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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, which is analyzed by classical Monte Carlo simulations. First, we discuss the phase diagrams as well as thermodynamic and magnetic properties. We show that the spin-glass transition temperature is largely enhanced by the spin-lattice coupling $b$ in the weakly disordered regime. 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, as increasing the strength of disorder, the system shows a concomitant transition of the nematic order and spin glass at a temperature determined by $b$, being almost independent of bond disorder. Although further-neighbor exchange interactions originating in the cooperative lattice distortions result in the spin-lattice order in the weakly disordered regime, the concomitant transition remains robust. We investigate the nature of the concomitant transition by analyzing the hysteresis of the magnetic susceptibility, the nonlinear susceptibility, and the specific heat. Furthermore, we discuss linear and nonlinear magnetic susceptibilities in the high-temperature paramagnetic phase as well as single-spin flip dynamics in the nematic phase. All these results are discussed in comparison with experiments for typical pyrochlore magnets, such as Y2Mo2O7 and ZnCr2O4.