Influence of disorder on anomalous Hall effect for Heusler compounds

The anomalous Hall effect (AHE) is a long known but still not fully understood transport effect. Most theory papers focus on the influence of one particular contribution to the AHE. Actual measured experimental data, however, often are not in accord with idealized assumptions. In this work we discuss the data analysis for materials with low residual resistivity ratios. As prototypical materials we study half metallic Heusler compounds. Here the influence of defects and disorder is apparent in a material with a complex topology of the Fermi surface. Using films of different degree of disorder, we show how different scattering mechanisms can be separated. For ${\text{Co}}_2{\text{FeSi}}_{0.6}{\text{Al}}_{0.4}$ and ${\text{Co}}_2{\text{FeGa}}_{0.5}{\text{Ge}}_{0.5}$ the AHE induced by $B2$-type disorder and temperature-dependent scattering is positive, while $\text{DO}3$-type disorder and possible intrinsic contributions possess a negative sign.

Figure 1

(a) $\theta -2\theta$ scan; inset, $\varphi$ scan of four equivalent (111) reflections. Both for ${\text{Co}}_2{\text{FeSi}}_{0.6}{\text{Al}}_{0.4}$ deposited at $600{}^{°}\mathrm{C}$. (b) Crystallographic analysis of ordering peaks determined in a four circle geometry for ${\text{Co}}_2{\text{FeSi}}_{0.6}{\text{Al}}_{0.4}$. Square symbols (left ordinate) represent the ratio of the integral intensity between (111) and (200) reflections. Circles symbols (right ordinate) represent the integral intensity measured for the (111) reflection. (c) Saturation magnetization for different compounds as a function of deposition temperature.

Figure 2

(a) ${\rho }_{\mathit{xx}}(T)$ for a set of ${\text{Co}}_2{\text{FeSi}}_{0.6}{\text{Al}}_{0.4}$ films deposited at different temperatures. (b) ${\rho }_{\mathit{xx}}$ (5 K) values as a function of deposition temperature. Inset shows Hall bar with a lateral size of $8\times 3$ mm${}^2$.

Figure 3

Representative set of Hall effect measurements of ${\text{Co}}_2{\text{FeSi}}_{0.6}{\text{Al}}_{0.4}$ deposited at (a) $700{}^{°}\text{C}$, (b) $667{}^{°}\text{C}$, (c) $612{}^{°}\text{C}$, (d) $550{}^{°}\text{C}$, (e) $520{}^{°}\text{C,}$ and (f) $480{}^{°}\text{C}$. The legend on Fig. 3a indicates the respective measurement temperatures and is valid for (a)–(f).

Figure 4

Anomalous Hall resistivity [(d) Anomalous Hall conductivity] against longitudinal resistivity [(d) longitudinal conductivity]. Each curve corresponds to one sample and consists of the data points extracted from measurements at 5, 55, 105, 155, 205, 240, and 280 K, respectively. In the legend the deposition temperature of each sample is noted [(c) and (d) share the legend]. The films are made of (a) ${\text{Co}}_2{\text{FeSi}}_{0.6}{\text{Al}}_{0.4}$ and (b) ${\text{Co}}_2{\text{FeGa}}_{0.5}{\text{Ge}}_{0.5}$ on $\text{MgO}$ and (c),(d) ${\text{Co}}_2{\text{FeGa}}_{0.5}{\text{Ge}}_{0.5}$ on ${\text{Al}}_2{\text{O}}_3$.

Figure 5

Left column: ${\rho }_{\mathit{xy}}^{\text{AHE}}(T)-{\rho }_{\mathit{xy}}^{\text{AHE}}(50\mathrm{K})$ against ${\rho }_{\mathit{xx}}(T)-{\rho }_{\mathit{xx}}(50\text{K})$. Each point represents data from one temperature curve of Fig. 3. The different lines represent samples deposited at different temperatures as given in the legend. Right column: linear (black squares, left ordinate) and quadratic ($\sigma {}^{\text{AH-}\mathit{bj}}$, red circles, right ordinate) fitting coefficients against deposition temperatures. ${\text{Co}}_2{\text{FeSi}}_{0.6}{\text{Al}}_{0.4}$ on $\text{MgO}$ (a) and ${\text{Co}}_2{\text{FeGa}}_{0.5}{\text{Ge}}_{0.5}$ on $\text{MgO}$ (b) and ${\text{Al}}_2{\text{O}}_3$ (c).