Complex anomalous Hall effect of CoGd alloy near the magnetization compensation temperature

In this article, the temperature-dependent complex Hall effect near the magnetization compensation temperature of CoGd alloy films is systematically studied. We find anomalies of Hall loops with characteristics similar to the topological Hall effect (THE), which is usually considered to indicate the occurrence of topological spin texture. However, the THE is ruled out by detailed magnetic and transport measurements on CoGd alloy films with different composition ratios. After considering the influence of the spin-flop effect and the inhomogeneity of the components naturally formed in the ferrimagnetic CoGd alloy, we constructed a phenomenological model that can explain the complex Hall effect near the magnetization compensation point without relying on the THE. The main result is helpful for explaining the microscopic magnetic properties and transport properties of rare-earth transition metal ferrimagnetic alloys near the compensation point.

Figure 1

(a) The Hall loops of ${\mathrm{Co}}_{79.7}{\mathrm{Gd}}_{20.3}$ at different temperatures, which are shifted longitudinally for convenience. The positions of the spin-flop field $H_{\mathrm{f}}$ are indicated by the red arrows. The abnormal humps indicated by the black arrows are observed at 240, 256, and 280 K, and we call them the type-I humps. The inset shows a locally enlarged loop at 256 K, where the humps marked by the blue arrows are defined as the type-II hump. (b) Temperature-dependent $H_{\mathrm{f}}$ for ${\mathrm{Co}}_{79.7}{\mathrm{Gd}}_{20.3}$. The black line is a guide for the eye, and the type-I hump appears in the temperature range marked by the gray shaded area. The cross-reference of $M-H$ loop and the Hall loop for ${\mathrm{Co}}_{79.7}{\mathrm{Gd}}_{20.3}$ at (c) 100 K and (d) 280 K. The loop at 100 K is reversed for comparison. The magnetic moment states within the corresponding magnetic field range are shown in dashed boxes, where the red, blue, and purple arrows represent ${\mathit{\mu }}_{\mathrm{Gd}}, {\mathit{\mu }}_{\mathrm{Co}}$, and ${\mathit{\mu }}_{\mathrm{net}}$, respectively.

Figure 2

The Hall loops of (a) ${\mathrm{Co}}_{79.7}{\mathrm{Gd}}_{20.3}$ and (b) ${\mathrm{Co}}_{80.7}{\mathrm{Gd}}_{19.3}$ at different temperatures, which are shifted longitudinally for convenience. The red and blue dotted lines with arrows represent the direction of the magnetic field scan. The definitions of $V_{\mathrm{H}}, V_{\mathrm{hump}}, H_{\mathrm{hump}}$, and $H_C$ are indicated.

Figure 3

Temperature-dependent $H_{\mathrm{hump}}$ of (a) ${\mathrm{Co}}_{79.7}{\mathrm{Gd}}_{20.3}$ and (b) ${\mathrm{Co}}_{80.7}{\mathrm{Gd}}_{19.3}$. Temperature-dependent $V_{\mathrm{hump}}$ and $V_{\mathrm{H}}$ of (c) ${\mathrm{Co}}_{79.7}{\mathrm{Gd}}_{20.3}$ and (d) ${\mathrm{Co}}_{80.7}{\mathrm{Gd}}_{19.3}$. The insets show $V_{\mathrm{H}}$ versus temperature within larger temperature range. (e) The dependence of magnetization compensation temperature $T_{\mathrm{M}}$ on Gd atom concentration $X$. The black line is a linear fit of the data.

Figure 4

The minor loops of ${\mathrm{Co}}_{79.7}{\mathrm{Gd}}_{20.3}$ at 254 K. The maximum positive magnetic field is fixed at 8.0 kOe and the maximum negative magnetic field ${H_{\mathrm{n}}}_{-\max }$ changes from 1.5 to 8.0 kOe.

Figure 5

Schematic diagram of a model based on inhomogeneous composition. (a)–(e) The relative variation in the proportions of the two phases with increasing temperature for a sample with average concentration $X_{\mathrm{S}}$. Model A and Model B correspond to the cases of ${\mathrm{Co}}_{79.1}{\mathrm{Gd}}_{20.9}$ and ${\mathrm{Co}}_{80.7}{\mathrm{Gd}}_{19.3}$, respectively.

Figure 6

Temperature-dependent $H_{\mathrm{C}}$ of (a) ${\mathrm{Co}}_{79.7}{\mathrm{Gd}}_{20.3}$ and (b) ${\mathrm{Co}}_{80.7}{\mathrm{Gd}}_{19.3}$. The red and blue lines are to guide the eyes.