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 dielectric non-linear susceptibilities, resolving the long-standing puzzle on the origin of the disorder-free spin glass.
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.
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…
Some frustrated pyrochlore antiferromagnets, such as Y2Mo2O7, show a spin-freezing transition and magnetic irreversibilities below a temperature Tf similar to what is observed nonlinear magnetization measurements on Y2Mo2O7 that provide strong evidence that there is an underlying thermodynamic phase transition at Tf, which is characterized by critical exponents γ\approx 2.8 and β\approx 0.8. These values are typical of those found in random spin glasses, despite the fact that the level of random disorder in Y2Mo2O7 is immeasurably small.
We study the impact of quenched disorder (random exchange couplings or site dilution) on easy-plane pyrochlore antiferromagnets. In the clean system, order-by-disorder selects a magnetically ordered state from a classically degenerate manifold. In the presence of randomness, however, different orders can be chosen locally depending on details of the disorder configuration. Using a combination of analytical considerations and classical Monte-Carlo simulations, we argue that any long-range-ordered magnetic state is destroyed beyond a critical level of randomness where the system breaks into magn…
By means of neutron scattering techniques we have investigated the frustrated pyrochlore magnet Ho_2Sn_2O_7, which was found to show a ferromagnetic spin-ice behavior below T \simeq 1.4 K by susceptibility measurements. High-resolution powder-neutron-diffraction shows no detectable disorder of the lattice, which implies appearance of a random magnetic state solely by frustrated geometry, i.e., the corner sharing tetrahedra. Magnetic inelastic-scattering spectra show that Ho magnetic moments behave as an Ising spin system at low temperatures, and that the spin fluctuation has static character. …
The classical Heisenberg antiferromagnet on the pyrochlore lattice is macroscopically and continuously degenerate and the system remains disordered at all temperatures, even in the presence of weak dilution with nonmagnetic ions. We show that, in stark contrast, weak bond disorder lifts the ground state degeneracy in favour of locally collinear spin configurations. We present a proof that for a single tetrahedron the ground state is perfectly collinear but identify two mechanisms which preclude the establishment of a globally collinear state; one due to frustration and the other due to higher-…
Experimental evidence from measurements of the a.c. and d.c. susceptibility, and heat capacity data show that the pyrochlore structure oxide, Gd_2Ti_2O_7, exhibits short range order that starts developing at 30K, as well as long range magnetic order at $T\sim 1$K. The Curie-Weiss temperature, $θ_{CW}$ = -9.6K, is largely due to exchange interactions. Deviations from the Curie-Weiss law occur below $\sim$10K while magnetic heat capacity contributions are found at temperatures above 20K. A sharp maximum in the heat capacity at $T_c=0.97$K signals a transition to a long range ordered state, with …
We study the ground-state and low-energy properties of classical vector spin models with nearest-neighbour antiferromagnetic interactions on a class of geometrically frustrated lattices which includes the kagome and pyrochlore lattices. We explore the behaviour of these magnets that results from their large ground-state degeneracies, emphasising universal features and systematic differences between individual models. We investigate the circumstances under which thermal fluctuations select a particular subset of the ground states, and find that this happens only for the models with the smallest…
The magnetothermodynamics of strongly frustrated classical Heisenberg antiferromagnets on kagome, garnet, and pyrochlore lattices is examined. The field induced adiabatic temperature change (dT/dH)_S is significantly larger for such systems compared to ordinary non-frustrated magnets and also exceeds the cooling rate of an ideal paramagnet in a wide range of fields. An enhancement of the magnetocaloric effect is related to presence of a macroscopic number of soft modes in frustrated magnets below the saturation field. Theoretical predictions are confirmed with extensive Monte Carlo simulations…
A frustrated system is one whose symmetry precludes the possibility that every pairwise interaction (``bond'') in the system can be satisfied at the same time. Such systems are common in all areas of physical and biological science. In the most extreme cases they can have a disordered ground state with ``macroscopic'' degeneracy, that is, one that comprises a huge number of equivalent states of the same energy. Pauling's description of the low temperature proton disorder in water ice was perhaps the first recognition of this phenomenon, and remains the paradigm. In recent years a new class of …
The magnetic insulator Gd2Sn2O7 is one of many geometrically frustrated magnetic materials known to exhibit a nonzero muon spin polarization relaxation rate, $λ(T)$, down to the lowest temperature (T) studied. Such behaviour is typically interpreted as a significant level of persisting spin dynamics (PSD) of the host material. In the case of Gd2Sn2O7, such PSD comes as a surprise since magnetic specific heat measurements suggest conventional gapped magnons, which would naively lead to an exponentially vanishing $λ(T)$ as $T \rightarrow 0$. In contrast to most materials that display PSD, the or…
Within the past 20 years or so, there has occurred an explosion of interest in the magnetic behavior of pyrochlore oxides of the type $A_{2}^{3+}$$B_{2}^{4+}$O$_{7}$ where $A$ is a rare-earth ion and $B$ is usually a transition metal. Both the $A$ and $B$ sites form a network of corner-sharing tetrahedra which is the quintessential framework for a geometrically frustrated magnet. In these systems the natural tendency to form long range ordered ground states in accord with the Third Law is frustrated, resulting in some novel short range ordered alternatives such as spin glasses, spin ices and s…
Recent elastic and inelastic neutron scattering studies of the highly frustrated pyrochlore antiferromagnet Tb2Ti2O7 have shown some very intriguing features that cannot be modeled by the local <111> classical Ising model, naively expected to describe this system at low temperatures. Using the random phase approximation to take into account fluctuations between the ground state doublet and the first excited doublet, we successfully describe the elastic neutron scattering pattern and dispersion relations in Tb2Ti2O7, semi-quantitatively consistent with experimental observations.
We consider magnon excitations in the spin-glass phase of geometrically frustrated antiferromagnets with weak exchange disorder, focussing on the nearest-neighbour pyrochlore-lattice Heisenberg model at large spin. The low-energy degrees of freedom in this system are represented by three copies of a U(1) emergent gauge field, related by global spin-rotation symmetry. We show that the Goldstone modes associated with spin-glass order are excitations of these gauge fields, and that the standard theory of Goldstone modes in Heisenberg spin glasses (due to Halperin and Saslow) must be modified in t…
The spin-1/2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram. Besides hosting several ordered phases, the model is debated to possess a spin-liquid ground state when only nearest-neighbor antiferromagnetic interactions are present. Here, we contest this hypothesis with an extensive numerical investigation using both exact diagonalization and complementary variational techniques. Specifically, we employ a RVB-like many-variable Monte Carlo ansatz and convolutional neural network quantum states for (variational) calculati…
The model 2d kagome system (H3O)Fe3(SO4)2(OH)6 and the 3d pyrochlore Y2Mo2O7 are two well characterized examples of low-disordered frustrated antiferromagnets which rather then condensing into spin liquid have been found to undergo a freezing transition with spin glass-like properties. We explore more deeply the comparison of their properties with those of spin glasses, by the study of characteristic rejuvenation and memory effects in the non-stationary susceptibility. While the pyrochlore shows clear evidence for these non-trivial effects, implying temperature selective aging, that is charact…
We study spin correlations for the highly frustrated classical pyrochlore lattice antiferromagnets with O(N) symmetry in the limit T->0. We conjecture that a local constraint obeyed by the extensively degenerate ground states dictates a dipolar form for the asymptotic spin correlations, at all N $\ne$ 2 for which the system is paramagnetic down to T=0. We verify this conjecture in the cases N=1 and N=3 by simulations and to all orders in the 1/N expansion about the solvable N=infinity limit. Remarkably, the N=infinity formulae are an excellent fit, at all distances, to the correlators at N=3 a…
In this paper we study the 3d frustrated lattice gas model in the annealed version, where the disorder is allowed to evolve in time with a suitable kinetic constraint. Although the model does not exhibit any thermodynamic transition it shows a diverging peak at some characteristic time in the dynamical non-linear susceptibility, similar to the results on the p-spin model in mean field and Lennard-Jones mixture recently found by Donati et al. [cond-mat/9905433]. Comparing these results to those obtained in the model with quenched interactions, we conclude that the critical behavior of the dynam…
