Chirality in new dimensions: magnetic enantiomorphs

We discuss a new class of magnetic systems, chiral magnetic crystals [1]. One speaks of chirality when a system exists in two versions (enantiomorphs) that cannot be superposed upon each other by proper (pure) rotations C. Ordinarily, this is tantamount to the case that the enantiomorphs are "space mirror" images of each other, i.e., the enantiomorphs are mapped onto each other by improper rotations iC, where i denotes space inversion. We call this case electrochirality because it arises from electric multipolar order. Electrochiral systems are invariant under "time mirror" images θC that combine rotations C with time inversion θ. By treating space inversion i, time inversion θ, and their combination iθ on the same footing, we identify magnetochirality and antimagnetochirality as new categories of chirality characterized by the existence of two distinct enantiomorphs. Each of these categories shows a distinct behavior under space mirrors iC, time mirros θC, and "space-time mirrors" iθC. In multichiral systems, all these inversion symmetries are absent so that these systems have four distinct enantiomorphs. The new forms of chirality identified here require magnetic multipole order; they are realized in magnetic crystals. More specifically it is the interplay of different electric and magnetic multipole densities that gives rise to the different categories of chirality; and we show that a new quantitative theory of electric and magnetic multipole densities in crystals [2] also provides quantitative measures of chirality. The spin-dependent electronic band structure in these materials directly reflects the distinct forms of chirality. We discuss material examples and experimental signatures. [1] arxiv:2405.20940. [2] arxiv:2509.17278.