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For disordered Heisenberg systems with small single ion anisotropy, two spinglass transitions below the long range ordered phase transition temperature hasbeen predicted theoretically for compositions close to the percolationthreshold. Experimental verification of these predictions is stillcontroversial for conventional spin glasses. We show that multiferroic spinglass systems can provide a unique platform for verifying these theoreticalpredictions via a study of change in magnetoelastic and magnetoelectriccouplings, obtained from an analysis of diffraction data, at the spin glasstransition temperatures. Results of macroscopic and microscopic (x-ray andneutron scattering) measurements are presented on disordered BiFeO3, acanonical Heisenberg system with small single ion anisotropy, which revealappearance of two spin glass phases SG1 and SG2 in coexistence with the LROphase below the A-T and G-T lines. It is shown that the temperature dependenceof the integrated intensity of the antiferromagnetic peak shows dips withrespect to the Brillouin function behaviour around the SG1 and SG2 transitiontemperatures. The ferroelectric polarisation changes significantly at the twospin glass transition temperatures. These results, obtained using microscopictechniques, clearly demonstrate that the SG1 and SG2 transitions occur on thesame magnetic sublattice and are intrinsic to the system. We also construct aphase diagram showing all the magnetic phases in BF-xBT system. While ourresults on the two spin glass transitions support the theoretical predictions,it also raises several open questions which need to be addressed by revisitingthe existing theories of spin glass transitions by taking into account theeffect of magnetoelastic and magnetoelectric couplings as well aselectromagnons.

physical review. b./physical review. b

Evidence for two spin-glass transitions with magnetoelastic and  magnetoelectric couplings in the multiferroic  (Bi$_{1-x}$Ba$_x$)(Fe$_{1-x}$Ti$_x$)O$_3$ system