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The usual starting point for understanding magnons in cuprate antiferromagnets such as La$_2$CuO$_4$ is a spin model incorporating cyclic exchange, which descends from a one-band Hubbard model, and has parameters taken from fits based on non-interacting spin wave theory. Here we explore whether this provides a reliable description of experiment, using matrix product states (MPS) to calculate magnon spectra beyond spin wave theory. We find that analysis based on low orders of spin wave theory leads to systematic overestimates of exchange parameters, with corresponding errors in estimates of Hubbard $t/U$. Once these are corrected, the ''standard'' model provides a good account of magnon dispersion and lineshape in La$_2$CuO$_4$, but fails to fully capture the continuum observed at high energies. The extension of this analysis to CaCuO$_2$ and Sr$_2$IrO$_4$ is also discussed.

Competing interactions in frustrated magnets can give rise to highly degenerate ground states from which correlated liquid-like states of matter often emerge. The scaling of this degeneracy influences the ultimate ground state, with extensive degeneracies potentially yielding quantum spin liquids, while sub-extensive or smaller degeneracies yield static orders. A longstanding problem is to understand how ordered states precipitate from this degenerate manifold and what echoes of the degeneracy survive ordering. Here, we use neutron scattering to experimentally demonstrate a new "nodal line" spin liquid, where spins collectively fluctuate within a sub-extensive manifold spanning one-dimensional lines in reciprocal space. Realized in the spin-orbit coupled, face-centered cubic iridate K$_2$IrCl$_6$, we show that the sub-extensive degeneracy is robust, but remains susceptible to fluctuations or longer range interactions which cooperate to select a magnetic order at low temperatures. Proximity to the nodal line spin liquid influences the ordered state, enhancing the effects of quantum fluctuations and stabilizing it through the opening of a large spin-wave gap. Our results demonstrate quantum fluctuations can act counter-intuitively in frustrated materials: instead of destabilizing ordering, at the brink of the nodal spin liquid they can act to stabilize it and dictate its low-energy physics., Comment: Main article: 9 pages, 3 figures. Supplemental material: 22 pages, 15 figures

A comprehensive set of muon spin spectroscopy and neutron scattering measurements supported by ab-initio and model Hamiltonian simulations have been used to investigate the magnetic ground state of Na$_2$PrO$_3$. $\mu$SR reveals N\'eel antiferromagnetic order below $T_{\rm N}\! \sim\! 4.9$ K, with a small static magnetic moment $m_{\rm static}\!\leq \! 0.22$~$\mu_{\rm B}/{\rm Pr}$ collinearly aligned along the $c-$axis. Inelastic neutron measurements reveal the full spectrum of crystal field excitations and confirm that the Pr$^{4+}$ ground state wave function deviates significantly from the $\Gamma_7$ limit relevant to the Kitaev model. Single and two magnon excitations are observed in the ordered state below $T_N=4.6$ K and are well described by non-linear spin wave theory from the N\'eel state using a magnetic Hamiltonian with Heisenberg exchange $J=1$ meV and symmetric anisotropic exchange $\Gamma/J=0.1$, corresponding to an XY model. Intense two magnon excitations are accounted for by $g$-factor anisotropy $g_\mathrm{z}/g_\pm = 1.29$. A fluctuating moment $\delta m^2 = 0.57(22)$ $\mu_{\rm B}^2/{\rm Pr}$ extracted from the energy and momentum integrated inelastic neutron signal is reduced from expectations for a local $J=1/2$ moment with average $g$-factor $g_{\rm avg}\approx 1.1$. Together, the results demonstrate that the small moment in Na$_2$PrO$_3$ arises from crystal field and covalency effects and that the material does not exhibit significant quantum fluctuations..

In this study, a novel material from the rare-earth based breathing pyrochlore family, Ba3Tm2Zn5O11, was successfully synthesized. Powder X-ray diffraction and high-resolution powder neutron diffraction confirmed phase purity and crystal structure, while thermogravimetric analysis revealed incongruent melting behavior compared to its counterpart, Ba3Yb2Zn5O11. High-quality single crystals of Ba3Tm2Zn5O11 were grown using the traveling solvent floating zone technique and assessed using Laue diffractometer and single crystal X-ray diffraction. Thermodynamic characterization indicated paramagnetic behavior down to 0.05 K, and inelastic neutron scattering measurements identified distinct crystal electric field bands. Additional low-energy excitation studies on single crystals revealed dispersionless bands at 0.8 and 1 meV. Computed phonon dispersions from first principles calculations ruled out phonons as the source of these modes, further illustrating the puzzling and unique properties of Ba3Tm2Zn5O11.

Compass models provide insights into the properties of Mott-insulating materials that host bond-dependent anisotropic interactions between their pseudospin degrees of freedom. In this article, we explore the classical and quantum ground state properties of one such model relevant to certain layered perovskite materials akin to Ba$_2$IrO$_4$ - namely, the Heisenberg-compass model on the square lattice. We first investigate the ground state phase diagram of this model using classical Monte Carlo simulations. These reveal that the low temperature classical phase diagram is divided into six different classes of long-range ordered phases, including four phases that exhibit an order by disorder selection and two phases that are stabilized energetically. This model admits a special duality transformation, known as the Klein duality, conveniently allowing to map one region of coupling parameters onto another and constraining the phase diagram, and which we exploit in our study. From the analysis of the zero-point energy and the free energy of the spin waves, we find that order by quantum disorder at zero temperature and order by thermal disorder select the same orderings as those found from classical Monte Carlo simulations. We further investigate the quantum ground states of this model using numerical exact diagonalization on small clusters by exploiting the translational symmetry of the square lattice. We obtain a ground state phase diagram bearing close resemblance to that found from the classical analysis., Comment: 18 pages, 6 figures

We formulate a Landau theory for altermagnets, a class of colinear compensated magnets with spin-split bands. Starting from the non-relativistic limit, this Landau theory goes beyond a conventional analysis by including spin-space symmetries, providing a simple framework for understanding the key features of this family of materials. We find a set of multipolar secondary order parameters connecting existing ideas about the spin symmetries of these systems, their order parameters and the effect of non-zero spin-orbit coupling. We account for several features of canonical altermagnets such as RuO$_2$, MnTe and CuF$_2$ that go beyond symmetry alone, relating the order parameter to key observables such as magnetization, anomalous Hall conductivity and magneto-elastic and magneto-optical probes. Finally, we comment on generalizations of our framework to a wider family of exotic magnetic systems deriving from the zero spin-orbit coupled limit., Comment: 5+ pages, 2 figures

Accidental ground state degeneracies -- those not a consequence of global symmetries of the Hamiltonian -- are inevitably lifted by fluctuations, often leading to long-range order, a phenomenon known as "order-by-disorder" (ObD). The detection and characterization of ObD in real materials currently lacks clear, qualitative signatures that distinguish ObD from conventional energetic selection. We show that for order-by-thermal-disorder (ObTD) such a signature exists: a characteristic temperature dependence of the fluctuation-induced pseudo-Goldstone gap. We demonstrate this in a minimal two-dimensional model that exhibits ObTD, the ferromagnetic Heisenberg-compass model on a square lattice. Using spin-dynamics simulations and self-consistent mean-field calculations, we determine the pseudo-Goldstone gap, $\Delta $, and show that at low temperatures it scales as the square root of temperature, $\sqrt{T} $. We establish that a power-law temperature dependence of the gap is a general consequence of ObTD, showing that all key features of this physics can be captured in a simple model of a particle moving in an effective potential generated by the fluctuation-induced free energy., Comment: Main text: 7 pages and 3 figures. Supplemental material: 8 pages and 3 figures

We investigate thermal transport in square ice, a two-dimensional analogue of spin ice, exploring the role played by emergent magnetic monopoles in transporting energy. Using kinetic Monte Carlo simulations based on energy preserving extensions of single-spin-flip dynamics, we explicitly compute the (longitudinal) thermal conductivity, $\kappa$, over a broad range of temperatures. We use two methods to determine $\kappa$: a measurement of the energy current between thermal baths at the boundaries, and the Green-Kubo formula, yielding quantitatively consistent values for the thermal conductivity. We interpret these results in terms of transport of energy by diffusion of magnetic monopoles. We relate the thermal diffusivity, $\kappa/C$ where $C$ is the heat capacity, to the diffusion constant of an isolated monopole, showing that the subdiffusive monopole implies $\kappa/C$ vanishes at zero temperature. Finally, we discuss the implications of these results for thermal transport in three-dimensional spin ice, in spin ice materials such as Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$, and outline some open questions for thermal transport in highly frustrated magnets., Comment: 18 pages, 8 figures

Ba3Yb2Zn5O11 is unique among breathing pyrochlore compounds for being in the nearly decoupled limit where inter-tetrahedron interactions are weak, hosting isolated clusters or "molecular magnet" like tetrahedra of magnetic ytterbium (Yb3+) ions. In this work, we present the first study carried out on single-crystal samples of the breathing pyrochlore Ba3Yb2Zn5O11, using a variety of magnetometry and neutron scattering techniques along with theoretical modeling. We employ inelastic neutron scattering to investigate the magnetic dynamics as a function of applied field (with respect to both magnitude and direction) down to a temperature of 70 mK, where inelastic scattering reveals dispersionless bands of excitations as found in earlier powder sample studies, in good agreement with a single-tetrahedron model. However, diffuse neutron scattering at zero field and dc-susceptibility at finite field exhibit features suggesting the presence of excitations at low-energy that are not captured by the single tetrahedron model. Analysis of the local structure down to 2 K via pair distribution function analysis finds no evidence of structural disorder. We conclude that effects beyond the single tetrahedron model are important in describing the low-energy, low temperature physics of Ba3Yb2Zn5O11, but their nature remains undetermined.

We study the effects of static magnetic and electric fields on Kitaev's honeycomb model. Using the electric polarization operator appropriate for Kitaev materials, we derive the effective Hamiltonian for the emergent Majorana fermions to second-order in both the electric and magnetic fields. We find that while individually each perturbation does not qualitatively alter Kitaev spin liquid, the cross-term induces a finite chemical potential at each Dirac node, giving rise to a Majorana-Fermi surface. We argue this gapless phase is stable and exhibits typical metallic phenomenology, such as linear in temperature heat capacity and finite, but non-quantized, thermal Hall response. Finally, we speculate on the potential for realization of this physics in Kitaev materials., Comment: 18 pages, 12 figures

We study magnetic behaviour of the Yb$^{3+}$ ions on a frustrated pyrochlore lattice in the spinel {\CYS}. The crystal-electric field parameters deduced from high-energy inelastic neutron scattering reveal well-isolated ytterbium ground state doublet with a weakly Ising character. Magnetic order studied by powder neutron diffraction evolves from the $XY$-type antiferromagnetic $\Gamma_5$ state to a splayed ice-like ferromagnet (both with k=0) in applied magnetic field with $B_c$=3 T. Low-energy inelastic neutron scattering identifies weakly dispersive magnetic bands around 0.72 meV starting at $\mid\bf{Q}\mid$ = 1.1 \AA$^{-1}$~ at zero field, which diminish with field and vanish above 3 T. We explain the observed magnetic behaviour in framework of the nearest-neighbour anisotropic exchange model for effective $S=1/2$ Kramers doublets on the pyrochlore lattice. The estimated exchanges position the {\CYS} spinel close to the phase boundary between the $\Gamma_5$ and splayed ferromagnet states, similar to the Yb-pyrochlores suggesting an important role of the competition between these phases., Comment: 24 pages, 7 Figures

Spontaneous magnon decay is a generic feature of the magnetic excitations of anisotropic magnets and isotropic magnets with non-collinear order. In this paper, we argue that the effect of interactions on one-magnon states can, under many circumstances, be treated in terms of an effective, energy independent, non-Hermitian Hamiltonian for the magnons. In the vicinity of Dirac or Weyl touching points, we show that the spectral function has a characteristic anisotropy arising from topologically protected exceptional points or lines in the non-Hermitian spectrum. Such features can, in principle, be detected using inelastic neutron scattering or other spectroscopic probes. We illustrate this physics through a concrete example: a honeycomb ferromagnet with Dzyaloshinskii-Moriya exchange. We perform interacting spin wave calculations of the structure factor and spectral function of this model, showing good agreement with results from a simple effective non-Hermitian model for the splitting of the Dirac point. Finally, we argue that the zoo of known topological protected magnon band structures may serve as a nearly ideal platform for realizing and exploring non-Hermitian physics in solid-state systems., Comment: 4+epsilon pages

The frustrated rare-earth pyrochlore Yb$_2$Ti$_2$O$_7$ is remarkable among magnetic materials: despite a ferromagnetically ordered ground state it exhibits a broad, nearly gapless, continuum of excitations. This broad continuum connects smoothly to the sharp one-magnon excitations expected, and indeed observed, at high magnetic fields, raising the question: how does this picture of sharp magnons break down as the field is lowered? In this paper, we consider the effects of magnon interactions in Yb$_2$Ti$_2$O$_7$, showing that their inclusion greatly extends the reach of spin-wave theory. First, we show that magnon interactions shift the phase boundary between the (splayed) ferromagnet (SFM) and the antiferromagnetic $\Gamma_5$ phase so that Yb$_2$Ti$_2$O$_7$ lies very close to it. Next, we show how the high-field limit connects to lower fields; this includes corrections to the critical fields for the $[111]$ and $[1\bar{1}0]$ directions, bringing them closer to the observed experimental values, as well as accounting for the departures from linear spin wave theory that appear in $[001]$ applied fields below 3 T [Thompson et al., Phys. Rev. Lett. 119, 057203 (2017)]. Turning to low-fields, though the extent of the experimentally observed broadening is not quite reproduced, we find a rough correspondence between non-linear spin-wave theory and inelastic neutron scattering data on both a single-crystal sample, as well as on a powder sample [Pe\c{c}anha-Antonio et al., Phys. Rev. B, 96, 214415 (2017)]. We conclude with an outlook on implications for future experimental and theoretical work on Yb$_2$Ti$_2$O$_7$ and related materials, highlighting the importance of proximity to the splayed ferromagnet-$\Gamma_5$ phase boundary and its potential role in intrinsic or extrinsic explanations of the low-field physics of Yb$_2$Ti$_2$O$_7$., Comment: 19 pages, 12 figures

In this review we provide an introduction to the physics of a series of frustrated quantum rare-earth pyrochlores. We first give a background on the microscopic single- and two-ion physics of these materials, discussing the origins and properties of their exchange interactions and their minimal low-energy effective models, before outlining what is known about their classical and quantum phases. We then make use of this understanding to discuss four important material examples: Er$_2$Ti$_2$O$_7$, Yb$_2$Ti$_2$O$_7$, Tb$_2$Ti$_2$O$_7$ and Pr$_2$Zr$_2$O$_7$, covering in some detail what is known experimentally and theoretically for each, and summarize some key questions that remain open. Finally, we offer an outlook on some alternative material platforms for realizing similar physics and discuss what we see as prospects for future investigations on these quantum rare-earth pyrochlores., Comment: 20 pages, 10 figures. To appear in Annual Reviews of Condensed Matter Physics

In systems with competing interactions, continuous degeneracies can appear which are accidental, in that they are not related to any symmetry of the Hamiltonian. Accordingly, the pseudo-Goldstone modes associated with these degeneracies are also unprotected. Indeed, through a process known as "order-by-quantum-disorder", quantum zero-point fluctuations can lift the degeneracy and induce a gap for these modes. We show that this gap can be exactly computed at leading order in $1/S$ in spin-wave theory from the mean curvature of the classical and quantum zero-point energies - without the need to consider any spin-wave interactions. We confirm this equivalence through direct calculations of the spin-wave spectrum to $O(1/S^2)$ in a wide variety of theoretically and experimentally relevant quantum spin models. We prove this equivalence through the use of an exact sum rule that provides the required mixing of different orders of $1/S$. Finally, we discuss some implications for several leading order-by-quantum-disorder candidate materials, clarifying the expected pseudo-Goldstone gap sizes in Er$_2$Ti$_2$O$_7$ and Ca$_3$Fe$_2$Ge$_3$O$_{12}$., Comment: 5 + 26 pages, 3 figures. Corrected discussion of cubic garnet, expanded supplemental material

We consider the structure of anisotropic exchange interactions in ytterbium-based insulating rare-earth magnets built from edge-sharing octahedra. We argue the features of trivalent ytterbium and this structural configuration allow for a qualitative determination of the different anisotropic exchange regimes that may manifest in such compounds. The validity of such super-exchange calculations is tested through comparison to the well-characterized breathing pyrochlore compound Ba$_3$Yb$_2$Zn$_5$O$_{11}$. With this in hand, we then consider application to three-dimensional pyrochlore spinels as well as two-dimensional honeycomb and triangular lattice systems built from such edge-sharing octahedra. We find an extended regime of robust emergent weak anisotropy with dominant antiferromagnetic Heisenberg interactions as well as smaller regions with strong anisotropy. We discuss the implications of our results for known compounds with the above structures, such as the spinels AYb$_2$X$_4$ (A = Cd, Mg, X = S, Se), the triangular compound YbMgGaO$_4$, which have recently emerged as promising candidates for observing unconventional magnetic phenomena. Finally, we speculate on implications for the R$_2$M$_2$O$_7$ pyrochlore compounds and some little studied honeycomb ytterbium magnets., Comment: 25 pages, 9 figures

We explore the physics of highly frustrated magnets in confined geometries, focusing on the Coulomb phase of pyrochlore spin ices. As a specific example, we investigate thin films of nearest-neighbor spin ice, using a combination of analytic large-N techniques and Monte Carlo simulations. In the simplest film geometry, with surfaces perpendicular to the [001] crystallographic direction, we observe pinch points in the spin-spin correlations characteristic of a two-dimensional Coulomb phase. We then consider the consequences of crystal symmetry breaking on the surfaces of the film through the inclusion of orphan bonds. We find that when these bonds are ferromagnetic, the Coulomb phase is destroyed by the presence of fluctuating surface magnetic charges, leading to a classical Z_2 spin liquid. Building on this understanding, we discuss other film geometries with surfaces perpendicular to the [110] or the [111] direction. We generically predict the appearance of surface magnetic charges and discuss their implications for the physics of such films, including the possibility of an unusual Z_3 classical spin liquid. Finally, we comment on open questions and promising avenues for future research., Comment: 17 pages, 11 figures. Minor improvements, typos corrected

The magnetic field response of the Mott-insulating honeycomb iridate Na$_{2}$IrO$_{3}$ is investigated using torque magnetometry measurements in magnetic fields up to 60 tesla. A peak-dip structure is observed in the torque response at magnetic fields corresponding to an energy scale close to the zigzag ordering ($\approx 15~K$) temperature. Using exact diagonalization calculations, we show that such a distinctive signature in the torque response constrains the effective spin models for these classes of Kitaev materials to ones with dominant ferromagnetic Kitaev interactions, while alternative models with dominant antiferromagnetic Kitaev interactions are excluded. We further show that at high magnetic fields, long range spin correlation functions decay rapidly, signaling a transition to a long-sought-after field-induced quantum spin liquid beyond the peak-dip structure. Kitaev systems are thus revealed to be excellent candidates for field-induced quantum spin liquids, similar physics having been suggested in another Kitaev material $\alpha-$RuCl$_{3}$., Comment: 12 pages, 20 figures; text modified, one figure shifted to main text, table added to main text

We develop a theory of the dynamical response of a minimal model of quantum spin ice (QSI) by means of inelastic light scattering. In particular, we are interested in the Raman response of the fractionalized U(1) spin liquid realized in the XXZ QSI. We show that the low-energy Raman intensity is dominated by spinon and gauge fluctuations. We find that the Raman response in the QSI state of that model appears only in the $T_{2g}$ polarization channel. We show that the Raman intensity profile displays a broad continuum from the spinons and coupled spinon and gauge fluctuations, and a low-energy peak arising entirely from gauge fluctuations. Both features originate from the exotic interaction between photon and the fractionalized excitations of QSI. Our theoretical results suggest that inelastic Raman scattering can in principle serve as a promising experimental probe of the nature of a U(1) spin liquid in QSI., Comment: 16 pages, 4 figures

We introduce a new classical spin liquid on the pyrochlore lattice by extending spin ice with further neighbour interactions. We find that this disorder free spin model exhibits a form of dynamical heterogeneity with extremely slow relaxation for some spins while others fluctuate quickly down to zero temperature. We thus call this state "spin slush", in analogy to the heterogeneous mixture of solid and liquid water. This behaviour is driven by the structure of the ground state manifold which extends the celebrated the two-in/two-out ice states to include branching structures built from three-in/one-out, three-out/one-in and all-in/all-out tetrahedra defects. Distinctive liquid-like patterns in the spin correlations serve as a signature of this intermediate range order. Possible applications to materials as well the effects of quantum tunneling are discussed., Comment: 8 pages + 7 pages

Conclusive evidence of order by disorder is scarce in real materials. Perhaps one of the strongest cases presented has been for the pyrochlore XY antiferromagnet Er2Ti2O7, with the ground state selection proceeding by order by disorder induced through the effects of quantum fluctuations. This identification assumes the smallness of the effect of virtual crystal field fluctuations that could provide an alternative route to picking the ground state. Here we show that this order by virtual crystal field fluctuations is not only significant, but competitive with the effects of quantum fluctuations. Further, we argue that higher-multipolar interactions that are generically present in rare-earth magnets can dramatically enhance this effect. From a simplified bilinear-biquadratic model of these multipolar interactions, we show how the virtual crystal field fluctuations manifest in Er2Ti2O7 using a combination of strong coupling perturbation theory and the random phase approximation. We find that the experimentally observed psi2 state is indeed selected and the experimentally measured excitation gap can be reproduced when the bilinear and biquadratic couplings are comparable while maintaining agreement with the entire experimental spin-wave excitation spectrum. Finally, we comments on possible tests of this scenario and discuss implications for other order-by-disorder candidates in rare-earth magnets., Comment: 16 pages, 6 figures

Recently, the effects of spin-orbit coupling (SOC) in correlated materials have become one of the most actively studied subjects in condensed matter physics, as correlations and SOC together can lead to the discovery of new phases. Among candidate materials, iridium oxides (iridates) have been an excellent playground to uncover such novel phenomena. In this review, we discuss recent progress in iridates and related materials, focusing on the basic concepts, relevant microscopic Hamiltonians, and unusual properties of iridates in perovskite- and honeycomb-based structures. Perspectives on SOC and correlation physics beyond iridates are also discussed., Comment: 34 pages, 9 figures; To appear in Annual Reviews of Condensed Matter Physics

Frustrated transition metal compounds in which spin-orbit coupling (SOC) and electron correlation work together have attracted much attention recently. In the case of 5$d$ transition metals, where SOC is large, $j_\text{eff}=1/2$ bands near the Fermi level are thought to encompass the essential physics of the material, potentially leading to a concrete realization of exotic magnetic phases such as the Kitaev spin liquid. Here we derive a spin model on a triangular lattice based on $j_\text{eff} = 1/2$ pseudospins that interact via antiferromagnetic Heisenberg ($J$) and Kitaev ($K$) exchanges, and crucially, an anisotropic $(\Gamma)$ exchange. Our classical analysis of the spin model reveals that, in addition to small regions of 120$^\circ$, $\mathbb{Z}_2$ / dual-$\mathbb{Z}_2$ vortex crystal and nematic phases, the stripy and ferromagnetic phases dominate the $J$-$K$-$\Gamma$ phase diagram. We apply our model to the 5$d$ transition metal compound, Ba$_3$IrTi$_2$O$_9$, in which the Ir$^{4+}$ ions form layered two-dimensional triangular lattices. We compute the band structure and nearest-neighbor hopping parameters using ab-initio calculations. By combining our ab-initio and classical analyses, we predict that Ba$_3$IrTi$_2$O$_9$ has a stripy ordered magnetic ground state., Comment: 8 pages, 5 figures

Two recent theoretical works studied the role of Kitaev interactions in the newly observed incommensurate magnetic order in the hyper-honeycomb ($\beta$-Li$_2$IrO$_3$) and stripy-honeycomb ($\gamma$-Li$_2$IrO$_3$) iridates. Each of these works analyzed a different model ($JK\Gamma$ versus coupled zigzag chain model) using a contrasting method (classical versus soft-spin analysis). The lack of commonality between these works precludes meaningful comparisons and a proper understanding of these unusual orderings. In this study, we complete the unfinished picture initiated by these two works by solving both models with both approaches for both 3D honeycomb iridates. Through comparisons between all combinations of models, techniques, and materials, we find that the bond-isotropic $JK\Gamma$ model consistently predicts the experimental phase of $\beta$-Li$_2$IrO$_3$ regardless of the method used, while the experimental phase of $\gamma$-Li$_2$IrO$_3$ can be generated by the soft-spin approach with eigenmode mixing irrespective of the model used. To gain further insights, we solve a 1D quantum spin-chain model related to both 3D models using the density matrix renormalization group method to form a benchmark. We discover that in the 1D model, incommensurate correlations in the classical and soft-spin analysis survive in the quantum limit only in the presence of the symmetric-off-diagonal exchange $\Gamma$ found in the $JK\Gamma$ model. The relevance of these results to the real materials are also discussed., Comment: 10 pages, 6 figures

If magnetic frustration is most commonly known for undermining long-range order, as famously illustrated by spin liquids, the ability of matter to develop new collective mechanisms in order to fight frustration is no less fascinating, providing an avenue for the exploration and discovery of unconventional properties of matter. Here we study an ideal minimal model of such mechanisms which, incidentally, pertains to the perplexing quantum spin ice candidate Yb2Ti2O7. Specifically, we explain how thermal and quantum fluctuations, optimized by order-by-disorder selection, conspire to expand the stability region of an accidentally degenerate continuous symmetry U(1) manifold against the classical splayed ferromagnetic ground state that is displayed by the sister compound Yb2Sn2O7. The resulting competition gives rise to multiple phase transitions, in striking similitude with recent experiments on Yb2Ti2O7 [Lhotel et al., Phys. Rev. B 89 224419 (2014)]. Considering the effective Hamiltonian determined for Yb2Ti2O7, we provide, by combining a gamut of numerical techniques, compelling evidence that such multiphase competition is the long-sought missing key to understanding the intrinsic properties of this material. As a corollary, our work offers a pertinent illustration of the influence of chemical pressure in rare-earth pyrochlores., Comment: 9 pages

The pyrochlore spin ice compounds Dy2Ti2O7 and Ho2Ti2O7 are well described by classical Ising models down to very low temperatures. Given the empirical success of this description, the question of the importance of quantum effects in these materials has been mostly ignored. We show that the common wisdom that the strictly Ising moments of Dy3+ and Ho3+ imply strictly Ising interactions is too naive; a more complex argument is needed to explain the close agreement between theory and experiment. From a microscopic picture of the interactions in rare-earth oxides, we show that the high-rank multipolar interactions needed to induce quantum effects are generated only very weakly by super-exchange. Using this framework, we formulate an estimate of the scale of quantum effects in Ho2Ti2O7 and Dy2Ti2O7, finding it to be well below experimentally relevant temperatures. We discuss the implications of these results for realizing quantum spin ice in other materials., Comment: 5 pages + 12 pages

The Kitaev honeycomb model has been suggested as a useful starting point to describe the honeycomb iridates. However, the zigzag ordering seen in Na2IrO3 and the magnetic transition in Li2IrO3 have raised questions to their connection to the Kitaev model and to the microscopic origin of these magnetic states, given their structural similarities. Here we study how the magnetic phases near the Kitaev spin liquid are affected by the inclusion of trigonal distortion of the oxygen octahedra within a purely nearest neighbour model. Using a combination classical analysis and exact diagonalization we show that near the ferromagnetic Kitaev limit a small amount of trigonal distortion, as found in Na2IrO3, stabilizes a zigzag phase. Decreasing the distortion destabilizes the zigzag phase toward a spiral phase that may be relevant for Li2IrO3. Using semi-classical spin-wave calculations we show that this regime is qualitatively consistent with experimentally known features of the dynamical structure factor in Na2IrO3 and speculate on implications for Li2IrO3., Comment: 10 pages, 5 figures

Recently, realizations of Kitaev physics have been sought in the A2IrO3 family of honeycomb iridates, originating from oxygen-mediated exchange through edge-shared octahedra. However, for the j = 1/2 Mott insulator in these materials exchange from direct d-orbital overlap is relevant, and it was proposed that a Heisenberg term should be added to the Kitaev model. Here we provide the generic nearest-neighbour spin Hamiltonian when both oxygen-mediated and direct overlap are present, containing a bond dependent off-diagonal exchange in addition to Heisenberg and Kitaev terms. We analyze this complete model using a combination of classical techniques and exact diagonalization. Near the Kitaev limit, we find new magnetic phases, 120 degree and incommensurate spiral order, as well as extended regions of zigzag and stripy order. Possible applications to Na2IrO3 and Li2IrO3 are discussed., Comment: 5 pages, 3 figures; added supplementary material and journal reference; fixed typos

In frustrated magnets when magnetic ordering is suppressed down to low temperature, the formation of a quantum spin liquid becomes a possibility. How such a spin liquid manifests in the presence of conduction electrons is a question with potentially rich physical consequences, particularly when both the localized spins and conduction electrons reside on frustrated lattices. We propose a novel mechanism for symmetry breaking in systems where conduction electrons hybridize with a quantum spin liquid through Kondo couplings. We apply this to the pyrochlore iridate Pr2Ir2O7, which exhibits an anomalous Hall effect without clear indications of magnetic order. We show that Kondo hybridization between the localized Pr pseudo-spins and Ir conduction electrons breaks some of the spatial symmetries, in addition to time-reversal regardless of the form ofthe coupling. These broken symmetries result in an anomalous Hall conductivity and induce small magnetic, quadrupolar and charge orderings. Further experimental signatures are proposed., Comment: 6 pages, 4 figures

Motivated by the nickel valence controversy in the perovskite nickelate RNiO_3, we consider a one-dimensional underscreened Kondo chain consisting of alternating spin-1 ("nickel") and electron ("oxygen") sites, which in addition to the usual electron hopping and spin-spin interaction between the S=1 spin and the electron also contains a spin mediated electron hopping term. Using the density-matrix renormalization group (DMRG), we obtained the zero temperature phase diagram of the model, as well as various correlation functions in each phase. Importantly, for a certain range of parameters the model exhibits a quasi-long-range spiral (QS) order. To understand the DMRG results, we construct a mean-field theory based on a Schwinger fermion decomposition of the S=1 spins, from which we argue that the QS phase corresponds to a phase in proximity to the spin Bose metal state proposed by D. N. Sheng, O. I. Motrunich, and M. P. A. Fisher [Phys. Rev. B 79, 205112 (2009)]. Notably, we find no evidence for a phase with the symmetry of "nickel"-centered charge order, which has been argued to arise due to site-selective Kondo screening of half the S=1 spins, and suggest that order of this type occurs only due to an additional energy gain from spontaneous lattice distortions, not present in this model., Comment: v2: 15 pages, Updated to essentially the published version

We propose a candidate for the hidden order in URu2Si2: a rank-5 E type spin density wave between Uranium 5f crystal field doublets breaking time reversal and lattice tetragonal symmetry in a manner consistent with recent torque measurements [R. Okazaki et al, Science 331, 439 (2011)]. We argue that coupling of this order parameter to magnetic probes can be hidden by crystal field effects, while still having significant effects on transport, thermodynamics and magnetic susceptibilities. In a simple tight-binding model for the heavy quasiparticles, we show the connection between the hidden order and antiferromagnetic phases arises since they form different components of this single rank-5 pseudo-spin vector. Using a phenomenological theory, we show the experimental pressure-temperature phase diagram can be qualitatively reproduced by tuning terms which break pseudo-spin rotational symmetry. As a test of our proposal, we predict the presence of small magnetic moments in the basal plane oriented in the [110] direction ordered at the wave-vector (0,0,1)., Comment: 5 pages

The recently studied material FeCrAs exhibits a surprising combination of experimental signatures, with metallic, Fermi liquid like specific heat but resistivity showing strong non-metallic character. The Cr sublattice posseses local magnetic moments, in the form of stacked (distorted) Kagome lattices. Despite the high degree of magnetic frustration, anti-ferromagnetic order develops below ~125K suggesting the non-magnetic Fe sublattice may play a role in stabilizing the ordering. From the material properties we propose a microscopic Hamiltonian for the low energy degrees of freedom, including the non-magnetic Fe sublattice, and study its properties using slave-rotor mean field theory. Using this approach we find a spin liquid phase on the Fe sublattice, which survives even in the presence of the magnetic Cr sublattice. Finally, we suggest that the features of FeCrAs can be qualitatively explained by critical fluctuations in the non-magnetic sublattice Fe due to proximity to a metal-insulator transition., Comment: 9 pages, 8 figures

The $\EtMeP$ and $\EtMeSb$ nearly triangular organic salts are distinguished from most other Pd[(dmit)$_2$] based salts, as they display valence bond and no long range order, respectively. Under pressure, a superconducting phase is revealed in EtMe$_3$P near the boundary of valence bond order. We use slave-rotor theory with an enlarged unit cell to study competition between uniform and broken translational symmetry states, offering a theoretical framework capturing the superconducting, valence bond order, spin liquid, and metallic phases on an isotropic triangular lattice. Our finite temperature phase diagram manifests a remarkable resemblance to the phase diagram of the EtMe$_3$P salt, where the re-entrant transitions of the type insulator-metal-insulator can be explained by an entropy difference between metal and the U(1) spin liquid. We find that the superconducting pairing symmetry is $d \pm id$, and predict different temperature dependences of the specific heat between the spin liquid and metal., Comment: minor changes, references added

An anisotropic metallic phase dubbed electronic nematic phase bounded by two consecutive metamagnetic transitions has been reported in the bilayer ruthenate Sr3Ru2O7. It has also been shown that the nematic and the accompanying metamagnetic transitions are driven by an effective momentum-dependent quadrupole-type interaction. Here, we study the microscopic origin of such an effective interaction. To elucidate the mechanism behind the spontaneous Fermi surface distortion associated with the nematic, we identify a simple tight binding model based on t2g orbitals, spin-orbit coupling and the rotation of RuO6 octahedra as starting point, consistent with the Fermi surface obtained from recent angle-resolved photoemission data. Within an extended Hubbard model the nematic state, characterized by an anisotropy between the bands near $(\pm \pi,0)$ and $(0,\pm \pi)$, then strongly competes with ferromagnetic order but pre-empts it via a finite nearest neighbor interaction. We discuss experimental means to confirm our proposal., Comment: 4+ pages, 3 figures