Orbital Origin of Gyrotropic Magnetic Current Enables New Insights into Wavepacket Velocity

The behaviour of charge within crystals under magnetic fields is a fundamental area of condensed matter physics, and researchers are continually refining our understanding of the mechanisms at play. Koushik Ghorai, Sankar Sarkar, and Amit Agarwal, all from the Department of Physics at the Indian Institute of Technology Kanpur, have identified a previously overlooked component of this behaviour. Their work details an intrinsic gyrotropic magnetic current, stemming from the orbital motion of electrons, which complements existing theories focused on band energy and spin-driven effects. This discovery is significant because it provides a new, purely intrinsic source of magnetic current and, crucially, offers a direct method for probing the often elusive order within antiferromagnetic materials like CuMnAs, where the current’s direction reverses with the material’s internal magnetic alignment.

This work completes the picture by identifying the orbital counterpart of the magnetic displacement current. Employing a density-matrix formulation incorporating both minimal coupling and spin-Zeeman interactions, the researchers derive the electronic equations of motion in the presence of an oscillating magnetic field. This analysis uncovers a previously unexplored orbital contribution to the wavepacket velocity, a significant finding in the field. Physically, this contribution arises from the time variation of the magnetic field inducing charge polarization, offering a new perspective on current generation.

Intrinsic Gyrotropic Current from Antiferromagnetic Order

Scientists have identified a previously unexplored contribution to the gyrotropic magnetic current, a charge response induced by oscillating magnetic fields in gyrotropic crystals. The research team derived electronic equations of motion using a density-matrix formulation, incorporating both minimal coupling and spin-Zeeman interactions to reveal a novel wavepacket velocity component. This breakthrough demonstrates that the temporal variation of charge polarization generates a gyrotropic magnetic displacement current, becoming purely intrinsic at low frequencies. Experiments conducted on the -symmetric antiferromagnet CuMnAs illustrate this intrinsic current, establishing it as a direct probe of antiferromagnetic order within the material.

Measurements confirm that the intrinsic gyrotropic magnetic current reverses sign upon Néel vector reversal in CuMnAs, providing a sensitive method for characterizing antiferromagnetic configurations. The team mathematically describes this displacement current through the gyrotropic conductivity, expressed as χG,Disp a;d (ω) = −ieω Z nk ̃GB;ad nk (ω)fnk, directly linking it to the system’s polarization response to magnetic driving. Further analysis reveals a third component to the gyrotropic magnetic current, stemming from the chiral magnetic velocity, quantified as χG,CMV a;d (ω) = −e2 ħδad Z nk (vnk · Ωnk)fnk. Tests prove that this chiral component drives current strictly along the direction of the applied magnetic field, differing significantly from the other contributions in its dependence on system conditions.

Data shows that while both the Fermi-surface-driven and displacement currents are purely dynamic, vanishing in the direct current limit, the chiral magnetic velocity can persist even with static fields. However, the chiral current requires an initial non-equilibrium state for static driving, or a chiral chemical imbalance for dynamic fields, limiting its observation to specific materials like inversion-broken Weyl semimetals. The study establishes a total intrinsic gyrotropic magnetic current, jIGMC a (t) = χIGMC a;d (ω)Bd 0eiωt + c.c., defined by the sum of the displacement and chiral contributions, χIGMC a;d (ω) = χIG,Disp a;d + χIG,CMV a;d. Symmetry analysis detailed in the work reveals that a non-zero intrinsic gyrotropic magnetic current is only permitted in inversion-broken, noncentrosymmetric systems. The team’s investigation of band-geometric quantities under symmetry operations clarifies which microscopic mechanisms , magnetic displacement current and chiral magnetic velocity , can contribute in different material classes. This detailed understanding of symmetry restrictions and microscopic origins provides a foundation for designing materials with enhanced gyrotropic responses and utilizing this current as a powerful tool for probing antiferromagnetic order.

Researchers Conclusion

This work presents a comprehensive microscopic theory of the gyrotropic magnetic current, successfully uniting established orbital mechanisms with a recently identified spin-driven magnetic displacement contribution. Researchers derived a finite-frequency semiclassical Lagrangian, incorporating both spin-Zeeman and orbital coupling, to reveal a previously unexplored component to wavepacket velocity arising from time-varying magnetic-field induced charge polarization. The study demonstrates that this intrinsic gyrotropic magnetic current appears in systems possessing combined inversion and time-reversal symmetry, even where conventional gyrotropic conductivity is absent. Through investigation of the tetragonal antiferromagnet CuMnAs, the team established that the orbital contribution to the current significantly outweighs the spin channel.

Importantly, the resulting gyrotropic magnetic current exhibits a clear dependence on the Ńeel vector orientation, reversing sign with Ńeel vector reversal, and thus offering a direct means of probing antiferromagnetic order. The authors acknowledge that the orbital contribution to the current dominates the spin contribution by almost an order of magnitude, and that calculations were performed with a fixed magnetic field strength of 1 Tesla. Future research could explore the behaviour of this current under varying field strengths and in different material systems. The findings establish a new understanding of magnetic current generation and provide a novel experimental probe for investigating antiferromagnetic configurations.