Effect of magnetoelastic coupling on spin-glass behavior in Heisenberg pyrochlore antiferromagnets with bond disorder

Motivated by puzzling aspects of spin-glass behavior reported in frustrated magnetic materials, we theoretically investigate effects of magnetoelastic coupling in geometrically frustrated classical spin models. In particular, we consider bond-disordered Heisenberg antiferromagnets on a pyrochlore lattice coupled to local lattice distortions. By integrating out the lattice degree of freedom, we derive an effective spin-only model, the bilinear-biquadratic model with bond disorder. The effective model is analyzed by classical Monte Carlo simulations using an extended loop algorithm. First, we discuss the phase diagrams in detail by showing the comprehensive Monte Carlo data for thermodynamic and magnetic properties. We show that the spin-glass transition temperature Tf is largely enhanced by the spin-lattice coupling b in the weakly disordered regime. By considering the limit of strong spin-lattice coupling, this enhancement is ascribed to the suppression of thermal fluctuations in semidiscrete degenerate manifold formed in the presence of the spin-lattice coupling. We also find that, by increasing the strength of disorder Δ, the system shows a concomitant transition of the nematic order and spin glass at a temperature determined by b, being almost independent of Δ. This is due to the fact that the spin-glass transition is triggered by the spin collinearity developed by the nematic order. Although further-neighbor exchange interactions originating in the cooperative lattice distortions result in spin-lattice order in the weakly disordered regime, the concomitant transition remains robust with Tf almost independent of Δ. We find that the magnetic susceptibility shows hysteresis between the field-cooled and zero-field-cooled data below Tf, and that the nonlinear susceptibility shows a negative divergence at the transition. These features are common to conventional spin-glass systems. Meanwhile, we find that the specific heat exhibits a broad peak at Tf, and that the Curie-Weiss temperature varies with Δ, even in the region where Tf is insensitive to Δ. In addition, we clarified that the concomitant transition remains robust against a substantial external magnetic field. These features are in clear contrast to the conventional spin-glass behavior. Furthermore, we show that the cubic susceptibility obeys a Curie-Weiss-type law and the estimated "Curie-Weiss" temperature gives a good measure of the spin-lattice coupling even in the presence of bond randomness. We also show, by studying single-spin-flip dynamics in the nematic phase, that the glassy spin dynamics may be observed at a rather high temperature in a realistic situation for weak disorder. All these results are discussed in comparison with experiments for typical pyrochlore magnets, such as Y2Mo2O7 and ZnCr2O4.