Physical properties of GdFe${}_2$(Al${}_x$Zn${}_{1-x}$)${}_{20}$

The high ferromagnetic ordering temperature of the dilute, rare-earth-bearing, intermetallic compound ${\mathrm{GdFe}}_2{\mathrm{Zn}}_{20}$ has been understood as being the consequence of the Gd${}^{3+}$ moment being embedded in a nearly ferromagnetic Fermi liquid. To test this understanding in detail, single crystals of the pseudoternary series ${\mathrm{GdFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$ ($x⩽0.122$) and ${\mathrm{YFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$ ($x⩽0.121$) were grown out of Zn-rich solution. Magnetization, heat capacity, and resistivity measurements show that, with Al doping, the ferromagnetic phase transition temperatures of the ${\mathrm{GdFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$ compounds decrease from 86 K ($x=$ 0) to 10 K ($x=$ 0.122); for the nonmagnetic analog, the ${\mathrm{YFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$ series, the Stoner enhancement factor $Z$ decreases from 0.88 ($x=$ 0) to 0.35 ($x=$ 0.121) in a similar manner. Tight-binding linear-muffin-tin orbital atomic-sphere approximation band structure calculations are used to rationalize this trend. These results, together with the earlier studies of the $R({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{Zn}}_{20}$ ($R=$ Gd and Y) series, clearly highlight the importance of band filling and the applicability of even a simple, rigid-band model to these compounds.

Figure 1

Room-temperature $M(H)$. The arrow draws attention to the slight nonlinearity of the $M(H)$ curve at room temperature.

Figure 2

Normalized lattice parameters measured at $~300$ K. For the ${\mathrm{GdFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$ series, $a_0=14.120$ $\AA$. For the ${\mathrm{YFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$ series, $a_0=14.097$ $\AA$. Inset: $x_{\mathrm{WDS}}$ vs $x_{\mathrm{nominal}}$.

Figure 3

(a) Temperature-dependent magnetic susceptibility data for ${\mathrm{GdFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$ taken at 1 kOe with $H$ along the [111] direction. (b) Field-dependent magnetization data for ${\mathrm{GdFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$ taken at 1.85 K with $H$ along the [111] direction. (c) Temperature-dependent $H/M$ data for ${\mathrm{GdFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$.

Figure 4

Isotherms of $M^2$ vs $H/M$ for the ${\mathrm{GdFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$ series. The temperature at which each measurement was taken is labeled.

Figure 5

Derivative of the resistivity for the ${\mathrm{GdFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$ series. The arrow shows the criterion used to infer critical temperature. Each subsequent data set is shifted downward by $1\times {10}^{-7}\hspace{0.5em}\mathrm{\mu }\mathrm{\Omega }\mathrm{\hspace{0.5em}}\mathrm{cm}/\mathrm{K}$ for clarity. Inset: Resistivity of ${\mathrm{GdFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$ from 1.85 to 300 K.

Figure 6

(a) $C_p$ vs $T$ for $x=0$, 0.005, 0.010, and 0.017 Al-doped ${\mathrm{GdFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$ series. Inset: $C_p$ vs $T$ for $x=0.047$, 0.069, and 0.122 Al-doped ${\mathrm{GdFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$ series. (b) $C_M$ vs $T$ for ${\mathrm{GdFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$ series. Arrows indicate $T_c$ values determined from the Arrot plot. Thin solid lines on $x=$ 0.005 and 0.017 data sets show criteria used to infer $T_c$.

Figure 7

(a) Temperature-dependent $\Delta M/\Delta H$ for ${\mathrm{YFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$ with $H$ parallel to the [111] direction. (b) $C_p/T$ vs $T^2$ for ${\mathrm{YFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$ series.

Figure 8

(a) $x$-dependent Stoner enhancement factor $z$ for Co-doped and Al-doped ${\mathrm{YFe}}_2{\mathrm{Zn}}_{20}$. (b) $x$-dependent $T_c$ for Co-doped and Al-doped ${\mathrm{GdFe}}_2{\mathrm{Zn}}_{20}$. The data for Co-doped ${\mathrm{YFe}}_2{\mathrm{Zn}}_{20}$ and ${\mathrm{GdFe}}_2{\mathrm{Zn}}_{20}$ are obtained from Ref. 9.

Figure 9

The total density of states (states/eV cell) of ${\mathrm{YCo}}_2{\mathrm{Zn}}_{20}$ and ${\mathrm{YFe}}_2({\mathrm{Al}}_x{\mathrm{Zn}}_{1-x}{)}_{20}$ ($x=0$, 0.05, and 0.1). The Fermi level is indicated as the vertical line.