Low-temperature scaling of the susceptibility of Ni films

Measurement of low field ac susceptibility of Ni thin films over the temperature range of $5–300\mathrm{K}$ reveals a surprising power law scaling. The temperature-dependent part of the normalized susceptibility, ${\chi }_{\parallel }∕M_S-{\chi }_{\mathrm{rot}}∕M_S$, where ${\chi }_{\parallel }$ is the initial susceptibility for in-plane magnetization, ${\chi }_{\mathrm{rot}}$ is the domain rotation contribution, and $M_S$ is the saturation magnetization, scales with the nonlinear reduced temperature as $t^{-2}$ over the entire temperature range, where $t=(T-T_C)∕(T+T_C)$ and $T_C$ is the Curie temperature. Thickness and reduced temperature dependences are completely decoupled. This result implies that domain wall motion does not contribute to the low field susceptibility.

Figure 1

(Color online) $M\text{−}H$ for $5\mathrm{nm}$ (inset) and $284\mathrm{nm}$ samples for both $H\parallel \text{film}$ and $H\perp \text{film}$.

Figure 2

(Color online) Reduced saturation magnetization as a function of reduced temperature $T∕T_C$ for Ni films. Dashed curve is bulk Ni. Inset: $T_C$ versus film thickness.

Figure 3

(Color online) Normalized low field anisotropic susceptibility versus temperature for a Ni film of thickness $151\mathrm{nm}$. Inset: Normalized low field out-of-plane susceptibility versus temperature for Ni films of different thicknesses.

Figure 4

(Color online) The normalized initial susceptibility at $T=10\mathrm{K}$ for $H\parallel \text{film}$ (black squares) and $H\perp \text{film}$ (red circles).

Figure 5

(Color online) Temperature-dependent part of the normalized susceptibility, ${\chi }_{\parallel }\left(T\right)∕M_S\left(T\right)-{\chi }_{\mathrm{rot}}\left(0\right)∕M_S\left(0\right)$, for Ni films of different thicknesses, as a function of $t=(T-T_C)∕(T+T_C)$. The data by Baberschke (Ref. 1) and for the bulk sample by Onnes and Perrier (Ref. 12) are also shown. Inset shows the data by Baberschke (Ref. 1) closer to the critical temperature. Solid curve is fitted using Eq. (2).

Figure 6

(Color online) Correlation between ${\chi }_{\mathrm{rot}}\left(0\right)∕M_S\left(0\right)$ and $\alpha$. The line shows linear correlation. Inset: Thickness dependence of both quantities.