Revealing emergent magnetic charge in an antiferromagnet with diamond quantum magnetometry

Topologically protected magnetic states are promising for next-generation spintronics. Antiferromagnets (AFMs) offer advantages such as enhanced stability and faster, richer dynamics relative to ferromagnets, but their vanishing net magnetization makes their textures challenging to detect. State-of-the-art synchrotron-based dichroic X-ray imaging has revealed two-dimensional (2D) AFM textures in α-Fe2O3, yet this approach is insensitive to the sign of the staggered magnetization and thus cannot access the associated vorticity. The authors propose diamond quantum magnetometry (DQM) with a single nitrogen–vacancy (NV) center as a minimally invasive, highly sensitive vector magnetometer capable of probing the weak fields generated by canted moments in AFMs.

The research question is whether DQM can directly read out the vorticity of AFM spin textures and, via a duality, reveal their emergent magnetic charge distributions. By reframing the AFM textures in terms of canted magnetization rather than the Néel vector, the study explores whether weak fields arising from the divergence of canted moments can be mapped and interpreted through an analogue of Gauss’s law, thereby uncovering monopolar, dipolar, and quadrupolar emergent magnetic charges in α-Fe2O3.

Previous work has established the importance of topological textures in magnetic materials and highlighted the advantages of AFM textures, though their detection is hampered by zero net magnetization. Synchrotron dichroic X-ray techniques have imaged 2D AFM textures in haematite (α-Fe2O3), but cannot determine the sign of the staggered magnetization, leaving vorticity inaccessible. Emergent magnetic monopoles have been studied in other systems such as spin ice, where they arise from distinct physics. Diamond NV magnetometry is a mature technique for nanoscale, vector-resolved magnetic field imaging with high sensitivity and low backaction, and prior works have developed methods to reconstruct vector fields and spin textures from single-component field data. This study builds on these advances to investigate emergent magnetic charges in a canted AFM, a class of materials not accessible to conventional magnetometry approaches for vorticity and charge mapping.

Material system and magnetic background: The archetypal AFM α-Fe2O3 (haematite) is studied across the Morin transition (TM ≈ 200 K). Below TM the ferromagnetic sublattices are mainly out of plane; above TM they are in-plane with a small canting induced by a Dzyaloshinskii–Moriya interaction (DMI) vector along the c-axis. The net canted magnetization is in-plane with average magnitude m∥ ≈ 2 × 10^−3 A m^−1, arising from a canting angle A ≈ 1.1 mrad. Due to symmetry, mz = 0 in α-Fe2O3 in the considered regime.

Diamond quantum magnetometry: A scanning diamond tip hosting a single NV center is rastered at a fixed height above the sample surface. Optically detected magnetic resonance (ODMR) is used to probe the Zeeman splitting of the NV ground states. In the weak-field approximation with negligible strain, the magnetic field projected onto the NV axis (BNV) is inferred from the transition frequency f+ using ΔE+ = ħ(f+ − D − Bbias) − γNV BNV, with D = 2.87 GHz, γNV = 28 MHz mT^−1, and a bias field Bbias = 0.5 mT applied along the NV axis to determine field orientation. ODMR line scans and raster scans provide maps of the NV-projected magnetic field. A Fourier-based reconstruction converts the measured component to laboratory-frame components, yielding Bz maps; z is aligned with the crystal c-axis.

Field–magnetization relation and thin-film model: In the thin-film approximation, Bz = αxy(t, d) * mxy + αz(t, d) * ∇^2 mz, where * denotes convolution with effective point spread functions αi that account for field decay and set spatial resolution by the NV–sample distance dNV. For α-Fe2O3 with mz = 0, Bz images directly reflect the (blurred) divergence of the in-plane canted magnetization mxy. The DMI symmetry (z-oriented) ensures m is in-plane, simplifying interpretation.

Spin-texture modeling and identification: Below TM, antiferromagnetic antiphase domain walls (ADWs) are modeled with a linear profile characterized by width w and a phase ξ controlling the variation of the Néel vector l, giving α-Néel (ξ = 0, π; mxy = 0) or α-Bloch (ξ = π/2, 3π/2; maximal mxy) wall types. Above TM, isolated merons (N = +1), antimerons (N = −1), and bimerons are modeled via a linear ansatz parameterized by phase ξ and winding number N. Analytical expressions for mxy divergence in polar coordinates and predicted Bz signatures are computed for each case.

Data acquisition and analysis: Bz images are acquired at T = 4 K and T = 300 K to probe textures below and above TM. Characteristic Bz signatures (e.g., sinusoidal with zero crossing for ADWs; radially symmetric monopolar-like for α-Bloch merons; twofold-symmetric for antimerons) are compared to model calculations. Where textures are not perfectly isolated, the authors reconstruct mxy distributions by fitting measured Bz with regularization to account for the convolution kernel and finite sensor height, and then forward-calculate Bz from the reconstructed mxy to validate fits. The mxy reconstruction leverages systematic regularization as detailed in Supplementary Section 7.

Emergent charge retrieval and 3D field visualization: The areal magnetic charge density is defined via the magnetic Gauss-law analogue: σm = ∇⋅mxy. Using Fourier deconvolution of measured Bz with the known transfer function α (and mz = 0), σm maps are retrieved without relying on the mxy reconstruction or the linear meron ansatz. Upward/downward continuation of the measured Bz plane yields 3D visualizations of the magnetic field B (= H in vacuum) above textures. Integrated charge Qm(r) is evaluated over circular regions of radius r centered on textures to study scaling and symmetry effects.

• DQM directly images AFM spin textures in α-Fe2O3, resolving distinct magnetic phases below and above TM ≈ 200 K. Below TM, narrow near-zero-field backgrounds with sinusoidal Bz profiles and zero crossings identify antiphase domain walls (ADWs). Above TM, larger features with non-zero background reveal merons, antimerons, and bimerons.
• The measured Bz corresponds to the divergence of the in-plane canted magnetization mxy (since mz = 0), enabling direct read-out of staggered vorticity and unambiguous determination of the topological winding number N for individual textures. DQM cannot determine the sign of the topological charge at the core because the canted moment vanishes there.
• Distinct field signatures: α-Néel ADWs and α-Néel merons (ξ = 0, π) are divergence-free with Bz ≈ 0; α-Bloch ADWs/merons (ξ = π/2, 3π/2) show maximal Bz amplitudes. Merons (N = +1) display radially symmetric Bz of either polarity depending on ξ; antimerons (N = −1) exhibit twofold-symmetric Bz patterns with azimuthal offsets set by ξ. Stable bimerons (meron–antimeron pairs) are observed.
• Emergent magnetic charge distributions retrieved from Bz via σm = ∇⋅mxy: α-Bloch merons host spatially extended monopolar (and anti-monopolar) charge distributions acting as sources/sinks of the magnetic field. ADWs exhibit dipolar charge character, whereas antimerons exhibit quadrupolar character.
• 3D visualizations of the magnetic field above textures confirm monopolar-like field lines for merons, dipolar for ADWs, and quadrupolar for antimerons. This is consistent with Maxwell’s equations: outside the material B = μ0 H with ∇⋅B = 0; apparent sources/sinks arise from ∇⋅m within the material (no violation of ∇⋅B = 0).
• Integrated 2D magnetic charge Qm(r) for isolated merons scales linearly with r, consistent with a 1/r dependence of fields from 2D charges. For isolated antimerons, symmetry enforces Qm = 0 at all r; experimentally observed deviations at larger r arise from interactions with neighboring textures and loss of ideal symmetry in dense ensembles.
• Quantitative parameters: DMI-induced canting A ≈ 1.1 mrad yields in-plane net magnetization m∥ ≈ 2 × 10^−3 A m^−1; ODMR uses D = 2.87 GHz, γNV = 28 MHz mT^−1, and bias Bbias = 0.5 mT; measured field contrasts are on the order of a few 10^−1 mT in the ODMR maps, with spatial resolution set by the NV–sample distance.

The study demonstrates that DQM can access the previously hidden vorticity of AFM spin textures and, through a formal duality, reveal their emergent magnetic charge distributions. This directly addresses the challenge left by X-ray dichroism imaging, which cannot determine the sign of the staggered magnetization. By showing that α-Bloch merons in α-Fe2O3 host emergent monopolar charges while ADWs and antimerons host dipolar and quadrupolar charges, respectively, the work introduces a paradigm where AFM textures form a 2D canvas of magnetic charges.

These findings are significant for AFM spintronics: the ability to map vorticity and emergent charges provides new handles for identifying, controlling, and potentially manipulating AFM textures for logic and memory devices. The observation that monopolar distributions can exist in a canted AFM (where demagnetizing fields are weak compared to AFM exchange) contrasts with ferromagnets, highlighting unique AFM physics. The scaling of integrated charge and the interaction-driven deviations underscore the collective behavior of textures in realistic ensembles, informing the design of devices where texture density and interactions are critical.

This work establishes diamond quantum magnetometry as a powerful tool to image AFM topological textures and directly retrieve their vorticity and emergent magnetic charge in α-Fe2O3. The authors identify a rich set of charge characters—monopolar (merons), dipolar (ADWs), and quadrupolar (antimerons)—and quantify integrated charge scaling, thereby defining a new class of systems for exploring 2D monopolar physics in antiferromagnets. The approach bridges local field imaging with topological and emergent electrodynamics concepts in quantum materials.

Future directions include: extending DQM to other canted AFMs and heterostructures; dynamic studies of texture creation, motion, and annihilation; controlled tuning of texture phase ξ and density via external fields or strain; integrating DQM with device operation to correlate emergent charge distributions with transport; and improving spatial resolution and reconstruction algorithms to resolve interacting multi-texture ensembles more precisely.

• DQM cannot determine the sign of the topological charge at the core because the canted moment vanishes there.
• Spatial resolution is limited by the NV–sample standoff distance (convolution with α blurring kernels); precise height and kernel estimation affect reconstruction fidelity.
• The mxy reconstruction uses simplifying assumptions and regularization; textures are often not perfectly isolated, and interactions with neighbors can bias retrieved σm and Qm.
• Upward/downward continuation and Fourier deconvolution can amplify noise and are sensitive to model parameters (thin-film approximation, mz = 0, transfer function accuracy).
• Dense texture ensembles complicate unambiguous classification and integrated charge evaluation at large radii due to overlap and symmetry breaking.