Fractional spin textures in the frustrated magnet SrCr(9p)Ga(12-9p)O₁₉

Evolution of magnetic surfboards and spin glass behavior in (Fe1-pGap)2TiO5

The unusual anisotropy of the spin glass (SG) transition in the pseudobrookite system Fe2TiO5has been interpreted as arising from an induced, van der Waals-like, interaction among magnetic clusters. Here we present susceptibility (χ) and specific heat data (C) for Fe2TiO5diluted with non-magnetic Ga, (Fe1-pGap)2TiO5, for disorder parameterp= 0, 0.11, and 0.42, and elastic neutron scattering data forp= 0.20. A uniform suppression ofTgis observed upon increasingp, along with a value ofχTgthat increases asTgdecreases, i.e.dχ(Tg)/dTg<0We also observeCT∝T2in the low temperature limit. The observed behavior places (Fe1-pGap)2TiO5in the category of a strongly geometrically frustrated SG.

Eminuscent phase in frustrated magnets: a challenge to quantum spin liquids

A geometrically frustrated (GF) magnet consists of localised magnetic moments, spins, whose orientation cannot be arranged to simultaneously minimise their interaction energies. Such materials may host novel fascinating phases of matter, such as fluid-like states called quantum spin-liquids. GF magnets have, like all solid-state systems, randomly located impurities whose magnetic moments may “freeze” at low temperatures, making the system enter a spin-glass state. We analyse the available data for spin-glass transitions in GF materials and find a surprising trend: the glass-transition temperature grows with decreasing impurity concentration and reaches a finite value in the impurity-free limit at a previously unidentified, “hidden”, energy scale. We propose a scenario in which the interplay of interactions and entropy leads to a crossover in the permeability of the medium that assists glass freezing at low temperatures. This low-temperature, “eminuscent”, phase may obscure or even destroy the widely-sought spin-liquid states in rather clean systems.

A spin-glass forms in frustrated magnetic systems when at low temperatures impurity sites “freeze” into a random spin configuration. Here, by looking back at previous experimental results, Syzranov and Ramirez show that the glass-transition temperature grows with decreasing impurity concentration.

Emergent Moments and Random Singlet Physics in a Majorana Spin Liquid

We exhibit an exactly solvable example of a SU(2) symmetric Majorana spin liquid phase, in which quenched disorder leads to random-singlet phenomenology of emergent magnetic moments. More precisely, we argue that a strong-disorder fixed point controls the low temperature susceptibility χ(T) of an exactly solvable S=1/2 model on the decorated honeycomb lattice with vacancy and/or bond disorder, leading to χ(T)=C/T+DT^{α(T)-1}, where α(T)→0 slowly as the temperature T→0. The first term is a Curie tail that represents the emergent response of vacancy-induced spin textures spread over many unit cells: it is an intrinsic feature of the site-diluted system, rather than an extraneous effect arising from isolated free spins. The second term, common to both vacancy and bond disorder [with different α(T) in the two cases] is the response of a random singlet phase, familiar from random antiferromagnetic spin chains and the analogous regime in phosphorus-doped silicon (Si:P).

PbFePO4F2 with a 1/6th bond depleted triangular lattice

A 1/6th bond depleted triangular lattice has been experimentally realized in the novel compound PbFePO₄F₂ with moderately strong frustration.

Fractionalized Z_{2} Classical Heisenberg Spin Liquids

Quantum spin systems are by now known to exhibit a large number of different classes of spin liquid phases. By contrast, for classical Heisenberg models, only one kind of fractionalized spin liquid phase, the so-called Coulomb or U(1) spin liquid, has until recently been identified: This exhibits algebraic spin correlations and impurity moments, "orphan spins," whose size is a fraction of that of the underlying microscopic degrees of freedom. Here, we present two Heisenberg models exhibiting fractionalization in combination with exponentially decaying correlations. These can be thought of as a classical continuous spin version of a Z_{2} spin liquid. Our work suggests a systematic search and classification of classical spin liquids as a worthwhile endeavor.

Classical Spin Liquid on the Maximally Frustrated Honeycomb Lattice

We show that the honeycomb Heisenberg antiferromagnet with J_{1}/2=J_{2}=J_{3}, where J_{1}, J_{2}, and J_{3} are first-, second-, and third-neighbor couplings, respectively, forms a classical spin liquid with pinch-point singularities in the structure factor at the Brillouin zone corners. Upon dilution with nonmagnetic ions, fractionalized degrees of freedom carrying 1/3 of the free moment emerge. Their effective description in the limit of low temperature is that of spins randomly located on a triangular lattice, with a frustrated sublattice-sensitive interaction of long-ranged logarithmic form. The XY version of this magnet exhibits nematic thermal order by disorder. This comes with a clear experimental diagnostic in neutron scattering, which turns out to apply also to the case of the celebrated planar order by disorder of the kagome Heisenberg antiferromagnet.

Maxwell electromagnetism as an emergent phenomenon in condensed matter

The formulation of a complete theory of classical electromagnetism by Maxwell is one of the milestones of science. The capacity of many-body systems to provide emergent mini-universes with vacua quite distinct from the one we inhabit was only recognized much later. Here, we provide an account of how simple systems of localized spins manage to emulate Maxwell electromagnetism in their low-energy behaviour. They are much less constrained by symmetry considerations than the relativistically invariant electromagnetic vacuum, as their substrate provides a non-relativistic background with even translational invariance broken. They can exhibit rich behaviour not encountered in conventional electromagnetism. This includes the existence of magnetic monopole excitations arising from fractionalization of magnetic dipoles; as well as the capacity of disorder, by generating defects on the lattice scale, to produce novel physics, as exemplified by topological spin glassiness or random Coulomb magnetism.This article is part of the themed issue 'Unifying physics and technology in light of Maxwell's equations'.

Kondo Impurities in the Kitaev Spin Liquid: Numerical Renormalization Group Solution and Gauge-Flux-Driven Screening

Kitaev's honeycomb-lattice compass model describes a spin liquid with emergent fractionalized excitations. Here, we study the physics of isolated magnetic impurities coupled to the Kitaev spin-liquid host. We reformulate this Kondo-type problem in terms of a many-state quantum impurity coupled to a multichannel bath of Majorana fermions and present the numerically exact solution using Wilson's numerical renormalization group technique. Quantum phase transitions occur as a function of Kondo coupling and locally applied field. At zero field, the impurity moment is partially screened only when it binds an emergent gauge flux, while otherwise it becomes free at low temperatures. We show how Majorana degrees of freedom determine the fixed-point properties, make contact with Kondo screening in pseudogap Fermi systems, and discuss effects away from the dilute limit.

Triangular antiferromagnet with nonmagnetic impurities

The effect of nonmagnetic impurities on the phase diagram of the classical Heisenberg antiferromagnet on a triangular lattice is investigated. We present analytical arguments confirmed by numerical calculations that at zero temperature vacancies stabilize a conical state providing an example of "order by quenched disorder" effect. Competition between thermal fluctuations and the site disorder leads to a complicated H-T phase diagram, which is deduced from the classical Monte Carlo simulations for a representative vacancy concentration. For the XY triangular-lattice antiferromagnet with an in-plane external field, nonmagnetic impurities stabilize the fanlike spin structure. We also briefly discuss the effect of quantum fluctuations.

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.

Neutron scattering and μSR investigations of the low temperature state of LuCuGaO₄

LuCuGaO₄ has magnetic Cu(2+) and diamagnetic Ga(3+) ions distributed on a triangular bilayer and is suggested to undergo a spin glass transition at Tg ∼ 0.4 K. Using μSR (muon spin rotation) and neutron scattering measurements, we show that at low temperature the spins form a short range correlated state with spin fluctuations detectable over a wide range of timescales: at 0.05 K magnetic fluctuations can be detected in both the μSR time window and also extending beyond 7 meV in the inelastic neutron scattering response, indicating magnetic fluctuations spanning timescales between ∼10(-5) and ∼10(-10) s. The dynamical susceptibility scales according to the form χ″(ω)T(α), with α = 1, throughout the measured temperature range (0.05-50 K). These effects are associated with quantum fluctuations and some degree of structural disorder in ostensibly quite different materials, including certain heavy fermion alloys, kagome spin liquids, quantum spin glasses, and valence bond glasses. We therefore suggest that LuCuGaO₄ is an interesting model compound for the further examination of disorder and quantum magnetism.

Quasispin glass in a geometrically frustrated magnet

The spin glass state in the spinel ZnCr(2(1-x))Ga(2x)O(4) is studied with magnetization and specific heat for x < 0.05. The freezing temperature is independent of disorder, despite a two-level-like density of states that varies linearly with x. This relationship implies the energy scale for freezing is independent of disorder, in contrast to mean field theories of spin glass. We suggest that the degrees of freedom are shielded spin vacancies, quasispins, which interact via an emergent long-range force mediated by the frustrated spin background.

Magnetic properties of hole-doped SCGO, SrCr(8)Ga(4-x)M(x)O(19) (M = Zn, Mg, Cu)

We report changes in the magnetic properties of hole-doped SCGO, SrCr8Ga4O19, induced by replacing non-magnetic Ga3+ with both non-magnetic (Mg2+ and Zn2+) and magnetic (Cu2+) cations. The resulting solid solutions, SrCr(8)Ga(4-x)M(x)O(19) (M = Zn, Mg, Cu) have been studied by x-ray diffraction and magnetic susceptibility measurements. For all cases, at least 10% of Ga can be replaced by divalent cations resulting in oxidation of ≥5% of the Cr3+ d3 to Cr4+ (d2). The hole doping results in an increase in ferromagnetic interactions and reduces the magnetic frustration. In the SrCr(8)Ga(4-x)Cu(x)O(19) series an enhancement of the spin-glass-like transition is observed, T(f)∼ 6 K, which we ascribe to the magnetic nature of the Cu2+ (d9) dopant.