactly as a gamma function quotient, while a Charlier series, using the convolution of two Gumbel distributions as the kernel, converges to the exact result over a restricted domain. These results can also be extended to calculate the temperature dependence of the distribution and give an insight into the origin of Gumbel-like distributions in steady-state and equilibrium quantities that are not extreme values.

The history of spin ice.

This review is a study of how the idea of spin ice has evolved over the years, with a focus on the scientific questions that have come to define the subject. Since our initial discovery of spin ice in 1997, there have been well over five thousand papers that discuss it, and in the face of such detail, it must be difficult for the curious observer to 'see the wood for the trees'. To help in this task, we go in search of the biggest insight to have emerged from the study of spin ice. On the way, we identify highlights and outstanding puzzles, and celebrate the inspirational role that Roger Cowley played in the early years.

Author Correction: Harmonic phase in polar liquids and spin ice.

The original version of this Article contained an error in the third sentence of the penultimate paragraph of the 'Definition of the harmonic phase' section of the Results, which incorrectly read 'In the Coulomb phase the tensor S αß (q) has one zero and two degenerate eigenvalues and it may be represented by an infinitely thin disc of radius 3/2 with its axis parallel to q.' The correct version states '[Formula: see text]' in place of '3/2.'Similarly, the second sentence in the legend of Fig. 3 originally incorrectly read 'In the Coulomb phase it is an infinitely thin disc with radius 3/2, but in the harmonic phase it becomes an oblate spheroid, that evolves from the disc in the low-temperature limit towards a unit sphere at high temperature (disc and example spheroid shown overlaid together).' The correct version states ' [Formula: see text] ' instead of '3/2'.This has been corrected in both the PDF and HTML versions of the Article.

Harmonic phase in polar liquids and spin ice.

Many liquid or liquid-like states remain stable down to temperatures well below the interaction energy scale, where mean-field theory predicts an ordering transition. In magnetism, correlated states such as spin ice and the spin liquid have been described as Coulomb phases, governed by an emergent gauge principle. In the physical chemistry of polar liquids, systems that evade mean field order have, in contrast, been described by Onsager's theory of the reaction field. Here we observe that in the low-temperature limit, Onsager's theory may be cast as a prototypical theory of the Coulomb phase. However at finite temperature, it describes a distinct geometrical state, characterised by harmonic functions. This state, labelled here the 'harmonic phase', is shown to occur experimentally in spin ice, a dipolar lattice system. It is suggested to be relevant to more general dipolar liquids.

An electric-field representation of the harmonic XY model.

The two-dimensional harmonic XY (HXY) model is a spin model in which the classical spins interact via a piecewise parabolic potential. We argue that the HXY model should be regarded as the canonical classical lattice spin model of phase fluctuations in two-dimensional condensates, as it is the simplest model that guarantees the modular symmetry of the experimental systems. Here we formulate a lattice electric-field representation of the HXY model and contrast this with an analogous representation of the Villain model and the two-dimensional Coulomb gas with a purely rotational auxiliary field. We find that the HXY model is a spin-model analogue of a lattice electric-field model of the Coulomb gas with an auxiliary field, but with a temperature-dependent vacuum (electric) permittivity that encodes the coupling of the spin vortices to their background spin-wave medium. The spin vortices map to the Coulomb charges, while the spin-wave fluctuations correspond to auxiliary-field fluctuations. The coupling explains the striking differences in the high-temperature asymptotes of the specific heats of the HXY model and the Coulomb gas with an auxiliary field. Our results elucidate the propagation of effective long-range interactions throughout the HXY model (whose interactions are purely local) by the lattice electric fields. They also imply that global spin-twist excitations (topological-sector fluctuations) generated by local spin dynamics are ergodically excluded in the low-temperature phase. We discuss the relevance of these results to condensate physics.

Generalized longitudinal susceptibility for magnetic monopoles in spin ice.

The generalized longitudinal susceptibility χ(q,ω) affords a sensitive measure of the spatial and temporal correlations of magnetic monopoles in spin ice. Starting with the monopole model, a mean field expression for χ(q,ω) is derived as well as expressions for the mean square longitudinal field and induction at a point. Monopole motion is shown to be strongly correlated, and both spatial and temporal correlations are controlled by the dimensionless monopole density x which defines the ratio of the magnetization relaxation rate and the monopole hop rate. Thermal effects and spin-lattice relaxation are also considered. The derived equations are applicable in the temperature range where the Wien effect for magnetic monopoles is negligible. They are discussed in the context of existing theories of spin ice and the following experimental techniques: DC and AC magnetization, neutron scattering, neutron spin echo and longitudinal and transverse field µSR. The monopole theory is found to unify diverse experimental results, but several discrepancies between theory and experiment are identified. One of these, concerning the neutron scattering line shape, is explained by means of a phenomenological modification to the theory.

Dimensional analysis, spin freezing and magnetization in spin ice.

Dimensional analysis is shown to give an insight into the non-ergodic behaviour of spin ice below its apparent 'spin freezing' temperature. Expressions are derived for the temperature-dependent magnetic susceptibility that are found to be highly consistent with the previously reported field cooled and zero field cooled magnetization of the spin ice dysprosium titanate, Dy(2)Ti(2)O(7), as well as with the theory of a 'magnetolyte', including Debye-Hückel screening and Wien dissociation. The spin freezing is inferred to reflect the inability of the quasi-free magnetic charges or 'monopoles' that comprise the magnetolyte to fully screen an applied magnetic field on the timescale of an experiment. The apparent freezing temperature (T(f)≈0.65 K) is identified as the point where the Debye screening length becomes greater than the Bjerrum association distance for charge pairs. Combining these dimensional arguments with Onsager's theory of the Wien effect, it is shown that magnetization data at relatively high field (Snyder et al 2004 Phys. Rev. B 69 064414) may be used to estimate the elementary magnetic charge of spin ice, as well as the temperature-dependent monopole density. Evidence is presented of a non-equilibrium population of monopoles below T≈0.2 K. It is also shown how Onsager's microscopic theory of field-induced monopole pair separation naturally suggests the 'magnetization jumps' in Dy(2)Ti(2)O(7) observed at applied fields of the order of ∼ 0.1 T. It is concluded that the results of dimensional analysis, when combined with Onsager's theory, provide an accurate, albeit approximate, description of the properties of Dy(2)Ti(2)O(7), that could be improved by the development of a lattice theory of the Wien effect, or tested on other spin ice materials.

Dy2Ti2O7 spin ice: a test case for emergent clusters in a frustrated magnet.

Dy2Ti2O7 is a geometrically frustrated magnetic material with a strongly correlated spin ice regime that extends from 1 K down to as low as 60 mK. The diffuse elastic neutron scattering intensities in the spin ice regime can be remarkably well described by a phenomenological model of weakly interacting hexagonal spin clusters, as invoked in other geometrically frustrated magnets. We present a highly refined microscopic theory of Dy2Ti2O7 that includes long-range dipolar and exchange interactions to third nearest neighbors and which demonstrates that the clusters are purely fictitious in this material. The seeming emergence of composite spin clusters and their associated scattering pattern is instead an indicator of fine-tuning of ancillary correlations within a strongly correlated state.

Crossover from positive to negative magnetoresistance in a spinel.

We present a new class of colossal magnetoresistance materials based on a series of frustrated spinels. The spin glass-like compound Zn0.95Cu0.05Cr2Se4, shows a field-induced transition to a ferromagnetic, which is associated with a highly unusual negative magnetoresistance effect (MR > 80%) in low magnetic field. At higher temperatures there is an unprecedented crossover to positive magnetoresistance (MR > 50%).