Magnetic properties of graphene nanodisk and nanocone powders at low temperatures

Our aim is the study of magnetization phenomena of carbon powders consisting of graphene nanocones and nanodisks. Magnetization measurements were carried out using a superconducting quantum interference device in magnetic fields $-5<B<5\mathrm{T}$ for temperatures in the range $0.5\le T<300\mathrm{K}$. We have observed that magnetization $M$ depends on temperature $T$ as a power law $M\propto T^{-\alpha }$ where the scaling exponent $\alpha =0.79\pm 0.04$ was determined. We found that the magnetization consists of a diamagnetic background and a paramagnetic contribution of localized spins. Considering saturation magnetization $M_S$ in the free spin magnetization model and diamagnetic susceptibility ${\chi }_D$ for independent of temperature $T$ we found that the effective spin value $S$ increases from $S=1/2$ at temperature $T>20\mathrm{K}$ to $S=3$ at low temperatures $0.5\le T\le 20\mathrm{K}$.

Figure 1

PIXE spectra of (a) the pure Cyclopore membrane and (b) typical PIXE spectra of HT-1600 carbon powder on a Cyclopore membrane.

Figure 2

Magnetizations $M_{\text{ZFC}}$ and $M_{\text{FC}}$ vs temperature $T$ in magnetic field $B=0.1\mathrm{T}$ after metallic impurity, gelatine capsule magnetizations, and the diamagnetic background are subtracted. (a) Magnetization $M_{\text{ZFC}}$ follows the power law $M_{\text{ZFC}}\propto T^{-\alpha },\alpha =0.83\pm 0.02$, for temperature $1.8\le T<60\mathrm{K}$. (b) Magnetization $M_{\text{ZFC}}$ at low temperature $T<1.8\mathrm{K}$ follows the power law $M_{\text{ZFC}}\propto T^{-\alpha }$ with exponent $\alpha =0.76\pm 0.05$.

Figure 3

Curves for carbon magnetization $M$ vs magnetic field $B$ for temperature (a) $T\ge 1.8\mathrm{K}$ and (b) $T=0.5$ and 1.0 K. The data shown here have been corrected by subtracting measured magnetization of the gelatine capsule and of metallic impurities from the measured carbon sample data. The solid lines represent fits of the experimental data considering effects of diamagnetic and paramagnetic free spin magnetizations [Eqs. (4) and (5)].

Figure 4

Magnetization $M$ vs magnetic field $B$ at selected temperatures in the intervals (a) $1.8\le T<50$ K and (b) $T=0.5$ and $1\mathrm{K}$. Here, the magnetization of the gelatin capsule, the ferromagnetic background of metallic impurities, and the diamagnetic background of the carbon powder have been subtracted from the measured data. Solid lines show approximations to these corrected data based on Eq. (2). For each temperature, the value of $S$ that gave the best fit is shown.

Figure 5

$M/M_S$ vs $B/T$ plots for temperatures (a) $1.8\le T\le 50$ K and (b) $T=0.5$ and $1\mathrm{K}$. Solid lines show approximations to these corrected data based on Eq. (2) using either $S=\frac{1}{2}$ or $S=3$. The inset shows a detail near origin of coordinate axes.

Figure 6

Arrott plots of the background corrected data in the temperature range $0.5\le T\le 10\mathrm{K}$.