Magnonic Black-Hole Horizons

• Magnonic black-hole horizons are engineered analog event horizons for spin waves that mimic gravitational phenomena, enabling tabletop studies of Hawking-like radiation.
• They rely on the linearized Landau–Lifshitz–Gilbert framework and effective acoustic metrics to simulate key aspects such as unidirectional propagation and antimagnon mixing.
• Experimental implementations in spintronic devices, superfluid ³He-B, and curvilinear ferromagnets have demonstrated signatures like enhanced reflection and black-hole lasing.

Magnonic black-hole horizons are analog event horizons engineered for spin-wave quasiparticles (magnons) in magnetically ordered systems. These horizons emulate aspects of gravitational black-hole physics—including unidirectional propagation, classical superradiance, and Hawking-like radiation—by exploiting flowing magnetic media, curvature, or spatial inhomogeneities that modulate the effective propagation velocity or spectrum of magnons. The construction and interpretation of magnonic black-hole horizons leverage the mathematically precise analogies between the equations governing spin waves in driven or textured magnets and the wave equations in curved spacetime, with the emergent spacetime metric encoded in the material and dynamical parameters of the magnet.

1. Theoretical Foundations and Emergent Metrics

The theoretical description of magnonic event horizons is rooted in the linearized Landau–Lifshitz–Gilbert (LLG) equation for magnetization dynamics, augmented by spin-transfer torque (STT) or spin–orbit torque (SOT) terms when a current is applied. For easy-plane ferromagnets, the equation can be cast as: $$\partial_t n = -\gamma n \times H_\text{eff} + \alpha n \times \partial_t n - (u \cdot \nabla)n + \beta n \times (u \cdot \nabla)n$$ where $n$ is the unit vector magnetization, $u$ parametrizes the drift velocity proportional to the applied current, and $\alpha,\ \beta$ are damping-like torques (Harms et al., 2022). Linearization about a magnetically ordered ground state leads, for long-wavelength excitations, to a Bogoliubov–de Gennes structure with magnonic ($\omega_+$) and "antimagnonic" ($\omega_-$) branches,

$\omega_{\pm}(k) = \pm c|k| + u k_x$

where $c$ is the spin-wave velocity (Harms et al., 2022, Roldán-Molina et al., 2016).

The resulting wave equations can be rewritten in the form of massless scalar field equations in an effective "acoustic" metric. In one spatial dimension, the line element takes a Painlevé–Gullstrand–like form: $ds^2 = (c^2 - U^2)dt^2 + 2U dx\,dt - dx^2 - dy^2$ with $U(x)$ the local flow velocity induced by current or spin superflow. The analog horizon forms at positions $n$0 where $n$1 (Harms et al., 2022, Roldán-Molina et al., 2016, Errani et al., 2024). For antiferromagnets, the same structure arises from the effective Klein–Gordon equation for deviations of the Néel vector (Errani et al., 2024).

Curvilinear magnonics, where spatial curvature or geometry generates inhomogeneous effective potentials, yield additional metric analogies. Here, the magnonic horizon is defined where the magnon group velocity vanishes due to the spatial variation of the curvature-induced Dzyaloshinskii–Moriya interaction (DMI) and anisotropy, resulting in a turning point analogous to a gravitational event horizon (Zhao et al., 16 Dec 2025).

2. Horizon Criteria and Physical Implementation

A magnonic black-hole horizon (or white-hole horizon) forms wherever the effective flow velocity equals the spin-wave group velocity: $n$2 For current-driven systems, $n$3 derives from the applied current density; for spin superfluids, it is set by the phase gradient between condensates; for systems with geometric curvature, the group velocity vanishes at the local band edge set by the effective potential (Harms et al., 2022, Človečko et al., 2018, Zhao et al., 16 Dec 2025).

Table: Key Physical Mechanisms for Magnonic Horizon Implementation

Physical Platform	Control Parameter	Horizon Condition
Ferromagnetic metal/insulator	Current density (STT/SOT)	$n$4
Superfluid $n$5He-B	Spin superflow velocity	$n$6
AFM insulator	Exchange/magnetic field, STT	$n$7
Curvilinear ferromagnets	Curvature gradient	$n$8

In systems based on STT/SOT, experimentally accessible current densities ($n$9–$u$0 A/m$u$1) and spin-wave velocities ($u$2–$u$3 km/s in YIG, CoFe) render the formation of horizons feasible at micron to sub-micron length scales (Harms et al., 2022, Roldán-Molina et al., 2016). In superfluid $u$4He-B, the horizon is formed as the spin-superflow between two magnon Bose–Einstein condensates (HPDs) reaches the local magnon group velocity ($u$5 m/s) (Človečko et al., 2018, Človečko et al., 2019). Curvature-induced horizons in YIG thin films occur at sub-100 nm radii, where the effective potential localizes a magnon bound state and blocks outgoing propagating modes (Zhao et al., 16 Dec 2025).

3. Antimagnons, Negative-Energy Modes, and Mode Mixing

In conventional ground states, spin waves correspond to positive-norm, energy-raising excitations (magnons). However, in dynamically stabilized or metastable states (e.g., magnetization antiparallel to the external field in a thin film, or for $u$6 in AFMs), branches of negative-norm, negative-energy excitations—antimagnons—emerge. Quantization in these regimes involves operators with commutators $u$7, and the antimagnons lower the net magnetic energy (Harms et al., 2022, Errani et al., 2024).

The essential feature at the horizon is the mixing of positive-energy (magnon) and negative-energy (antimagnon) branches. An incident magnon at the horizon scatters such that part of the amplitude is transmitted as an antimagnon, which is trapped inside the $u$8 region. This mixing is the analogue of the process responsible for Hawking radiation and classical superradiant amplification (Harms et al., 2022, Errani et al., 2024, Roldán-Molina et al., 2016).

4. Observable Signatures: Hawking Radiation and Black-Hole Lasing

Quantum field theory in curved spacetime predicts that mode mixing at the horizon yields spontaneous emission of magnon–antimagnon pairs, with an occupation number given by: $u$9 where the Hawking temperature $\alpha,\ \beta$0 is set by the “surface gravity,” the gradient of the velocity at the horizon

$\alpha,\ \beta$1

For patterned magnetic films and typical device parameters, $\alpha,\ \beta$2 can reach 10–100 mK (Harms et al., 2022); in superfluid $\alpha,\ \beta$3He-B the estimate is $\alpha,\ \beta$4 nK, within four orders of magnitude of the bath temperature $\alpha,\ \beta$5K (Človečko et al., 2018, Človečko et al., 2019). In current-driven ferromagnetic systems, $\alpha,\ \beta$6 can be $\alpha,\ \beta$70.1–1 K for sufficiently sharp current gradients ($\alpha,\ \beta$8–$\alpha,\ \beta$9 nm) (Roldán-Molina et al., 2016, Harms et al., 2021, Errani et al., 2024).

In finite cavities defined by a black–white hole horizon pair, negative-energy antimagnon modes become resonant and unstable, yielding “black-hole lasing:” a self-amplifying, exponentially growing oscillation at discrete, quantized frequencies

$\omega_+$0

with instability growth rates given by tunneling probabilities at the horizons (Harms et al., 2022).

Horizon-induced amplification is observed experimentally as enhanced reflection (gain) or suppression of transmitted spin-wave power. In superfluid $\omega_+$1He-B, reflected power at the white-hole horizon can exceed incident power by 20–30%, in accordance with classical superradiant predictions (Človečko et al., 2018, Človečko et al., 2019). In solid-state devices, horizon-amplification can be detected via Brillouin light scattering or network-analyzer FMR (Errani et al., 2024).

5. Experimental Platforms and Parameter Regimes

Magnonic black-hole horizons have been realized or proposed in multiple platforms:

• Ferromagnetic metals and insulators: STT/SOT-driven horizons in thin films, realizing negative-energy modes at current densities as low as $\omega_+$2 A/m$\omega_+$3 for ultrathin (nm-scale) films with strong interfacial DMI. Material parameters: $\omega_+$4–$\omega_+$5 A/m, exchange length $\omega_+$6 nm, Gilbert damping $\omega_+$7, DMI $\omega_+$81–3 mJ/m$\omega_+$9. Gradient engineering at the 100 nm scale achieves $\omega_-$0–1 K (Harms et al., 2021).
• Superfluid $\omega_-$1He-B: Phase-locked magnon BECs in cylinders, connected by a microchannel. Event horizon formation at spin supercurrents $\omega_-$2 m/s, with spatial gradients over $\omega_-$3 mm, yielding $\omega_-$4 nK (Človečko et al., 2018, Človečko et al., 2019).
• Antiferromagnets: Horizons via spatially varying exchange or field, with STT or SOT induced background “flows.” Relevant for materials such as NiO, CuMnAs, with spin-wave velocity $\omega_-$5 m/s and current densities $\omega_-$6–$\omega_-$7 A/m$\omega_-$8. Hawking temperatures $\omega_-$9 in the sub-Kelvin to several-Kelvin range (Errani et al., 2024).
• Curvilinear (geometrically textured) ferromagnets: Smooth curvature gradients generate effective DMI and anisotropy, producing localized bound magnon modes and an analog event horizon at radii where the propagating magnon group velocity vanishes. For YIG films with tailored curvature, $\omega_{\pm}(k) = \pm c|k| + u k_x$0 mK is achievable; robust frequency combs and enhanced nonlinear mixing highlight the concentration of interactions at the horizon (Zhao et al., 16 Dec 2025).

6. Experimental Observations and Measurement Strategies

Key experimental signatures include:

• Suppression of transmission and enhanced reflection: Directly observable in power spectral density measurements, both in magnonic superfluids and thin-film devices (Človečko et al., 2018, Človečko et al., 2019, Errani et al., 2024).
• Thermal emission spectra: Thermal occupation of magnonic modes upstream of the horizon, detectable via microwave photon counting, Brillouin light scattering, or spin-pumping-induced inverse spin Hall effect (Harms et al., 2022, Errani et al., 2024).
• Black-hole lasing: Instabilities in the finite negative-energy region between horizons, manifesting as quantized, exponentially growing spin-wave modes in GHz regimes (Harms et al., 2022).
• Quantum entanglement: Correlated emission of magnon pairs at $\omega_{\pm}(k) = \pm c|k| + u k_x$1, measurable via spin–spin correlators (neutron or Brillouin scattering), is predicted as a quantum Hawking signature (Roldán-Molina et al., 2016).

Engineered device geometries include patterned current-carrying strips, spatially inhomogeneous magnetic field gates, and geometrically curved nanomagnets. Detection methods span micro-focused BLS, time-resolved MOKE, and transport measurements of enhanced gain or induced thermal currents (Harms et al., 2022, Errani et al., 2024).

7. Significance, Limitations, and Outlook

Magnonic black-hole horizons offer a precise platform to study analog Hawking radiation, mode mixing, and nontrivial quantum effects in a controlled tabletop setting. Material parameter regimes—especially in thin-film spintronic devices—are within reach of current fabrication and measurement technology (Harms et al., 2022, Harms et al., 2021, Errani et al., 2024). Curvature-based approaches open new, texture-independent pathways for horizon engineering (Zhao et al., 16 Dec 2025).

Principal challenges include achieving sharp gradients (high $\omega_{\pm}(k) = \pm c|k| + u k_x$2 or $\omega_{\pm}(k) = \pm c|k| + u k_x$3) without destructive Joule heating, isolating quantum Hawking signals from background thermal noise, and stabilizing negative-energy states against collapse or domain formation. Superfluid $\omega_{\pm}(k) = \pm c|k| + u k_x$4He-B stands out for its ultra-low dissipation and favorable Hawking temperature to bath temperature ratio, currently providing the cleanest platform for direct quantum observation (Človečko et al., 2018, Človečko et al., 2019).

Future prospects center on direct detection of Hawking spectra, quantum entanglement of magnon pairs, controlled amplification for magnonic lasing, and potential integration into magnonic logic architectures exploiting horizon-based gain and nonreciprocal transmission. The field bridges condensed matter, quantum optics, and analog gravity, offering insights into both fundamental and applied aspects of nonequilibrium many-body physics (Harms et al., 2022, Roldán-Molina et al., 2016, Errani et al., 2024).