Carrier doping to the Mott insulator is essential to produce highly correlated metals with emergent properties. Pyrochlore ruthenates, Pr$_{2}$Ru$_{2}$O$_{7}$ (Ru-$4d$ electron number, $n=4$) and Ca$_{2}$Ru$_{2}$O$_{7}$ ($n=3$), are a Mott insulator and a magnetic bad metal, respectively, due to the strong electron correlation. We investigate magneto-transport properties of (Pr$_{1-x}$Ca$_{x}$)$_{2}$Ru$_{2}$O$_{7}$ in a whole band-filling range, $0<x<1$. With increasing hole-doping $x$, the system undergoes an insulator-metal transition. When Ca$_{2}$Ru$_{2}$O$_{7}$ is doped with electrons ($0.5<x<0.9$), the enhanced coupling among Ru-$4d$ spins produces a ferromagnetic-metal phase with a large anomalous-Hall angle up to 2 %. We discuss the electronic phase transitions in (Pr$_{1-x}$Ca$_{x}$)$_{2}$Ru$_{2}$O$_{7}$ in view of Hund's metal.
The magnetic ground states of $R_2$Ru$_2$O$_7$ and $A_2$Ru$_2$O$_7$ with $R=$ Pr, Gd, Ho, and Er, as well as $A=$ Ca, Cd are predicted devising a combination of the cluster-multipole (CMP) theory and spin-density-functional theory (SDFT). The strong electronic correlation effects are estimated by the constrained-random-phase approximation (cRPA) and taken into account within the dynamical-mean-field theory (DMFT). The target compounds feature $d$-orbital magnetism on Ru$^{4+}$ and Ru$^{5+}$ ions for $R$ and $A$, respectively, as well as $f$-orbital magnetism on the $R$ site, which leads to an …
We discuss the origin of spin correlations observed in neutron scattering experiments on the paramagnetic phase of a number of frustrated spinel compounds, most notably ZnCr2O4. These correlations are striking for two reasons. First, they have been interpreted as evidence for the formation of weakly interacting hexagonal clusters of spins. Second, they are very different from those calculated for the nearest neighbour Heisenberg pyrochlore antiferromagnet, in which Coulomb phase correlations generate sharp scattering features known as pinch points. Using large-$n$ calculations and Monte Carlo …
The pyrochlore ruthenate In$_2$Ru$_2$O$_7$ displays a subtle competition between spin-orbital entanglement and molecular orbital formation. At room temperature, a spin-orbit-entangled singlet state was identified. With decreasing temperature, In$_2$Ru$_2$O$_7$ undergoes multiple structural transitions and eventually forms a nonmagnetic ground state with semi-isolated Ru$_2$O units on the pyrochlore lattice. The dominant hopping through the Ru-O-Ru linkage leads to molecular orbital formation within the Ru$_2$O units. This molecular orbital formation is unique in that it involves the O$^{2-}$ a…
We examine the appearance of superconductivity in the strong-coupling limit of the Hubbard model on the pyrochlore lattice. We focus upon the limit of half filling, where the normal-state band structure realizes a $j=3/2$ semimetal. Introducing doping, we show that the pairing is favored in a $J=2$ quintet $E_g$ state. The attractive interaction in this channel relies on the fact that $E_g$ pairing on the pyrochlore lattice avoids the detrimental on-site repulsion. Our calculations show that a time-reversal symmetry-breaking superconducting phase is favored, which displays Bogoliubov Fermi sur…
We study the Mott transition from a metal to cluster Mott insulators in the 1/4- and 1/8-filled pyrochlore lattice systems. It is shown that such Mott transitions can arise due to charge localization in clusters or in tetrahedron units, driven by the nearest-neighbor repulsive interaction. The resulting cluster Mott insulator is a quantum spin liquid with a spinon Fermi surface, but at the same time a novel fractionalized charge liquid with charge excitations carrying half the electron charge. There exist two emergent U(1) gauge fields or "photons" that mediate interactions between spinons and…
We present optical conductivity spectra for $Pb_{2}Ru_{2}O_{7-δ}$ single crystal at different temperatures. Among reported pyrochlore ruthenates, this compound exhibits metallic behavior in a wide temperature range and has the least resistivity. At low frequencies, the optical spectra show typical Drude responses, but with a knee feature around 1000 \cm. Above 20000 \cm, a broad absorption feature is observed. Our analysis suggests that the low frequency responses can be understood from two Drude components arising from the partially filled Ru $t_{2g}$ bands with different plasma frequencies a…
Employing large-scale quantum Monte Carlo simulations, we reveal the full phase diagram of the extended Hubbard model of hard-core bosons on the pyrochlore lattice with partial fillings. When the intersite repulsion is dominant, the system is in a cluster Mott insulator phase with an integer number of bosons localized inside the tetrahedral units of the pyrochlore lattice. We show that the full phase diagram contains three cluster Mott insulator phases with 1/4, 1/2, and 3/4 boson fillings, respectively. We further demonstrate that all three cluster Mott insulators are Coulomb liquid phases an…
Emergent Vortex Ordering in a Multiflavor Pyrochlore-Lattice Compound GeCo$_2$O$_4$
University of Science and Technology of China（中国科学技术大学）；Comprehensive Research Organization for Science and Society (CROSS)（综合研究组织科学社会）；Rutherford Appleton Laboratory（鲁瑟福阿普顿实验室）；Peking University（北京大学）；China Institute of Atomic Energy（中国原子能科学研究院）
Fractonic phases of matter are novel quantum ground states supporting sub-dimensional emergent excitations with mobility restrictions. Due to a sub-extensive ground state degeneracy that is dependent on the geometry of the underlying lattice, fractonic phases are considered as models for quantum memory or quantum glass. While there exist a number of exactly solvable models with interactions between multiple particles/spins, the realization of such models in real materials is extremely challenging. In this work, we provide a realistic quantum model of quadratic spin interactions on the breathin…
Using $\rm Er_2Ti_2O_7$ as a motivation, we investigate finite-field properties of $XY$ pyrochlore antiferromagnets. In addition to a fluctuation-induced six-fold anisotropy present in zero field, an external magnetic field induces a combination of two-, three-, and six-fold clock terms as a function of its orientation providing for a rich and controllable magnetothermodynamics. For $\rm Er_2Ti_2O_7$, we predict a new phase transition for ${\bf H}\parallel [001]$. Re-entrant transitions are also found for ${\bf H}\parallel [111]$. We extend these results to the whole family the $XY$ pyrochlore…
The antiferromagnetic system on a rare-earth pyrochlore has been focused as a strong candidate of U(1) quantum spin liquid. Here, we study the phase transitions driven by external magnetic field and discuss the large thermal Hall effect due to emergent spinon excitations with staggered gauge fields. Despite the spinons, the charge excitations of the effective action that carry spin-1/2 quantum number, do not couple to the external field, the emergent U(1) gauge field is influenced in the presence of external magnetic field. Especially along [111] and [110]-directions, we discuss the possible p…
Spontaneous symmetry breakings, metal-insulator transitions, and transport properties of magnetic-domain-wall states in pyrochlore iridium oxides are studied by employing a symmetry adapted effective hamiltonian with a slab perpendicular to the (111) direction of the pyrochlore lattice. Emergent metallic domain wall, which has unconventional topological nature with a controllable and mobile metallic layer, is shown to host Fermi surfaces with modulated helical spin textures resembling Rashba metals. The helical nature of the domain-wall Fermi surfaces is experimentally detectable by anomalous …
The XY pyrochlore antiferromagnet Er$_2$Ti$_2$O$_7$ exhibits a rare case of $Z_6$ discrete symmetry breaking in its $ψ_2$ magnetic ground state. Despite being well-studied theoretically, systems with high discrete symmetry breakings are uncommon in nature and, thus, Er$_2$Ti$_2$O$_7$ provides an experimental playground for the study of broken $Z_n$ symmetry, for $n>2$. A recent theoretical work examined the effect of a magnetic field on a pyrochlore lattice with broken $Z_6$ symmetry and applied it to Er$_2$Ti$_2$O$_7$. This study predicted multiple domain transitions depending on the crystall…
"Magnetic monopole" is an exotic quantum excitation in pyrochlore U(1) spin liquid, and its emergence is purely of quantum origin and has no classical analogue. We predict topological thermal Hall effect (TTHE) of "magnetic monopoles" and present this prediction through non-Kramers doublets. We observe that, when the external magnetic field polarizes the Ising component of the local moment, internally this corresponds to the induction of emergent dual U(1) gauge flux for the "magnetic monopoles". The motion of "magnetic monopoles" is then twisted by the induced dual gauge flux. This emergent L…
The spin ice materials, including Ho2Ti2O7 and Dy2Ti2O7, are rare earth pyrochlore magnets which, at low temperatures, enter a constrained paramagnetic state with an emergent gauge freedom. Remarkably, the spin ices provide one of very few experimentally realised examples of fractionalization because their elementary excitations can be regarded as magnetic monopoles and, over some temperature range, the spin ice materials are best described as liquids of these emergent charges. In the presence of quantum fluctuations, one can obtain, in principle, a quantum spin liquid descended from the class…
Two quintessential ingredients governing the topological invariant of a system are the dimensionality and the symmetry of the system. Due to the recent development of thin film and artificial superstructure growth technique, it is possible to control the dimensionality of the system, smoothly between the two-dimensions (2D) and three-dimensions (3D). In this work we unveil the dimensional crossover of emergent topological phenomena in correlated topological materials. In particular, by focusing on the thin film of pyrochlore iridate antiferromagnets grown along the [111] direction, we demonstr…
We report on the epitaxial growth, structural and electrical properties of metallic pyrochlore bismuth ruthenate heterostructures grown along both the [001] and [111] directions. Ordered pyrochlore thin films were obtained with highly oriented texture along the [001] and [111] crystallographic directions. Density functional theory calculations of the electronic band structure and density of states indicated that Bi$_2$Ru$_2$O$_7$ is semimetallic and that hybridization of the Ru 4$d$ and Bi 6$p$ orbitals via the anion network at the Fermi energy was responsible for the metallicity. Electrical c…
We study the effects of a uniform electric field on the the ground state and excitations of the three-dimensional U(1) spin liquid phase of a breathing pyrochlore lattice, arising due to the coupling between the conventional (Maxwell) electric field and the emergent electrodynamics of the quantum spin ice material. This is an extension of the studies for isotropic pyrochlores in Phys. Rev. B 96, 125145 (2017) to the anisotropic case, as the lattice inversion symmetry is broken in breathing pyrochlores. The emergent photons are found to exhibit birefringence, analogous to the isotropic case. Ho…
Magnetic fluctuations and electrons couple in intriguing ways in the vicinity of zero temperature phase transitions - quantum critical points - in conducting materials. Quantum criticality is implicated in non-Fermi liquid behavior of diverse materials, and in the formation of unconventional superconductors. Here we uncover an entirely new type of quantum critical point describing the onset of antiferromagnetism in a nodal semimetal engendered by the combination of strong spin-orbit coupling and electron correlations, and which is predicted to occur in the iridium oxide pyrochlores. We formula…
A quantum melting of the spin ice is proposed for pyrochlore-lattice magnets Pr$_2TM_2$O$_7$ ($TM=$Ir, Zr, and Sn). The quantum superexchange Hamiltonian having a nontrivial magnetic anisotropy is derived in the basis of atomic non-Kramers magnetic doublets. The ground states exhibit a cooperative ferroquadrupole and pseudospin chirality, forming a magnetic analog of smectic liquid crystals. Our theory accounts for dynamic spin-ice behaviors experimentally observed in Pr$_2TM_2$O$_7$.
The rich physics manifested by 5d oxides falls outside the Mott-Hubbard paradigm used to successfully explain the electronic and magnetic properties of 3d oxides. Much consideration has been given to the extent to which strong spin-orbit coupling (SOC), in the limit of increased bandwidth and reduced electron correlation, drives the formation of novel electronic states, as manifested through the existence of metal-insulator transitions (MITs). SOC is believed to play a dominant role in 5d5 systems such as iridates (Ir4+), undergoing MITs which may or may not be intimately connected to magnetic…
Quantum spin liquids (QSL) have generated considerable excitement as phases of matter with emergent gauge structures and fractionalized excitations. In this context, phase transitions out of QSLs have been widely discussed as Higgs transitions from deconfined to confined phases of a lattice gauge theory. However the possibility of a wider range of novel phases, occuring between these two limits, has yet to be systematically explored. In this Letter, we develop a formalism which allows for interactions between fractionalised quasiparticles coming from the constraint on the physical Hilbert spac…
We theoretically investigate emergent quantum phases in the thin film geometries of the pyrochore iridates, where a number of exotic quantum ground states are proposed to occur in bulk materials as a result of the interplay between electron correlation and strong spin-orbit coupling. The fate of these bulk phases as well as novel quantum states that may arise only in the thin film platforms, are studied via a theoretical model that allows layer-dependent magnetic structures. It is found that the magnetic order develop in inhomogeneous fashions in the thin film geometries. This leads to a varie…
Although initially introduced to mimic the spin-ice pyrochlores, no artificial spin ice has yet exhibited the expected degenerate ice-phase with critical correlations similar to the celebrated Coulomb phase in the pyrochlore lattice. Here we study a novel artificial spin ice based on a vertex-frustrated rather than pairwise frustrated geometry and show that it exhibits a quasicritical ice phase of extensive residual entropy and, significantly, algebraic correlations. Interesting in its own regard as a novel realization of frustration in a vertex system, our lattice opens new pathways to study …
We study the pyrochlore series (Eu$_{1-x}$Bi$_x$)$_2$Ir$_2$O$_7$ for $ 0 \leq x \leq 1$. We show that for small $x$, the lattice undergoes an anomalous contraction but the all-in/all-out and metal-to-insulator transitions remain robust, and the resistivity approaches a $1/T$ dependence at low-T, suggesting proximity to the Weyl semimetallic phase, as previously predicted theoretically. At the boundary between Eu$_2$Ir$_2$O$_7$ and Bi$_2$Ir$_2$O$_7$ a qualitatively different ground state emerges, which is characterized by its unusual metallic behavior and absence of magnetic ordering at least d…
Pyrochlore systems ($A_{2}B_{2}O_{7}$) with $A$-site rare-earth local moments and $B$-site $5d$ conduction electrons offer excellent material platforms for the discovery of exotic quantum many-body ground states. Notable examples include U(1) quantum spin liquid of the local moments and semimetallic non-Fermi liquid of the conduction electrons. Here we investigate emergent quantum phases and their transitions driven by the Kondo lattice coupling between such highly entangled quantum ground states. Using the renormalization group method, it is shown that weak Kondo lattice coupling is irrelevan…
Condensed matter exhibits a wide variety of exotic emergent phenomena such as the fractional quantum Hall effect and the low temperature cooperative behavior of highly frustrated magnets. I consider the classical Hamiltonian dynamics of spins of the latter phenomena using a method introduced by Dirac in the 1950s by assuming they are constrained to their lowest energy configurations as a simplifying measure. Focusing on the kagome antiferromagnet as an example, I find it is a gauge system with topological dynamics and non-locally connected edge states for certain open boundary conditions simil…
We study the two-dimensional kagome-ice model derived from a pyrochlore lattice with second- and third-neighbor interactions. The canted moments align along the local $\langle 111 \rangle$ axes of the pyrochlore and respond to both in-plane and out-of-plane external fields. We find that the combination of further-neighbor interactions together with the external fields introduces a rich phase diagram with different spin textures. Close to the phase boundaries, metastable $\textit{"snake"}$ domains emerge with extremely long relaxation time. Our kinetic Monte Carlo analysis of the magnetic-field…
The evolution between Fermi liquid and non-Fermi-liquid states in correlated electron systems has been a central subject in condensed matter physics because of the coupled intriguing magnetic and electronic states. An effective pathway to explore the nature of non-Fermi liquid behavior is to approach its phase boundary. Here we report a crossover from non-Fermi liquid to Fermi-liquid state in metallic CaRuO3 through ionic liquid gating induced protonation with electric field. This electronic transition subsequently triggers a reversible magnetic transition with the emergence of an exotic ferro…
When a conduction electron couples with a non-coplanar localized magnetic moment, the realspace Berry curvature is exerted to cause the geometrical Hall effect, which is not simply proportional to the magnetization. So far, it has been identified in the case mostly where the non-coplanar magnetic order is present on the sublattice of conduction electrons. Here, we demonstrate that the geometrical Hall effect shows up even without long-range magnetic order of conduction electrons, as induced by non-coplanar exchange fields from the localized magnetic moments, in hole-doped phyrochlore molybdate…
While there is compelling evidence for the existence of magnetic monopoles in spin ice, the direct observation of a point-like source of magnetic field in these systems remains an open challenge. One promising approach is electron holography, which combines atomic-scale resolution with extreme sensitivity to magnetic vector potentials, through the Aharonov-Bohm effect. Here we explore what holography can teach us about magnetic monopoles in spin ice, through experiments on artificial spin ice, and numerical simulations of pyrochlore spin ice. In the case of artificial spin ice, we show that ho…
We study possible quantum $U(1)$ spin liquids in three dimensions with time-reversal symmetry. We find a total of 7 families of such $U(1)$ spin liquids, distinguished by the properties of their emergent electric/magnetic charges. We show how these spin liquids are related to each other. Two of these classes admit nontrivial protected surface states which we describe. We show how to access all of the 7 spin liquids through slave particle (parton) constructions. We also provide intuitive loop gas descriptions of their ground state wave functions. One of these phases is the `topological Mott ins…
A correlated insulator at the surface of the polar metal Ca$_3$Ru$_2$O$_7$
University of St Andrews（圣安德鲁斯大学）；Diamond Light Source Ltd（钻石光源有限公司）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；National Institute for Materials Science（国立材料研究所）；MAX IV Laboratory, Lund University（隆德大学MAX IV实验室）
Experimental and theoretical aspects of Hall-type transport of spins in magnetic insulators are reviewed, with emphasis on their spin chirality origin. A general formalism for linear response theory of thermal Hall transport in the spin model is developed, which can be applied to both the magnon and the paramagnetic, spin-liquid regimes. Recent experiments on magnon-mediated thermal Hall transport in the two-dimensional kagome, and three-dimensional pyrochlore ferromagnetic insulators are reviewed in light of the multi-band magnon theory of Hall transport, and compared to the more mysterious t…
Quantum spin liquids are highly entangled ground states of quantum systems with emergent gauge structure, fractionalized spinon excitations, and other unusual properties. While these features clearly distinguish quantum spin liquids from conventional, mean-field-like states at zero temperature (T), their status at T>0 is less clear. Strictly speaking, it is known that most quantum spin liquids lose their identity at non-zero temperature, being in that case adiabatically transformable into a trivial paramagnet. This is the case for the U(1) quantum spin liquid states recently proposed to occur …
Topological insulators, in contrast to ordinary semiconductors, accompany protected metallic surfaces described by Dirac-type fermions. Here, we theoretically show another emergent two-dimensional metal embedded in the bulk insulator is realized at a magnetic domain wall. The domain wall has long been studied as ingredients of both old-fashioned and leading-edge spintronics. The domain wall here, as an interface of seemingly trivial antiferromagnetic insulators, emergently realizes a functional interface preserved by zero modes with robust two-dimensional Fermi surfaces, where pyrochlore iridi…
