Altermagnetism in 6H perovskites

npj | quantum materials Article Published in partnership with Nanjing University https://doi.org/10.1038/s41535-025-00821-z Altermagnetism in 6H perovskites Check for updates 1234567890():,; 1234567890():,; Sergey V. Streltsov1,2 & Sang-Wook Cheong3 The combination of a centrosymmetric crystallographic structure with local structural alternations and collinear antiferromagnetism can lead to broken PT (Parity × Time-reversal) symmetry, resulting in altermagnets with non-relativistic spin-split bands. The 6H perovskites with composition A3BB’2O9 exhibit unique layered structural alternations and typically adopt an antiferromagnetic ground state. Here, we report the discovery that several 6H perovskites are indeed altermagnets exhibiting nonrelativistic spin-split bands. We also explore the possible presence of net magnetization due to spinorbit coupling in these materials, as well as the manifestation of giant piezomagnetism. Since the single crystals of 6H perovskites can be readily grown and cleavable, our findings provide a new avenue to study the cleaved atomically-flat surfaces of altermagnets with advanced experimental techniques such as spin-resolved scanning tunneling microscopy (STM) or spin-resolved angleresolved photoemission spectroscopy (ARPES) to explore their spin splitting nature. Perovskites are one of the most studied structural classes, encompassing not only the popular perovskite solar cells and the famous cuprate superconductors but also many other materials important for various applications. In so-called cubic perovskites, such as SrTiO3 or LaMnO3, transition metal ions are surrounded by ligand’s octahedra, forming a cubic or distorted cubic lattice where the octahedra share corners. Depending on the ionic radii of the A and B elements in the general formula ABX3, other types of packing can be realized1. In hexagonal perovskites, such as BaNiO3, AX3 layers form a hexagonal close-packed structure, and the BX6 octahedra share faces rather than corners. Both cubic and hexagonal perovskites demonstrate extraordinary physical properties such as magnetoresistance2, high dielectric constant3, unusual magnetic, charge, and orbital orders4, many of them were found to be not only ferroelectrics, but also multiferroics5,6, other perovskites turned out half-metals with record high Curie temperatures7. Very recently, a new notion of altermagnetism was introduced to characterize materials which exhibit ferromagnet behavior, but have zero net magnetization8–13. This class of magnetic materials demonstrate anomalous electronic and spin transport, Nernst and magneto-optical effects etc.13–15 Different perovskites have been suggested to be altermagnets: CaCrO316,17, LaTiO318, HgMnO319, (La,Ca)MnO320,21, and many others. However, the simplest ABX3 perovskites are a tip of iceberg and progress in chemistry resulted in synthesis of mixed structures, when layers of cubic perovskites are intertwined with one or few layers of hexagonal (H) perovskites. In this paper we discuss altermagnetism in some of these mixed perovskites, so-called 6H perovskites1,22,23 with general formula A3BB’2O9 and the unit cell (u.c.) consisting of 6 repeating layers as shown in Fig. 1. Magnetic ions can occupy B and B0 positions, both having octahedral coordination. Two B’O6 octahedra share their faces and form B’2O9 dimers. Both dimers and “isolated” B ions form their own triangular lattices. While the magnetic structure for most of 6H perovskites remains unsolved, we argue that many of them can be altermagnets. Detailed ab initio calculations for two of them show not only corresponding spin-split band structure, various magneto-optical effects, but also a giant piezomagnetic response, which makes a whole class of 6H perovskite interesting for further experimental and theoretical studies. Results Symmetry analyses There are three possible structures characterized by the hexagonal P63/ mmc, orthorhombic Cmcm, and monoclinic C2/c space groups, which describe A3BB’2O9 perovskites with B0 ions forming dimers (the hexagonal P63mc, where only half of the sites in dimers are occupied by transition metals, and the monoclinic P21/c structures without dimers are not considered in this study)1. There is no inversion center (I) connecting the magnetic B sites, but C2 rotation axes perpendicular to the c-axis (located at 1/4 and 3/4 of c for Cmcm and C2/c, and additionally at the origin and c/2 for P63/mmc). There is also a mirror plane, mz, for P63/mmc group; mz combined with time-reversal (T) guarantees vanishing total magnetization in the collinear case. This makes 6H perovskites altermagnetic if the two ab planes of magnetic B ions (at the origin and c/2) are antiferromagnetically ordered and the spins are (mostly) aligned along the c-axis. The same C2 rotation or mz mirror plane rather than inversion transforms B0 sites of the same dimer into each other. 1 Institute of Metal Physics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia. 2Department of theoretical physics and applied mathematics, Ural Federal University, Ekaterinburg, Russia. 3Keck Center for Quantum Magnetism and Department of Physics and Astronomy, Rutgers University, Piscataway, e-mail: NJ, USA. npj Quantum Materials | (2025)10:102 1 Article https://doi.org/10.1038/s41535-025-00821-z While there are many 6H perovskites with magnetic ions occupying B or B0 sites, and many of them show clear signatures of dominating antiferromagnetic (AFM) interactions, a detailed study of the ground-state magnetic structure has been performed for only 15 AFM 6H perovskites. Detailed lists of ferromagnetic, ferrimagnetic, antiferromagnetic 6H perovskites, as well as those that do not exhibit long-range magnetic order, being potential candidates for quantum spin-liquid behavior or showing thermal-induced magnetization, are presented in Tables S1–S3 of the supplemental materials (See Supplementary Information). Symmetry analysis by magnetic point groups (MPG) according to24 shows that 4 out of 15 AFM 6H perovskites appear to be altermagnets. Their properties are summarized in Table 1. There are two M-type altermagnets, Ba3CoIr2O9 and Ba3SrIr2O9, with broken time-reversal symmetry and ferromagnetic point groups, where one would expect non-vanishing magnetization due to orbital magnetism (spin-orbit coupling). In addition, timereversal symmetry is broken in Ba3NiRu2O9 and Ba3TbRu2O9, which must be S-type altermagnets with symmetric non-relativistic spin splitting. Next, we use density functional theory (DFT) calculations to verify these conclusions and study the implications of altermagnetism in one representative from each class. Fig. 1 | The crystal structure of 6H perovskites. Magnetic ions can occupy B positions to form triangular lattice and B0 constituting dimers, indexes numerate layers. For clarity a primitive unit cell (which is two times smaller than the crystallographic unit cell) is shown. The primitive cp (...truncated)