In gyrotropic crystals, an oscillating magnetic field induces a charge response known as the gyrotropic magnetic current. While its conventional origin is attributed to magnetic-field-modified band energy and shifts in the Fermi surface, a recent study identified an additional spin-driven magnetic displacement contribution. Here, we complete the picture by identifying the orbital counterpart of the magnetic displacement current. Using a density matrix formulation that incorporates both minimal coupling and spin-Zeeman interactions, we derive the electronic equations of motion in the presence of an oscillating magnetic field and uncover an orbital contribution to the wave-packet velocity. Physically, this contribution arises from the time variation of the magnetic-field-induced charge polarization. In the low-frequency transport regime, this mechanism becomes purely intrinsic. We illustrate this intrinsic gyrotropic current of orbital origin in the $\mathcal{P}\mathcal{T}$-symmetric antiferromagnet CuMnAs. We show that the intrinsic gyrotropic magnetic current reverses sign upon Néel vector reversal, establishing it as a direct probe of antiferromagnetic order in CuMnAs and other $\mathcal{PT}$-symmetric antiferromagnets.

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• Electrical conductivity
• Magnetism
• Transport phenomena
• Bloch wave theory
• Boltzmann theory
• Density matrix methods
• Discrete symmetries in condensed matter