Correlation between compensation temperatures of magnetization and angular momentum in GdFeCo ferrimagnets

Determining the angular momentum compensation temperature of ferrimagnets is an important step towards ferrimagnetic spintronics, but it is not generally easy to achieve it experimentally. We propose a way to estimate the angular momentum compensation temperature of ferrimagnets without a dynamical characterization technique. We derive a simple equation that relates the magnetization compensation temperature, the Curie temperature, and the angular momentum compensation temperature based on the critical exponent approximation. We show that the derived equation can explain our experimental results and can be used to estimate the angular momentum compensation temperature from the temperature dependence of magnetization.

Figure 1

(a) Schematic of the GdFeCo microwire device, and (b) anomalous Hall effect resistance $R_{\mathrm{H}}$ as a function of the perpendicular magnetic field ${\mu }_0{H}_z$ at room temperature (300 K). The orange arrow indicates the coercive field ${\mu }_0{H}_{\mathrm{c}}$ and the black up-down arrow indicates the Hall resistance difference $\mathrm{\Delta }{R}_{\mathrm{H}}\equiv R_{\mathrm{H}}\left(+{\mu }_0{H}_{z,\mathrm{sat}}\right)-R_{\mathrm{H}}\left(-{\mu }_0{H}_{z,\mathrm{sat}}\right)$, where $+{\mu }_0{H}_{z,\mathrm{sat}}$ and $-{\mu }_0{H}_{z,\mathrm{sat}}$ are the saturation fields with the condition ${\mu }_0{H}_{\mathrm{c}}<{\mu }_0{H}_{z,\mathrm{sat}}$.

Figure 2

(a) $\mathrm{\Delta }{R}_{\mathrm{H}}$ as a function of the temperature $T$ for sample II. The blue dot indicates the magnetization compensation temperature $T_{\mathrm{M}}$, and (b) DW speed $v$ as a function of $T$ for sample II at ${\mu }_0{H}_z=80\mathrm{mT}$. The blue dot indicates the magnetization compensation temperature $T_{\mathrm{M}}$, and the purple arrow indicates the angular momentum compensation temperature $T_{\mathrm{A}}$.

Figure 3

(a) $T_{\mathrm{A}}$ with respect to $T_{\mathrm{M}}$. The red line is the best linear fit. (b) $T_{\mathrm{A}}/T_{\mathrm{C}}$ with respect to $T_{\mathrm{M}}/T_{\mathrm{C}}$. The red line is the best linear fit.

Figure 4

(a) Temperature $T$ dependence of the total magnetization $M_{\mathrm{net}}$. The solid red line indicates the best fitting based on Eq. (5). (b) Temperature $T$ dependence of the extracted sub-magnetic moments. (c) $\eta$ with respect to the sample number (the red dot indicates $\eta =0.19$).

Figure 5

$T_{\mathrm{A}}^{*}$ with respect to $T_{\mathrm{A}}$. The red line is the linear fit with slope $=1$ and $y$-axis interception $=0$.