arXiv subjects

Jeffrey G. Rau

Publications and source records attributed to Jeffrey G. Rau.

At least 37 records · Page 2Linked to original sources

arXiv2020

Magnetoelectric generation of a Majorana-Fermi surface in Kitaev's honeycomb model

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.

cond-mat.str-el↗

arXiv2019

Multi-phase competition in quantum $XY$ pyrochlore antiferromagnet CdYb$_{2}$Se$_{4}$: zero and applied magnetic field study

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 $Γ_5$ 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 Å$^{-1}$~ 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 $Γ_5$ and splayed ferromagnet states, similar to the Yb-pyrochlores suggesting an important role of the competition between these phases.

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arXiv2019

Non-Hermitian topology of spontaneous magnon decay

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.

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arXiv2019

Magnon interactions in the frustrated pyrochlore ferromagnet Yb$_2$Ti$_2$O$_7$

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 $Γ_5$ 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 [Peçanha-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-$Γ_5$ phase boundary and its potential role in intrinsic or extrinsic explanations of the low-field physics of Yb$_2$Ti$_2$O$_7$.

cond-mat.str-el↗

arXiv2018

Pseudo-Goldstone gaps and order-by-quantum-disorder in frustrated magnets

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$_{12}$.

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arXiv2018

Frustrated quantum rare-earth pyrochlores

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.

cond-mat.str-el↗

arXiv2018

Spin ice thin films: Large-N theory and Monte Carlo simulations

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.

cond-mat.str-el↗

arXiv2018

Frustration and anisotropic exchange in ytterbium magnets with edge-shared octahedra

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.

cond-mat.str-el↗

arXiv2017

Fingerprints of quantum spin ice in Raman scattering

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.

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arXiv2016

Spin slush in an extended spin ice model

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.

cond-mat.stat-mech↗

arXiv2015

Order by virtual crystal field fluctuations in pyrochlore XY antiferromagnets

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.

cond-mat.str-el↗

arXiv2015

Magnetic Orders Proximal to the Kitaev Limit in Frustrated Triangular Systems: Application to Ba$_3$IrTi$_2$O$_9$

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 $(Γ)$ 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 $J$-$K$-$Γ$ 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.

cond-mat.str-el↗

arXiv2015

Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials

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.

cond-mat.str-el↗

arXiv2015

Two iridates, two models, two approaches: a comparative study on magnetism in 3D honeycomb materials

Two recent theoretical works studied the role of Kitaev interactions in the newly observed incommensurate magnetic order in the hyper-honeycomb ($β$-Li$_2$IrO$_3$) and stripy-honeycomb ($γ$-Li$_2$IrO$_3$) iridates. Each of these works analyzed a different model ($JKΓ$ 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 $JKΓ$ model consistently predicts the experimental phase of $β$-Li$_2$IrO$_3$ regardless of the method used, while the experimental phase of $γ$-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 $Γ$ found in the $JKΓ$ model. The relevance of these results to the real materials are also discussed.

cond-mat.str-el↗

arXiv2015

Are multiphase competition & order-by-disorder the keys to understanding Yb2Ti2O7?

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.

cond-mat.str-el↗

arXiv2015

How quantum are classical spin ices?

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.

cond-mat.str-el↗

arXiv2014

Trigonal distortion in the honeycomb iridates: Proximity of zigzag and spiral phases in Na2IrO3

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.

cond-mat.str-el↗

arXiv2014

Generic spin model for the honeycomb iridates beyond the Kitaev limit

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.

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