Elasto-Hall conductivity and the anomalous Hall effect in altermagnets

Abstract

Altermagnets break time-reversal symmetry, preserve the crystal translation invariance, and have a spin density with $d$-wave, $g$-wave, etc. momentum dependencies which do not contribute to the magnetization. When an $s$-wave spin-density contribution cannot be excluded by symmetry a small magnetization and an anomalous Hall effect (AHE) emerge. However, for so-called "pure" altermagnets, where the $s$-wave component is symmetry forbidden even in the presence of SOC, both the zero-field magnetization and the AHE vanish. We show that altermagnets generally exhibit a non-zero elasto-Hall-conductivity, by which application of strain leads to a non-zero AHE. For pure altermagnets it is the only contribution to the AHE. This elasto-Hall-conductivity is caused by strain coupling to the Berry curvature quadrupole that characterizes altermagnets and allows for the determination of the altermagnetic order using transport measurements that are linear in the electrical field. We further show that the emergence of a non-zero magnetization in the presence of strain arises from a different response function: piezomagnetism. While this magnetization gives rise to an additional contribution to the elasto-Hall conductivity, the corresponding Berry curvature is qualitatively different from the distorted Berry curvature quadrupole originating from the altermagnetic order parameter. This insight also helps to disentangle AHE and weak ferromagnetism for systems with symmetry-allowed $s$-wave contribution. Quantitatively, the elasto-Hall conductivity is particularly pronounced for systems with a Dirac spectrum in the altermagnetic state. The same mechanism gives rise to anomalous elasto-thermal Hall, Nernst, and Ettinghausen effects.

17 pages, 12 figures

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Cited by in corpus (16)

• Tuning of altermagnetism by strain
• Hybrid d/p-wave altermagnetism in Ca${}_3$Ru${}_2$O${}_7$ and strain-controlled spin splitting
• Spin and pair density waves in 2D altermagnetic metals
• Relativistic Spin-momentum locking in altermagnets
• Activation of anomalous Hall effect and orbital magnetization by domain walls in altermagnets
• Observation of mirror-odd and mirror-even spin texture in ultrathin epitaxially strained RuO2 films
• Magnetic-field-tuned randomness in inhomogeneous altermagnets
• Zeeman-type spin splittings in strained d-wave altermagnets
• Approximate half-integer quantization in anomalous planar transport in $d$-wave altermagnets
• Multipole analysis of spin currents in altermagnetic MnTe
• Spin-resolved quasiparticle interference patterns on altermagnets via non-spin-resolved scanning tunneling microscopy
• Formulation of spin Nernst effect for spin-nonconserving insulating magnets
• Strain-tunable anomalous Hall effect in hexagonal MnTe
• Spontaneous emergence of altermagnetism in the single-orbital extended Hubbard model
• Superconducting States and Intertwined Orders in Metallic Altermagnets
• Electric field controlled second-order anomalous Hall effect in altermagnets