Spatial Evolution of the Ferromagnetic Phase Transition in an Exchange Graded Film

A combination of experiments and numerical modeling was used to study the spatial evolution of the ferromagnetic phase transition in a thin film engineered to have a smooth gradient in exchange strength. Mean-field simulations predict, and experiments confirm, that a 100 nm ${\mathrm{Ni}}_x{\mathrm{Cu}}_{1-x}$ alloy film with Ni concentration that varies by 9% as a function of depth behaves predominantly as if composed of a continuum of uncoupled ferromagnetic layers with continuously varying Curie temperatures. A mobile boundary separating ordered and disordered regions emerges as the temperature is increased. We demonstrate continuous control of the boundary position with temperature, and reversible control of the magnetization on both sides of the boundary with the magnetic field.

Figure 1

Derivative of magnetic moment with respect to temperature for the uniform $x=0.61$ (black), graded $x=0.61–0.70$ (purple), and uniform $x=0.70$ (pink) samples.

Figure 2

Exchange strength gradient model. (a) Depth-dependent exchange strength. (b), (c) Magnetization profiles at 0.84 $T_C$ and 0.91 $T_C$, respectively. Symbols in (b) and (c) are the results of mean-field simulations, solid curves are fits using a closed-form function. Dashed vertical lines in (b) and (c) indicate $z_C$.

Figure 3

(a) Fitted PNR data. Inset shows best-fit magnetic parameters. $2\sigma$ fitting uncertainties are $<3\mathrm{K}$ for $T_{Ci}$ and $T_{Cf}$, $<2\mathrm{kA}{\mathrm{m}}^{-1}$ for $M_S$, and $<0.002$ for $h$. (b),(c) Fitted data in (a) plotted as spin asymmetry. Error bars correspond to $\pm 1\sigma$.

Figure 4

Nuclear (a) and magnetic (b) profiles corresponding to the fits in Fig. 3. (c) Temperature dependence of the depth corresponding to half the maximum magnetization. Solid curve is a guide to the eye.

Figure 5

(a), (b) Fitted PNR data plotted as spin asymmetry show clear reversible behavior, as well as a strong field-dependent amplitude. Error bars correspond to $\pm 1\sigma$. (c) Magnetic profiles corresponding to the fits in (a) and (b).