Disentangling topological and anomalous Hall contributions of skyrmions using Kerr microscopy and thermal transport measurements

Technical Summary: Disentangling Topological and Anomalous Hall Contributions of Skyrmions Using Kerr Microscopy and Thermal Transport Measurements

Problem Statement
The topological Hall effect (THE) serves as a critical transport signature for identifying topologically protected magnetic structures, such as skyrmions. However, in single-layer ferromagnetic films like Ta/CoFeB/MgO, the THE is extremely weak and is often obscured by the dominant anomalous Hall effect (AHE). Unlike bulk or multilayer systems where THE peaks may be distinct, in these single-layer systems, the THE manifests as small deviations at the edges of hysteresis loops where magnetic signals change rapidly. Conventional electrical transport measurements cannot easily separate the THE from the AHE because both effects influence electron trajectories in the same manner, resulting in overlapping signals. Furthermore, while imaging techniques like magnetic force microscopy (MFM) or Kerr microscopy can visualize magnetic domains, they do not inherently verify the topological nature of these structures or their contribution to charge transport. The challenge lies in reliably extracting the minute THE signal from the total Hall resistivity in single-nanometer-thick films at room temperature without high-resolution imaging being the sole verification method.

Methodology
The authors employed a multi-modal approach combining electrical transport measurements with magneto-optical Kerr effect (MOKE) microscopy and thermal transport measurements to isolate the THE.

1. Sample Fabrication: Ta/CoFeB/MgO single-layer stacks were deposited on thermally oxidized silicon substrates. A key feature of the deposition process was the creation of opposing thickness gradients in the Ta and CoFeB layers (approx. ±21.2%/cm). This gradient creates a transition region between in-plane and out-of-plane magnetic anisotropy, a condition favorable for skyrmion nucleation. Samples were annealed at 473 K to optimize material properties.
2. Electrical and Optical Measurements (MOKE-Hall): A Hall cross device was patterned for simultaneous Hall resistivity ($\rho_{Hall}$) measurement and MOKE imaging. By cycling an out-of-plane magnetic field, the authors recorded $\rho_{Hall}$ hysteresis loops and simultaneously captured Kerr images of the surface magnetization.
   • Separation Technique: The magnetization ($M$) was reconstructed from the average brightness of the MOKE images. Since the AHE is proportional to $M$ and the ordinary Hall effect (OHE) is negligible in the low-field regime, the authors normalized the measured $\rho_{Hall}$ and the MOKE-derived magnetization. The difference between these normalized signals yielded the isolated THE ($\rho_{THE}$).
3. Thermal Transport Measurements (Nernst-Hall): A second set of samples with integrated Joule heaters and resistive thermometers was used to measure the Nernst effect. The total Nernst signal ($N_{xy}$) contains ordinary, anomalous, and topological contributions. By normalizing the Nernst and Hall signals to their saturation values and calculating the difference, the authors derived a "topological quantity" ($N_{TQ}$). This quantity isolates the combined topological contributions (THE and topological Nernst effect, TNE) by eliminating normal and anomalous parts.
4. Verification and Analysis: The presence of skyrmions was confirmed via particle detection algorithms applied to the Kerr images. The authors also investigated magnetic relaxation (creep) to ensure that the observed peaks were not artifacts of time-dependent magnetization changes, determining a relaxation time constant to standardize measurement timing.

Key Results

• Extraction of THE: The study successfully extracted a topological Hall resistivity of 249(18) pΩ m for Ta/CoFeB/MgO single-layer films at room temperature. This value is approximately one order of magnitude lower than values reported for multilayer systems, explaining why it is difficult to detect without the proposed separation method.
• Correlation with Skyrmions: The peaks in the extracted THE signal align temporally with the nucleation and growth of skyrmions observed in the Kerr microscopy images. The number of detected skyrmions peaks at the same magnetic field values where the THE signal is maximal, confirming that the transport anomaly originates from these topological textures.
• Validation via Thermal Transport: The topological quantity ($N_{TQ}$) derived from thermal transport measurements exhibited characteristic peaks consistent with the electrical THE measurements. Although the units differ and the exact peak shapes vary due to slight thickness differences between samples, the independent confirmation via the Nernst effect validates the existence of topological contributions in this material system.
• Relaxation and Deformation: The authors observed that skyrmions undergo deformation and magnetic creep over time. However, by accounting for relaxation times (approx. 0.5 s to reach negligible decay), they confirmed that the observed THE peaks are not artifacts of magnetic relaxation but are intrinsic to the skyrmion formation process.

Significance and Claims
The paper claims to demonstrate a robust method for disentangling the weak topological Hall effect from the dominant anomalous Hall effect in single-layer nanometer-thick ferromagnetic films at room temperature. The primary significance lies in:

1. Methodological Advancement: The work establishes that combining MOKE microscopy with electrical transport allows for the separation of THE without requiring high-resolution imaging techniques (like LTEM or MFM) to be the primary detection tool. This makes the technique applicable even to very thin films where other imaging methods might struggle.
2. Material Verification: The study provides the first reported evidence of THE in single-layer Ta/CoFeB/MgO films at room temperature, supporting the topological nature of the magnetic structures in this system.
3. Independent Verification: By cross-referencing electrical Hall measurements with thermal Nernst measurements, the authors verify that the observed effects are indeed topological in origin, rather than artifacts of domain wall scattering or other non-topological mechanisms.

The authors conclude that while the THE in single-layer systems is small and sensitive to domain morphology and skyrmion density, the proposed dual-method approach (MOKE-Hall and Nernst-Hall) successfully isolates these contributions, confirming the presence of topologically protected skyrmions in the investigated material.