Chapter 4: Electrical transport studies of Magnetic
4.2 Transport studies of bilayer (𝐵𝐵𝑖𝑖 , 𝑆𝑆𝑆𝑆) 2 𝑇𝑇𝑒𝑒 3 / Cr- (𝐵𝐵𝑖𝑖, 𝑆𝑆𝑆𝑆) 2 𝑇𝑇𝑒𝑒 3
4.2.5 Comparison of the field cooling curves taken on the
dRxx was also seen in the 0.05 T warm-up Rxx curve after − 0.5 T field-cool, as shown in Figure 4.13(d), the latter was less significant in the peak height.
4.2.5 Comparison of the field cooling curves taken on the (3+6)-10% ternary TI/MTI
for |B| < 0.5 T and then turned into classical magnetoresistance for |B| > 0.5 T. Above 14.8 K, Rxx increased with |B| and showing AWL behavior for all fields. Comparing Figure 14.15(d) with the high-resolution Rxx vs. B curve at T = 14 K in Figure 4.10(d), we note that the curve was actually not flat and showing AWL behavior for |B| < 0.1 T. Our findings of predominantly AWL behavior for T > 14 K and WL behavior for T ≤ 14 K suggest that there were competing mechanisms that determined the electrical transport properties of the (3+6)- 10% ternary TI/MTI sample.
Figure 4.15: (a) Field-cool Rxy vs. T curves of the (3+6)-10% ternary TI/MTI sample at different magnetic fields. (b) Field-cool Rxx vs. T curves of the same sample at different magnetic fields.
(c) Rxy vs. B isotherms constructed from different field-cool Rxy vs. T curves. (d) Rxx vs. B isotherms constructed from different field-cool Rxy vs. T curves.
To better understand the temperature evolution of R vs. B curves and the magnetic field evolution of R vs. T curves, we constructed the 3D plots of Rxy and Rxx as a function of B and T, as shown in Figure 4.16. From the Rxy (B, T) data shown in Figures 4.16(a) and 4.16(c), it is clear that the color maps were not symmetrical relative to B = 0. Due to AHE, spontaneous magnetization is along the negative field direction. Taking the light blue color line (corresponding to Rxy = 0) as the onset of the AHE for negative fields and the yellow color line as the onset of the AHE for positive fields, we found that the onset of AHE with a negative applied field appeared at a higher temperature than that with a positive field.
Figure 4.16: Rxy (B, T) and Rxx (B, T) maps derived from the field-cooled Rxy vs. T and Rxx vs. T curves in different fields. (a) 2D map of Rxy (B, T), where the color bar represents the magnitude of Rxy in units of kΩ. (b) 2D map of Rxx (B, T), where the color bar represents the magnitude of Rxx in units of kΩ. (c) 3D map of Rxy (B, T). (d) 3D map of Rxx (B, T).
For the evolution of Rxy with B and T, it is as we described before. Nevertheless, the transition from weak anti-localization to weak localization is quite smooth without any apparent transition. This again implies the ratios of both contributions from somewhere cause the transition of the curve.
Figure 4.17: (a) 2D map of Rxy (B, T) as derived from field-cooled Rxy vs. T curves. (b) 2D map of Rxx (B, T) as derived from field-cooled Rxx vs. T curves. (c) 2D map of Rxy (B, T) as derived from zero-field-warming Rxy vs. T curves after field cooling. Here B represents the field applied before zero-field warming. (d) 2D map of Rxx (B, T) as derived from zero-field-warming Rxx vs.
T curves after field cooling. Here B represents the field applied before zero-field warming.
To obtain a more complete picture, we conducted resistive measurements using temperature sweeps again by first cooling the sample in a much stronger magnetic field up to 8T and then measuring the resistance while warming up in zero fields, as shown in Figure 4.17. For field
cooling, the value of |Rxy| decreased with increasing fields in the large field limit, as shown in Figure 4.17(a), which is consistent with what we had observed before. Similar studies of the Rxx (B, T) data is shown in Figure 4.17 (b), which revealed how the Rxx (B, T) curve transitioned from a W-shape at low temperatures to a V-shape at high temperatures by considering horizontal cuts in Figure 4.17 (b).
It is interesting to note that the zero-field warming Rxy map (after field cooling) shown in Figure 4.17(c), the |Rxy| value became independent of the applied magnetic field for B > 1 T in the positive field response and for |B| > 0.5 T in the negative field response, which implies the saturation of the magnetization.
For the positive field response shown in Figure 4.17(c), Rxy evolved from negative to positive values between T = 7 K to 15 K, which corresponded to negative coercive fields, consistent with what we had observed from the hysteretic Rxy vs. B isotherms over this temperature range. In the case of negative field response, |Rxy| decreased monotonously with increasing temperature. However, the Rxy value after cooled in negative fields was found to be smaller than that after cooled in the positive fields for 10 K < T < 15 K. The asymmetric dependence of the AHE and spontaneous magnetization on positive and negative field responses is interesting, which may be associated with the asymmetric interfaces of both the TI and MTI layers, leading to Rashba-like splitting[87].
In the case of the Rxx (B, T) map shown in Figure 4.17(d), Rxx vs. B was independent of the pre-applied field for B > 0.1 T. This is not surprising because after field-cooled by sufficiently high magnetic fields, a saturation of magnetization completely suppressed disorder spin scattering and so Rxx obtained under zero-field warming would be only dependent on the temperature and would be independent of -the magnetic fields applied during field-cooling.
4.3 Effects of circularly polarized light on the AHE of bilayer ternary