Magnonic Crystals: Fundamentals & Applications

• Magnonic crystals are artificial, periodic magnetic materials designed to modulate spin waves via engineered band structures and induced band gaps.
• They are fabricated using advanced techniques such as nanofabrication, ion implantation, voltage control, and optical writing to tailor magnetic parameters.
• These structures enable applications like reconfigurable spin-wave filtering, topological spintronics, and integration in quantum hybrid devices.

A magnonic crystal (MC) is an artificial, periodic magnetic material designed to modulate and control the propagation of spin waves (magnons) via engineered band structures. The spatial periodicity in one, two, or three dimensions gives rise to frequency bands and band gaps in the spin wave spectrum, analogous to electronic band structures in solids or photonic band structures in photonic crystals. Ongoing research explores diverse MC geometries, interactions, material platforms, and control mechanisms, spanning linear and nonlinear dynamics, topology, disorder effects, quantum information applications, and advanced reconfigurability.

1. Fundamental Structure and Band Engineering

MCs are realized by imposing spatially periodic modulations of magnetic parameters (such as saturation magnetization $M_s$, exchange stiffness $A$, anisotropy $K$, or Dzyaloshinskii–Moriya interaction $D$) within a ferromagnetic, ferrimagnetic, or synthetic antiferromagnetic host. This can be achieved by nanofabrication (e.g., arrays of nanoholes (Levchenko et al., 12 Jun 2025), nanocylinders (Tiwari et al., 2010), or etched grooves (Kosen et al., 2017)), ion implantation (Obry et al., 2013), voltage-induced anisotropy (Wang et al., 2016, Merbouche et al., 2021), laser patterning (Bublikov et al., 2023), or emergence of intrinsic nanoscale magnetic textures (domain walls, skyrmions, vortices) (Wang et al., 2014, Mruczkiewicz et al., 2015, Chen et al., 2021, Wang et al., 24 Sep 2025).

The resulting periodic potential leads to magnonic band formation, with Bragg reflections at wavevectors: $k_n = \frac{n\pi}{a}$ where $a$ is the lattice period and $n$ is an integer. Band gaps emerge at these Brillouin zone boundaries, their locations and widths being determined by both lattice geometry and magnetic contrast.

The spin-wave dispersion in thin films, especially in the Damon–Eshbach or backward-volume geometries, may be modified by the periodic patterning: $$\omega(k) = \omega_0 + D k^2 + \gamma M_s \Lambda(kt)$$ with $\omega_0$ the ferromagnetic resonance, $D$ the exchange stiffness, $\gamma$ the gyromagnetic ratio, $t$ the film thickness, and $\Lambda(kt)$ encapsulating dipolar effects (Levchenko et al., 12 Jun 2025).

The control of bandgaps and transmission characteristics underpins the function of MCs as frequency-selective filters, microwave phase shifters, magnonic waveguides, and logic devices.

2. Material Platforms, Fabrication, and Tunability

Experimentally, MCs are fabricated on diverse scales. Yttrium iron garnet (YIG) is the archetypal low-damping platform for long-range spin-wave propagation, supporting bandgap engineering via nanohole arrays (Levchenko et al., 12 Jun 2025), etched grooves (Kosen et al., 2017), or semiconductor overlays (Bublikov et al., 2023). Permalloy (Ni$_{80}$Fe$_{20}$) is frequently used for exchange-dominated nanowire arrays (Ding et al., 2011), with controlled disorder and tunable magnetic ground states.

Magnetoelectric and voltage control is realized using epitaxial ferroelectric/ferromagnet heterostructures such as BiFeO$_3$/LSMO (Merbouche et al., 2021), or via gate-induced perpendicular magnetic anisotropy in ultrathin Co/MgO stacks (Wang et al., 2016). Voltage pulses can also reversibly nucleate or annihilate chiral textures, such as domain wall skyrmions (DWSKs), by modulating DMI strength (Wang et al., 24 Sep 2025).

Optical writing of MCs is demonstrated through spatial light interference and local heating, allowing transient, user-defined periodic modulation of $M_s(x)$ (Chang et al., 2019, Bublikov et al., 2023). The laser-tuned charge carrier concentration in semiconductors directly modifies the magnonic band gap nonreciprocally in hybrid YIG/GaAs MCs (Bublikov et al., 2023).

Dynamic, on-demand, and reconfigurable MCs can therefore be realized by voltage control, local heating, optical writing, or direct gating of anisotropy energies.

3. Advanced Linear and Nonlinear Spin-Wave Dynamics

MCs support rich linear dynamics—band crossing, mode hybridization, and gap opening—observable by techniques such as propagating spin-wave spectroscopy (PSWS), Brillouin light scattering (BLS), and ferromagnetic resonance (FMR) (Levchenko et al., 12 Jun 2025, Ding et al., 2011). Structures with multimode crossovers exhibit anticrossings in the dispersion at critical $k$ values, with spin-wave energy channeled into select quantized width modes, enabling efficient and mode-selective transmission (Levchenko et al., 12 Jun 2025).

Disorder and defect engineering—in the form of programmable magnetic ground states, such as antiferromagnetic (AFM) versus ferromagnetic (FM) nanowire order—yield changes in the dynamic magnonic response and enable studies of localization, impurity states, and Anderson-like phenomena (Ding et al., 2011).

Nonlinear dynamics have recently come to the forefront. In twisted MCs (formed by stacking two magnetic layers with finite twist angles, leading to moiré-type superlattices), three-magnon interactions are dramatically enhanced by noncollinear ground states, giving rise to magnonic frequency combs (MFCs) upon two-tone microwave driving (Li et al., 15 Jul 2025). The MFCs, with up to 22 comb teeth, exhibit plateau-like dependence on twist angle and excitation frequency, controlled by the saturation of the three-magnon scattering processes within a range of twist geometries and frequencies.

4. Topological and Chiral Magnon Modes

Periodic modulation in MCs, especially when combined with broken time-reversal or inversion symmetry, can result in nontrivial topological phases for magnons. Topological magnonic crystals exhibit volume bands with nonzero Chern numbers, supporting protected chiral edge modes that propagate unidirectionally and are robust to backscattering and disorder (Shindou et al., 2012). These edge modes, predicted in dipolar-interacting systems (e.g., 2D MCs with tailored geometry), arise from the bosonic Bogoliubov–de Gennes Hamiltonian framework, with Berry curvature and Chern invariants guaranteeing the existence of topological boundary modes.

The ability to engineer topologically protected magnon transport opens the way for fault-tolerant spintronic elements, spin current splitters, and reconfigurable circuits, with analogies to quantum Hall systems and topological electronics.

In domain-wall- and skyrmion-based MCs, topological effects further manifest: (i) domain wall-based periodic textures generate a quantized Berry phase for spin waves, introducing a geometric vector potential and allowing dynamic reconfiguration of the magnonic band structure via domain wall nucleation or annihilation (Wang et al., 2014); (ii) periodic skyrmion arrays support dispersive magnonic bands with band gaps dependent on skyrmion configuration, tunable by magnetic field or current (Mruczkiewicz et al., 2015, Chen et al., 2021).

5. Complex Textures: Domain Wall and Skyrmion Magnonic Crystals

MCs based on complex, nanoscale spin textures exploit the interplay between topology, DMI, and magnetic anisotropy to structure magnon propagation:

• Domain Wall Skyrmion-based MCs (DWSK-MCs): Formed by embedding a chain of skyrmions within a chiral Néel-type domain wall in a magnetic strip, periodically modulating the wall's internal spin structure (Wang et al., 24 Sep 2025). The total energy density is:

$$\varepsilon_{tot} = A (\nabla \mathbf{m})^2 - D \mathbf{m} \cdot \left[(\hat{z} \times \nabla) \times \mathbf{m}\right] - K m_z^2$$

Dynamic control of DMI via voltage pulses nucleates DWSKs at prescribed positions, creating a periodic potential for domain-wall-confined spin waves, thereby opening magnonic band gaps. The band structure can be tuned in real time by varying the external field to modulate DWSK size, with robustness maintained even in curved geometries.

• Skyrmion-Based MCs: Periodic arrays of skyrmions in multilayer dots or films enable dispersive magnonic bands due to coherent coupling between confined breathing and gyrotropic skyrmion modes (Mruczkiewicz et al., 2015). These bands feature both positive and negative group velocities, enabling direction-dependent signal transmission and frequency filtering (Chen et al., 2021).
• Topological signatures: Quantized Berry phases (e.g., $\varphi = 4 n_w \pi$ for domain-wall configurations (Wang et al., 2014)) further enrich the behavior of magnonic bands, facilitating switchable band gap architectures.

6. Nonreciprocal, Quantum, and Hybrid Information Devices

MCs are increasingly being integrated into quantum and hybrid information systems. Nonreciprocal magnon propagation—arising from Dzyaloshinskii–Moriya interaction or asymmetric boundary conditions—enables directional transmission and functionalities such as quantum information diodes (Shukla et al., 2023). In these devices, the magnon dispersion is asymmetric for left- and right-propagating waves, leading to selective reflection (by Bragg condition) and quantum information rectification that can be controlled with external electric fields or magnetoelectric effects.

At millikelvin temperatures, YIG-based MCs exhibit magnonic bandgaps and can be interfaced with superconducting circuits for quantum information processing, provided spin-wave damping is minimized (Kosen et al., 2017). Proposals exist for magnonic quantum networks, in which superconducting loops mediate long-range interactions between magnetic particles, forming tunable magnonic lattices suitable for coupling distant spin qubits or acting as a quantum information bus (Rusconi et al., 2018).

7. Prospects: Reconfigurability, Metrology, and Novel Functionality

The unique degree of control in MCs—ranging from geometric reconfiguration (Ciubotaru et al., 2012, Wang et al., 2016), dynamic voltage-induced switching (Wang et al., 2016, Merbouche et al., 2021), optically written band structures (Chang et al., 2019, Bublikov et al., 2023), and quantum coherent manipulation (Liu et al., 2023)—places them at the forefront of spintronic device platform research.

Emergent nonlinearities (MFCs in twisted MCs (Li et al., 15 Jul 2025)), topological transport, on-chip integration, and adaptive filtering expand potential use cases. MCs are now central to studies of wave-based logic, quantum state transfer, low-loss RF nanodevices, and as model systems for wave propagation in disordered and topologically nontrivial media.

An active area for future exploration is the extension to 2D and 3D magnonic nanoarrays, the interface with CMOS-compatible platforms, and the exploitation of magnonic band engineering for high-precision sensors and frequency standards, leveraging the intrinsic frequency comb phenomena and robust, voltage/optical tunability.