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• Gd-content gradients influence PMA in both "+δ" and "−δ" samples. • "+δ" has lower H C due to closer T comp , suggesting different Gd-content. • Reversal of AHE loop near T comp indicates sublattice dominance shift. • Decrease in H SF suggests weakened exchange interaction near T comp. • Strong ΔR XY at ± 4 kOe and ± 30 kOe for "−δ" indicates enhanced PMA. Ferrimagnetic rare-earth (RE) – transition-metal (TM) alloys are considered small ferromagnets with antiferromagnetic exchange in sublattices, which makes them a preferable choice for future ultrafast memory-related applications. Here, we explore the magnetic properties of two GdFeCo thin films with tailored vertical composition gradients, achieved by gradually varying Gd concentration across the film thickness. The temperature-dependent magnetic behavior of these films is investigated using anomalous Hall effect (AHE) measurements and SQUID magnetometry. Both films exhibit perpendicular magnetic anisotropy with distinct coercivities, indicating variations in their magnetic properties. The films show RE-dominant behavior at 300 K. Moreover, for the positive composition gradient (+δ) film, the compensation temperature is around 350 K, while the film with a negative gradient (−δ) exhibits a compensation temperature above 400 K. Furthermore, the spin-flop behavior and AHE sign reversal provide insights into the sublattice dominance and exchange interactions within the films. The magnitude of ΔR XY (the difference in AHE resistance at different magnetic fields) is shown to be sensitive to the composition gradient, indicating stronger perpendicular magnetic anisotropy for the "−δ" sample. This study demonstrates the potential of composition engineering to tailor the magnetic characteristics of ferrimagnetic materials for specific spintronics applications. [ABSTRACT FROM AUTHOR]

• Investigate the temperature-dependent AHE in sandwich structures composed of two RE-TM FIM layers. • Complex AHE phenomena explained by the magnetization reversal of individual layers, Hall sign reversal, and the SF transition in the GdFeCo layer. • A model is developed to provide a simplified explanation of the origin of these complex AHE loops. • The model unravels the complexity in AHE loops near and far from the T comp. • The model fits well with the experimental results. The anomalous Hall effect (AHE) has been a remarkable tool for characterizing the magnetic properties of thin films with perpendicular magnetic anisotropy. In this study, we investigate the temperature-dependent AHE in sandwich structures composed of two ferrimagnetic (FIM) layers with different coercivities, using rare-earth-transition-metal (RE-TM) materials. Complex triple AHE loops are obtained near the compensation temperature of GdFeCo, and these loops are explained by considering the magnetization reversal of the individual layers, Hall sign reversal, and the spin-flop transition in the GdFeCo layer. A model is developed to provide a simplified explanation of the origin of these complex AHE loops. This study elucidates the mechanism behind the unusual temperature-dependent AHE response of the technologically important RE-TM FIM films for spintronics applications. [ABSTRACT FROM AUTHOR]

• Identification of Hall-contributor from TEM analysis and AHE measurements in RE-TM FIMs. • Novel sandwich structure of FeCo-compensated GdFeCo and TbFeCo. • ΔR AHE drops towards zero when FeCo-content compensate in the two layers. • FeCo is the major contributor of the anomalous Hall signal. • Temperature dependence of ΔR AHE further supports the claim. The contribution of magnetic sublattices in rare-earth-transition-metal (RE-TM) ferrimagnets (FIMs) has long been debated and is still unclear. The spin-split of 3d conducting electrons in TMs has been known for the anomalous Hall effect (AHE) response, yet in FIMs the contribution from RE is unclear. Here we try to solve the problem by applying a novel sandwich structure of TbFeCo and GdFeCo using Ta spacer. FeCo-content in the two layers is changed from unequal to equal and the AHE resistance (R AHE) of the structure is studied. The difference in R AHE of the two layers is compared with their FeCo-content ratio. This study shows that when the FeCo-content of the two magnetic layers is close, the ΔR AHE is greatly reduced. The results indicate that the AHE signal is majorly contributed by the FeCo-sublattices. The novel approach followed here adds crucial information to the ongoing debate on Hall-contribution in RE-TM FIMs. [ABSTRACT FROM AUTHOR]

• Magnetization relaxation in Hf/GdFeCo/SiN as a function of current polarity, probe widths, and notch in the device. • In notched Hall bar, the smaller H C for positive current seems due to valve-like behavior from notch. • Notch provides smaller delays for nucleation and switching compared to the no-notch Hall bar. • Narrow probe shows the advantage of comparatively faster and less stochastic switching. • Sense current is another important key to controlling the nucleation delay. The race-track memory concept relies on domain wall propagation through a magnetic track, which has the potential to change the future course of memory-related applications. Therefore, the materials where one can control the propagation of domain walls are crucial. Further, the stochastic nature of magnetization switching has potential applications in neuromorphic computing. Here we study the propagation of magnetic domains and the stochastic magnetization relaxation in the Gd-Fe-Co Hall bar. The magnetic relaxation of Hall bar devices is studied using anomalous Hall resistance measurements. This study highlights the behavior of magnetization relaxation under various parameters viz., at different magnitudes and directions of sensing currents, Hall probe aspect ratios, and the presence of a notch in the Hall bar. This study shows that the stochastic nature and delay in magnetization relaxation can be controlled by the sensing currents and the Hall bar geometry, which is crucial for magnetization switching-based applications. [ABSTRACT FROM AUTHOR]

• Temperature dependent anomalous Hall effect (AHE) in GdFeCo. • Magnetic compensation temperature for sheet film ~240 K and device ~118 K. • In sheet film, spin-flopping is witnessed at 0.6 Tesla close to compensation temperature. • Triple loops are observed in AHE hysteresis for the device. • The zero-field and 3 Tesla R AHE scan suggests the Hall signal generates solely from the FeCo moment. • Drop in the 3Tesla R AHE near the compensation is explained by considering the low field spin-flopping. Here we investigate the temperature dependence of anomalous Hall effect in Hf/GdFeCo/MgO sheet film and Hall bar device. The magnetic compensation temperature (T comp) for the sheet film and device is found to be ~240 K and ~118 K, respectively. In sheet film, spin-flopping is witnessed at a considerably lower field, 0.6 T, close to T comp. The AHE hysteresis loops in the sheet film have a single loop whereas in the Hall bar device, hystereses consist of triple loops are observed just above the T comp. Moreover, the temperature-dependent anomalous Hall resistance (R AHE) responds unusually when a perpendicular magnetic field is applied while recording the R AHE. The zero-field R AHE scan suggests the Hall signal generates solely from the FeCo moment. However, the behavior of 3T-field R AHE scan in which the R AHE drops close to zero near the T comp seems to be following the net magnetization response of the device, is explained by considering the low field spin-flopping around the compensation temperature. The results presented here give important insight to understand the complex AHE behavior of ferrimagnets for their spintronic applications. [ABSTRACT FROM AUTHOR]

• Magnetization relaxation at different probe widths, sensing currents, and Hall geometries. • Current shunting, Joule heating, and current-induced SOT are responsible for coercivity response. • Dependence of domain wall propagation on probe widths. • Device behavior at different circumstances is crucial for practical use. The understanding of the characteristics of a magnetic layer in a different environment is crucial for any spintronics application. Before practical applications, thorough scrutiny of such devices is compulsory. Here we study such a potential Hall device of MgO-capped Hf/GdFeCo bilayer (FeCo-rich) for magnetization relaxation around nucleation fields at different voltage probe line widths and dc sensing currents. The device is characterized by anomalous Hall measurements in transverse and longitudinal Hall geometries for two different probe widths A (5 µ m) and B (1 µ m). The coercivities of the Hall loops (ρ xy - H and R xx - H) drop with increasing the sense current for both the probes. For probe B, the sharp and large drop in coercivity (ρ xy - H loops) at comparatively lower sensing currents is observed, which is attributed to the negligible current shunting and presence of pinning site at B caused by the patterning process. The average domain wall velocities at various sensing currents for probe B are found to be smaller than probe A, from the transverse and longitudinal Hall geometry magnetization relaxation measurements, which agrees with pinning sites and Joule heating effect at probe B. The notch position in the pattern and the longitudinal Hall resistance curve peak shape suggest the domain wall propagation direction from probe B to probe A in the current channel. This study highlights the domain wall propagation at different nucleation fields, sensing currents, and the Hall probe aspect ratios. [ABSTRACT FROM AUTHOR]

• Modulation of anisotropic magnetoresistance by anomalous Hall signal. • Asymmetric magnetoresistance peaks appear at coercivity. • Magnetization relaxation at different nucleation fields. • Domain wall velocity measurement from magnetization relaxation. We present here a way to modulate the anisotropic magnetoresistance (AMR) by anomalous Hall signal and thus measure the domain wall (DW) motion velocity at near-coercivity. We study the magnetization relaxation at the constant field in the longitudinal (R xx) Hall geometry. We observed asymmetric R xx peaks that appear at the DW pinning fields. This unusual magnetoresistance behavior is explained by considering the AMR modulation by the anomalous Hall voltage. In the proposed method, using the magnetization relaxation, the real-time DW velocity measurement is much easier in comparison to the other microscopy methods. Moreover, the additional signal from anomalous Hall voltage makes this technique simpler and sensitive for DW velocity measurements, which can be useful for various spintronic sensing applications. [ABSTRACT FROM AUTHOR]

In this study, the interfacial PMA in (Ta or Hf)/TbFeCo/MgO/Ta structures are investigated and the effectiveness of two kinds of heavy-metal Hf and Ta underlayers are explored. The PMA of TbFeCo is found to critically rely on several aspects like Tb-concentration (Tb sputtering power), underlayer material (Ta/Hf), annealing temperature and heating rate of annealing. The crystalline phase of the underlayer is investigated by XRD and resistivity measurements and optimized by changing the film thickness. It was observed that for the Hf underlayer the PMA could be obtained in as-deposited samples irrespective of the Tb-concentration with squareness close to unity. The post-annealing results show improved PMA in FeCo-dominant films; however, the PMA reduces when Tb-content is increased. [ABSTRACT FROM AUTHOR]

• AHE in TbFeCo thin film is studied with a series of dc sense currents. • H C and ρ AHE are found to be decreasing with increasing the dc sense current. • The ρ AHE behavior is explained by considering the current induced SOT and Joule heating. • The switching speed is estimated by the reciprocal of difference in the saturation and nucleation fields. The control of magnetic properties by electric current in nanoscale devices is critical for advanced applications of spintronics. Here, we study the anomalous Hall effect in amorphous TbFeCo/Ta/MgO structure for various dc sense currents using the Hall bar pattern. The aspect ratio of the Hall bar structure is changed by simply interchanging the current and voltage terminals. It is found that the increase in the sense current decreases both the anomalous Hall resistivity and the coercivity in the TbFeCo. The decreasing trend of resistivity and coercivity with sense current is unusual which is explained on the basis of Joule heating and spin-orbit torque. In addition, a simple analysis is performed to relate the magnetization switching speed as a function of dc sense current. [ABSTRACT FROM AUTHOR]

• Magnetic domain wall can be detected well by employing anomalous Hall effect. • The domain wall velocity grows exponentially with respect to the field. • The AHE and MR signals can be efficiently employed to investigate the magnetic homogeneity and pinning effect of the device. We present a powerful method to detect the magnetic domain wall (DW), based on the intrinsic characteristic of anomalous Hall effect (AHE), by employing magneto-transport measurement on a device of double Hall cross geometry. We demonstrate that DW propagation manifests its behavior in the distinctive AHE hysteresis and longitudinal magnetoresistance (MR). As DW propagates along the Hall channel, the AHE hysteresis varies considerably depending on the voltage-pickup position while MR displays abnormal asymmetric peaks. Utilizing this direct correlation, we formulate simple models for AHE switching path and MR peak so that they can be efficiently used to characterize DW behavior. It is revealed that at the nucleation stage, the DW velocity grows exponentially with respect to the field. Additionally, the effects of magnetic pinning sites are taken into account and shed light on. The proposed method could be potentially employed for the detection of DW behavior in nanoscale devices. [ABSTRACT FROM AUTHOR]