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[en] We report on the Moessbauer spectra and magnetization properties of single-crystalline (BiFeO3)x-(BaTiO3)1-x solid solution nanostructures in the form of nanocubes, measuring approximately 150 to 200 nm on a side, prepared by a molten salt solid-state reaction method in the compositional range wherein 0.5 (le) x (le) 1. Powder x-ray diffraction (XRD) and monochromatic synchrotron XRD studies indicate products of high purity, which undergo gradual, well-controlled structural transformations from rhombohedral to tetragonal structures with decreasing 'x.' For all solid solution products, room-temperature magnetization studies exhibit hysteretic behavior with remnant magnetization values of Mr (ge) 0.32 emu/g, indicating that the latent magnetization locked within the toroidal spin structure of BiFeO3 has been released. Room-temperature Moessbauer spectra show composition-dependent characteristics with decreasing magnetic hyperfine field values and increasing absorption linewidths due to a decrease in the magnetic exchange interaction strength with decreasing x. For the lowest x=0.5 composition studied, the Moessbauer spectra show paramagnetic behavior, indicating a Neel temperature for this composition below 300 K. However, room-temperature magnetization studies with applied fields of up to 50 kOe show hysteretic behavior for all compositions, including the x=0.5 composition, presumably due to field-induced ordering. Furthermore, hysteresis loops for all compositions exhibit smaller coercivities at 10 K than at 300 K, an observation that may suggest the presence of magnetoelectric coupling in these systems.