Dielectric relaxations of charge-ordered Ln1.5Sr0.5NiO4 (Ln=La and Nd) ceramics were investigated over a broad temperature range. The giant dielectric constant (over 70000) with a low dielectric loss of 0.1 was determined at high frequencies (up to 5 MHz) over a broad temperature range. There are two dielectric relaxations in the vicinity of charge ordering temperatures. The thermal activated small polaronic hopping between two charge ordering temperatures should contribute to the giant dielectric response in the present ceramics. Compared to other giant dielectric constant materials, the present materials have the notable advantage for high frequency applications.

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