Revealing emergent magnetic charge in an antiferromagnet with diamond quantum magnetometry

Topologically protected states in magnetic materials are highly promising for next-generation spintronics. Antiferromagnets (AFMs) offer advantages over ferromagnets due to their enhanced stability and faster dynamics, but their vanishing net magnetic moment makes studying their topological textures challenging. Previous techniques like synchrotron-based dichroic X-ray methods have revealed 2D topological AFM spin textures in haematite, but lacked the sensitivity to detect vorticity. This study addresses this limitation by employing DQM, a highly sensitive vectorial magnetic field sensing technique with negligible backaction. The research explores the concept of emergent magnetic charges in canted AFMs, where a slight canting of magnetization, arising from the Dzyaloshinskii-Moriya interaction (DMI), leads to weak magnetic fields. These fields can be described using a magnetic analogue of Gauss's law, suggesting the existence of emergent magnetic charges. DQM, utilizing a nitrogen-vacancy (NV) center in diamond as a point field sensor, is ideally suited to investigate these weak fields and the emergent magnetic charges associated with AFM topological textures. The overarching aim is to define a new class of magnetic systems for investigating 2D monopolar physics and showcasing the transformative power of DQM in the field of quantum materials research. The unique capability of DQM to directly measure the weak magnetic fields generated by the divergence of the canted moments offers a pathway to explore these previously inaccessible phenomena.

The literature review highlights prior work on topological textures in magnetic materials and the potential of antiferromagnets for spintronic applications. It emphasizes the challenges associated with detecting the spin textures in antiferromagnets due to their zero net magnetization. Existing techniques such as synchrotron-based dichroic X-ray techniques are discussed, acknowledging their limitations in measuring vorticity. The review also introduces diamond quantum magnetometry (DQM) as a novel technique capable of measuring weak magnetic fields, setting the stage for its application in this study. The existing literature on emergent magnetic monopoles in systems like spin ice is referenced, providing a comparative context for the current findings. The concept of canted antiferromagnets and the role of DMI in generating weak magnetic fields is reviewed, establishing the theoretical foundation for the study’s approach.

The experimental methodology involves using DQM to image topological textures in haematite (α-Fe₂O₃). A single NV center in a diamond is used as a highly sensitive sensor, scanned at a constant height above the sample surface. Optically detected magnetic resonance (ODMR) is employed to measure the magnetic field projected onto the NV axis. A bias field is applied to extract field orientation. Raster scans provide Bz images, which are transformed to laboratory coordinates via Fourier reconstruction. The study utilizes a thin-film approximation to relate the measured Bz to the in-plane and out-of-plane components of the magnetization. Due to the symmetry of the DMI in α-Fe₂O₃, the Bz images primarily reflect the divergence of the canted magnetization. The analysis involves modelling the Bz images with various AFM spin textures, including antiphase domain walls (ADWs), merons, antimerons, and bimerons. The models account for the topological charge and winding number of these textures, allowing for their identification and characterization. A systematic procedure is developed to distinguish between these spin textures based on their characteristic Bz signatures. Magnetization reconstruction is performed using a regularization technique to obtain the mxy distribution, which is then used to calculate the expected Bz distribution for comparison with experimental data. Finally, a magnetic analogue of Gauss's law is employed to relate the divergence of magnetization to the emergent magnetic charge density. Downward continuation of the planar Bz distribution allows for three-dimensional visualization of the magnetic field above the sample surface, revealing the spatial distribution of emergent magnetic charges.

The key findings of the research include the direct visualization and characterization of diverse emergent magnetic charge distributions in haematite (α-Fe₂O₃). DQM imaging reveals a rich tapestry of monopolar, dipolar, and quadrupolar charge distributions associated with various AFM topological textures. The researchers demonstrate a duality relation between staggered vorticity and magnetic charge, linking the vorticity of AFM spin textures to their associated magnetic charge density. They identify antiferromagnetic Bloch merons as carriers of spatially extended emergent magnetic monopoles. Positively and negatively charged monopolar textures are shown to be topologically equivalent, unlike their ferromagnetic counterparts, while antimerons exhibit a quadrupolar character. The study quantifies the magnetic charge density using a thin-film approximation and downward continuation of the measured magnetic field data. Three-dimensional visualizations of the magnetic field lines provide a clear depiction of the monopolar, dipolar, and quadrupolar charge distributions. The radial dependence of the integrated magnetic charge (Qm) is analyzed for merons and antimerons, revealing a linear scaling with radius for merons and a near-zero value for antimerons, consistent with theoretical predictions. Deviations from the zero Qm for antimerons are attributed to interactions with neighboring spin textures. The study concludes that the observed emergent monopoles are consistent with theoretical models and do not violate Maxwell's equations. The interactions between different spin textures within the 2D magnetic charge canvas modify the net magnetic charge of individual constituents.

The findings of this research directly address the challenges of imaging and characterizing AFM spin textures, which are known for their vanishing net moment. The successful application of DQM provides a significant advancement in the field of antiferromagnetic spintronics. The observation of emergent magnetic monopoles in α-Fe₂O₃ opens new avenues for exploring 2D monopolar physics. The results highlight the transformative potential of DQM in unveiling emergent phenomena in quantum materials, pushing the boundaries of materials characterization and potentially impacting the development of next-generation spintronic devices. The close agreement between experimental observations and theoretical models supports the interpretation of emergent magnetic charges and their association with topological spin textures. The study demonstrates the power of combining advanced experimental techniques with sophisticated theoretical models to gain deeper insights into complex magnetic phenomena.

This paper demonstrates the successful application of diamond quantum magnetometry for imaging topological textures and revealing emergent magnetic charges in the antiferromagnet haematite. The identification of monopolar, dipolar, and quadrupolar charge distributions associated with distinct AFM spin textures showcases the power of this technique. Future research could explore the dynamics of these emergent magnetic charges under varying conditions, investigate other antiferromagnetic materials with different DMI symmetries, and further explore the potential applications of this knowledge in spintronics and other fields.

The thin-film approximation used in the analysis may introduce some limitations in accurately quantifying the emergent magnetic charge density for thicker samples. The magnetization reconstruction technique relies on several simplifying assumptions and regularization steps, which might affect the precision of the obtained mxy distributions. The analysis focuses primarily on isolated spin textures, while the actual system comprises a complex multi-textural ensemble where interactions between textures modify the net charge of individual constituents. The study doesn't directly measure the topological charge sign of the spin textures, limiting the complete characterization of their topological properties.