The dielectric constant of the Kagome staircase-like Co3V2O8 polycrystalline compound has been measured as function of temperature and magnetic field up to 14T. It is found that the application of an external magnetic field suppresses the anomaly for the dielectric constant beyond 6.1K. Furthermore, its magnetic field dependence reveals a negative magnetocapacitance which is proportional to the magnetic susceptibility, suggesting a common magnetostrictive origin for the magnetic field dependence of the two quantities. This result is very different from that obtained from the isostructural compound Ni3V2O8 that presents a peak in the dielectric constant at the incommensurate magnetic phase transition coupled to a sign change of the magnetocapacitance.
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