Coupling Chirality, Polar Order, and Altermagnetic Spin Splitting in a Hybrid Manganese Chloride

Abstract: Hybrid manganese halides enable the coexistence of molecular chirality, polar order, and magnetic exchange within a single lattice. Here, we combine first-principles calculations with spin-space-group analysis to investigate the synthesized enantiomeric pair [(R)/(S)-MPA]2MnCl4(H2O). We predict that its compensated magnetic state hosts altermagnetic spin splitting in the nonrelativistic limit, and that the coupled chiral, polar, and magnetic degrees of freedom define a symmetry-related manifold. From this manifold, we derive simple sign rules for the electronic and magneto-optical response: reversing both chirality and polarity, or reversing the magnetic domain alone, inverts the spin splitting throughout the Brillouin zone, whereas reversing chirality alone or polarity alone changes the spin-splitting sign only in symmetry-selected regions. With spin-orbit coupling, reversing chirality or magnetic order flips the Kerr rotation angle, while changing the polar variant leaves it unchanged. These results reveal a chemically accessible route to translate molecular handedness into symmetry-controlled spin splitting and magneto-optical readout in hybrid manganese halides. Critically, we show that the sign and momentum pattern of the splitting are governed by the interplay of the chiral, polar, and magnetic degrees of freedom. This interplay opens the possibility to control the spin splitting through a judicious design of the organic cations, by modulating their chirality and polarity.