A linear magnetoelectric (ME) response emerges when both space inversion and time-reversal symmetries are broken, enabling a symmetry-allowed coupling between electric and magnetic fields. In this work, a substantial linear ME coupling of up to 12%, accompanied by an unconventional glassy behavior in the dynamic ME response, is observed in the cluster-glass (CG) compound ${\mathrm{CuMn}}_2{\mathrm{O}}_4$. The CG state is identified through the frequency-dependent behavior of ac susceptibility, the memory effect in the relaxation of dc magnetization, and neutron depolarization measurements. Neutron diffraction confirms the absence of long-range magnetic order and reveals a structural transition to a polar $I{4}_{1}md$ phase from the high-temperature centrosymmetric $I{4}_1/amd$ phase, which is supported by the synchrotron x-ray diffraction as well as x-ray absorption spectroscopy. The emergence of this polar structure leads to ferroelectric ordering at the onset of the structural and CG transition. The concurrent observation of a static linear ME response and a glassy ME response in the CG state raises a fundamental question regarding the symmetry-driven ME coupling in disordered magnetic systems.

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• Magnetism
• Magnetoelectric effect
• Manganites
• Dielectric constant measurements
• Magnetization measurements
• Neutron diffraction
• X-ray absorption spectroscopy