[논문 리뷰] Altermagnets and beyond: Nodal magnetically-ordered phases

T. Jungwirth, Rafael M. Fernandes외 2명|arXiv (Cornell University)|2024. 09. 16.

Magnetic and transport properties of perovskites and related materials인용 수 5

한 줄 요약

알터마그넷이 nodal even-parity-wave magnetic ordering을 갖는 포괄적 검토로, 대칭 기반 식별, 물질 실현, 전자구조 서명, relativistic/topological 효과 및 비정렬 스핀 밀도에 대한 확장을 자세히 다룬다.

ABSTRACT

The recent discovery of altermagnets has opened new perspectives in the field of ordered phases in condensed matter. In strongly-correlated superfluids, the nodal p-wave and d-wave ordered phases of $^{3}$He and cuprates play a prominent role in physics for their rich phenomenology of the symmetry-breaking order parameters. While the p-wave and d-wave superfluids have been extensively studied over the past half a century, material realizations of their magnetic counterparts have remained elusive for many decades. This is resolved in altermagnets, whose recent discovery was driven by research in the field of spintronics towards highly scalable information technologies. Altermagnets feature d, g or i-wave magnetic ordering, with a characteristic alternation of spin polarization and spin-degenerate nodes. Here we review how altermagnetism can be identified from symmetries of collinear spin densities in crystal lattices, and can be realized at normal conditions in a broad family of insulating and conducting materials. We highlight salient electronic-structure signatures of the altermagnetic ordering, discuss extraordinary relativistic and topological phenomena that emerge in their band structures, and comment on strong-correlation effects. We then extend the discussion to non-collinear spin densities in crystals, including the prediction of p-wave magnets, and conclude with a brief summary of the reviewed physical properties of the nodal magnetically-ordered phases.

연구 동기 및 목표

• ALtermagnetism를 nodal spin-polarized electronic structure와 vanishing net magnetization을 갖는 독립된 대칭 클래스로 연구 의의를 제시한다.
• spin-대칭군이 collinear magnet을 ferromagnets, antiferromagnets, and altermagnets로 분류하는 방식을 설명한다.
• altermagnetic ordering의 물질 실현을 가능하게 하는 밴드-구조 특성 및 원리들을 요약한다.
• Relativistic spin-orbit coupling, topology, and strong correlations이 altermagnetic bands에 미치는 영향을 논의한다.
• 비정렬(spin) 밀도에 대한 논의를 확장하고 p-wave magnetic ordering를 예측한다.

제안 방법

• collinear magnets에 대한 3-way spin-group symmetry classification을 설명하고, altermagnets의 non-trivial spin Laue groups를 강조한다.
• even-parity l>0 magnetic order (d, g, i waves)가 crystals의 spin densities에서 어떻게 유도되고 momentum-space band structures에 어떻게 반영되는지 설명한다.
• collinear spin densities의 대칭과 normal conditions에서의 금속 및 절연 물질에서 altermagnetism를 식별하고 실현하는 방법을 요약한다.
• altermagnetic band structures에 대한 relativistic spin-orbit coupling의 영향과 가능의 topological phenomena를 개관한다.
• material predictions 및 실험 검증을 지원하는 계산(DFT) 및 분광학적 접근법을 논의한다.]
• research_questions: ["What symmetry principles distinguish altermagnets from ferromagnets and antiferromagnets in collinear spin systems?","How can d-, g-, and i-wave altermagnetic order manifest in real materials and what are their band-structure signatures?","What roles do spin-density symmetries and crystal potentials play in enabling altermagnetic phases under ambient conditions?","How does spin-orbit coupling influence non-relativistic altermagnetic band structures and emergent topological phenomena?","Can the framework be extended to non-collinear spin densities to predict p-wave magnetic ordering?"]
• key_findings: [

Figure 1: Altermagnets and ferromagnets. a, Nodal altermagnetic ordering in the crystal space (top) and in the momentum-space energy iso-surfaces/Fermi surfaces (bottom). The cartoons illustrate a d-wave ordering. Spin-degenerate nodes are highlighted by black lines in the 2D cartoons. Arrows and co

실험 결과

연구 질문

• RQ1 What symmetry principles distinguish altermagnets from ferromagnets and antiferromagnets in collinear spin systems?
• RQ2 How can d-, g-, and i-wave altermagnetic order manifest in real materials and what are their band-structure signatures?
• RQ3 What roles do spin-density symmetries and crystal potentials play in enabling altermagnetic phases under ambient conditions?
• RQ4 How does spin-orbit coupling influence non-relativistic altermagnetic band structures and emergent topological phenomena?
• RQ5 Can the framework be extended to non-collinear spin densities to predict p-wave magnetic ordering?

주요 결과

• Altermagnets form a distinct symmetry class with nodal spin-polarized band structures and zero net magnetization.
• Nodal altermagnetic ordering features even-parity-wave spin densities (d, g, i) with spin-degenerate nodes and opposite-spin iso-surfaces.
• Relativistic spin-orbit coupling can lift spin degeneracy on nodal surfaces and produce large spin-polarization magnitudes and Berry-curvature effects.
• Experimental signatures include anomalous Hall and Nernst effects, dichroism measurements, and spin-resolved ARPES confirming spin textures and nodal features.
• Material candidates hosting altermagnetic order have been identified by symmetry analyses (spin Laue groups) and DFT, with realizations in MnTe, Mn5Si3, CrSb, RuO2, MnTe, FeSe, and MnTe-based systems, among others.
• Extensions to non-collinear spin densities predict p-wave magnetism and broaden the landscape beyond strictly collinear altermagnetic order

Figure 2: Nodal ordering in superfluids and magnets. Schematic comparison of the Cooper-pairing Fermi-liquid instabilities with p-wave and d-wave gap functions ( $\pm$ refers to the phase of the order parameter), their searched-for counterpart magnetic Pomeranchuk Fermi-liquid instabilities, and the