Magnetic properties of ${\mathrm{Gd}}_x{\mathrm{Y}}_{1-x}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}$: Dilute, large-$\mathbf{S}$ moments in a nearly ferromagnetic Fermi liquid

Single crystals of the dilute, rare earth bearing, pseudoternary series ${\mathrm{Gd}}_x{\mathrm{Y}}_{1-x}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}$ were grown out of Zn-rich solution. Measurements of magnetization, resistivity, and heat capacity on ${\mathrm{Gd}}_x{\mathrm{Y}}_{1-x}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}$ samples reveal ferromagnetic order of the ${\mathrm{Gd}}^{3+}$ local moments across virtually the whole series $(x⩾0.02)$. The magnetic properties of this series, including the ferromagnetic ordering, the reduced saturated moments at base temperature, the deviation of the susceptibilities from Curie-Weiss law, and the anomalies in the resistivity, are understood within the framework of dilute, $\mathbf{S}$ moments $\left({\mathrm{Gd}}^{3+}\right)$ embedded in a nearly ferromagnetic Fermi liquid $\left(\mathrm{Y}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}\right)$. The $s\text{−}d$ model is employed to further explain the variation of $T_C$ with $x$ as well as the temperature dependences of the susceptibilities.

Figure 1

(Color online) (a) Powder x-ray diffraction pattern of $\mathrm{Gd}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}$ with a Si internal standard (using $\mathrm{Cu}K\alpha$ radiation) with main peaks indexed. (b) The normalized intensity of the (117) peak of ${\mathrm{Gd}}_x{\mathrm{Y}}_{1-x}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}$ for representative $x$ values, with the positions calibrated by the nearby Si(002) peak.

Figure 2

Magnetization $M$ with respect to applied field $H$ for a sample of ${\mathrm{Gd}}_{0.5}{\mathrm{Y}}_{0.5}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}$ at 150, 200, and $300\mathrm{K}$. The solid lines are guides to the eye. (a) Detailed magnetization of two samples of ${\mathrm{Gd}}_{0.5}{\mathrm{Y}}_{0.5}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}$ at $300\mathrm{K}$. The data set shown as solid squares (same data as in main figure) has slope change feature (indicated by an arrow); while the data set shown as open circles does not. (b) The difference of the two data sets reveals the saturation of ferromagnetic impurity above $5\mathrm{kOe}$.

Figure 3

Gd concentration inferred from EDS (solid squares) and high-temperature magnetic susceptibility (solid circles). The open triangles represent lattice constants. The dashed line is the location where inferred $x$ equals nominal $x$ and also represents a linear dependence of the lattice parameter.

Figure 4

(Color online) $1∕{\chi }_{{\mathrm{Gd}}^{3+}}$ vesus temperature for representative members of the ${\mathrm{Gd}}_x{\mathrm{Y}}_{1-x}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}$ series. Note that data are normalized to mole Gd using $x$ inferred from high-temperature data. From right-down to left-up: $x=1$, 0.75, 0.5, 0.25, 0.1, 0.05, and 0.035. (a) Obtained under high magnetic field. (b) Solid lines: obtained under $1\mathrm{kOe}$ applied field; dashed lines: under high magnetic field.

Figure 5

(Color online) Temperature dependent magnetization of ${\mathrm{Gd}}_x{\mathrm{Y}}_{1-x}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}$, $H=1000\mathrm{Oe}$, for (a) $1.0⩾x⩾0.175$ and (b) $x⩽0.175$.

Figure 6

(Color online) [(a) and (b)] Field-dependent magnetization of ${\mathrm{Gd}}_x{\mathrm{Y}}_{1-x}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}$ at $1.85\mathrm{K}$. (c) Field-dependent magnetization of ${\mathrm{Gd}}_x{\mathrm{Y}}_{1-x}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}$ at $1.85\mathrm{K}$, normalized to ${\mathrm{Gd}}^{3+}$ content (see text). The error bars were estimated by allowing for a $\pm 0.02$ variation of $x$.

Figure 7

Arrott plots for representative members of the ${\mathrm{Gd}}_x{\mathrm{Y}}_{1-x}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}$ series: $x=\left(\mathrm{a}\right)$ 0.5, (b) 0.035, and (c) 0.02.

Figure 8

(Color online) Zero-field resistivity for current along the [110] direction. The arrows represent $T_C$ determined from Arrott plot analyses.

Figure 9

(Color online) Temperature variation of $\Delta \rho$ (see text). The arrows represent $T_C$ determined from Arrott plot analysis of magnetization measurements.

Figure 10

(Color online) Temperature variation of specific heat $C_p$ of the ${\mathrm{Gd}}_x{\mathrm{Y}}_{1-x}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}$ series for $x=1$, 0.75, 0.5, and 0. The arrows represent $T_C$ determined from Arrott plot analyses.

Figure 11

(Color online) Temperature variation of $\Delta C$. (a) From right to left, $x=1$, 0.75, 0.5, 0.25, and 0.175. (b) From right to left, $x=0.175$, 0.1, 0.05, 0.0375, and 0.02. The arrows represent $T_C$ values determined from the Arrott analysis of magnetization measurements.

Figure 12

(Color online) $\Delta C∕x$ versus $T∕T_C$ for representative $x$ values.

Figure 13

(Color online) (a) Paramagnetic Curie temperature, ${\theta }_C$, (b) ferromagnetic ordering temperature, $T_C$, (c) saturated moment per Gd, ${\mu }_{\mathit{sat}}$, and (d) magnetic entropy, $S_M$, with respect to $x$ for the ${\mathrm{Gd}}_x{\mathrm{Y}}_{1-x}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}$ series. The values of $T_C$ in (b) were determined by Arrott plot analyses (black circle) and the resistivity measurements (open circle). The solid line in (d) represents $S_M=xR\ln 8$ ($R$ is gas constant), the magnetic entropy of ${\mathrm{Gd}}^{3+}$ Hund’s ground state. The error bars are estimated as 1% of the total entropy, $S={\int }_0^{T_C}\frac{C_p}{T}dT$.

Figure 14

$T_C$ of ${\mathrm{Gd}}_x{\mathrm{Y}}_{1-x}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}$ versus $x{\chi }_{\mathrm{Y}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}}\left(T_C\right)$. The solid line is a linear fit through the origin point.

Figure 15

(Color online) $1∕\chi$ of ${\mathrm{Gd}}_x{\mathrm{Y}}_{1-x}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}$ versus $T$ for representative $x$ values. Dotted lines: measured under $1\mathrm{kOe}$ applied field; dash lines: obtained under high magnetic field; solid lines: calculated results (see text).