Ultralight Dark Matter Detection with a Ferromagnet Lattice

Abstract

A levitated ferromagnet provides an exceptionally sensitive probe of ultralight dark matter (ULDM) through measuring weak magnetic-like field signals. We propose a ferromagnet lattice magnetometer that coherently combines multiple levitated ferromagnets to enhance effective sensitivity. By replacing a single ferromagnet with a lattice, we increase the total polarized spin while preserving the intrinsic dynamical response of each constituent ferromagnet. We show that magnetic dipole-dipole interactions within the lattice can be dynamically suppressed through a high-frequency magnetic field, rendering the system effectively noninteracting, at the cost of only a moderate reduction in signal amplitude due to the distinct renormalization of linear and quadratic spin responses. We analyze the noise properties of the lattice and demonstrate that collective readout leads to favorable scaling with the number of ferromagnets. Interpreted in terms of axion-electron, dark photon, and axion-photon couplings, our results yield projected sensitivities that significantly exceed existing single-ferromagnet implementations. In particular, for axion-photon interactions, we find a nontrivial lattice-induced enhancement of the signal itself, leading to sensitivities that surpass existing constraints over a broad mass range.

Figures (2)

• Figure 1: Magnetic-field noise power spectral density $S_{B}(f)$ for the ferromagnet lattice. The total spectrum (black) is shown together with its dominant contributions: thermal, backaction, and imprecision components. The imprecision term is computed using the frequency-dependent susceptibility $\chi(\omega)$ in Eq. (\ref{['eq:chi']}), leading to a pronounced rise at high frequencies. For $v_{\theta\theta} = v_{\phi\phi}$, the system exhibits a single resonance frequency. The low-frequency regime is thermally limited, whereas at higher frequencies the imprecision term determines the sensitivity. Frequencies above $10\ \mathrm{kHz}$ are not considered reliable due to overlap with the high-frequency modulation.
• Figure 2: Projected sensitivity to ultralight dark matter couplings as a function of the dark matter mass $m_\mathrm{DM}$, derived from the projected noise of the proposed ferromagnet lattice magnetometer. The solid red curve shows the constraints obtained from this work. Shaded regions indicate existing constraints from the literature caputo_dark_2021-1AxionLimits. The blue curve denotes the existing experimental constraints from a single ferromagnet magnetometer kaliaUltralightDarkMatter2024. In our calculations, we take the size of the shield as $L = 1\ \mathrm{m}$, and use the same parameter setups as the existing single ferromagnet.