Fermionic mean-field theory and variational Monte Carlo calculations are employed to shed light on the possible uniform ground states of the Heisenberg model on the pyrochlore lattice. Among the various flux configurations, we find the chiral spin states carrying \pm pi/2 flux through each triangular face to be the most stable both within the mean-field theory and the projected wave-function studies. Properties of the spin-spin correlation function and the chirality order parameter are calculated for the projected wave functions. Mean-field band structures are examined.
The one-band Hubbard model on the pyrochlore lattice contains an extended quantum spin-liquid phase formed from the manifold of singlet dimer coverings. We demonstrate that the massive and deconfined spinon excitations of this system have fermionic statistics. Holonic quasiparticles introduced by doping are also fermions and we explain the origin of this counterintuitive result.
We study the uniform time reversal invariant $U(1)$ quantum spin liquid (QSL) with low energy fermionic quasi-particles for rare earth pyrochlore magnets and explore its magnetic instability employing an augmented fermionic parton mean field theory approach. Self consistent calculations stabilise an uniform $U(1)$ QSL with both gapped and gapless parton excitations as well as fractionalised magnetically ordered phases in an experimentally relevant part of the phase diagram near the classical phase boundaries of the magnetically ordered phases. The gapped QSL has a band-structure with a non-zer…
This short note documents some of the pyrochlore magnetization plateaus resulting from the arguments of Pal & Lal that were not mentioned in arxiv:1902.06475v1. These are (layered) "Kagome"-like plateaus that are commensurate with the pyrochlore lattice, including an exact wavefunction for the $\frac{m}{m_s} = \frac{5}{6}$ plateau state.
We have performed a detailed transverse magnetization study of the pyrochlore antiferromagnet Gd2Ti2O7. A transverse magnetization of about 10^{-3}M_{sat} is observed in the low-temperature ordered phases. These measurements result in the refinement of the Gd2Ti2O7 phase diagrams. Observation of a transverse magnetization indicates loss of the cubic symmetry in some of the magnetic phases and provides new information for a better understanding of the complicated magnetic ordering of Gd2Ti2O7.
The ground state of a spin 1/2 nearest neighbor quantum Heisenberg antiferromagnet on the pyrochlore lattice is investigated using a large $N$ SU(N) fermionic mean field theory. We find several mean field states, of which the state of lowest energy upon Gutzwiller projection, is a parity and time reversal breaking chiral phase with a unit monopole flux exiting each tetrahedron. This "monopole flux" state has a Fermi surface consisting of 4 lines intersecting at a point. At mean field the low-energy excitations about the Fermi surface are gapless spinons. An analysis using the projective symmet…
Above 40K, the magnetic susceptibility of the heavy Fermion spinel LiV2O4 has many features in common with those of geometrically frustrated magnetic insulators, while its room temperature resistivity comfortably exceeds the Mott-Regel limit. This suggests that local magnetic moments, and the underlying geometry of the pyrochlore lattice, play an important role in determining its magnetic properties. We extend a recently introduced tetragonal mean field theory for insulating pyrochlore antiferromagnets to the case where individual tetrahedra contain spins of different lengths, and use this as …
We report low-temperature susceptibility and magnetisation data for the cubic pyrochlore Er2Ti2O7. By performing the measurements on single crystals we are able to establish the degree of magnetic anisotropy present in this compound and to determine the critical values for magnetic field induced transitions below the magnetic ordering temperature of 1.2 K. We also present a magnetic H-T phase diagram of this quantum XY antiferromagnet for different directions of an applied field.
We report magnetization data for several titanium pyrochlore systems measured down to 0.5 K. The measurements, performed on single crystal samples in fields of up to 7 T, have captured the essential elements of the previously reported phase transitions in these compounds and have also revealed additional important features overlooked previously either because of the insufficiently low temperatures used, or due to limitations imposed by polycrystalline samples. For the spin-ice pyrochlores Dy2Ti2O7 and Ho2Ti2O7, an unusually slow relaxation of the magnetization has been observed in lower fields…
The antiferromagnetic Heisenberg model on a pyrochlore lattice under external magnetic field is studied by classical Monte Carlo simulation. The model includes bilinear and biquadratic interactions; the latter effectively describes the coupling to lattice distortions. The magnetization process shows a half-magnetization plateau at low temperatures, accompanied with strong suppression of the magnetic susceptibility. Temperature dependence of the plateau behavior is clarified. Finite-temperature phase diagram under the magnetic field is determined. The results are compared with recent experiment…
Two geometrically frustrated pyrochlore stannates, undergoing long range magnetic order below 1K, were investigated at very low temperature. Anomalies in the behaviour of hyperfine quantities are found, by 155Gd Mossbauer spectroscopy in Gd2Sn2O7 and by low temperature specific heat measurements in Tb2Sn2O7. They are interpreted in terms of fluctuations of the correlated Gd or Tb spins, using a model two-level system (the nuclear spins) submitted to a randomly fluctuating (hyperfine) field.
We study the $S=1/2$ pyrochlore Heisenberg antiferromagnet in a magnetic field. Using large scale density-matrix renormalization group (DMRG) calculations for clusters up to $128$ spins, we find indications for a finite triplet gap, causing a threshold field to nonzero magnetization in the magnetization curve. We obtain a robust saturation field consistent with a magnon crystal, although the corresponding $5/6$ magnetization plateau is very slim and possibly unstable. Most remarkably, there is a pronounced and apparently robust $\frac 1 2$ magnetization plateau where the groundstate breaks (re…
We present a detailed symmetry analysis of the degeneracy lifting due to higher order spin exchanges in the pyrochlore lattice in applied magnetic field. Under the assumption of the 4 sublattice ordering, the criteria for a stable half-magnetization plateau are deduced. The higher order exchange terms may originate from spin-lattice coupling, or can describe quantum and thermal fluctuations.
We derive analytic forms for spin waves in pyrochlore magnets with dipolar-octupolar interactions, such as ${\rm Nd}_2{\rm Zr}_2{\rm O}_7$. We obtain full knowledge of the diagonalized magnonic Hamiltonian within the linear spin wave approximation. We also consider the effect of a "breathing mode" as a perturbation of this system. The breathing mode lifts the degeneracy of the upper band of the spin wave dispersion along the direction $X\to W$ in $k$-space.
We propose the idea of a spin-lattice liquid, in which spin and lattice degrees of freedom are strongly coupled and remain disordered and fluctuating down to low temperatures. We show that such a state arises naturally from a microscopic analysis of a class of molybdate pyrochlore compounds, and is driven by a giant magnetoelastic effect. Finally, we argue that this could explain some of the experimental features of Y$_2$Mo$_2$O$_7$.
A quantum mean field theory of the pyrochlore lattice is presented. The starting point is not the individual magnetic ions, as in the usual Curie-Weiss mean field theory, but a set of interacting corner sharing tetrahedra. We check the consistency of the model against magnetic susceptibility data, and find a good agreement between the theoretical predictions and the experimental data. Implications of the model and future extensions are also discussed.
Electron spin resonance study of frustrated pyrochlore Gd2Ti2O7 is performed in a wide frequency band for a temperature range 0.4-30 K, which covers paramagnetic and magnetically ordered phases. The paramagnetic resonance reveals the spectroscopic g-factor about 2.0 and a temperature dependent linewidth. In ordered phases magnetic resonance spectra are distinctive for a nonplanar cubic (or tetrahedral) antiferromagnet with an isotropic susceptibility. In the high-field saturated phase, weakly-dispersive soft modes are observed and their field evolution is traced.
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…
Exchange interaction tends to favor collinear or coplanar magnetic orders in rotationally invariant spin systems. Indeed, such magnetic structures are usually selected by thermal or quantum fluctuations in highly frustrated magnets. Here we show that a complex noncoplanar magnetic order with a quadrupled unit cell is stabilized by itinerant electrons on the pyrochlore lattice. Specifically we consider the Kondo-lattice and Hubbard models at quarter filling. The electron Fermi 'surface' at this filling factor is topologically equivalent to three intersecting Fermi circles. Perfect nesting of th…
We study magnetic order in the Heisenberg antiferromagnet on the checkerboard lattice, a two-dimensional version of the pyrochlore network with strong geometric frustration. By employing the semiclassical (1/S) expansion we find that quantum fluctuations of spins induce a long-range order that breaks the four-fold rotational symmetry of the lattice. The ordered phase is a valence-bond crystal. We discuss similarities and differences with the extreme quantum case S = 1/2 and find a useful phenomenology to describe the bond-ordered phases.
The magnetization processes of the spin-3/2 antiferromagnet LiInCr4O8 comprising a "breathing" pyrochlore lattice, which is an alternating array of small and large tetrahedra, are studied under ultrahigh magnetic fields of up to 130 T using state-of-the-art pulsed magnets. A half magnetization plateau is observed above 90 T to 130 T, suggesting that LiInCr4O8 has a strong spin-lattice coupling, similar to conventional chromium spinel oxides. The magnetization of LiGa0.125In0.875Cr4O8, in which the structural and magnetic transitions at low temperatures have been completely suppressed, shows a …
Gd2Ti2O7 is a highly frustrated antiferromagnet on a pyrochlore lattice, where apart from the Heisenberg exchange the spins also interact via dipole-dipole forces. We report on low-temperature specific heat measurements performed on single crystals of Gd2Ti2O7 for three different directions of an applied magnetic field. The measurements reveal the strongly anisotropic behaviour of Gd2Ti2O7 in a magnetic field despite the apparent absence of a significant single-ion anisotropy for Gd3+. The H-T phase diagrams are constructed for H//111], H//[110] and H//[112]. The results indicate that further …
We consider the quantum spin-$s$ $XXZ$ Heisenberg antiferromagnet on the two- and three-dimensional pyrochlore lattices and examine a spin-Peierls mechanism of lowering the total energy by a lattice distortion in a high magnetic field. For the exact eigenstates consisting of several independent localized magnons in a ferromagnetic environment we show the existence of a spin-Peierls instability by rigorous analytical calculations. In addition we report on exact diagonalization data for finite two-dimensional pyrochlore lattices up to N=64 sites. We discuss a scenario of the field-tuned changes …
The pyrochlore materials have long been predicted to harbor a quantum spin liquid, an intrinsic long-range-entangled state supporting fractionalized excitations. Existing pyrochlore experiments, on the other hand, have discovered several weakly ordered states and a tendency of close competition amongst them. Motivated by these facts, we give a complete classification of spin-orbit-coupled $\mathbb{Z}_2$ spin-liquid states on the pyrochlore lattice by using the projective symmetry group (PSG) approach for bosonic spinons. For each spin liquid, we construct a mean-field Hamiltonian that can be u…
The ytterbium pyrochlore magnets, Yb2B2O7 (B = Sn, Ti, Ge) are well described by S_eff = 1/2 quantum spins decorating a network of corner-sharing tetrahedra and interacting via anisotropic exchange. Structurally, only the non-magnetic B-site cation, and hence, primarily the lattice parameter, is changing across the series. Nonetheless, a range of magnetic behaviors are observed: the low temperature magnetism in Yb2Ti2O7 and Yb2Sn2O7 has ferromagnetic character, while Yb2Ge2O7 displays an antiferromagnetically ordered Neel state at low temperatures. While the static properties of the ytterbium …
Nematic spin liquid in a spin-1 pyrochlore magnet and its realization in $\mathrm{NaCaNi}_2\mathrm{F}_7$
Creative Science Unit, Faculty of Science, Shizuoka University（静冈大学理学院创意科学单元）；Institute for Materials Research, Tohoku University（东北大学材料研究所）；Theory of Quantum Matter Unit, Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学量子物质理论单元）
We report measurements performed on a polycrystalline sample of the pyrochlore compound Nd2Sn2O7. It undergoes a second order magnetic phase transition at Tc ~ 0.91 K to a noncoplanar all-in-all-out magnetic structure of the Nd3+ magnetic moments. The thermal behavior of the low temperature specific heat fingerprints excitations with linear dispersion in a three-dimensional lattice. The temperature independent spin-lattice relaxation rate measured below Tc and the anomalously slow paramagnetic spin dynamics detected up to ~ 30 Tc are suggested to be due to magnetic short-range correlations in …
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 $\mi…
Muon spin relaxation measurements on Bi2Ir2O7 show that it undergoes a bulk magnetic transition at 1.84(3) K. This is accompanied by increases in the muon spin relaxation rate and the amplitude of the non-relaxing part of the signal. The magnetic field experienced by muons is estimated to be 0.7 mT at low-temperature, around two orders of magnitude smaller than that in other pyrochlore iridates. These results suggest that the low-temperature state represents ordering of exceptionally small magnetic moments with persistent weak dynamics. The relaxation rate increases further below 0.23(4) K, co…
Materials with strong spin-orbit interactions are presently a main target in the search for systems with novel magnetic properties. Magnetic anisotropies can be very large in such compounds, ranging from strongly frustrated Kitaev exchange in honeycomb iridates and the associated spin-liquid states to robust antisymmetric couplings in square-lattice Sr_2IrO_4 . Here we predict from ab initio quantum chemistry calculations that another highly unusual regime is realized in pyrochlore iridium oxides: the nearest-neighbor Heisenberg interaction can vanish whilst the antisymmetric Dzyaloshinskii- M…
Muon-spin relaxation results on the pyrochlore iridate Nd$_2$Ir$_2$O$_7$ are reported. Spontaneous coherent muon-spin precession below the metal-insulator transition (MIT) temperature of about 33 K is observed, indicating the appearance of a long-ranged magnetic ordering of Ir$^{4+}$ moments. With further decrease in temperature, the internal field at the muon site increases again below about 9 K. The second increase of internal field suggests the ordering of Nd$^{3+}$ moments, which is consistent with a previous neutron experiment. Our results suggest that the MIT and magnetic ordering of Ir$…
Muon spin rotation and relaxation experiments in the pyrochlore iridate Eu2Ir2O7 yield a well-defined muon spin precession frequency below the metal-insulator/antiferromagnetic transition temperature TM = 120 K, indicative of long-range commensurate magnetic order and thus ruling out quantum spin liquid and spin-glass-like ground states. The dynamic muon spin relaxation rate is temperature-independent between 2 K and ~TM and yields an anomalously long Ir^{4+} spin correlation time, suggesting a singular density of low-lying spin excitations. Similar behavior is found in other pyrochlores and g…
We report synchrotron radiation diffraction and muon spin rotation (muSR) measurements on the frustrated pyrochlore magnet Tb2Ti2O7. The powder diffraction study of a crushed crystal fragment does not reveal any structural change down to 4 K. The muSR measurements performed at 20 mK on a mosaic of single crystals with an external magnetic field applied along a three-fold axis are consistent with published a.c. magnetic-susceptibility measurements at 16 mK. While an inflection point could be present around an internal field intensity slightly above 0.3 T, the data barely support the presence of…
Neutron scattering has been used to study the magnetic order and spin dynamics of the colossal magnetoresistive pyrochlore Tl_2Mn_2O_7. On cooling from the paramagnetic state, magnetic correlations develop and appear to diverge at T_C (123 K). In the ferromagnetic phase well defined spin waves are observed, with a gapless ($Δ<0.04$ meV) dispersion relation E=Dq^{2} as expected for an ideal isotropic ferromagnet. As T approaches T_C from low T, the spin waves renormalize, but no significant central diffusive component to the fluctuation spectrum is observed in stark contrast to the La$_{1-x}$(C…
Pyrochlores offer an ideal playground to investigate the magnetic ground state of frustrated magnetic systems. In this class of materials, competition between various magnetic interactions remains frustrated and prevents an ordered magnetic state at low temperatures. Tb2Sn2O7 has recently attracted significant attention due to its ordered spin-ice state. Additionally, in such systems, application of external magnetic field might result in exotic magnetic states. Our current investigation on Tb2Sn2O7 reveal the presence of a new phase associated with fifth order susceptibility at low temperatur…
Neutron scattering measurements show the ferromagnetic XY pyrochlore Yb2Ti2O7 to display strong quasi-two dimensional (2D) spin correlations at low temperature, which give way to long range order (LRO) under the application of modest magnetic fields. Rods of scattering along < 111 > directions due to these 2D spin correlations imply a magnetic decomposition of the cubic pyrochlore system into decoupled kagome planes. A magnetic field of ~0.5 T applied along the [1-10] direction induces a transition to a 3D LRO state characterized by long-lived, dispersive spin waves. Our measurements map out a…
The Heisenberg nearest neighbour antiferromagnet on the pyrochlore (3D) lattice is highly frustrated and does not order at low temperature where spin-spin correlations remain short ranged. Dzyaloshinsky-Moriya interactions (DMI) may be present in pyrochlore compounds as is shown, and the consequences of such interactions on the magnetic properties are investigated through mean field approximation and monte carlo simulations. It is found that DMI (if present) tremendously change the low temperature behaviour of the system. At a temperature of the order of the DMI a phase transition to a long ra…
The spin dynamics in the geometrically frustrated pyrochlore antiferromagnet $\rm Gd_2Sn_2O_7$ is studied by means of the electron spin resonance. In the ordered phase ($T_N = 1$ K), we have detected three gapped resonance modes. Their values agree well with the developed spin-wave theory which takes into account the Heisenberg nearest-neighbor exchange, the single-ion anisotropy and the long-range dipolar interactions. The theory also predicts a fourth lowest-frequency gap, which lies beyond the experimental range of frequencies, but determines the exponential decrease of the specific heat at…
In an ideal classical pyrochlore antiferromagnet without perturbations, an infinite degeneracy at a ground state leads to absence of a magnetic order and spin-glass transition. Here we present Na$_3$Mn(CO$_3$)$_2$Cl as a new candidate compound where classical spins are coupled antiferromagnetically on the pyrochlore lattice, and report its structural and magnetic properties.The temperature dependences of the magnetic susceptibility and heat capacity, and the magnetization curve are consistent with those of an $S$ = 5/2 pyrochlore lattice antiferromagnet with nearest-neighbor interactions of 2 …
In a ferromagnet, the spin excitations are the well-studied magnons. In frustrated quantum magnets, long-range magnetic order fails to develop despite a large exchange coupling between the spins. In contrast to the magnons in conventional magnets, their spin excitations are poorly understood. Are they itinerant or localized? Here we show that the thermal Hall conductivity $κ_{xy}$ provides a powerful probe of spin excitations in the "quantum spin ice" pyrochlore Tb$_2$Ti$_2$O$_7$. The thermal Hall response is large even though the material is transparent. The Hall response arises from spin exc…
Weyl semimetals are three dimensional analogs of graphene where the energy of the excitations are a linear function of their momentum. Pyrochlore Iridates $(A_{2}Ir_{2}O_{7})$ with A =yttrium or lanthanide element) are conjectured to be examples of such a system, with the low energy physics described by twenty four Weyl nodes. An intriguing possibility is that these materials provide a physical realization of the Adler-Bell-Jackiw anomaly. In this letter we investigate the properties of pyrochlore iridates in an applied magnetic field. We find that the dispersion of the lowest landau level dep…
Despite a well-ordered pyrochlore crystal structure and strong magnetic interactions between the Dy$^{3+}$ or Ho$^{3+}$ ions, no long range magnetic order has been detected in the pyrochlore titanates Ho$_2$Ti$_2$O$_7$ and Dy$_2$Ti$_2$O$_7$. To explore the actual magnetic phase formed by cooling these materials, we measure their magnetization dynamics using toroidal, boundary-free magnetization transport techniques. We find that the dynamical magnetic susceptibility of both compounds has the same distinctive phenomenology, that is indistinguishable in form from that of the dielectric permittiv…
The magnetic behavior of polycrystalline samples of Er$_2$Ir$_2$O$_7$ and Tb$_2$Ir$_2$O$_7$ pyrochlores is studied by magnetization measurements and neutron diffraction. Both compounds undergo a magnetic transition at 140 and 130 K respectively, associated with an ordering of the Ir sublattice, signaled by thermomagnetic hysteresis. In Tb$_2$Ir$_2$O$_7$, we show that the Ir molecular field leads the Tb magnetic moments to order below 40 K in the all-in/all-out magnetic arrangement. No sign of magnetic long range order on the Er sublattice is evidenced in Er$_2$Ir$_2$O$_7$ down to 0.6 K where a…
The charge ordered structure of ions and vacancies characterizing rare-earth pyrochlore oxides serves as a model for the study of geometrically frustrated magnetism. The organization of magnetic ions into networks of corner-sharing tetrahedra gives rise to highly correlated magnetic phases with strong fluctuations, including spin liquids and spin ices. It is an open question how these ground states governed by local rules are affected by disorder. In the pyrochlore Tb$_2$Hf$_2$O$_7$, we demonstrate that the vicinity of the disordering transition towards a defective fluorite structure translate…
We present magnetization and Hall effect measurements on the pyrochlore iridate Nd2Ir2O7. Previous muon spin rotation measurements have shown that the system undergoes an unusual transition at T$_M$ = 110 K into a magnetic phase lacking long-range order, followed by a transition at T$_LRO$ = 6 K into a state with long-range magnetic order. We observe a small remnant magnetization when cycling through zero magnetic field at temperatures below T$_M$. Below T$_LRO$, this remnant magnetization increases sharply, and new hysteresis effects appear at a higher field B$_c$ = 2.5 T, while the Hall resi…
The electronic and magnetic properties of spin-1/2 pyrochlores R2V2O7 were investigated on the basis of density-functional calculations. Contrary to the common belief, the spin-1/2 V4+ ions are found to have a substantial easy-axis single-ion anisotropy. The |D/J| ratio deduced from the magnon quantum Hall effect of Lu2V2O7, where J is the nearest-neighbor spin exchange and D is the Dzyaloshinskii-Moriya parameter, is much greater than the value estimated from our calculations (i.e., 0.32 vs. 0.05). We show that this discrepancy is due to the neglect of the single-ion anisotropy of the V4+ ion…
We predict magnetisation plateaux ground states for $S=1/2$ Heisenberg antiferromagnets on pyrochlore lattices by formulating arguments based on gauge and spin-parity transformations. We derive a twist operator appropriate to the pyrochlore lattice, and show that it is equivalent to a large gauge transformation. Invariance under this large gauge transformation indicates the sensitivity of the ground state to changes in boundary conditions. This leads to the formulation of an Oshikawa-Yamanaka-Affleck (OYA)-like criterion at finite external magnetic field, enabling the prediction of plateaux in…
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 report experimental signatures of topological transitions among the Weyl semimetal states of pyrochlore Pr2Ir2O7, where the Kondo coupling between the Ir topological electrons and the spin-ice like orders of Pr moments plays a decisive role. The magnetic-field dependence of resistivity and the Hall conductivity exhibits a plateau and a sharp jump associated with a magnetic-field hysteresis, similar to a liquid-gas-like transition in dipolar spin ice system. Furthermore, the Kondo coupling is controlled by the hydrostatic pressure, revealing that the field-induced displacement of Weyl points…
We present a comprehensive neutron scattering study of the breathing pyrochlore magnet LiGaCr4S8. We observe an unconventional magnetic excitation spectrum with a separation of high and low-energy spin dynamics in the correlated paramagnetic regime above a spin-freezing transition at 12(2) K. By fitting to magnetic diffuse-scattering data, we parameterize the spin Hamiltonian. We find that interactions are ferromagnetic within the large and small tetrahedra of the breathing pyrochlore lattice, but antiferromagnetic further-neighbor interactions are also essential to explain our data, in qualit…
Recent neutron scattering measurements on the spinel CdCr2O4 revealed a rare example of helical magnetic order in geometrically frustrated pyrochlore antiferromagnet. The spin spiral characterized by an incommensurate wavevector Q = 2pi (0, delta, 1) with delta ~0.09 is accompanied by a tetragonal distortion. Here we conduct a systematic study on the magnetic ground state resulting from the interplay between the Dzyaloshinskii-Moriya interaction and further neighbor exchange couplings, two of the most important mechanisms for stabilizing incommensurate spin orders. We compute the low-energy sp…
Building a full understanding of the complex magnetism in the rare-earth pyrochlore iridates, A2Ir2O7, is an ongoing issue in condensed matter physics. The possibility of two interpenetrating and interacting frustrated magnetic pyrochlore sublattices, connected with the strong spin-orbit coupling of the 5d Ir4+ ion, lends itself to a wide array of potential electronic and magnetic states. In this paper, we present longitudinal field and zero field muSR measurements of Er2Ir2O7. The muSR response of Er2Ir2O7 is dominated by the strong fluctuating fields of the Er3+ (J = 15/2) moments, showing a…
All interpretations of extensive magnetic neutron scattering data in the cited paper are at fault [Phys. Rev. X 12, 021015]. For, the expressions for scattered intensities therein do not contain the cerium multipole whose likely contribution to the magnetic state of the pyrochlore is a principal goal of the published investigation. The Comment includes a brief look at essential corrections to the theory.
Pyrochlore iridates and pyrochlore ices are two families of materials where novel quantum phenomena are intertwined with strong spin-orbit coupling, substantial electron correlation and geometrical frustration. Motivated by the puzzling experiments on two pyrochlore systems Pr2Ir2O7 and Yb2Ti2O7, we study the proximate Ising orders and the quantum phase transition out of quantum spin ice U(1) quantum spin liquid (QSL). We apply the electromagnetic duality of the compact quantum electrodynamics to analyze the "magnetic monopoles" condensation for U(1) QSL. The monopole condensation transition r…
We have explored the critical metal-insulator phenomena for pyrochlore-type $R_2$Ir$_2$O$_7$, in which electron correlation strength and magnetic configuration are systematically controlled by varying the average rare-earth ionic radius ($R$=Nd$_{1-x}$Pr$_{x}$ and Sm$_{y}$Nd$_{1-y}$), external pressure, and magnetic field. Metal-insulator transitions in bulk are caused by increasing $x$ or tuning external pressure, indicating that the effective electron correlation is responsible for the transition. The metallic state intervenes between the paramagnetic insulating and antiferromagnetically ord…
