A hidden order that emerges in the frustrated pyrochlore Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ with $T_{\text{c}}=0.53$ K is studied using specific heat, magnetization, and neutron scattering experiments on a high-quality single crystal. Semi-quantitative analyses based on a pseudospin-1/2 Hamiltonian for ionic non-Kramers magnetic doublets demonstrate that it is an ordered state of electric quadrupole moments. The elusive spin liquid state of the nominal Tb$_2$Ti$_2$O$_7$ is most likely a U(1) quantum spin-liquid state.
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 have studied the hidden long-range order (LRO) of the frustrated pyrochlore magnet Tb$_2$Ti$_2$O$_7$ by means of specific-heat experiments and Monte-Carlo (MC) simulations, which has been discussed as the LRO of quadrupole moments inherent to the non-Kramers ion of Tb$^{3+}$. We have found that the sharp specific-heat peak is collapsed into a broad hump by magnetic fields above 0.3 T for $H//[001]$. This result, qualitatively reproduced by MC simulations, suggests that a field-induced magnetic state overcomes the quadrupolar LRO state, as a similar case of a classical spin ice. The present …
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…
We investigate quantum phase transitions for the $s=1/2$ antiferromagnetic Heisenberg model on a pyrochlore lattice. By means of a series expansion starting from isolated tetrahedra, the ground-state phase diagram is determined. When the ratio of the two competing exchange couplings is varied, the first-order (second-order) quantum phase transition occurs between the two spin gap phases (the spin-gap and the antiferromagnetic phases). We also discuss some properties expected for the s=1 pyrochlore spin system.
The crystal structures of the A2B2O7-x Niobium-based pyrochlores Y2(Nb0.86Y0.14)2O6.91, CaYNb2O7, and Y2NbTiO7 are reported, determined by powder neutron diffraction. These compounds represent the first observation of B-site displacements in the pyrochlore structure: the B-site ions are found to be displaced from the ideal pyrochlore positions, creating electric dipoles. The orientations of these dipoles are fully analogous to orientations of the magnetic moments in Ising spin based magnetically frustrated pyrochlores. Diffuse scattering in electron diffraction patterns shows that the displace…
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 present an extensive numerical study of a new type of frustrated itinerant magnetism on the pyrochlore lattice. In this theory, the pyrochlore magnet can be viewed as a cross-linking network of Kondo or double-exchange chains. Contrary to models based on Mott insulators, this itinerant magnetism approach provides a natural explanation for several spin and orbital superstructures observed on the pyrochlore lattice. Through extensive Monte Carlo simulations, we obtain the phase diagrams at two representative electron filling fractions $n = 1/2$ and 2/3. In particular, we show that an intrigui…
As an example of ordering due to quantum fluctuations, we examine the nearest-neighbor antiferromagnetic quantum O(n) rotor model on the pyrochlore lattice. Classically, this system remains disordered even at zero temperature; we find that adding quantum fluctuations induces an ordered phase that survives to positive temperature, and we determine how its phase diagram scales with the coupling constant and the number of spin components. We demonstrate, using quantum Monte Carlo simulations, that this phase has long-range spin-nematic order, and that the phase transition into it appears to be fi…
Frustrated rare-earth pyrochlore titanates, Yb$_2$Ti$_2$O$_7$, and Tb$_2$Ti$_2$O$_7$ have been proposed as promising candidates to realize quantum spin ice (QSI). Multiple exotic quantum phases, including Coulombic ferromagnet, quantum valence-bond solid, and quadrupolar ordering, have been predicted to emerge in the QSI state upon application of a (111)-oriented external magnetic field. Here, we report on the primal successful layer-by-layer growth of ultra-thin films of frustrated quantum pyrochlores, R$_2$Ti$_2$O$_7$ (R = Er, Yb, and Tb), along the (111) direction. We confirm their high cry…
We report low-temperature thermal conductivity $κ$ of pyrochlore Yb$_2$Ti$_2$O$_7$, which contains frustrated spin-ice correlations with significant quantum fluctuations. In the disordered spin-liquid regime, $κ(H)$ exhibits a nonmonotonic magnetic field dependence, which is well explained by the strong spin-phonon scattering and quantum monopole excitations. We show that the excitation energy of quantum monopoles is strongly suppressed from that of dispersionless classical monopoles. Moreover, in stark contrast to the diffusive classical monopoles, the quantum monopoles have a very long mean …
MuSR experiments have been performed on powder sample of the "ordered spin ice" Tb$_2$Sn$_2$O$_7$ pyrochlore compound. At base temperature (T=35mK) the muon relaxation is found to be of dynamical nature which demonstrates that strong fluctuations persist below the ferromagnetic transition (T_C=0.87K). Hints of long range order appear as oscillations of the muon polarization when an external field is applied and also as a hysteretic behavior below T_C. We propose a dynamical and strongly correlated scenario where dynamics results from fluctuation of large spin clusters with the "ordered spin ic…
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…
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 e…
Competition between the ferromagnetic double-exchange interaction and the super-exchange antiferromagnetic interaction is theoretically studied in the presence of geometrical frustration. As increasing the super-exchange interaction, the ferromagnetic metal becomes unstable, and is taken over by a cooperative paramagnetic metal, in sharp contrast with a discontinuous transition to the antiferromagnetic insulator in the absence of frustration. In the critical region, the system exhibits a peculiar temperature-independent behavior with highly incoherent transport, suggesting a large residual ent…
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…
We report neutron scattering studies of the spin correlations of the geometrically frustrated pyrochlore Tb2Mo2O7 using single crystal samples. This material undergoes a spin-freezing transition below Tg~24 K, similar to Y2Mo2O7, and has little apparent chemical disorder. Diffuse elastic peaks are observed at low temperatures, indicating short-range ordering of the Tb moments in an arrangement where the Tb moments are slightly rotated from the preferred directions of the spin ice structure. In addition, a Q-independent signal is observed which likely originates from frozen, but completely unco…
A "supercooled" liquid develops when a fluid does not crystallize upon cooling below its ordering temperature. Instead, the microscopic relaxation times diverge so rapidly that, upon further cooling, equilibration eventually becomes impossible and glass formation occurs. Classic supercooled liquids exhibit specific identifiers including microscopic relaxation times diverging on a Vogel-Tammann-Fulcher (VTF) trajectory, a Havriliak-Negami (HN) form for the dielectric function, and a general Kohlrausch-Williams-Watts (KWW) form for time-domain relaxation. Recently, the pyrochlore Dy2Ti2O7 has be…
Three-dimensionally (3D) frustrated magnets generally exist in the magnetic diamond and pyrochlore lattices, in which quantum fluctuations suppress magnetic orders and generate highly entangled ground states (GS). LiYbSe2 in a previously unreported pyrochlore lattice was discovered from LiCl flux growth. Distinct from the quantum spin liquid (QSL) candidate NaYbSe2 hosting a perfect triangular lattice of Yb3+, LiYbSe2 crystallizes in the cubic pyrochlore structure with space group Fd-3m (No. 227). The Yb3+ ions in LiYbSe2 are arranged on a network of corner-sharing tetrahedra, which is particu…
Although materials that exhibit nearest-neighbor-only antiferromagnetic interactions and geometrical frustration theoretically should not magnetically order in the absence of disorder, few such systems have been observed experimentally. One such system appears to be the pyrochlore Tb2Ti2O7. However, previous structural studies indicated that Tb2Ti2O7 is an imperfect pyrochlore. To clarify the situation, we performed neutron powder diffraction (NPD) and x-ray absorption fine structure (XAFS) measurements on samples that were prepared identically to those that show no magnetic order. The NPD mea…
The geometrically-frustrated spin glass Y2Mo2O7 has been considered widely to be crystallographically ordered with a unique nearest neighbor magnetic exchange interaction, J. To test this assertion, we present x-ray-absorption fine-structure results for the Mo and Y K edges as a function of temperature and compare them to results from a well-ordered pyrochlore, Tl2Mn2O7. We find that the Mo-Mo pair distances are significantly disordered at approximately right angles to the Y-Mo pairs. These results strongly suggest that lattice disorder nucleates the spin-glass phase in this material.
We have studied long range orders of electric quadrupole moments described by an effective pseudospin-$\frac{1}{2}$ Hamiltonian representing pyrochlore magnets with non-Kramers ions under [111] magnetic field, in relevance to Tb$_{2}$Ti$_{2}$O$_{7}$. Order parameters and phase transitions of this frustrated system are investigated using classical Monte-Carlo simulations. In zero field, the model undergoes a first-order phase transition from a paramagnetic state to an ordered state with an antiparallel arrangement of pseudospins. This pseudospin order is characterized by the wavevector $\boldsy…
We use a Monte Carlo simulation to study the diluted antiferromagnetic Ising model on the frustrated lattices including the pyrochlore lattice to show the dilution effects. Using the Wang-Landau algorithm, which directly calculates the energy density of states, we accurately calculate the entropy of the system. We discuss the nonmonotonic dilution concentration dependence of residual entropy for the antiferromagnetic Ising model on the pyrochlore lattice, and compare it to the generalized Pauling approximation proposed by Ke et al. [Phys. Rev. Lett. 99, 137203 (2007)]. We also investigate othe…
The low-temperature thermodynamic properties of the frustrated pyrochlore Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ have been studied using the single crystal of $x=0.005$ sitting in a long range ordered phase in the $x$-$T$ phase diagram. We observed that the specific heat exhibits a minimum around 2 K and slightly increases on cooling, similar to a Schottky-like anomaly for canonical spin ices. A clear specific-heat peak observed at $T_{\rm c} = 0.53$ K is ascribable to the phase transition to a quadrupolar state, which contributes to a relatively large change in entropy, $S \simeq 2.7$ J K$^{-1}$mol$^{…
In this study, we performed powder neutron diffraction and inelastic scattering measurements of frustrated pyrochlore Nd$_2$Ir$_2$O$_7$, which exhibits a metal-insulator transition at a temperature $T_{\rm MI}$ of 33 K. The diffraction measurements revealed that the pyrochlore has an antiferromagnetic long-range structure with propagation vector $\vec{q}_{0}$ of (0,0,0) and that it grows with decreasing temperature below 15 K. This structure was analyzed to be of the all-in all-out type, consisting of highly anisotropic Nd$^{3+}$ magnetic moments of magnitude $2.3\pm0.4$$μ_{\rm B}$, where $μ_{…
The frustrated pyrochlore magnet Yb$_2$Ti$_2$O$_7$ has the remarkable property that it orders magnetically, but has no propagating magnons over wide regions of the Brillouin zone. Here we use inelastic neutron scattering to follow how the spectrum evolves in cubic-axis magnetic fields. At high fields we observe in addition to dispersive magnons also a two-magnon continuum, which grows in intensity upon reducing the field and overlaps with the one-magnon states at intermediate fields leading to strong renormalization of the dispersion relations, and magnon decays. Using heat capacity measuremen…
We review the mechanism of spin-lattice coupling in relieving the geometrical frustration of pyrochlore antiferromagnets, in particular spinel oxides. The tetrahedral unit, which is the building block of the pyrochlore lattice, undergoes a spin-driven Jahn-Teller instability when lattice degrees of freedom are coupled to the antiferromagnetism. By restricting our considerations to distortions which preserve the translational symmetries of the lattice, we present a general theory of the collective spin-Jahn-Teller effect in the pyrochlore lattice. One of the predicted lattice distortions breaks…
Lattice-coupled antiferromagnetic spin model is analyzed for a number of frustrated lattices: triangular, Kagome, and pyrochlore. In triangular and Kagome lattices where ground state spins are locally ordered, the spin-lattice interaction does not lead to a static deformation of the lattice. In the pyrochlore structure, spin-lattice coupling supports a picture of the hexagon spin cluster proposed in the recent experiment[S. H. Lee et al. Nature, 418, 856 (2002)]. Through spin-lattice interaction a uniform contraction of the individual hexagons in the pyrochlore lattice can take place and reduc…
We report the growth of large high quality crystals of the frustrated magnet, Pr2Zr2O7 by the floating zone technique. Several crystals have been produced starting with varying levels of excess of Pr6O11 to compensate for the loss of Pr2O3 during the growth process. X-ray diffraction analysis of the crystals shows that the Pr composition in our crystals, as determined by the Pr site occupancy in the pyrochlore structure, is always slightly less than 1. Fits to the magnetic sus-ceptibility data below 10 K using a Curie-Weiss law reveal an antiferromagnetic coupling between the Pr moments, with …
The effect of site dilution by non magnetic impurities on the susceptibility of geometrically frustrated antiferromagnets (kagome and pyrochlore lattices) is discussed in the framework of the Generalized Constant Coupling model, for both classical and quantum Heisenberg spins. For the classical diluted pyrochlore lattice, excellent agreement is found when compared with Monte Carlo data. Results for the quantum case are also presented and discussed.
A new charge-ordered magnetically frustrated mixed-metal fluoride with a pyrochlore-related structure has been synthesized and characterized. The material, RbFe2F6 (RbFe2+Fe3+F6) was synthesized through mild hydrothermal conditions. The material exhibits a three-dimensional pyrochlore-related structure consisting of corner-shared Fe2+F6 and Fe3+F6 octahedra. In addition to single crystal diffraction data, neutron powder diffraction and magnetometry measurements were carried out. Magnetic data clearly reveal strong antiferromagnetic interactions (a Curie-Weiss temperature of -270 K) but suffici…
We show theoretically that spin and orbital degrees of freedom in the pyrochlore oxide Y2Mo2O7, which is free of quenched disorder, can exhibit a simultaneous glass transition, working as dynamical randomness to each other. The interplay of spins and orbitals is mediated by the Jahn-Teller lattice distortion that selects the choice of orbitals, which then generates variant spin exchange interactions ranging from ferromagnetic to antiferromagnetic ones. Our Monte Carlo simulations detect the power-law divergence of the relaxation times and the negative divergence of both the magnetic and dielec…
We report detailed measurements of the low temperature magnetic phase diagram of Er$_2$Ti$_2$O$_7$. Heat capacity and time-of-flight neutron scattering studies of single crystals, subject to magnetic fields applied along the crystallographic [110] direction, reveal unconventional low energy states. Er$^{3+}$ magnetic ions reside on a pyrochlore lattice in Er$_2$Ti$_2$O$_7$, where local XY anisotropy and antiferromagnetic interactions give rise to a unique frustrated system. In zero field, the ground state exhibits coexisting short and long range order, accompanied by soft collective spin excit…
Our polycrystalline sample study on the Yb-based chalcogenide spinels $A$Yb$_2$$X_4$ ($A =$ Cd, Mg, $X =$ S, Se) has revealed frustrated magnetism due to the antiferromagnetically coupled Heisenberg spin on the pyrochlore lattice. Our crystal electric field analysis indicates the Yb ground state has nearly Heisenberg spins with a strong quantum character of the ground doublet. All the materials exhibit an antiferromagnetic order at 1.4-1.8 K, much lower temperature than the antiferromagnetic exchange coupling scale of $\sim 10$ K. The magnetic specific heat $C_{\rm M}$ shows a $T^{3}$ dependen…
We perform a general study of spin ordering on the pyrochlore lattice with a 3:1 proportionality of two spin polarizations. Equivalently, this describes valence bond solid conformations of a quantum dimer model on the diamond lattice. We determine the set of likely low temperature ordered phases, on the assumption that the ordering is weak, i.e the system is close to a ``U(1)'' quantum spin liquid in which the 3:1 proportionality is maintained but the spins are strongly fluctuating. The nature of the 9 ordered states we find is determined by a ``projective symmetry'' analysis. All the phases e…
The magnetic ground state of oxynitride pyrochlore Lu$_2$Mo$_2$O$_{5-y}$N$_2$, a candidate compound for the quantum spin liquid ($S=1/2$, Mo$^{5+}$), was studied by muon spin rotation/relaxation experiment. In contrast to Lu$_2$Mo$_2$O$_7$ ($S=1$, Mo$^{4+}$) which exhibits the spin-glass behavior with a freezing temperature $T_g\simeq16$ K, no such spin freezing or long range magnetic order was observed down to 0.3 K. Moreover, two separate magnetic domains were detected below $\sim$13 K, which were characterized by differences in spin dynamics. The first is the "sporadic" spin fluctuation see…
We have studied (Tb$_{1-x}$La$_x$)$_2$Mo$_2$O$_7$ pyrochlores by neutron diffraction and $μ$SR at ambient and under applied pressure. Substitution of Tb for La expands the lattice and induces a change from a spin-glass like state ({\itshape x}=0) to a non collinear ferromagnet ({\itshape x}=0.2). In the ferromagnetic structure, the Tb moments orient close to their local anisotropy axis as for an ordered spin ice, while the Mo moments orient close to the net moment. The $μ$SR dynamical relaxation rate shows a cusp-like peak at the Curie temperature T$_C$ and a broad anomaly at T$^\star$$<$T$_C$…
We report on the study of unusual spin glass properties in the geometrically frustrated pyrochlore Tb$_{2}$Mo$_{2}$O$_{7}$, $T$$_{g}$$\simeq$24 K. The analysis of the nonlinear part of dc and complex susceptibilities, near the glass transition regime, suggests the existence of a statistical distribution of relaxation times in short-range ordered ferromagnetic clusters. In addition, the magnetic spins are not sufficiently frozen below the glass transition temperature; apparently, responsible for the non-equilibrium scaling behavior of the static critical exponents of nonlinear susceptibilities.…
Geometrically Frustrated Quadrupoles on the Pyrochlore Lattice and Generalized Spin Liquids
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Laboratoire Léon Brillouin, CEA, CNRS, Université Paris-Saclay（里昂·布里渊实验室，法国原子能和替代能源委员会，法国国家科学研究中心，巴黎萨克雷大学）；Université Grenoble Alpes, CNRS, Institut Néel（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，尼尔研究所）
We have investigated the origin of the magnetic dipole correlations $\langle σ_{\boldsymbol{Q}}^z σ_{\boldsymbol{-Q}}^z \rangle$ characterized by the modulation wave vector $\boldsymbol{k} \sim (\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})$ observed in the frustrated pyrochlore magnet Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$. This magnetic short-range order cannot be accounted for by adding further-neighbor exchange interactions to the nearest-neighbor pseudospin-$\tfrac{1}{2}$ Hamiltonian for quantum pyrochlore magnets. Using classical Monte Carlo simulation and quantum simulation based on thermally pure qua…
Longitudinal-field muon spin relaxation experiments have been carried out in the paramagnetic state of single-crystal Gd_2Ti_2O_7 just above the phase transition at T_m = 1.0 K. At high applied fields the exponential relaxation time T_1 is proportional to field, whereas T_1 saturates below a crossover field B_c that is ~2.5 T at 1.5 K and decreases as T_m is approached. At low fields the relaxation rate increases markedly as the freezing temperature is approached, as expected for critical slowing down of the spin fluctuations, but the increase is suppressed by applied field. This behavior is c…
We investigate the Sp(N) mean-field theory for frustrated quantum magnets. First, we establish some general properties of its solutions; in particular, for small spin we propose simple rules for determining the saddle points of optimal energy. We then apply these insights to the pyrochlore lattice. For spins on a single tetrahedron, we demonstrate a continuous ground state degeneracy for any value of the spin length. For the full pyrochlore lattice, this degeneracy translates to a large number of near-degenerate potential saddle points. Remarkably, it is impossible to construct a saddle point …
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…
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…
We report on infrared, Raman, magnetic susceptibility, and specific heat measurements on CdCr2O4 and ZnCr2O4 single crystals. We estimate the nearest-neighbor and next-nearest neighbor exchange constants from the magnetic susceptibility and extract the spin-spin correlation functions obtained from the magnetic susceptibility and the magnetic contribution to the specific heat. By comparing with the frequency shift of the infrared optical phonons above TN , we derive estimates for the spin-phonon coupling constants in these systems. The observation of phonon modes which are both Raman and infrar…
We used a local susceptibility approach in extensive polarized neutron diffraction studies of the spin liquid \tbti. For a magnetic field applied along the [110] and [111] directions, we found that, at high temperature, all Tb moments are collinear and parallel to the field. With decreasing temperature, the Tb moments reorient from the field direction to their local anisotropy axes. For the [110] field direction, the field induced magnetic structure at 10 K is spin ice-like, but with two types of Tb moments of very different magnitudes. For a field along [111], the magnetic structure resembles…
We report the magnetic characterization of the frustrated transition metal pyrochlore NaCaCo$_2$F$_7$. This material has high spin Co$^{2+}$ in CoF$_6$ octahedra in a pyrochlore lattice, and disordered non-magnetic Na and Ca on the large-atom sites in the structure. Large crystals grown by the floating zone method were studied. The magnetic susceptibility is isotropic, the Co moment is larger than the spin-only value, and in spite of the large Curie Weiss theta (-140 K), freezing of the spin system, as characterized by peaks in the ac and dc susceptibility and specific heat, does not occur unt…
From a microscopic model for the pyrochlore antiferromagnet Tb2Sn2O7, including the crystal field Hamiltonian and interactions between the angular momenta, we compute an effective pseudospin-1/2 Hamiltonian Heff$ that incorporates perturbatively in the effective interactions the effect of excited crystal field levels. We obtain the semiclassical ground states of Heff and find a region of parameter space with a two-in/two-out spin ice configuration on each tetrahedron with ordering wavevector q=0 and with spins canted away from the local Ising axes as found in Tb2Sn2O7. This ground state can al…
In frustrated magnetic systems, geometric constraints or the competition amongst interactions introduce extremely high degeneracy and prevent the system from readily selecting a low-temperature ground state. The most frustrated known spin arrangement is on the pyrochlore lattice, but nearly all magnetic pyrochlores have unquenched orbital angular momentum, constraining the spin directions through spin-orbit coupling. Pyrochlore Mn$_2$Sb$_2$O$_7$ is an extremely rare Heisenberg pyrochlore system, with directionally-unconstrained spins and low chemical disorder. We show that it undergoes a spin-…
FeF$_3$, with its half-filled Fe$^{3+}$ $3d$ orbital, hence zero orbital angular momentum and $S=5/2$, is often put forward as a prototypical highly-frustrated classical Heisenberg pyrochlore antiferromagnet. By employing {\it ab initio} density functional theory (DFT), we obtain an effective spin Hamiltonian for this material. This Hamiltonian contains nearest-neighbor antiferromagnetic Heisenberg, bi-quadratic and Dzyaloshinskii-Moriya interactions as dominant terms and we use Monte Carlo simulations to investigate the nonzero temperature properties of this minimal model. We find that upon d…
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…
Spin liquid state in a three-dimensional pyrochlore-like frustrated magnet
Indian Institute of Technology Madras（马德拉斯理工学院）；Institute for Basic Science（基础科学研究院）；CEA（法国原子能和替代能源委员会）；CNRS（法国国家科学研究中心）；Université Paris-Saclay（巴黎萨克雷大学）；Institut Laue-Langevin（朗之万研究所）；STFC Rutherford Appleton Laboratory（STFC卢瑟福阿普尔顿实验室）；Sungkyunkwan University（成均馆大学）；Quantum Centre of Excellence for Diamond and Emergent Materials, Indian Institute of Technology Madras（马德拉斯理工学院钻石与新兴材料量子卓越中心）
Quantum spin ice materials, pyrochlore magnets with competing Ising and transverse exchange interactions, have been widely discussed as candidates for a quantum spin-liquid ground state. Here, motivated by quantum chemical calculations for Pr pyrochlores, we present the results of a study for frustrated transverse exchange. Using a combination of variational calculations, exact diagonalisation, numerical linked-cluster and series expansions, we find that the previously-studied U(1) quantum spin liquid, in its pi-flux phase, transforms into a nematic quantum spin liquid at a high-symmetry, SU(2…
We present the benchmark of the polynomial expansion Monte Carlo method to a Kondo lattice model with classical localized spins on a geometrically frustrated lattice. The method enables to reduce the calculation amount by using the Chebyshev polynomial expansion of the density of states compared to a conventional Monte Carlo technique based on the exact diagonalization of the fermion Hamiltonian matrix. Further reduction is brought by a real-space truncation of the vector-matrix operations. We apply the method to the model with spin-ice type Ising spins on a three-dimensional pyrochlore lattic…
The spin ice system Dy$_{2}$Ti$_{2}$O$_{7}$ exhibits strong frequency-dependent spin-freezing at $\sim$ 16 K temperature. Although it has been a matter of discussion for years, the origin of this unusual spin freezing is still unknown. The replacement of Ti with isovalent Zr leads to the dynamic magnetic ground state at low temperatures in Dy$_{2}$Zr$_{2}$O$_{7}$ and prevents the formation of high-temperature spin freezing. Interestingly the high-temperature spin freezing re-emerges in the presence of the magnetic field. In this direction, we have studied a series of disordered pyrochlore oxid…
We investigate the dynamical quadrupole structure factor of a spin-1/2 $J_{1}$-$J_{2}$ Heisenberg chain with competing ferromagnetic $J_{1}$ and antiferromagnetic $J_{2}$ in a magnetic field by exploiting density-matrix renormalization group techniques. In a field-induced spin nematic regime, we observe gapless excitations at $q=π$ according to quasi-long-range antiferro-quadrupole correlations. The gapless excitation mode has a quadratic form at the saturation, while it changes into a linear dispersion as the magnetization decreases.
