Gyrotropic Thin Films in Photonics and Spintronics

• Gyrotropic thin films are engineered nanostructures with off-diagonal tensor components that break reciprocity and induce optical and spin-dependent phenomena.
• They are synthesized using multilayer stacks, garnet deposition, and metallic films under magnetic fields to fine-tune magneto-optic and gyrotropic responses.
• Their unique properties drive innovations in photonics, magnonics, and spintronics, powering devices like microwave isolators and skyrmion-based oscillators.

Gyrotropic thin films are engineered nanostructures in which the dielectric or magnetic response includes antisymmetric (off-diagonal) tensor components, breaking optical reciprocity and enabling effects such as optical activity, nonreciprocal emission, and topological spin excitations. Such films encompass a diverse class of materials systems: from chiral atomic-layer heterostructures with strong spin-orbit coupling, to magnetic multilayers supporting topologically protected skyrmions, to metallic thin films subjected to out-of-plane magnetic fields. Gyrotropy in these contexts manifests as magneto-optic rotation, nonreciprocal photon emission, and gyrotropic magnetic resonances, with device applications spanning photonics, magnonics, and spintronics.

1. Fundamental Concepts and Constitutive Tensors

The essential property of gyrotropic thin films is the presence of off-diagonal imaginary elements in their permittivity or permeability tensors. This structure underpins natural optical activity, nonreciprocal absorption, and spin-dependent transport.

In photonic contexts, the permittivity tensor typically takes the form

$$\varepsilon(\omega) = \begin{pmatrix} \varepsilon_d & +i\,\varepsilon_g & 0 \ -i\,\varepsilon_g & \varepsilon_d & 0 \ 0 & 0 & \varepsilon_z \end{pmatrix}$$

where $\varepsilon_g$ is proportional to either external magnetic field (for Drude metals), the macroscopic magnetization (for ferromagnets), or the microscopic chirality (for chiral organic/inorganic films). For gyrotropic chiral dielectrics, gyrotropy may instead be described by a gyrotropy factor $g$ in the constitutive relation $$\mathbf{D} = \epsilon_0 \epsilon \mathbf{E} + i \epsilon_0 g\, \hat{\mathbf{u}} \times \mathbf{E}$$, with the axis $\hat{\mathbf{u}}$ set by the film symmetry or stacking direction (Babaei, 2018).

The gyrotropic response can be microscopically linked to the orbital magnetic moment of Bloch electrons in chiral or twisted layered systems, as formalized by the gyrotropic magnetic effect (GME). The corresponding low-frequency current response is

$$j_i^{\rm GME}(\omega) = \alpha^{\rm GME}_{ij} B_j(\omega)$$

with the GME tensor $\alpha^{\rm GME}_{ij}$ given by Fermi-surface integrals over velocity and the orbital moment (Wang et al., 2020).

2. Synthetic Realizations: Multilayer Structures and Growth Parameters

Several platforms realize gyrotropic thin films with tailored magneto-optic, gyroelectric, or gyromagnetic properties:

Magnetic Multilayers and Skyrmionic Films:

Multilayer stacks such as [Ir/Fe/Co/Pt]$_{20}$, with per-layer thicknesses at nanometer scale, leverage interfacial Dzyaloshinskii-Moriya interaction (DMI) and interlayer dipolar coupling to stabilize nanoscale Néel skyrmions at room temperature (Satywali et al., 2018). The detailed stack protocol involves:

• Substrate: Si/SiO$_2$
• Seed layers: Ta(3nm)/Pt(10nm)
• $20\times$ repetitions of Ir(1nm)/Fe($x$Å)/Co($y$Å)/Pt(1nm)
• Capping: Pt(2nm)

Magnetic parameters are $M_\mathrm{s} \approx (0.8–1.2) \times 10^6$ A/m, effective anisotropy $K_\mathrm{eff} \approx 0.4–0.6$ MJ/m$^3$, DMI $D \approx 1.8–2.2$ mJ/m$^2$, exchange stiffness $A \approx 10–15$ pJ/m, and Gilbert damping $\alpha_\mathrm{eff} \approx 0.03–0.05$.

Magneto-optic Garnet Films:

Bi-substituted yttrium iron garnet (Bi-YIG) thin films, such as Bi$_{0.1}$Y$_{2.9}$Fe$_5$O$_{12}$, are grown via pulsed-laser deposition (PLD) on Gd$_3$Ga$_5$O$_{12}$ (GGG) substrates with (100) or (111) orientation at $825^{\circ}$C, oxygen pressure $0.15$ mbar, and thicknesses $20$–$150$ nm (Gurjar et al., 2022). AFM confirms rms roughness $<0.5$ nm. In-plane lattice constants increase with Bi$^{3+}$ content, especially for (111), due to dodecahedral site occupancy and ionic radius mismatch.

Metallic Films under Magnetic Fields:

Gyrotropy in Drude metals (e.g., bismuth) is engineered by applying a perpendicular magnetic field, inducing cyclotron off-diagonal terms in the permittivity tensor and breaking reciprocity. The thin-film is treated analytically as a 2D emitter, with optical properties governed by a combination of plasma and cyclotron frequencies, and relaxation time (Zhang et al., 1 Jan 2026).

3. Optical and Magneto-Optical Gyrotropy in Thin Films

Natural Optical Activity and the Gyrotropic Magnetic Effect (GME):

In nonmagnetic chiral or twisted thin films, optical rotation arises from the GME, where the gyrotropic response is controlled by the Fermi-surface orbital magnetic moment. The multi-band Kubo formalism yields a current proportional to $v_x m_x$ at the Fermi level, with the rotatory power scaling up to $10^3$ rad/m in optimized systems such as magic-angle twisted bilayer graphene (Wang et al., 2020).

Key dependencies for large optical rotation include:

• Layer thickness ($\sim$ nanometers to $100$ nm)
• Small twist angle (enhancing flat bands)
• Frequency $\omega$ in the low-energy (intraband) regime Materials platforms include twisted van der Waals structures, chiral atomically thin films, and Weyl semimetal slabs.

Polygonal Chiral Thin Films:

Polygonal chiral films demonstrate selective circular Bragg reflection and pronounced optical rotation, with their dielectric tensors explicitly incorporating both biaxiality and gyrotropy: $$\epsilon_{yz} = +\epsilon_g, \quad \epsilon_{zy} = -\epsilon_g$$ Fabry–Pérot oscillations, Bragg band splitting, and bandgap positions are controlled by the gyrotropy factor $g$ and film porosity $p$. The transfer-matrix method allows calculation of reflection/transmission for right and left circular polarizations, with quantifiable band positions and optical rotation angles (Babaei, 2018).

4. Magnetic Gyrotropy: Skyrmions and Magnetization Dynamics

Gyrotropic Modes in Skyrmionic Films:

Néel skyrmions confined to multilayer stacks exhibit discrete gyrotropic resonances observable as Lorentzian absorption peaks in broadband FMR, with frequencies $f_G \sim 0.5–3$ GHz and typical quality factors $Q = 10–30$. These modes, fundamentally distinct from uniform FMR or radial breathing, are softened (reduced in frequency) by interlayer dipolar coupling—up to $50$–$70\%$ lower compared to single-layer films. Analytical modeling via the Thiele equation yields

$$G\,\hat z\times \dot{\mathbf{R}} - D\alpha\,\dot{\mathbf{R}} + \partial U/\partial \mathbf{R} = 0,$$

with $\omega_G = \kappa/G$, where stiffness $\kappa$ combines exchange, DMI, dipolar, and confinement energies (Satywali et al., 2018).

Micromagnetic simulations confirm that the fundamental mode is a rigid-core ($\mu=-1$ azimuthal quantum number, CCW) gyration with negligible breathing or edge localization.

Ferromagnetic Resonance in Magneto-Optic Garnet Films:

Bi-YIG thin films demonstrate tunable FMR linewidth ($\Delta H_0$), effective magnetization, and Gilbert damping: | Thickness (nm) | $\Delta H_0$ (mT, 100) | $\alpha$ (100) | $\Delta H_0$ (mT, 111) | $\alpha$ (111) | |---|---|---|---|---| | 20 | 1.8 | $2.5 \times 10^{-4}$ | 2.5 | $5.0 \times 10^{-4}$ | | 50 | 1.5 | $1.5 \times 10^{-4}$ | 2.0 | $4.0 \times 10^{-4}$ | |100 | 1.1 | $1.2 \times 10^{-4}$ | 1.4 | $3.0 \times 10^{-4}$ | |150 | 0.8 | $1.06 \times 10^{-4}$| 1.1 | $2.30 \times 10^{-4}$| Higher Bi$^{3+}$ content and (111) orientation maximize the permittivity tensor's gyrotropic parameter, favoring large Faraday rotation, while (100) yields lower damping for microwave devices (Gurjar et al., 2022).

5. Nonreciprocal and Radiative Phenomena in Gyrotropic Thin Films

Gyrotropy gives rise to nonreciprocal electromagnetic response and modified radiative properties. For Drude metals under magnetic fields, the nonreciprocal permittivity allows for radiative emission of angular momentum, calculable via the Keldysh NEGF formalism.

Key analytical flux densities (per unit area $\Sigma$) are: $$\frac{\langle I \rangle}{\Sigma} = \int_0^\infty \frac{d\omega}{\pi} \hbar \omega N(\omega) \int_{k_\parallel < \omega/c} \frac{d^2 k_\parallel}{(2\pi)^2} A_I(k_\parallel,\omega)$$

$$\frac{\langle M_z \rangle}{\Sigma} = \int_0^\infty \frac{d\omega}{\pi} \hbar N(\omega) \int_{k_\parallel < \omega/c} \frac{d^2 k_\parallel}{(2\pi)^2} A_M(k_\parallel,\omega)$$

with $A_I$ and $A_M$ determined by gyrotropic transmission coefficients. For bismuth films (thickness 1 nm, $T=300$ K), $\langle M_z\rangle$ increases in magnitude with magnetic field, and vanishes as $B\to0$ (Zhang et al., 1 Jan 2026).

An important physical consequence is that Kirchhoff’s law generalizes under gyrotropy: reciprocity is broken ($t_{sp}\neq0$), and emission/absorption must be described with cross-polarized coefficients.

6. Applications and Practical Implications

Gyrotropic thin films underpin several device classes:

• Microwave isolators and circulators: Optimized Bi-YIG (100) films, with narrow FMR linewidth and low $\alpha$, provide low-loss channels for nonreciprocal signal routing (Gurjar et al., 2022).
• Magneto-optical modulators: Maximizing Bi substitution and (111) orientation enhances Faraday rotation via increased gyrotropy.
• Skyrmion-based microwave oscillators: Exploiting gyrotropic resonance modes in multilayers enables compact GHz-frequency sources and selective filters (Satywali et al., 2018).
• Chiro-optical metasurfaces: Polygonal chiral films and GME-active twisted multilayers are exploited for polarization control and current-induced orbital switching (Wang et al., 2020).
• Radiative angular momentum sources: Tuning gyrotropy in metallic films allows for the active generation and manipulation of photonic torque in nanophotonic and optomechanical contexts (Zhang et al., 1 Jan 2026).

Device optimization is fundamentally constrained by intrinsic/extrinsic damping, control of the gyrotropic parameter via composition and structure, and the balance between high gyrotropy and low loss.

7. Outlook and Materials Engineering Strategies

Advances in gyrotropic thin-film science derive from the engineered control of tensorial permittivity and magnetization, whether through artificial stacking (twisted bi- or multilayers), atomic substitution (e.g., Bi$^{3+}$ for Y$^{3+}$ in garnets), or external fields (cyclotron gyrotropy in metals). Key strategies include:

• Band flattening and Fermi surface engineering to enhance orbital moment and thus optical gyrotropy
• High-quality epitaxial growth to minimize damping and inhomogeneity
• Structural chirality or discrete rotational symmetry (polygonal stacks) to realize tailored polarization-dependent Bragg effects

The unification of these approaches yields versatile platforms for studying and exploiting natural optical activity, topological magnetization dynamics, and nonreciprocal radiative phenomena in low-dimensional quantum and mesoscopic systems (Satywali et al., 2018, Babaei, 2018, Wang et al., 2020, Gurjar et al., 2022, Zhang et al., 1 Jan 2026).