[Paper Review] Emerging research landscape of altermagnetism

Libor Šmejkal, Jairo Sinova+1 more|arXiv (Cornell University)|Apr 22, 2022

Magnetic and transport properties of perovskites and related materials45 citations

TL;DR

This Perspective introduces altermagnetism, a third magnetic phase with compensated antiparallel order and momentum-space spin splitting, and surveys its symmetry foundations, material candidates, and potential impact across condensed-matter physics.

ABSTRACT

Magnetism is one of the largest, most fundamental, and technologically most relevant fields of condensed-matter physics. Traditionally, two basic magnetic phases have been considered -- ferromagnetism and antiferromagnetism. The breaking of the time-reversal symmetry and spin splitting of the electronic states by the magnetization in ferromagnets underpins a range of macroscopic responses in this extensively explored and exploited type of magnets. By comparison, antiferromagnets have vanishing net magnetization. This Perspective reflects on recent observations of materials hosting an intriguing ferromagnetic-antiferromagnetic dichotomy, in which spin-split spectra and macroscopic observables, akin to ferromagnets, are accompanied by antiparallel magnetic order with vanishing magnetization, typical of antiferromagnets. An unconventional non-relativistic symmetry-group formalism offers a resolution of this apparent contradiction by delimiting a third basic magnetic phase, dubbed altermagnetism. Our Perspective starts with an overview of the still emerging unique phenomenology of the phase, and of the wide array of altermagnetic material candidates. In the main part of the article, we illustrate how altermagnetism can enrich our understanding of overarching condensed-matter physics concepts, and have impact on prominent condensed-matter research areas.

Motivation & Objective

• Summarize the emergence and phenomenology of altermagnetism as a distinct magnetic phase beyond ferromagnetism and antiferromagnetism.
• Outline the non-relativistic spin-group symmetry framework that defines altermagnetism and protects spin-split band features.
• Identify material candidates and ab initio evidence supporting altermagnetic spin splitting.
• Discuss connections to key condensed-matter concepts (Kramers theorem, Berry phase, quasiparticles) and implications for research areas like spintronics and superconductivity.

Proposed method

• Describe non-relativistic spin-group symmetry as a generalization of relativistic magnetic groups.
• Explain how opposite-spin sublattice transformations connected by rotation yield altermagnetic order.
• Present identification rules for recognizing altermagnets in crystal structures and ab initio data.
• Survey predicted and identified altermagnetic materials across dimensionalities and conduction types.

Experimental results

Research questions

• RQ1 What distinguishes altermagnetism from ferromagnetism and conventional antiferromagnetism in terms of spin splitting and symmetry?
• RQ2 How do non-relativistic spin-group symmetries protect momentum-space spin splitting while maintaining zero net magnetization?
• RQ3 What are the characteristic material candidates and their predicted or observed spin-splitting magnitudes?
• RQ4 How can altermagnetism influence broader condensed-matter physics concepts and applied fields like spintronics and thermoelectrics?

Key findings

• Altermagnetism exhibits spin-split, time-reversal symmetry broken band structures with zero net magnetization in materials with compensated antiparallel order.
• Spin splitting in altermagnets is strongly momentum-dependent and can reach magnitudes comparable to ferromagnets in parts of the Brillouin zone (e.g., ~1 eV in RuO2).
• Non-relativistic spin-group symmetries provide a robust framework to classify and describe altermagnetic phases, distinguishing them from ferromagnets and conventional antiferromagnets.
• Spin-up and spin-down Fermi-surface sectors are anisotropic but equally populated, with spin degeneracies preserved along certain high-symmetry lines or surfaces.
• Ab initio calculations show altermagnetic spin splitting persists without strong dependence on relativistic spin-orbit coupling and survives correlation effects in several materials.
• A variety of material candidates spanning 2D/3D, insulators to metals, and diverse chemistries are predicted to host altermagnetism, including RuO2, Mn5Si3, CrSb, MnTe, La2CuO4, and others (Table 3).