Piezomagnetism-driven magnetoelectric coupling in altermagnetic multiferroic K 3 Cr 2 F 7

Ferroelectric control of altermagnetism in momentum space has been studied widely, while the control of magnetism in real space of altermagnets is still rare. We present a design rule to identify multiferroicity in $n=2$ Ruddlesden-Popper halides. Our results show that a Jahn-Teller distortion can cooperate with oxygen octahedral rotations to break inversion symmetry, which we demonstrate in ${\mathrm{K}}₃\mathrm{C}{\mathrm{r}}₂{\mathrm{F}}₇$ and cation-ordered ${\mathrm{KAg}}₂{\mathrm{Cu}}₂{\mathrm{Cl}}₇$, and leads to a ferrielectric-to-ferroelectric phase transition in ${\mathrm{K}}₃\mathrm{C}{\mathrm{r}}₂{\mathrm{F}}₇$. Altermagnetic spin order in the ferrielectric phase of ${\mathrm{K}}₃\mathrm{C}{\mathrm{r}}₂{\mathrm{F}}₇$ transforms into a conventional antiferromagnetic order in the ferroelectric phase, at which strain/pressure engineered sizable changes of weak ferromagnetism can occur. Our study is not only conducive to realize strong magnetoelectric coupling in multiferroics but also reveals more functionalities in altermagnetic materials.