Recent years have seen a proliferation in investigations on Altermagnetism due to its exciting prospects both from an applications perspective and theoretical standpoint. Traditionally, altermagnets are distinguished from collinear antiferromagnets using the central concept of halving subgroups within the spin space group formalism. In this work, we propose the Fundamental Lemma of Altermagnetism (FLAM) deriving the exact conditions required for the existence of altermagnetic phase in a magnetic material on the basis of site-symmetry groups and halving subgroups for a given crystallographic space group. The spin group formalism further clubs ferrimagnetism with ferromagnetism since the same-spin and opposite-spin sublattices lose their meaning in the presence of multiple magnetic species. As a consequence of FLAM, we further propose a class of fully compensated ferrimagnets, termed as Alterferrimagnets (AFiMs), which can show alternating momentum-dependent spin-polarized non-relativistic electronic bands within the first Brillouin zone. We show that alterferrimagnetism is a generalization of traditional collinear altermagnetism where multiple magnetic species are allowed to coexist forming fully compensated magnetic-sublattices, each with individual up-spin and down-spin sublattices.
Comments
Chanchal K. Barman and Bishal Das contributed equally to this work. 38 pages (27 pages main, 11 pages supplement), 17 figures (11 figures main, 6 figures supplement), 2 tables (all in main)
Recent years have seen a proliferation in investigations on Altermagnetism due to its exciting prospects both from an applications perspective and theoretical standpoint. Traditionally, altermagnets are distinguished from collinear antiferromagnets using the central concept of halving subgroups within the spin space group formalism. In this work, we propose the Fundamental Lemma of Altermagnetism (FLAM) deriving the exact conditions required for the existence of altermagnetic phase in a magnetic material on the basis of site-symmetry groups and halving subgroups for a given crystallographic space group. The spin group formalism further clubs ferrimagnetism with ferromagnetism since the same-spin and opposite-spin sublattices lose their meaning in the presence of multiple magnetic species. As a consequence of FLAM, we further propose a class of fully compensated ferrimagnets, termed as Alterferrimagnets (AFiMs), which can show alternating momentum-dependent spin-polarized non-relativistic electronic bands within the first Brillouin zone. We show that alterferrimagnetism is a generalization of traditional collinear altermagnetism where multiple magnetic species are allowed to coexist forming fully compensated magnetic-sublattices, each with individual up-spin and down-spin sublattices.
Altermagnetism represents a type of collinear magnetism, that is in some aspects distinct from ferromagnetism and from conventional antiferromagnetism. In contrast to the latter, sublattices of opposite spin are related by spatial rotations and not only by translations and inversions. As a result, altermagnets have spin-split bands leading to unique experimental signatures. Here, we show theoretically how a d-wave altermagnetic phase can be realized with ultracold fermionic atoms in optical lattices. We propose an altermagnetic Hubbard model with anisotropic next-nearest neighbor hopping and obtain the Hartree-Fock phase diagram. The altermagnetic phase separates in a metallic and an insulating phase and is robust over a large parameter regime. We show that one of the defining characteristics of altermagnetism, the anisotropic spin transport, can be probed with trap-expansion experiments.
The behavior of spin quantum in k-space is key to identifying altermagnets (AMs) as the third kind of fundamental collinear magnetism. In contrast, non-collinear magnets,though abundant in nature,lack well-defined spin quantum numbers, and the resulting spin textures are often highly complex, which limits their potential for next-generation spintronic applications. Here we propose hyperspin, which lives in a higher-dimensional space, to address these drawbacks. Through analyzing the commutation relations between spin and Hamiltonian for a class of non-collinear magnets, we reveal it is a hyperspin, rather than the usual spin, that commutes with Hamiltonian. Unexpectedly, these non-collinear magnets should also show collinear spin-split bands in k-space like collinear AMs. We therefore classify such non-collinear magnets as hyperspin altermagnets (HAMs), as opposed to the usual collinear AMs. Our theory elucidates the fundamental physics of AMs and HAMs and provides a framework for exploring the wide range of non-collinear magnets that may possess other kinds of conserved quantities.
Altermagnets, a newly classified type of collinear magnet, exhibit zero magnetization, akin to antiferromagnets, but have spin-split electronic bands, akin to ferromagnets. Their low-energy excitations are predicted to be magnons, but with linear energy-momentum dispersion, typical of antiferromagnets, and additional chiral splitting analogous to those of electronic bands. However, such predictions are made using linear spin wave theory, which considers infinitely long-lived noninteracting magnons. This study employs nonperturbative quantum many-body calculations, via tensor network algorithms, to find how a chiral magnon will acquire finite lifetime and how the bands will shift due to magnon-magnon interaction. Such corrections to noninteracting magnon bands could be detected by Raman scattering experiments, for which the recipe is provided. Although the same interaction effects are often described in magnetism by nonlinearity of the Landau-Lifshitz-Gilbert equation, direct comparison using altermagnetic magnons as the testbed, shows how such classical methods cannot fully reproduce the results of quantum many-body calculations.
We study quantum ferrimagnets in one, two, and three dimensions by using a variety of methods and approximations. These include: (i) a treatment based on the spin coherent state path-integral formulation of quantum ferrimagnets by taking into account the leading order quantum and thermal fluctuations (ii) a field-theoretical (non-linear σ-model type) formulation of the special case of one-dimensional quantum ferrimagnets at zero temperature (iii) an effective description in terms of dimers and quantum rotors, and (iv) a quantum renormalization group study of ferrimagnetic Heisenberg chains. Some of the formalism discussed here can be used for a unified treatment of both ferromagnets and antiferromagnets in the semiclassical limit. We show that the low (high) energy effective Hamiltonian of a (S_1, S_2) Heisenberg ferrimagnet is a ferromagnetic (antiferromagnetic) Heisenberg model. We also study the phase diagram of quantum ferrimagnets in the presence of an external magnetic field h (hc1<h<hc2) and show that the low- and the high-field phases correspond respectively to the classical Néel and the fully polarized ferromagnetic states. We also calculate the transition temperature for the Berezinskii-Kosterlitz-Thouless phase transition in the special case of two-dimensional quantum ferrimagnets.
Altermagnetism, known for its non-relativistic spin-split band structures with yet compensated moments, is being intensively investigated. Discovering new altermagnetic materials with characteristics suitable for practical use remains an important ongoing task. Recently a metallic room-temperature altermagnet candidate Rb1-xV2Te2O with a layered structure and d-wave spin symmetry has been reported based on experimental results from the spin-resolved photoemission spectroscopy and scanning tunnelling microscopy/spectroscopy (STM/STS) measurements. Here we report neutron powder diffraction (NPD) investigations on the magnetic structure of Rb1-xV2Te2O, which shows a G-type antiferromagnetic structure below the transition temperature of 337 K. The result is different from the original theoretical expectation, which might lead to new insights on the physics of this altermagnet candidate.
Altermagnets are a new class of symmetry-compensated magnets with large spin splittings. Here, we show that the notion of altermagnetism extends beyond the realm of Landau-type order: we study exactly solvable Z_{2} quantum spin(-orbital) liquids (QSLs), which simultaneously support magnetic long-range order as well as fractionalization and Z_{2} topological order. Our symmetry analysis reveals that in this model three distinct types of "fractionalized altermagnets (AM^{*})" emerge, which can be distinguished by their residual symmetries. Importantly, the fractionalized excitations of these states carry an emergent Z_{2} gauge charge, which implies that they transform projectively under symmetry operations. Consequently, we show that "altermagnetic spin splittings" are now encoded in a momentum-dependent particle-hole asymmetry of the fermionic parton bands. We discuss consequences for experimental observables such as dynamical spin structure factors and (nonlinear) thermal and spin transport.