Cobalt pyrochlore fluoride NaCaCo$_2$F$_7$ is a disordered frustrated magnet composed of Co$^{2+}$ ions with an effective spin-$\frac{1}{2}$ magnetic moment and exhibits spin freezing below $T_f \sim$2.4 K. We perform ultrasound velocity measurements on a single crystal of the cubic NaCaCo$_2$F$_7$. The temperature dependence of the bulk modulus (the breathing elastic mode) exhibits Curie-type softening upon cooling below $\sim$20 K down to $T_f$, which is suppressed by the magnetic field. This Curie-type softening should be a precursor to the enhancement of the strength of exchange disorder via the spin-lattice coupling, which causes the spin freezing. In contrast to the magnetic-field-suppressed Curie-type softening in the bulk modulus, the trigonal shear modulus exhibits softening with a characteristic minimum upon cooling, which is enhanced by the magnetic field at temperatures below $\sim$20 K. This magnetic-field-enhanced elastic anomaly in the trigonal shear modulus suggests a coupling of the lattice to the dynamical spin-cluster state. For NaCaCo$_2$F$_7$, the observed elastic anomalies reveal an occurrence of magnetic-field-induced crossover from an isostructural lattice instability toward the spin freezing to a trigonal lattice instability arising from the emergent dynamical spin-cluster state.
We present time-of-flight neutron total scattering and polarized neutron scattering measurements of the magnetically frustrated compounds NaCaCo$_2$F$_7$ and NaSrCo$_2$F$_7$, which belong to a class of recently discovered pyrochlore compounds based on transition metals and fluorine. The magnetic pair distribution function (mPDF) technique is used to analyze and model the total scattering data in real space. We find that a previously-proposed model of short-range XY-like correlations with a length scale of 10-15 Å, combined with nearest-neighbor collinear antiferromagnetic correlations, accurat…
We present results of $^{23}$Na and $^{19}$F nuclear magnetic resonance (NMR) measurements on NaCaCo$_2$F$_7$, a frustrated pyrochlore magnet with a Curie-Weiss temperature, $T_{cw}$ ~-140 K, and intrinsic bond disorder. Below 3.6 K both the $^{23}$Na and $^{19}$F spectra broaden substantially in comparison to higher temperatures accompanied by a considerable reduction (80 \%) of the NMR signal intensity: This proves a broad quasi-static field distribution. The $^{19}$F spin-lattice relaxation rate $^{19}(1/T_1$) exhibits a peak at 2.9 K already starting to develop below 10 K. We attribute the…
We report high-frequency/high-field electron spin resonance (ESR) and high-field magnetization studies on single crystals of the bond-disordered pyrochlore NaCaCo$_2$F$_7$. Frequency- and temperature-dependent ESR investigations above the freezing temperature $T_f \sim 2.4$ K reveal the coexistence of two distinct magnetic phases. A cooperative paramagnetic phase, evidenced by a gapless excitation mode, is found as well as a spin-glass phase developing below 20 K which is associated with a gapped low-energy excitation. Effective $g$-factors close to 2 are obtained for both modes in line with p…
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…
We present an analytical model of orbital ordering in vanadium spinel MnV2O4. The model is based on recent first-principles calculation indicating a strong trigonal distortion at the vanadium sites of this compound [Phys. Rev. Lett. 102, 216405 (2009)]. At the single-ion level, the trigonal crystal field leaves a doubly degenerate atomic ground state and breaks the approximate rotational symmetry of t2g orbitals. We find that the effective interaction between the low-energy doublets is described by a quantum antiferromagnetic 120-degree model on the pyrochlore lattice. We obtain the classical …
The antiferromagnetic pyrochlore material NaCaCo$_2$F$_7$ is a thermal spin liquid over a broad temperature range (~ 140 K down to $T_F = 2.4 $K), in which magnetic correlations between Co$^{2+}$ dipole moments explore a continuous manifold of antiferromagnetic XY states. The thermal spin liquid is interrupted by spin freezing at a temperature that is ~ 2 % of the mean field interaction strength, leading to short range static XY clusters with distinctive relaxation dynamics. Here we report the low energy inelastic neutron scattering response from the related compound NaSrCo$_2$F$_7$, confirmin…
The possible existence of topological insulators in cubic pyrochlore iridates A$_{2}$Ir$_{2}$O$_{7}$ (A = Y or rare-earth elements) is investigated by taking into account the strong spin-orbit coupling and trigonal crystal field effect. It is found that the trigonal crystal field effect, which is always present in real systems, may destabilize the topological insulator proposed for the ideal cubic crystal field, leading to a metallic ground state. Thus the trigonal crystal field is an important control parameter for the metal-insulator changeover. We propose that this could be one of the reaso…
Cerium electronic multipoles in trigonal symmetry viewed in magnetic neutron diffraction are investigated. Analytic expressions for all the magnetic multipoles, and radial integrals calculated with an established atomic code, are used to scrutinize a recent claim to have observed an octupole-ice configuration in a powder sample of pyrochlore Ce2Sn2O7. Three equally plausible suites of multipoles belonging to uncorrelated cerium ions give equally satisfactory accounts of the available diffraction pattern. Our multipoles are suitable for future experiments using Bragg diffraction from a compound…
The pyrochlore compound \tbti\ is known to remain in a spin-liquid state down to the lowest attainable temperature (0.05\,K), whereas current theories predict it should order into an antiferromagnetic structure. A number of models have been developed in order to resolve this discrepancy, but they could not obtain a spin-liquid ground state. We present here an explanation for the lack of magnetic order in \tbti\ based on the presence of a Jahn-Teller-like distortion from the local trigonal symmetry and on the physics of the two-singlet system coupled by exchange.
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…
By many-body quantum-chemical calculations, we investigate the role of two structural effects - local ligand distortions and the anisotropic Cd-ion coordination - on the magnetic state of Cd2Os2O7, a spin S=3/2 pyrochlore. We find that these effects strongly compete, rendering the magnetic interactions and ordering crucially depend on these geometrical features. Without trigonal distortions a large easy-plane magnetic anisotropy develops. Their presence, however, reverses the sign of the zero-field splitting and causes a large easy-axis anisotropy (D = -6.8 meV), which in conjunction with the …
We report the low temperature magnetic properties of Ce$_2$Sn$_2$O$_7$, a rare-earth pyrochlore. Our susceptibility and magnetization measurements show that due to the thermal isolation of a Kramers doublet ground state, Ce$_2$Sn$_2$O$_7$ has Ising-like magnetic moments of $\sim1.18$ $μ_\mathrm{B}$. The magnetic moments are confined to the local trigonal axes, as in a spin ice, but the exchange interactions are antiferromagnetic. Below 1 K the system enters a regime with antiferromagnetic correlations. In contrast to predictions for classical $\langle 111 \rangle$-Ising spins on the pyrochlore…
We study the prototype 5d pyrochlore iridate Y2Ir2O7 from first principles using the local density approximation and dynamical mean-field theory (LDA+DMFT). We map out the phase diagram in the space of temperature, onsite Coulomb repulsion U, and filling. Consistent with experiments, we find that an all-in-all-out ordered insulating phase is stable for realistic values of U. The trigonal crystal field enhances the magnetic moments of the jeff=1/2 doublet, and strong inter-band correlations are induced by the Coulomb interaction, which indicates that a three-band description is important. We de…
The results of studies of Y$_{2}$Ti$_2$O$_7$ single crystals doped with Er$^{3+}$ and Yb$^{3+}$ ions by means of electron paramagnetic resonance (EPR) and dc-magnetometry are reported. EPR signals of the trigonal centers with the characteristic hyperfine structure of Er$^{3+}$ or Yb$^{3+}$ ions were observed. Field dependences of magnetization of single crystals for magnetic fields directed along the crystallographic axes and temperature dependences of magnetic susceptibilities were measured. Spin Hamiltonian parameters ($g$-factors and parameters of the hyperfine interaction) for Er$^{3+}$ an…
Cubic Y$_{2}$Ti$_{2}$O$_{7}$ single crystals doped with Er$^{3+}$ and Yb$^{3+}$ ions have been studied by the methods of electron spin resonance (ESR) and selective laser spectroscopy. ESR spectra exhibit signals from rare-earth ions that substitute for yttrium ions in sites with local trigonal symmetry. The $g$ tensor components are determined. The results of optical investigations indicate that impurity centers of several types are formed; the sublevel energies of the ground and excited multiplets of these centers are found. Among the great variety of detected optical centers, the centers th…
We present AC and DC magnetometry, heat capacity, muon spin relaxation ($μ$SR) and resonant inelastic X-ray scattering (RIXS) studies of the pyrochlore osmate Y$_2$Os$_2$O$_7$. We observe a non-zero effective moment governed by $\sqrt{f}μ_{\rm{eff}} = 0.417(1)\,μ_{\rm{B}}$ where $f$ is the fraction of Os sites which exhibit a spin, and spin freezing at temperature $T_{\rm f} \simeq 5\,$K, consistent with previous results. The field dependence of magnetisation data shows that the paramagnetic moment is most likely due to large moments $μ_{\rm eff} \simeq 3\,μ_{\rm B}$ on only a small fraction $…
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 present a neutron diffraction study of FeV2O4, which is rare in exhibiting spin and orbital degrees of freedom on both cation sublattices of the spinel structure. Our data confirm the existence of three structural phase transitions previously identified with x-ray powder diffraction, and reveal that the lower two transitions are associated with sequential collinear and canted ferrimagnetic transitions involving both cation sites. Through consideration of local crystal and spin symmetry, we further conclude that Fe2+ cations are ferro-orbitally ordered below 135K and V3+ orbitals order at 60…
Geometrical frustration is a central challenge in contemporary condensed matter physics, a crucible favourable to the emergence of novel physics. The pyrochlore magnets, with rare earth magnetic moments localized at the vertices of corner-sharing tetrahedra, play a prominent role in this field, with a rich variety of exotic ground states ranging from the "spin ices" \hoti\ and \dyti\ to the "spin liquid" and "ordered spin ice" ground states in \tbti\ and \tbsn. Inelastic neutron scattering provides valuable information for understanding the nature of these ground states, shedding light on the …
We have studied the field-induced magnetic structures of Tb2Ti2O7 pyrochlore by single-crystal neutron diffraction under a field applied along the [111] local anisotropy axis, up to H=12T and down to T=40mK. We collected a hundred magnetic Bragg peaks for each field and temperature value and refined the magnetic structures with k=0 propagation vector by performing a symmetry analysis in the space group R-3m, reducing the number of free parameters to three only. We observe a gradual reorientation of the Tb magnetic moments towards the field direction, close to a "3-in, 1-out / 1-in, 3-out" spin…
Continuous quantum phase transitions involving all-in-all-out (AIAO) antiferromagnetic order in strongly spin-orbit-coupled 5d compounds could give rise to various exotic electronic phases and strongly-coupled quantum critical phenomena. Here we experimentally trace the AIAO spin order in Sm2Ir2O7 using direct resonant x-ray magnetic diffraction techniques under high pressure. The magnetic order is suppressed at a critical pressure Pc=6.30 GPa, while the lattice symmetry remains in the cubic Fd-3m space group across the quantum critical point. Comparing pressure tuning and the chemical series …
The magnetic properties of the pyrochlore iridate material Eu$_2$Ir$_2$O$_7$ (5$d^5$) have been studied based on the first principle calculations, where the crystal field splitting $Δ$, spin-orbit coupling (SOC) $λ$ and Coulomb interaction $U$ within Ir 5$d$ orbitals are all playing significant roles. The ground state phase diagram has been obtained with respect to the strength of SOC and Coulomb interaction $U$, where a stable anti-ferromagnetic ground state with all-in/all-out (AIAO) spin structure has been found. Besides, another anti-ferromagnetic states with close energy to AIAO have also…
Ytterbium-based delafossites with effective S=1/2 moments are investigated intensively as candidates for quantum spin-liquid ground states. While the synthesis of related cerium compounds has also been reported,many important details concerning their crystal, electronic, and magnetic structures are unclear. Here we analyze the S=1/2 system KCeO2, combining complementary theoretical methods. The lattice geometry was optimized and the band structure investigated using density functional theory extended to the level of a GGA+U calculation in order to reproduce the correct insulating behavior. The…
