Disorder-induced depression of the Curie temperature in mechanically milled $\mathrm{Gd}{\mathrm{Al}}_2$

The effect of disorder on the ferromagnetic transition is investigated in mechanically milled $\mathrm{Gd}{\mathrm{Al}}_2$. $\mathrm{Gd}{\mathrm{Al}}_2$ is a ferromagnet when crystalline and a spin glass when amorphous. Mechanical milling progressively disorders the alloy, allowing observation of the change from ferromagnetic to a disordered magnetic state. X-ray diffraction and pair-distribution-function analysis are used to determine the grain size, lattice parameter, and mean-squared atomic displacements. The magnetization as a function of temperature is described by a Gaussian distribution of Curie temperatures. The mean Curie temperature decreases with decreasing lattice parameter, where lattice parameter serves as a measure of defect concentration. Two different rates of change with lattice parameter are observed: the first, slower rate occurs while grain size is changing, and the grain size is constant in the second regime. The breadth of the Curie temperature distribution is linear with lattice parameter. Milled and annealed $\mathrm{Gd}{\mathrm{Al}}_2$ shows that the mean Curie temperature has the same general dependence on lattice parameter as milled, but unannealed $\mathrm{Gd}{\mathrm{Al}}_2$, while the breadth of the Curie temperature distribution is different in annealed samples compared to the unannealed materials.

Figure 1

X-ray diffraction patterns showing the decrease in peak height and peak broadening as the sample is milled.

Figure 2

(a) The root-mean-square microstrain and (b) the grain size as functions of milling time.

Figure 3

Reduced structure functions for unmilled $\mathrm{Gd}{\mathrm{Al}}_2$ (bottom) and $\mathrm{Gd}{\mathrm{Al}}_2$ milled for times of $100\mathrm{h}$ (middle) and $400\mathrm{h}$ (top).

Figure 4

(a) Mean-squared atomic displacement and (b) lattice parameter as functions of milling time. The lines are guides to the eye.

Figure 5

$M_{\mathit{ZFC}}\left(T\right)$. The lower figure shows details of the behavior near $T_C$.

Figure 6

$d{M}_{\mathit{ZFC}}\left(T\right)∕dT$ for various milling times as a function of temperature. All measurements were made at a field of $100\mathrm{Oe}$.

Figure 7

Changes in (a) ${\overline{T}}_C$ and (b) grain size with milling time in mechanically milled $\mathrm{Gd}{\mathrm{Al}}_2$.

Figure 8

${\overline{T}}_C$ as a function of percent change of lattice parameter. Different symbols represent samples from different milling runs. The open symbols represent samples milled and subsequently annealed. The letter A refers to a group of points with similar values of $T_C$ and $a$, but very different grain sizes.

Figure 9

The dependence of the distribution breadth $\Delta T_C$ on percent change in lattice parameter in mechanically milled $\mathrm{Gd}{\mathrm{Al}}_2$. Different symbols represent samples from different milling runs. Open symbols represent samples that were milled and subsequently annealed.

Figure 10

The real (top) and imaginary (bottom) susceptibilities of a sample milled for $350\mathrm{h}$ measured at $1\mathrm{Oe}$ with no dc bias field.

Figure 11

The dependence of the real (top) and imaginary (bottom) susceptibility as a function of temperature and dc bias field measured at $55\mathrm{Hz}$ for a sample milled for $350\mathrm{h}$.

Figure 12

$\chi \left(T\right)$ for $\mathrm{Gd}{\mathrm{Al}}_2$ milled for $590\mathrm{h}$ (triangles), then annealed $400°\mathrm{C}$ (squares), $600°\mathrm{C}$, (diamonds), and $800°\mathrm{C}$ (right-pointing triangles). All annealing times were for $10\min$ with the exception of the $800°\mathrm{C}$ anneal, which was for $48\mathrm{h}$. Open symbols represent ZFC and closed symbols FC measurements.