Elastic neutron scattering, ac susceptibility, and specific heat experiments on the pyrochlores Er$_{2}$Ge$_{2}$O$_{7}$ and Yb$_{2}$Ge$_{2}$O$_{7}$ show that both systems are antiferromagnetically ordered in the $Γ_5$ manifold. The ground state is a $ψ_{3}$ phase for the Er sample and a $ψ_{2}$ or $ψ_{3}$ phase for the Yb sample, which suggests "Order by Disorder"(ObD) physics. Furthermore, we unify the various magnetic ground states of all known R$_{2}$B$_{2}$O$_{7}$ (R = Er, Yb, B = Sn, Ti, Ge) compounds through the enlarged XY type exchange interaction $J_{\pm}$ under chemical pressure. The mechanism for this evolution is discussed in terms of the phase diagram proposed in the theoretical study [Wong et al., Phys. Rev. B 88, 144402, (2013)].
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.
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 study the ground state properties of an anisotropic, quasi-2D version of the quantum (S=1/2) pyrochlore antiferromagnet. In the presence of Dzyaloshinsky-Moriya interactions, in addition to the Heisenberg exchanges, it is shown that two types of ordered magnetic states are generally possible: non coplanar "chiral," and coplanar antiferromagnetic order. The magnetic moments in all cases are determined by the Dzyaloshinsky-Moriya interactions and in this sense the antiferromagnetic order is "weak."
We investigate the zero- and finite-temperature properties of the bond-random $s=1/2$ Heisenberg antiferromagnet on the pyrochlore lattice by the exact diagonalization and the Hams--de Raedt methods. We find that the randomness induces the gapless quantum spin liquid (QSL) state, the random-singlet state. Implications to recent experiments on the mixed-anion pyrochlore-lattice antiferromagnet Lu$_2$Mo$_2$O$_5$N$_2$ exhibiting gapless QSL behaviors are discussed.
It is shown that the mechanism of order out of disorder is at work in the antisymmetric pyrochlore antiferromagnet. Quantum as well as thermal fluctuations break the continuous degeneracy of the classical ground state manifold and reduce its symmetry to $\mathbb{Z}_3 \times \mathbb{Z}_2$. The role of anisotropic symmetric exchange is also investigated and we conclude that this discrete like ordering is robust with respect to these second order like interactions. The antisymmetric pyrochlore antiferromagnet is therefore expected to order at low temperatures, whatever the symmetry type of its in…
Our single crystal study of the magneto-thermal and transport properties of the pyrochlore iridate Eu2Ir2O7 reveals a continuous phase transition from a paramagnetic metal to an antiferromagnetic insulator for a sample with stoichiometry within ~1% resolution. The insulating phase has strong proximity to an antiferromagnetic semimetal, which is stabilized by several % level of the off-stoichiometry. Our observations suggest that in addition to electronic correlation and spin-orbit coupling the magnetic order is essential for opening the charge gap.
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…
The quantum pyrochlore antiferromagnet is studied by perturbative expansions and exact diagonalization of small clusters. We find that the ground state is a spin-liquid state: The spin-spin correlation functions decay exponentially with distance and the correlation length never exceeds the interatomic distance. The calculated magnetic neutron diffraction cross section is in very good agreement with experiments performed on Y(Sc)Mn2. The low energy excitations are singlet-singlet ones, with a finite spin gap.
\ersn\, is considered, together with \erti, as a realization of the XY antiferromagnet on the pyrochlore lattice. We present magnetization measurements confirming that \ersn\, does not order down to 100 mK but exhibits a freezing below 200 mK. Our neutron scattering experiments evidence the strong XY character of the \er moment and point out the existence of short range correlations in which the magnetic moments are in peculiar configurations, the Palmer-Chalker states, predicted theoretically for an XY pyrochlore antiferromagnet with dipolar interactions. Our estimation of the \ersn\, paramet…
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.
The stability of the disordered ground state of the classical Heisenberg pyrochlore antiferromagnet is studied within extensive Monte Carlo simulations by introducing an additional exchange interaction $J'$ that interpolates between the pyrochlore lattice ($J'=0$) and the face-centered cubic lattice ($J'=J$). It is found that for $J'/J$ as low as $J'/J\ge 0.01$, the system is long range ordered : the disordered ground state of the pyrochlore antiferromagnet is unstable when introducing very small deviations from the pure $J'=0$ limit. Furthermore, it is found that the selected phase is a colli…
Single-ion anisotropy is of importance for the magnetic ordering of the frustrated pyrochlore antiferromagnets Gd2Ti2O7 and Gd2Sn2O7. The anisotropy parameters for the Gd2Sn2O7 were measured using the electron spin resonance (ESR) technique. The anisotropy was found to be of the easy plane type, with the main constant D=140mK. This value is 35% smaller than the value of the corresponding anisotropy constant in the related compound Gd2Ti2O7.
We show using quantum free energy calculation that the quantum phase transition between U(1) quantum spin liquid (QSL) and antiferromagnet (AFM) phases in pyrochlore quantum antiferromagnet (QAFM) is a first order rather than second order. This change in order from second to first order is induced by gauge fluctuations, which are explicitly taken into account at gauge theory level in our effective low energy theory. We therefore have discovered a fluctuation-induced first order quantum phase transition in pyrochlore QAFM. We explicitly derive the quantum free energy description of this QSL to …
The synthesis and characterization of a new Yb-based material Ba3Yb2Zn5O11 are reported. This material is identified as the first model system of a pseudospin-1/2 quantum antiferromagnet on "breathing" pyrochlore lattice characterized by an alternating array of small and large Yb tetrahedra. Despite dominant antiferromagnetic interactions J ~ 7 K, a large amount of magnetic entropy (25%) remains at 0.38 K, indicating that each small Yb tetrahedron forms a unique doubly degenerate singlet state. These results are well described by the Heisenberg pseudospin-1/2 single tetrahedron model.
In the highly frustrated pyrochlore magnet spins form a lattice of corner sharing tetrahedra. We show that the tetrahedral ``molecule'' at the heart of this structure undergoes a Jahn-Teller distortion when lattice motion is coupled to the antiferromagnetism. We extend this analysis to the full pyrochlore lattice by means of Landau theory and argue that it should exhibit spin-Peierls phases with bond order but no spin order. We find a range of Neel phases, with collinear, coplanar and noncoplanar order. While collinear Neel phases are easiest to generate microscopically, we also exhibit an int…
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.
In the Heisenberg antiferromagnet $Gd_2Ti_2O_7$, the exchange interactions are geometrically frustrated by the pyrochlore lattice structure. This ESR study reveals a strong temperature dependent anisotropy with respect to a [111] body diagonal below a temperature $T_A=80$ K, despite the spin only nature of the $Gd^{3+}$ ion. Anisotropy and symmetry breaking can nevertheless appear through the superexchange interaction. The presence of short range planar correlation restricted to specific Kagomé planes is sufficient to explain the two ESR modes studied in this work.
The ground-state properties of the spin-1 pyrochlore antiferromagnet are studied by applying the VBS-like tetrahedron-unit decomposition to the original spin system. The symmetrization required on every vertex is taken into account by introducing a ferromagnetic coupling. The pairwise effective Hamiltonian between the adjacent tetrahedrons is obtained by considering the next nearest neighbor and the third neighbor exchange interactions. We find that the transverse component of the spin chirality exhibits a long-range order, breaking the parity symmetry of the tetrahedral group, while the chira…
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…
We show that the S=1/2 pyrochlore lattice with both Heisenberg and antisymmetric, Dzyaloshinsky-Moriya (DM) interactions, can order antiferromagnetically into a state with chiral symmetry, dictated by the distribution of the DM interactions. The chiral antiferromagnetic state is characterized by a small staggered magnetic moment induced by the DM interaction. An external magnetic field can also lead to characteristic field-induced ordering patterns, strongly dependent on the field direction, and generally separated by a quantum phase transition from the chiral ordered phase. The phase diagram …
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…
We investigate theoretically the ordering effect of quantum spin fluctuations in a Heisenberg antiferromagnet on a two-dimensional network of corner sharing tetrahedra. This network is obtained as a {111} slice of the highly frustrated pyrochlore lattice, from which it inherits the equivalence of all three pairs of opposite bonds of each tetrahedron. The lowest-order (in 1/S) quantum corrections partially lift the huge degeneracy of the classical ground state and select an ensemble of states with long-range valence-bond order.
We show that the low-energy sector of the S=1/2, antiferromagnetic Heisenberg model on a one-dimensional lattice of coupled tetrahedra consists of 2^N replica of the spectrum of the dimerized Heisenberg chain, where N is the number of tetrahedra. This provides a proof of the following properties: i) there is a residual ground-state entropy per spin equal to 2^{1/4}; ii) there is a singlet-triplet gap as long as the coupling between the tetrahedra is smaller than the internal one. These properties are compared to available results on the pyrochlore lattice.
We study the semiclassical limit of the $Sp(N)$ generalization of the pyrochlore lattice Heisenberg antiferromagnet by expanding about the $N \to \infty$ saddlepoint in powers of a generalized inverse spin. To leading order, we write down an effective Hamiltonian as a series in loops on the lattice. Using this as a formula for calculating the energy of any classical ground state, we perform Monte-Carlo simulations and find a unique collinear ground state. This state is not a ground state of linear spin-wave theory, and can therefore not be a physical (N=1) semiclassical ground state.
We study possible quantum phases of the Heisenberg antiferromagnet on the planar pyrochlore lattice, also known as the checkerboard lattice or the square lattice with crossings. It is assumed that the exchange coupling on the square-lattice-links is not necessarily the same as those along the crossing links. When all the couplings are the same, this model may be regarded as a two dimensional analog of the pyrochlore antiferromagnet. The large-N limit of the Sp($N$) generalized model is considered and the phase diagram is obtained by analyzing the fluctuation effects about the $N \to \infty$ li…
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…
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 present a mean-field theory for magnetic field driven transitions in dipolar coupled gadolinium titanate Gd$_2$Ti$_2$O$_7$ pyrochlore system. Low temperature neutron scattering yields a phase that can be regarded as a 8 sublattice antiferromagnet, in which long-ranged ordered moments and fluctuating moments coexist. Our theory gives parameter regions where such a phase is realized, and predicts several other phases, with transitions amongst them driven by magnetic field as well as temperature. We find several instances of {\em local} disorder parameters describing the transitions.
We study the effects of magnetoelastic couplings on pyrochlore antiferromagnets. We employ Landau theory, extending an investigation begun by Yamashita and Ueda for the case of S=1, and semiclassical analyses to argue that such couplings generate bond order via a spin--Peierls transition. This is followed by, or concurrent with, a transition into one of several possible low-temperature Neel phases, with most simply collinear, but also coplanar or mixed spin patterns. In a collinear Neel phase, a dispersionless string-like magnon mode dominates the resulting excitation spectrum, providing a dis…
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 …
Motivated by puzzling characteristics of spin-glass transitions widely observed in pyrochlore-based frustrated materials, we investigate effects of coupling to local lattice distortions in a bond-disordered antiferromagnet on the pyrochlore lattice by extensive Monte Carlo simulations. We show that the spin-glass transition temperature $\TSG$ is largely enhanced by the spin-lattice coupling, and furthermore, becomes almost independent of $Δ$ in a wide range of the disorder strength $Δ$. The critical property of the spin glass transition is indistinguishable from that of the canonical Heisenber…
The (three-dimensional) pyrochlore lattice antiferromagnet with Heisenberg spins of large spin length $S$ is a highly frustrated model with an macroscopic degeneracy of classical ground states. The zero-point energy of (harmonic order) spin wave fluctuations distinguishes a subset of these states. I derive an approximate but illuminating {\it effective Hamiltonian}, acting within the subspace of Ising spin configurations representing the {\it collinear} ground states. It consists of products of Ising spins around loops, i.e has the form of a $Z_2$ lattice gauge theory. The remaining ground sta…
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…
We present the results of an exact diagonalization study of the spin-1/2 Heisenberg antiferromagnet on a two-dimensional version of the pyrochlore lattice, also known as the square lattice with crossings or the checkerboard lattice. Examining the low energy spectra for systems of up to 24 spins, we find that all clusters studied have non-degenerate ground states with total spin zero, and big energy gaps to states with higher total spin. We also find a large number of non-magnetic excitations at energies within this spin gap. Spin-spin and spin-Peierls correlation functions appear to be short-r…
The crystal structures and magnetic properties of three previously unreported A2B2F7 pyrochlore materials, NaSrMn2F7, NaCaFe2F7, and NaSrFe2F7 are presented. In these compounds, either S=2 Fe2+ or S=5/2 Mn2+ is on the B site, while nonmagnetic Na and Ca (Na and Sr) are disordered on the A site. The materials, which were grown as crystals via the floating zone method, display high effective magnetic moments and large Curie-Weiss thetas. Despite these characteristics, freezing of the magnetic spins, characterized by peaks in the susceptibility or specific heat, is not observed until low temperat…
Frustrated quantum magnets not only provide exotic ground states and unusual magnetic structures, but also support unconventional excitations in many cases. Using a physically relevant spin model for a breathing pyrochlore lattice, we discuss the presence of topological linear band crossings of magnons in antiferromagnets. These are the analogs of Weyl fermions in electronic systems, which we dub Weyl magnons. The bulk Weyl magnon implies the presence of chiral magnon surface states forming arcs at finite energy. We argue that such antiferromagnets present a unique example in which Weyl points…
The pyrochlore lattice Heisenberg antiferromagnet has a massive classical ground state degeneracy. We summarize three approximation schemes, valid for large spin length $S$, to capture the (partial) lifting of this degeneracy when zero-point quantum fluctuations are taken into account; all three are related to analytic loop expansions. The first is harmonic order spin waves; at this order, there remains an infinite manifold of degenerate collinear ground states, related by a gauge-like symmetry. The second is anharmonic (quartic order) spin waves, using a self-consistent approximation; the har…
We investigate the ground-state properties of the nearest-neighbor $S=1$ pyrochlore Heisenberg antiferromagnet using two complementary numerical methods, density-matrix renormalization group (DMRG) and pseudofermion functional renormalization group (PFFRG). Within DMRG, we are able to reliably study clusters with up to 48 spins by keeping 20 000 SU(2) states. The investigated 32-site and 48-site clusters both show indications of a robust $C_3$ rotation symmetry breaking of the ground-state spin correlations and the 48-site cluster additionally features inversion symmetry breaking. Our PFFRG an…
We discuss the origin of spin correlations observed in neutron scattering experiments on the paramagnetic phase of a number of frustrated spinel compounds, most notably ZnCr2O4. These correlations are striking for two reasons. First, they have been interpreted as evidence for the formation of weakly interacting hexagonal clusters of spins. Second, they are very different from those calculated for the nearest neighbour Heisenberg pyrochlore antiferromagnet, in which Coulomb phase correlations generate sharp scattering features known as pinch points. Using large-$n$ calculations and Monte Carlo …
The 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 …
The Goldstone mode in a helical magnetic phase, also known as the helimagnon, is a propagating mode with a highly anisotropic dispersion relation. Here we study theoretically the helimagnon excitations in a complex chiral ground state of pyrochlore antiferromagnets such as spinel CdCr2O4 and itinerant magnet YMn2. We show that the effective theory of the soft modes in the helical state possesses a symmetry similar to that of smectic liquid crystals. We compute the low-energy spin-wave spectrum based on a microscopic spin Hamiltonian and find a dispersion relation characteristic of the helimagn…
In the classical pyrochlore lattice Heisenberg antiferromagnet, there is a macroscopic continuous ground state degeneracy. We study semiclassical limit of large spin length $S$, keeping only the lowest order (in 1/S) correction to the classical Hamiltonian. We perform a detailed analysis of the spin-wave modes, and using a real-space loop expansion, we produce an effective Hamiltonian, in which the degrees of freedom are Ising variables representing fluxes through loops in the lattice. We find a family of degenerate collinear ground states, related by gauge-like $Z_2$ transformations and provi…
The ground states of Klein type spin models on the pyrochlore and checkerboard lattice are spanned by the set of singlet dimer coverings, and thus possess an extensive ground--state degeneracy. Among the many exotic consequences is the presence of deconfined fractional excitations (spinons) which propagate through the entire system. While a realistic electronic model on the pyrochlore lattice is close to the Klein point, this point is in fact inherently unstable because any perturbation $ε$ restores spinon confinement at $T = 0$. We demonstrate that deconfinement is recovered in the finite--te…
In the pyrochlore lattice Heisenberg antiferromagnet, for large spin length $S$, the massive classical ground state degeneracy is partly lifted by the zero-point energy of quantum fluctuations at harmonic order in spin-waves. However, there remains an infinite manifold of degenerate collinear ground states, related by a gaugelike symmetry. We have extended the spin-wave calculation to quartic order, assuming a Gaussian variational wavefunction (equivalent to Hartree-Fock approximation). Quartic calculations \emph{do} break the harmonic-order degeneracy of periodic ground states. The form of th…
We study the low-temperature physics of the $SU(2)$-symmetric spin-$1/2$ Heisenberg antiferromagnet on a pyrochlore lattice and find fingerprint evidence for the thermal spin-ice state in this frustrated quantum magnet. Our conclusions are based on the results of bold diagrammatic Monte Carlo simulations, with good convergence of the skeleton series down to the temperature $T/J=1/6$. The identification of the spin-ice state is done through a remarkably accurate microscopic correspondence for the static structure factor between the quantum Heisenberg, classical Heisenberg, and Ising models at a…
Low-temperature powder neutron diffraction measurements are performed in the ordered magnetic state of the pyrochlore antiferromagnet Gd2Sn2O7. Symmetry analysis of the diffraction data indicates that this compound has the ground state predicted theoretically for a Heisenberg pyrochlore antiferromagnet with dipolar interactions. The difference in magnetic structures of Gd2Sn2O7 and of nominally analogous Gd2Ti2O7 is found to be determined by a specific type of third-neighbor superexchange interaction on the pyrochlore lattice between spins across empty hexagons.
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…
We report inelastic neutron scattering measurements from our newly synthesized single crystals of the structurally metastable antiferromagnetic pyrochlore Yb$_{2}$Ge$_{2}$O$_{7}$. We determine the four symmetry-allowed nearest-neighbor anisotropic exchange parameters via fits to linear spin wave theory supplemented by fits of the high-temperature specific heat. The exchange parameters so-determined are strongly correlated to the values determined for the $g$-tensor components, as previously observed for the related Yb pyrochlore Yb$_{2}$Ti$_{2}$O$_{7}$. To address this issue, we directly deter…
The gadolinium pyrochlores, Gd$_2B_2$O$_7$, are amongst the best realizations of antiferromagnetically coupled Heisenberg spins on a pyrochlore lattice. We present a magnetic characterization of Gd$_2$Pt$_2$O$_7$, a unique member of this family. Magnetic susceptibility, heat capacity, and muon spin relaxation measurements show that Gd$_2$Pt$_2$O$_7$ undergoes an antiferromagnetic ordering transition at $T_N = 1.6$ K. This transition is strongly first order, as indicated by the sharpness of the heat capacity anomaly, thermal hysteresis in the magnetic susceptibility, and a non-divergent relaxat…
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…
Quantum Heisenberg antiferromagnets on pyrochlore and checkerboard lattices in a strong external magnetic field are mapped onto hard-core lattice gases with an extended exclusion region. The effective models are studied by the exchange Monte Carlo simulations and by the transfer matrix method. The transition point and the critical exponents are obtained numerically for a square-lattice gas of particles with the second-neighbor exclusion, which describes a checkerboard antiferromagnet. The exact structure of the magnon crystal state is determined for a pyrochlore antiferromagnet.
We study quantum effects in a spin-3/2 antiferromagnet on the pyrochlore lattice in an external magnetic field, focusing on the vicinity of a plateau in the magnetization at half the saturation value, observed in CdCr$_2$O$_4$, and HgCr$_2$O$_4$. Our theory, based on quantum fluctuations, predicts the existence of a symmetry-broken state on the plateau, even with only nearest-neighbor microscopic exchange. This symmetry broken state consists of a particular arrangement of spins polarized parallel and antiparallel to the field in a 3:1 ratio on each tetrahedron. It quadruples the lattice unit c…
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 $\mi…
We investigate the ultrafast dynamics of Cd$_2$Os$_2$O$_7$, a prototype material showing a Lifshitz-type transition as a function of temperature. In the paramagnetic metallic state, the photo-reflectivity shows a sub-picosecond relaxation, followed by a featureless small offset. In the antiferromagnetic state slightly below $T_N$, however, the photo-reflectivity resurges over hundreds of picoseconds, which goes beyond the usual realm of the effective-temperature model. Our observations are consistent with the Lifshitz phase transition of Cd$_2$Os$_2$O$_7$ driven by the evolution of the local m…
High resolution time-of-flight neutron scattering measurements on Tb2Ti2O7 reveal a rich low temperature phase diagram in the presence of a magnetic field applied along [110]. In zero field at T=0.4 K, terbium titanate is a highly correlated cooperative paramagnet with disordered spins residing on a pyrochlore lattice of corner-sharing tetrahedra. Application of a small field condenses much of the magnetic diffuse scattering, characteristic of the disordered spins, into a new Bragg peak characteristic of a polarized paramagnet. At higher fields, a magnetically ordered phase is induced, which s…
We study low energy excitations in the quantum breathing pyrochlore antiferromagnet Ba$_3$Yb$_2$Zn$_5$O$_{11}$ by combination of inelastic neutron scattering (INS) and thermodynamical properties measurements. The INS spectra are quantitatively explained by spin-1/2 single-tetrahedron model having $XXZ$ anisotropy and Dzyaloshinskii-Moriya interaction. This model has a two-fold degeneracy of the lowest-energy state per tetrahedron and well reproduces the magnetization curve at 0.5 K and heat capacity above 1.5 K. At lower temperatures, however, we observe a broad maximum in the heat capacity ar…
The XY-pyrochlore antiferromagnet \ETO\ is studied by heat capacity measurements and electron spin resonance spectroscopy performed on single crystal samples. The magnetic phase diagrams are established for two directions of applied field, $H\parallel [100]$ and $H\parallel [111]$. In the magnetically ordered phase observed below $T_N=1.2$ K, the magnetic excitation spectrum consists of a Goldstone mode acquiring an isotropic gap in an applied field, and another mode with a gap softening in the vicinity of a field-induced phase transition. This second-order transition takes place at a critical…
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…
Correlation functions (CFs) of the classical Heisenberg antiferromagnet on the pyrochlore lattice are studied by solving exactly the infinite-component spin-vector model. % As in many Fully Frustrated Lattices, the constraint due to the minimization of the energy and the particular structure based on corner sharing tetrahedra both contribute to the creation of local degrees of freedom. % The resulting degeneracy destroys any magnetic order at all temperature and we obtain no sign of criticality, even at $T = 0$. % Calculated neutron scattering cross sections have their maxima beyond the first …
