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Motivated by puzzling aspects of spin-glass behavior reported in frustratedmagnetic materials, we theoretically investigate effects of magnetoelasticcoupling in geometrically frustrated classical spin models. In particular, weconsider bond-disordered Heisenberg antiferromagnets on a pyrochlore latticecoupled to local lattice distortions. By integrating out the lattice degree offreedom, we derive an effective spin-only model, the bilinear-biquadratic modelwith bond disorder, which is analyzed by classical Monte Carlo simulations.First, we discuss the phase diagrams as well as thermodynamic and magneticproperties. We show that the spin-glass transition temperature is largelyenhanced by the spin-lattice coupling $b$ in the weakly disordered regime. Thisenhancement is ascribed to the suppression of thermal fluctuations insemidiscrete degenerate manifold formed in the presence of the spin-latticecoupling. We also find that, as increasing the strength of disorder, the systemshows a concomitant transition of the nematic order and spin glass at atemperature determined by $b$, being almost independent of bond disorder.Although further-neighbor exchange interactions originating in the cooperativelattice distortions result in the spin-lattice order in the weakly disorderedregime, the concomitant transition remains robust. We investigate the nature ofthe concomitant transition by analyzing the hysteresis of the magneticsusceptibility, the nonlinear susceptibility, and the specific heat.Furthermore, we discuss linear and nonlinear magnetic susceptibilities in thehigh-temperature paramagnetic phase as well as single-spin flip dynamics in thenematic phase. All these results are discussed in comparison with experimentsfor typical pyrochlore magnets, such as Y2Mo2O7 and ZnCr2O4.

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