Gyrotropy

Gyrotropy is the property of a medium in which left- and right-rotating elliptical polarizations propagate at different speeds. The source digest introduces it through Wikipedia's magneto-optic effect entry: a magneto-optic effect is any phenomenon in which an electromagnetic wave propagates through a medium altered by a quasistatic magnetic field. Such a medium is also called gyrotropic or gyromagnetic.

Magneto-optic effects

When light is transmitted through a layer of magneto-optic material the result is the Faraday effect — the plane of polarization can be rotated, forming a Faraday rotator. Reflection from a magneto-optic material gives the magneto-optic Kerr effect (not to be confused with the nonlinear Kerr effect). In general, magneto-optic effects break time-reversal symmetry locally (considering only light propagation, not the source of the magnetic field) and break Lorentz reciprocity, which is the necessary condition for devices such as optical isolators, through which light passes in one direction but not the other. Two gyrotropic materials with reversed rotation directions of the two principal polarizations, corresponding to complex-conjugate ε tensors for lossless media, are called optical isomers.

Gyrotropic order in condensed matter

A distinct but related use of the term appears in condensed matter physics. A crystalline electronic system is geometrically chiral when it lacks mirror planes, space-inversion centres or rotoinversion axes; typically this chirality is predefined by the lattice and fixed on crystal formation. In materials with gyrotropic order, electrons spontaneously organize to exhibit macroscopic chirality in an originally achiral lattice — proposed as the quantum analogue of cholesteric liquid crystals. The 2020 Nature paper by Su-Yang Xu et al. reported optical chiral induction and observation of a gyrotropically ordered phase in 1T-TiSe₂, confirmed by an out-of-plane Circular Photogalvanic Effect current.

The gyrotropic magnetic effect

The Gyrotropic Magnetic Effect (GME) (GME) is the low-frequency limit of optical gyrotropy in metals and semimetals coupled to chiral spin textures. Paul, Park, Han and Balents (Phys. Rev. Lett. 135, 246704, 2025) derive rotatory power in terms of universal scaling functions and estimate experimentally viable values with realistic material parameters. Ghorai, Sarkar and Agarwal (arXiv:2601.04787) identify an intrinsic gyrotropic magnetic current of orbital origin, illustrated in the PT-symmetric antiferromagnet CuMnAs.

Engineering gyrotropy

Several approaches in the digest aim to produce or enhance gyrotropic response without the bulky magnetic bias that conventional gyrotropic materials require:

• Epsilon-near-zero heterostructures. Katsantonis et al. (Sci. Rep. 13, 21986, 2023) alternate gyrotropic and metallic or plasmonic films to form an Epsilon-Near-Zero (ENZ) Effective Medium, averaging diagonal permittivities of opposite sign toward zero while leaving off-diagonal permittivities unaltered, thereby amplifying Nonreciprocity.
• Magnet-less gyrotropy. Boshgazi, Mehrany and Memarian (Opt. Express 33, 24370) time-modulate the permittivity tensor of a static achiral, non-gyrotropic crystal, emulating gyrotropy through temporal rotation of the principal axes, with a proposed realization via modulated electro-optic effects in a nonlinear crystal.
• Plasma-based tunable media. Rodriguez et al. (APS DPP 2022) build a tunable bulk gyrotropic medium from magnetized low-temperature plasma discharge tubes in a 2D photonic crystal, operating at 2–10 GHz, with evidence for topologically protected edge states.
• 1D anisotropic and gyrotropic photonic crystals. Vinogradov et al. describe Yeh band gaps, magneto-optical and birefringence effects, and tunable switchable filters and magnetic superlenses.

Related phenomena

• Acoustical activity. Kumaraswamy and Krishnamurthy (Acta Cryst. A36, 760–762, 1980) describe the acoustic gyrotropic tensor, a fifth-rank tensor d_ij,l = −d_ji,l controlling acoustical activity in crystals, with a group-theoretical classification of acoustically active classes.
• Magnetic vortex gyration. Skorokhodov et al. study the collective gyrotropic oscillation mode of vortices in two coupled ferromagnetic disks, measuring resonant frequency versus separation by magnetic resonance force spectroscopy and estimating interaction energy via the Thiele equation.
• Superconducting nonreciprocity. Kokkeler, Tokatly and Bergeret (SciPost Phys. 16, 055) treat gyrotropic symmetry in a lateral Josephson junction, linking the Superconducting Diode Effect to the spin Hall effect, spin galvanic effect and spin Hall magnetoresistance.

Simulation

The open-source FDTD package Meep provides a documentation tutorial on gyrotropic media, describing how gyrotropy is supported in its Materials module.