Unveiling ferroelectric and altermagnetic coexistence in multiferroic HfMnO₃ perovskite

Multiferroic materials, which simultaneously exhibit electric and magnetic ordering, have garnered increasing attention due to their potential to revolutionize next-generation spintronic, memory, and multifunctional devices. Their unique ability to couple electric polarization and magnetic states offers low-power operation, electric field control of magnetism, and enhanced device scalability. Among these, altermagnetic multiferroics are particularly promising for enabling spin-polarized transport without stray fields. In this context, we have systematically investigated the structural, electronic, ferroelectric, and optical properties of the trigonal R3c-phase HfMnO₃ using first-principles density functional theory. The compound is found to be thermodynamically and dynamically stable, with a Goldschmidt tolerance factor of 0.88 supporting a distorted perovskite framework. The spin-resolved band structure revealed energy-dependent spin splitting without net magnetization, which is characteristic of altermagnetic behavior. Furthermore, our Berry phase calculations predict a robust spontaneous polarization of approximately 104 μC cm^-2 along the [111] direction, positioning HfMnO₃ as a strong ferroelectric candidate. Remarkably, the polarization-switched state retains both dynamic and electronic stability while preserving the altermagnetic signatures, confirming the multiferroic nature of the material. Optical analyses show high UV absorption, a notable refractive index, and plasmonic features above 7.5 eV, suggesting potential applications in optoelectronics and UV photodetectors. These findings establish HfMnO₃ as a promising altermagnetic multiferroic oxide for multifunctional applications in spintronic and optoelectronic technologies.