Effect of carrier localization on anomalous Hall effect in the structurally chiral $\beta \text{−}\mathrm{Mn}$ type ${\mathrm{Co}}_7{\mathrm{Zn}}_7{\mathrm{Mn}}_6$ alloy

The effect of carrier localization due to electron-electron interaction in the anomalous Hall effect is elusive and there are contradictory results in the literature. To address the issue, we report here the detailed transport study including the Hall measurements on $\beta$-Mn type cubic compound ${\mathrm{Co}}_7{\mathrm{Zn}}_7{\mathrm{Mn}}_6$ with a chiral crystal structure, which lacks global mirror symmetry. The alloy orders magnetically below $T_c$ = 204 K, and is reported to show spin glass state at low temperature. The longitudinal resistivity (${\rho }_{xx}$) shows a pronounced upturn below $T_{\text{min}}$ = 75 K, which is found to be associated with carrier localization due to quantum interference effect. The upturn in ${\rho }_{xx}$ shows a $T^{1/2}$ dependence and it is practically insensitive to the externally applied magnetic field, which indicates that electron-electron interaction is primarily responsible for the low-$T$ upturn. The studied sample shows a considerable value of the anomalous Hall effect below $T_c$. We found that the localization effect is present in the ordinary Hall coefficient ($R_0$), but we failed to observe any signature of localization in the anomalous Hall resistivity or conductivity. The absence of localization effect in the anomalous Hall effect in ${\mathrm{Co}}_7{\mathrm{Zn}}_7{\mathrm{Mn}}_6$ may be due to large carrier density, and it warrants further theoretical investigations, particularly with systems having broken mirror symmetry.

Figure 1

(a) Crystal structure of ${\mathrm{Co}}_7{\mathrm{Zn}}_7{\mathrm{Mn}}_6$) (${\mathrm{P}4}_{1}32$-right-handed structure) as viewed along the [111] direction. (b) Powder x-ray diffraction pattern of ${\mathrm{Co}}_7{\mathrm{Zn}}_7{\mathrm{Mn}}_6$ (data points) and Rietveld refinement curves (solid line) at 10 K. (c) Thermal variation of lattice parameter ($a$).

Figure 2

(a) The magnetization ($M$) as a function of the temperature ($T$) measured in zero field-cooled-heating (ZFCH), field-cooled (FC), and field-cooled-heating (FCH) protocols under $H$ = 100 Oe. The inset shows the temperature derivative of $M\left(T\right)$. (b) Susceptibility ($\chi$) versus temperature ($T$) fitted with modified Curie-Weiss law (left axis) and inverse susceptibility (${\chi }^{-1}$) versus temperature ($T$) data with liner fitting (right axis), measured at $H$ = 1 kOe. (c) Isothermal magnetization at different temperatures measured between $\pm 50$ kOe. (d) Enlarged view of the $M$ vs $H$ curve at 3 K and 100 K plotted between $\pm$ 5 kOe. (e) Shows isothermal magnetization data measured at 3 K after being cooled at zero and $+1$ k Oe. (f) Shows the variation of exchange bias field (${\mathrm{H}}_{\text{EB}}$) on left axis and coercive field (${\mathrm{H}}_C$) on right axis as a function of cooling field (${\mathrm{H}}_{\text{cool}}$) at 3K.

Figure 3

(a) The $T$ variation of resistivity (${\rho }_{xx}$). The inset a(i) shows the $\frac{d{\rho }_{xx}}{dT}$ vs $T$ curve and a(ii) shows ${\rho }_{xx}$ vs $T^{1/2}$ plot below 50 K, along with a linear fit to the data. (b) ${\rho }_{xx}$ vs $T$ data at $H$= 0, 50 kOe fitted with Eq. (2).

Figure 4

(a) Isothermal field dependent MR. (b) Main panel shows $H^{2/3}$ dependence of $MR$ vs $H$ near the transition temperature, inset shows the $H^2$ dependence of $MR$ vs $H$ at 300 K. (c) Linear field dependence of MR well below the transition temperature.

Figure 5

(a) Hall resistivity (${\rho }_{xy}$) vs $H$ at different constant $T$. (b) ${\rho }_{xy}$ vs $H$ at $T=5$ K with a linear fit to the high field data. (${\rho }_{xy}$) vs $H, {\rho }_{xy}^{\text{AHE}}/{\rho }_{xx}$ vs ${\rho }_{xx}$ plot with linear fit. (c) $T$ variation of ${\rho }_{xy}^{\text{AHE}}$. (d) ${\sigma }_{xy}^{\text{AHE}}$ vs $T$ fitted with Eq. (4) and the inset shows the saturation magnetization ($M_s$) as a function of $T$ and fitted with Eq. (4). (e) $T$ variation of ordinary Hall coefficient ($R_0$) and anomalous Hall coefficient ($R_s$).