The pyrochlore oxides $A_2B_2$O$_7$ exhibit a complex interplay between geometrical frustration, electronic correlations, and spin-orbit coupling, due to the lattice structure and active charge, spin, and orbital degrees of freedom. Understanding the properties of these materials is a theoretical chalenge, because their intricate nature depends on material-specific details and quantum many-body effects. Here we review our recent studies based on first-principles calculations and quantum many-body theories for 4$d$ and 5$d$ pyrochlore oxides with $B$=Mo, Os, and Ir. In these studies, the spin-orbit coupling and local electron correlations are treated within the LDA+$U$ and LDA+dynamical mean-field theory formalisms. We also discuss the technical aspects of these calculations.
Evidence for another phase transition at 120 K in the metallic pyrochlore oxide Cd2Re2O7, following the structural transition at 200 K and followed by the superconducting transition at 1.0 K, is given through resistivity, magnetoresistance, specific heat, and X-ray diffraction measurements. The results indicate unique successive structural and electronic transitions occurring in the pyrochlore compound, revealing an interesting interplay between the crystal and electronic structures on the itinerant electron system in the pyrochlore lattice.
We report the X-ray study for the pyrochlore oxide Cd2Re2O7. Two symmetry-lowering structural transitions were observed at Ts1=200K and Ts2=120K. The former is of the second order from the ideal cubic pyrochlore structure with space group Fd-3m to a tetragonally distorted structure with I-4m2, while the latter is of the first order likely to another tetragonal space group I4122. We discuss the feature of the lattice deformation.
A new pyrochlore ruthenium oxide, Hg2Ru2O7 was synthesized under a high pressure of 6 GPa. In contrast to the extensively studied Ru4+ oxides, this compound possesses a novel Ru5+ valence state, corresponding to a half-filled t_2g_3 electron configuration. Hg2Ru2O7 exhibits a first order metal-insulator transition at 107 K, accompanied by a structural transition from cubic to lower symmetry. The behavior of the magnetic susceptibility suggests the possible formation of a spin singlet in the insulating low temperature state.
We report on the muon spin rotation/relaxation study of a pyrochlore oxide, Cd2Os2O7, which exhibits a metal-insulator (MI) transition at T_{MI}~225 K without structural phase transition. It reveals strong spin fluctuation (>10^8/s) below the MI transition, suggesting a predominant role of geometrical spin frustration amongst Os^{5+} ions. Meanwhile, upon further cooling, a static spin density wave discontinuously develops below T_{SDW}~150 K. These observations strongly suggest the occurrence of an anomalous magnetic transition and associated change in the local spin dynamics in undistorted 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 …
Motivated by recent observation of a new high field phase near saturation in chromium spinels $A$Cr$_2$O$_4$ ($A=$ Zn, Cd, Hg), we study the $S = 3/2$ pyrochlore Heisenberg antiferromagnet with biquadratic interactions. Magnon instability analysis at the saturation field reveals that a very small biquadratic interaction can induce magnon pairing in pyrochlore antiferromagnets, which leads to the emergence of a ferro-quadrupolar phase, or equivalently a spin nematic phase, below the saturation field. We present the magnetic phase diagram in an applied field, studying both $S=3/2$ and $S=1$ spin…
Na-based osmium oxide pyrochlore was synthesized for the first time by an ion-exchange method. KOs2O6 was used as a host compound. Elelectron probe micro-analysis, synchrotron x-ray diffraction analysis, and thermo-gravimetric analysis confirmed its structure not as the beta-type but as the defect-type pyrochlore. The composition was identified as Na1.4Os2O6.H2O. Electrical resistivity, heat capacity, and magnetization measurements of the polycrystalline Na1.4Os2O6.H2O clarified absence of superconductivity above 2 K, being in contrast to what were found for the beta-pyrochlore AOs2O6 (A = Cs,…
The superconducting pyrochlore oxide Cd2Re2O7 (Tc = 1 K), which is now considered as a candidate of the spin-orbit-coupled metal, shows an inversion-symmetry-breaking structural transition at Ts1 = 200 K. Ts1 decreases with increasing pressure and disappears at around Pc = 4:2GPa, where at least four high-pressure phases with tiny structural distortions are suggested by means of powder X-ray diffraction [Yamaura PRB 2017]. We have carried out Raman scattering experiments to investigate changes in the crystal symmetry under high pressures up to 4.8 GPa. A structural transition at 1.9-3.0 GPa an…
We investigate the metal-insulator transition (MIT) of the osmium pyrochlore oxide Cd2Os2O7 through transport and magnetization measurements. The MIT and a magnetic transition to the all-in/all-out (AIAO) order occur simultaneously at 227 K. We propose a mechanism based on a Lifshitz transition induced by the AIAO magnetic order probably via strong spin-orbit couplings in the specific semimetallic band structure. It is suggested, moreover, that two observed puzzles, a finite conductivity near T = 0 and an emergence of weak ferromagnetic moments, are not bulk properties but originate at magneti…
We present our theoretical results on an effective two-band double-exchange model on a pyrochlore lattice for understanding intricate phase competition in Mo pyrochlore oxides. The model includes the twofold degeneracy of $e_g'$ orbitals under trigonal field splitting, the interorbital Coulomb repulsion, the Hund's-rule coupling between itinerant $e_g'$ electrons and localized $a_{1g}$ spins, and the superexchange antiferromagnetic interaction between the $a_{1g}$ spins. By Monte Carlo simulation with treating the Coulomb repulsion at an unrestricted-type mean-field level, we obtain the low-te…
Motivated by the heavy fermion Fermi liquid (HFFL) features observed at low-$T$ in the pyrochlore $LiV_{2}O_{4}$, we consider a material-specific model that includes aspects of the local quantum chemistry, the geometrically frustrated lattice structure, and strong correlations in a {\it single} approach. In particular, we show how geometrical frustration (GF) gives rise to a crossover scale, $T^{*}<<J$, the intersite (AF) exchange, below which the metallic system shows HFFL features. Our scenario is a specific realization of the importance of GF effects in driving HFFL behavior in $LiV_{2}O_{4…
We report results of NMR experiments on the ruthenium oxide Hg2Ru2O7 with the pyrochlore structure, which exhibits a metal-insulator transition at TMI = 107 K. In the metallic phase above TMI, the nuclear spin-lattice relaxation rate 1/T1 and the Knight shift at the Hg sites follow the Korringa relation, indicating the absence of substantial spatial spin correlation. At low temperatures in the insulating phase, 99,101Ru-NMR signals are observed at zero magnetic field, providing evidence for a commensurate antiferromagnetic order. The estimated ordered moment is about 1 muB per Ru, much smaller…
We report the filling control of the pyrochlore oxide Y2Ir2O7. Metallic ground state appears with increasing substitution content x (x >= 0.3). We have revealed that the density of states at the Fermi level rapidly changes with x by this filling control of Y2Ir2O7.
Semimetallic osmium pyrochlore oxide Cd2Os2O7 undergoes a magnetic transition to an all-in-all-out (AIAO)-type order at 227 K, followed by a crossover to an AIAO insulator at around 210 K. Here, we studied the isostructural and isoelectronic compound Hg2Os2O7 through thermodynamic measurements, muSR spectroscopy and neutron diffraction experiments. A similar magnetic transition, probably to an AIAO-type order, was observed at 88 K, while the resistivity showed a decrease at the transition and remained metallic down to 2 K. Thus, the ground state of Hg2Os2O7 is most likely an AIAO semimetal, wh…
In frustrated systems, some or many states are competed due to frustration of exchange interactions, and this competition often results in exotic states, such as spin liquid and chiral orders. We consider a pyrochlore oxide, a three-dimensional frustrated system, and study its $S=\frac{1}{2}$ effective model, consisting of the Heisenberg-type and Dzyaloshinsky-Moriya-type superexchange interactions between the nearest-neighbor transition-metal ions. We show that by using new multiorbital effects of the $t_{2g}$ orbitals on coefficients of those interactions, we can change the effective dimensi…
Recently new pyrochlore oxides superconductors AOs2O6 (A=K,Rb,Cs) were found and we measured the pressure dependence of magnetization up to 1.2 GPa in order to deduce the pressure effect of Tc in the three beta-pyrochlore oxides. It is found that the initial pressure dependence of Tc is positive for all the compounds. Only KOs2O6 exhibits a saturation in Tc at 0.56 GPa and the downturn at higher pressure
Electronic properties of the metallic pyrochlore oxide Cd2Re2O7 are studied by means of electrical resistivity and Hall measurements. Semimetallic band structures are revealed as expected from band structure calculations. It is found that large changes in carrier density and mass occur at the structural phase transition at Ts1 = 200 K. A large mass enhancement is observed, particularly for the high-temperature phase with the ideal pyrochlore structure, suggesting that an anomalous correlation has an important effect on the itinerant electrons in the pyrochlore lattice.
In this work we investigate the phase diagram of heavy (4d and 5d) transition metal oxides on the pyrochlore lattice, such as those of the form $\mathrm{A_2M_2O_7}$, where A is a rare earth element and M is a transition metal element. We focus on the competition between Coulomb interaction, spin-orbit coupling, and lattice distortion when these energy scales are comparable. Strong spin-orbit coupling entangles the spin and the $t_{2g}$ $d$-orbitals giving rise to doublet $j=1/2$ and quadruplet $j=3/2$ states. In contrast to previous works which focused on the doublet manifold, we also discuss …
The superconducting transition of the ?-pyrochlore oxide KOs2O6 with Tc = 9.60 K is studied by resistivity measurements under various magnetic fields using a high-quality single crystal. The reentrant behavior of superconductivity is observed near Tc in low magnetic fields below 2 T. The recovered resistance probably due to flux flow exhibits an anomalous angle dependence, indicating that flux pinning is enhanced in magnetic fields along certain crystallographic directions such as [110], [001] and [112]. It is suggested that there is an intrinsic pinning mechanism coming from the specific crys…
We theoretically study a multi-band Hubbard model of pyrochlore oxides of the form A$_2$B$_2$O$_7$, where B is a heavy transition metal ion with strong spin-orbit coupling, in a thin film geometry orientated along the [111] direction. Along this direction, the pyrochlore lattice consists of alternating kagome and triangular lattice planes of B ions. We consider a single kagome layer, a bilayer, and the two different trilayers. As a function of the strength of the spin-orbit coupling, the direct and indirect $d$-orbital hopping, and the band filling, we identify a number of scenarios where a no…
We report the single-crystal X-ray analysis of the structure of the pyrochlore oxide superconductor KOs$_2$O$_6$. The structure was identified as the $β$-pyrochlore structure with space group $Fd\bar{3}m$ and lattice constant $a$ = 10.089(2)~Åat 300 K: the K atom is located at the 8$b$ site, not at the 16$d$ site as in conventional pyrochlore oxides. We found an anomalously large atomic displacement parameter $U_\mathrm{iso}$ = 0.0735(8)~Å$^2$ at 300 K for the K cation, which suggests that the K cation weakly bound to an oversized Os$_{12}$O$_{18}$ cage exhibits intensive rattling, as recently…
We make the first report that a metallic pyrochlore oxide \Cd2Re2O7, exhibits type II superconductivity at 1.1 K. The pyrochlore oxide is known to be a geometrical frustrated system, which includes the tetrahedral network of magnetic ions. A large number of compounds are classified in the family of pyrochlore oxides, and these compounds exhibit a wide variety of physical properties ranging from insulator through semiconductor and from bad metal to good metal. Until now, however, no superconductivity has been reported for frustrated pyrochlore oxides. The bulk superconductivity of this compound…
Electronic phase separation and related inhomogeneity is ubiquitously seen in strongly-correlated systems. A typical example is found between ferromagnetic metal and antiferromagnetic insulator in CMR manganese oxides. Here we demonstrate that the geometrical frustration brings distinctive aspects into the phase separation phenomena. From Monte Carlo simulation and a simple energy comparison for the pyrochlore double-exchange model, we show that such phase separation takes place between ferromagnetic and paramagnetic metals. We discuss the relevance of our results to a spin-glassy metallic pha…
The structural, electronic, and optical properties of pyrochlore-type Pb$_{2}$Ir$_{2}$O$_{6}$O'$_{0.55}$, which is a metal without spatial inversion symmetry at room temperature, were investigated. Structural analysis revealed that the structural distortion relevant to the breakdown of the inversion symmetry is dominated by the Pb-O' network but is very small in the Ir-O network. At the same time, gigantic second-harmonic generation signals were observed, which can only occur if the local environment of the Ir 5$d$ electrons features broken inversion symmetry. First-principles electronic struc…
We study orbital Mott transition in two dimensional pyrochlore lattice, using a two orbital Hubbard model with only inter-orbital electronic hopping. We use a real space Monte Carlo based approach to study the model at finite temperature, and establish temperature-interaction phase diagrams that highlight the Mott transition, orbital ordering, and spectral trends, and possible window of pseudo gap. Due to only inter-orbital hopping, the Mott insulator `generates' ferro exchange resulting in ferro-orbital ordering, with T$_{corr}/t$ peaked at $\approx$ 0.2 around $U/t \approx 6$. The optical co…
The double-exchange model, which has been extensively studied in the context of colossal magneto-resistance in perovskite manganese oxides, is known to exhibit a ferromagnetic metallic state at low temperatures because of the interplay between localized moments and itinerant electrons through the Hund's-rule coupling. Here we investigate numerically the ferromagnetic transition in the double-exchange model defined on the frustrated pyrochlore lattice as a simple model for ferromagnetic pyrochlore oxides. We demonstrate that the finite-size corrections are largely reduced by implementing averag…
Two beta-pyrochlore oxide superconductors, CsOs2O6 and RbOs2O6, are studied thermodynamically by measuring specific heat on polycrystalline samples. It is found that a Sommerfeld coefficient ? is nearly equal, 20 mJ/K2 mol Os, in the two oxides with different superconducting transition temperatures; Tc = 3.3 K and 6.3 K, respectively. This suggests that the density of states at the Fermi level is not a crucial parameter to determine the Tc of the beta-pyrochlore oxide superconductors, which is incompatible with the general expectation for a conventional BCS-type superconductor. Anomalous latti…
An effective quantum pseudospin-1/2 Hamiltonian for Yb_2TM_2O_7 (TM = Ti and Sn) is obtained in terms of the atomic Kramers ground doublet of the LS coupling and the crystalline electric field, which is almost described with J^z=\pm 1/2. It is calculated microscopically as the sum of Anderson's superexchange interaction and the magnetic dipole interaction. It is found that it shows a strong exchange anisotropy.
We discuss the ground state of a pyrochlore lattice of threefold-orbitally-degenerate $S=1/2$ magnetic ions. We derive an effective spin-orbital Hamiltonian and show that the orbital degrees of freedom can modulate the spin exchange, removing the infinite spin-degeneracy characteristic of pyrochlore structures. The resulting state is a collection of spin-singlet dimers, with a residual degeneracy due to their relative orientation. This latter is lifted by a magneto-elastic interaction, induced in the spin-singlet phase-space, that forces a tetragonal distortion. Such a theory provides an expla…
Magnetism of ruthernium pyrochlore oxides A2Ru2O7 (A = Hg, Cd, Ca), whose electronic properties within a localized ion picture are characterized by non-degenerate t2g orbitals (Ru5+, 4d3) and thereby subject to geometrical frustration, has been investigated by muon spin rotation/relaxation (muSR) technique. The A cation (mostly divalent) was varied to examine the effect of covalency (Hg > Cd > Ca) on their electronic property. In a sample with A = Hg that exhibits a clear metal-insulator (MI) transition below >> 100 K (which is associated with a weak structural transition), a nearly commensura…
Pyrochlore lattices, which are found in two important classes of materials -- the $A_2B_2X_7$ pyrochlore family and the $AB_2X_4$ spinel family -- are the quintessential 3-dimensional frustrated lattice architecture. While historically oxides ($X =$~O) have played the starring role in this field, the past decade has seen materials synthesis breakthroughs that have lead to the emergence of fluoride ($X =$~F) and chalcogenide ($X =$~S, Se) pyrochlore lattice materials. In this Research Update, we summarize recent progress in understanding the magnetically frustrated ground states in three famili…
A unique type of frustrated lattice is found in two A-site ordered spinel oxides, LiGaCr4O8 and LiInCr4O8. Because of the large size mismatch between Li+ and Ga3+/In3+ ions at the A site, the pyrochlore lattice, made up of Cr3+ ions carrying spin 3/2, becomes an alternating array of small and large tetrahedra, i.e., a "breathing" pyrochlore lattice. We introduce a parameter, the breathing factor Bf, which quantifies the degree of frustration in the pyrochlore lattice: Bf is defined as J'/J, where J' and J are nearest-neighbor magnetic interactions in the large and small tetrahedra, respectivel…
Resistivity and specific heat have been measured on a single crystalline sample of the beta-pyrochlore oxide superconductor, KOs2O6. It is found that a second peak in specific heat, which may evidence an unknown phase transition, appears around Tp ~ 7.5 K below the superconducting transition temperature Tc = 9.53 K. Applying magnetic fields up to 14 T, Tc is reduced gradually down to 7.1 K, while Tp is raised a little and becomes even higher than Tc at 14 T, which implies that the second anomaly is not associated directly with the superconductivity. It is demonstrated, however, that there is s…
High pressure effects on the superconducting transitions of beta-pyrochlore superconductors AOs2O6 (A = Cs, Rb, K) are studied by measuring resistivity under high pressures up to 10 GPa. The superconducting transition temperature Tc first increases with increasing pressure in all the compounds and then exhibits a broad maximum at 7.6 K (6 GPa), 8.2 K (2 GPa) and 10 K (0.6 GPa) for A = Cs, Rb and K, respectviely. Finally, the superconductivity is suppressed completely at a critical pressure near 7 GPa and 6 GPa for A = Rb and K and probably above 10 GPa for A = Cs. Characteristic changes in the…
We investigated the magnetoresistance (MR) effect of the pyrochlore oxide Nd2Ir2O7, which shows a metal-insulator transition at T_MI =33 K. A small positive MR effect was observed in the metallic state above T_MI, while a large negative MR effect was observed in the insulating state below T_MI . MR effects exceeding 3000% were found at 1 K at a field of 9 T. As a result, we confirmed the crossover from the insulating state to a state with a small or partial band gap in a field up to 56 T. Furthermore, from the MR effect in Eu2Ir2O7 (T_MI = 120 K) and Gd$_2$Ir$_2$O$_7$ (T_MI = 127 K), we reveal…
The Bragg diffraction of neutrons and x-rays are well-suited to the task of determining the distribution of magnetization in crystals. Applications of the two techniques proceed by contrasting observed intensities with intensities calculated with a specific model, and changing the model as need be to achieve satisfactory agreement. An all-in-all-out (AIAO) magnetic configuration of magnetic dipoles on a cubic face-centred lattice with networks of corner-sharing tetrahedra is often mentioned in the context of pyrochlore oxides, for example, but the corresponding neutron and x-ray diffraction pa…
We investigate heavy fermion behaviors in the vanadium spinel LiV_2O_4. We start from a three-orbital Hubbard model on the pyrochlore lattice and derive its low-energy effective Hamiltonian by an approach of real-space renormalization group type. One important tetrahedron configuration in the rochlore lattice has a three-fold orbital degeneracy and spin S=1, and correspondingly, the effective Hamiltonian has spin and orbital exchange interactions of Kugel-Khomskii type as well as correlated electron hoppings. Analyzing the effective Hamiltonian, we find that ferromagnetic double exchange proce…
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…
Paramagnetic correlations in the magnetic material Yb2Ti2O7 have been investigated via neutron scattering, revealing a [111] rod of scattering intensity. Assuming interactions between the Yb^{3+} ions composed of all symmetry-allowed nearest neighbor exchange interactions and long-range dipolar interactions, we construct a model Hamiltonian that allows for an excellent description of the neutron scattering data. Our results provide compelling evidence for significant anisotropic exchange interactions in an insulating magnetic pyrochlore oxide. We also compute the real space correlations leadin…
In this study, we have performed the magnetocaloric effect and the specific heat measurements of chromium spinel oxide HgCr$_2$O$_4$, wherein the magnetic Cr$^{3+}$ ions form a highly frustrated pyrochlore lattice with significant spin-lattice coupling. In addition to the known magnetic-field-induced phases, our thermodynamic measurements detect a novel quantum phase just before the saturation of the magnetization, which has not been expected from the classical theories of the pyrochlore lattice antiferromagnet with spin-lattice coupling. Based on recent theoretical model calculation, we discu…
Pyrochlore oxides show several fascinating phenomena, such as the formation of heavy fermions and the thermal Hall effect. Although a key to understanding some phenomena may be the Dzyaloshinsky-Moriya (DM) interaction, its microscopic origin is unclear. To clarify the microscopic origin, we constructed a $t_{2g}$-orbital model with the kinetic energy, the trigonal-distortion potential, the multiorbital Hubbard interactions, and the $LS$ coupling, and derived the low-energy effective Hamiltonian for a $d^{1}$ Mott insulator with the weak $LS$ coupling. We first show that lack of the inversion …
We investigated the electronic and magnetic properties of the pyrochlore oxide Cd$_2$Os$_2$O$_7$ using the density-functional theory plus on-site repulsion ($U$) method, and depict the ground-state phase diagram with respect to $U$. We conclude that the all-in/all-out non-collinear magnetic order is stable in a wide range of $U$. We also show that the easy-axis anisotropy arising from the spin-orbit (SO) coupling plays a significant role in stabilizing the all-in/all-out magnetic order. A \textit{pseudo gap} was observed near the transition between the antiferromagnetic metallic and insulating…
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…
We have performed photoemission and soft x-ray absorption studies of pyrochlore-type Ru oxides, namely, the filling-control system Sm$_{2-x}$Ca$_x$Ru$_2$O$_7$ and the bandwidth-control system Sm$_{2-x}$Bi$_x$Ru$_2$O$_7$, which show insulator-to-metal transition with increasing Ca and Bi concentration, respectively. Core levels and the O 2$p$ valence band in Sm$_{2-x}$Ca$_x$Ru$_2$O$_7$ show almost the same amount of monotonous upward energy shifts with Ca concentration, which indicates that the chemical potential is shifted downward due to hole doping. The Ru 4$d$ band in Sm$_{2-x}$Ca$_x$Ru$_2$…
Magnetic pyrochlore oxides, including the spin ice materials, have proved to be a rich field for the study of geometrical frustration in 3 dimensions. Recently, a new family of magnetic oxides has been synthesised in which the half of the tetrahedra in the pyrochlore lattice are inflated relative to the other half, making an alternating array of small and large tetrahedra. These "breathing pyrochlore" materials such as LiGaCr4O8, LiInCr4O8 and Ba3Yb2Zn5O11 provide new opportunities in the study of frustrated magnetism. Here we provide an analytic theory for the ground state phase diagram and s…
We discuss the ground state properties of a spin 1/2 magnetic ion with threefold $t_{2g}$ orbital degeneracy on a highly frustrated pyrochlore lattice, like Ti$^{3+}$ ion in B-spinel MgTi$_2$O$_4$. We formulate an effective spin-orbital Hamiltonian and study its low energy sector by constructing several exact-eigenstates in the limit of vanishing Hund's coupling. We find that orbital degrees of freedom modulate the spin-exchange energies, release the infinite spin-degeneracy of pyrochlore structure, and drive the system to a non-magnetic spin-singlet manifold. The latter is a collection of spi…
Pyrochlore oxides are fascinating systems where strong, multi-orbital correlations in concert with geometrical frustration give rise to unanticipated physical properties. The detailed mechanism of the insulator-metal transitions (IMT) underpinning these phenomena is, however, ill-understood in general. Motivated thereby, we study the IMT in the pyrochlore ${\rm Hg_{2}Ru_{2}O_{7}}$ using LDA+DMFT. In contrast to the well-known examples of Mott transitions in TMO, we show that, in the negative charge-transfer situation characteristic of \hg, self-doping plays a crucial role in the emergence of a…
Electronic and magnetic properties of molybdenum pyrochlores A2Mo2O7 are studied by the fully relativistic density-functional theory plus on-site repulsion (U) method, with focusing on the spin-glass insulating material Y2Mo2O7. We find that the system exhibits peculiar competition in energy between different magnetic states in the large-U insulating region. The magnetic competition cannot be explained by the conventional picture based on the geometrical frustration of isotropic Heisenberg antiferromagnetic exchange interactions. Through an analysis by using a generalized spin model, we find t…
We present new magnetic heat capacity and neutron scattering results for two magnetically frustrated molybdate pyrochlores: $S=1$ oxide Lu$_2$Mo$_2$O$_7$ and $S={\frac{1}{2}}$ oxynitride Lu$_2$Mo$_2$O$_5$N$_2$. Lu$_2$Mo$_2$O$_7$ undergoes a transition to an unconventional spin glass ground state at $T_f {\sim} 16$ K. However, the preparation of the corresponding oxynitride tunes the nature of the ground state from spin glass to quantum spin liquid. The comparison of the static and dynamic spin correlations within the oxide and oxynitride phases presented here reveals the crucial role played by…
We report neutron scattering measurements of the spinel oxide LiGaCr$_{4}$O$_{8}$, in which magnetic ions Cr$^{3+}$ form a breathing pyrochlore lattice. Our experiments reveal the coexistence of a nearly dispersionless resonance mode and dispersive spin wave excitations in the magnetically ordered state, which can be quantitatively described by a quantum spin model of hexagonal loops and linear spin wave theory with the same set of exchange parameters, respectively. Comparison to other Cr spinel oxides reveals a linear relationship between the resonance energy and lattice constant across all t…
Spin ice materials are the model systems that have a zero-point entropy as \textit{T} $\rightarrow$ 0 K, owing to the frozen disordered states. Here, we chemically alter the well-known spin ice Ho$_{2}$Ti$_{2}$O$_{7}$ by replacing Ti sites with isovalent but larger Zr ion. Unlike the Ho$_{2}$Ti$_{2}$O$_{7}$ which is a pyrochlore material, Ho$_{2}$Zr$_{2}$O$_{7}$ crystallizes in disordered pyrochlore structure. We have performed detailed structural, ac magnetic susceptibility and heat capacity studies on Ho$_{2}$Zr$_{2}$O$_{7}$ to investigate the interplay of structural disorder and frustrated …
A novel macroscopically degenerate state called kagome ice, which was recently found in a spin ice compound Dy2Ti2O7 in a magnetic field applied along the [111] direction of the cubic unit cell, is studied by specific heat measurements. The residual entropy of the kagome ice is estimated to be 0.65 J/K mol Dy, which is nearly 40 % of that for the tetrahedral spin ice obtained in a zero field (1.68 J/K mol Dy) and is in good agreement with a theoretical prediction. It is also reported that the kagom ice state, which is stabilized at a range of magnetic field of 0.3 ~ 0.6 T, is a 'gas' phase and…
The two orbital Hubbard model, with the electrons additionally coupled to a complex magnetic background, arises in the pyrochlore molybdates. The background involves local moments Hund's coupled to the electrons, driving double exchange ferromagnetism, and antiferromagnetic (AF) tendency arising from competing superexchange. The key scales include the Hubbard repulsion and the superexchange, both of which can be tuned in these materials. They control the phase transition from a ferromagnetic metal to a spin glass metal and then to a spin glass (Mott) insulator. We provide a comprehensive descr…
The family of magnetic rare-earth pyrochlore oxides R2M2O7 plays host to a diverse array of exotic phenomena, driven by the interplay between geometrical frustration and spin-orbit interaction, which leads to anisotropy in both magnetic moments and their interactions. In this article we establish a general, symmetry--based theory of pyrochlore magnets with anisotropic exchange interactions. Starting from a very general model of nearest-neighbour exchange between Kramers ions, we find four distinct classical ordered states, all with q=0, competing with a variety of spin-liquids and unconvention…
We study double-exchange models with itinerant t2g electrons in spinel and pyrochlore crystals. In both cases the localized spins form a network of corner-sharing tetrahedra. We show that the strong directional dependence of t2g orbitals leads to unusual Fermi surfaces that induce spin superstructures and noncoplanar orderings for a weak coupling between itinerant electrons and localized spins. Implications of our results to ZnV2O4 and Cd2Os2O7 are also discussed.
The effective quantum pseudospin-1/2 model for interacting rare-earth magnetic moments, which are locally described with atomic doublets, is studied theoretically for magnetic pyrochlore oxides. It is derived microscopically for localized Pr^{3+} 4f moments in Pr_2TM_2O_7 (TM = Zr, Sn, Hf, and Ir) by starting from the atomic non-Kramers magnetic doublets and performing the strong-coupling perturbation expansion of the virtual electron transfer between the Pr 4f and O 2p electrons. The most generic form of the nearest-neighbor anisotropic superexchange pseudospin-1/2 Hamiltonian is also constru…
The dipolar-octupolar pyrochlore oxides R$_2$M$_2$O$_7$ (R=Ce, Sm, Nd) represent an important opportunity in the search for three dimensional Quantum Spin Liquid (QSL) ground states. Their low energy physics is governed by an alluringly simple XYZ Hamiltonian, enabling theoretical description with only a small number of free parameters. Meanwhile, recent experiments on Ce pyrochlores strongly suggest QSL physics. Motivated by this, we present here a complete analysis of the ground state phase diagram of dipolar-octupolar pyrochlores. Combining cluster mean field theory, variational arguments a…
