Magnetic properties of $R{\text{Fe}}_2{\text{Zn}}_{20}$ and $R{\text{Co}}_2{\text{Zn}}_{20}$ $\left(R=\text{Y},\text{Nd},\text{Sm},\text{Gd}\text{–}\text{Lu}\right)$

Magnetization, resistivity, and specific heat measurements were performed on solution-grown single crystals of $R{\text{Fe}}_2{\text{Zn}}_{20}$ and $R{\text{Co}}_2{\text{Zn}}_{20}$ $\left(R=\text{Y},\text{Nd},\text{Sm},\text{Gd-Lu}\right)$. Whereas ${\text{LuCo}}_2{\text{Zn}}_{20}$ and ${\text{YCo}}_2{\text{Zn}}_{20}$ manifest unremarkable metallic behavior, ${\text{LuFe}}_2{\text{Zn}}_{20}$ and ${\text{YFe}}_2{\text{Zn}}_{20}$ display behaviors such as characteristic of nearly ferromagnetic Fermi liquids. When the well-defined $4f$ local moments $\left({\text{Gd}}^{3+}{\text{-Tm}}^{3+}\right)$ are embedded into this strongly polarizable host, they manifest enhanced ferromagnetic ordering and the values of $T_{\text{C}}$ for $R{\text{Fe}}_2{\text{Zn}}_{20}$ $\left(R=\text{Gd-Tm}\right)$ scale with the de Gennes factor. In addition, data on the $R{\text{Fe}}_2{\text{Zn}}_{20}$ compounds indicate a small crystal electric field (CEF) effect compared with the interaction energy scale. On the other hand, the local moment bearing members of $R{\text{Co}}_2{\text{Zn}}_{20}$ $\left(R=\text{Nd},\text{Sm},\text{Gd-Tm}\right)$ manifest weak magnetic interactions and the magnetic properties for $R=\text{Dy-Tm}$ members are strongly influenced by the CEF effect on the $R$ ions. The magnetic anisotropy and specific heat data for the Co series were used to determine the CEF coefficient of $R$ ion with its cubic point symmetry. These CEF coefficients, determined for the Co series, are consistent with the magnetic anisotropy and specific heat data for the Fe series, which indicates similar CEF effects for the Fe and Co series. Such analysis, combined with specific heat and resistivity data, indicates that for $R=\text{Tb-Ho}$, the CEF splitting scale is smaller than their $T_{\text{C}}$ values, whereas for ${\text{ErFe}}_2{\text{Zn}}_{20}$ and ${\text{TmFe}}_2{\text{Zn}}_{20}$ the $4f$ electrons lose part of their full Hund’s rule ground state degeneracy above $T_{\text{C}}$. ${\text{YbFe}}_2{\text{Zn}}_{20}$ and ${\text{YbCo}}_2{\text{Zn}}_{20}$ manifest typical but distinct heavy fermion behaviors associated with different Kondo temperatures.

Figure 1

(Color online) (a) The cubic unit cell of $R{T}_2{\text{Zn}}_{20}$. (b) The CN-16 Frank-Kasper polyhedron of rare-earth ions.

Figure 2

(Color online) The lattice constants (a) for $R{\text{Fe}}_2{\text{Zn}}_{20}$ and $R{\text{Co}}_2{\text{Zn}}_{20}$ versus the radius of the trivalent rare-earth ion with $\text{CN}=9$ (Ref. 15). The error bars were estimated from the standard variation in four separate measurement made on one batch of sample.

Figure 3

(Color online) (a) Temperature-dependent magnetization $M$ divided by the applied field $H$ for ${\text{YFe}}_2{\text{Zn}}_{20}$ and ${\text{LuFe}}_2{\text{Zn}}_{20}$ as well as their Co analogs for $H=10$ and 50 kOe. Inset: a blow-up plot at low temperature. (b) $H/M$ for ${\text{YFe}}_2{\text{Zn}}_{20}$ and ${\text{LuFe}}_2{\text{Zn}}_{20}$. The solid lines present the modified Curie-Weiss $\left[\chi \left(T\right)=C/\left(T-{\theta }_{\text{C}}\right)+{\chi }_0\right]$ fit for the data above 100 K. Inset: field-dependent magnetization at 1.85 K.

Figure 4

(Color online) $M/H$ for ${\text{LuFe}}_2{\text{Zn}}_{20}$. From right to left: $H=2$, 5, 10, 20, and 30 kOe. Inset: $\chi \left(H\right)$ for ${\text{LuFe}}_2{\text{Zn}}_{20}$ at varied temperature.

Figure 5

(Color online) Low temperature specific heat data of ${\text{YFe}}_2{\text{Zn}}_{20}$ and ${\text{LuFe}}_2{\text{Zn}}_{20}$ (plotted as $C_p/T$ versus $T^2$), as well as the Co analogs.

Figure 6

(Color online) (a) Temperature-dependent resistivity of ${\text{YFe}}_2{\text{Zn}}_{20}$ and ${\text{LuFe}}_2{\text{Zn}}_{20}$, as well as their Co analogs. Inset: $\rho$ versus $T^2$. The solid lines present the linear fit of the data sets from 2 to 9 K. (b) Estimated spin fluctuation contribution to the resistivity for ${\text{YFe}}_2{\text{Zn}}_{20}$ and ${\text{LuFe}}_2{\text{Zn}}_{20}$. The error bars were estimated as $\pm 10\%$ of the values of the resistivity for ${\text{YCo}}_2{\text{Zn}}_{20}$ and ${\text{LuCo}}_2{\text{Zn}}_{20}$, respectively.

Figure 7

(Color online) Temperature-dependent magnetization of $R{\text{Co}}_2{\text{Zn}}_{20}$ ($R=\text{Nd}$ and Sm) compounds divided by applied field $H=10000\text{Oe}$. Inset: applied field $\left(H=10000\text{Oe}\right)$ divided by the magnetizations of $R{\text{Co}}_2{\text{Zn}}_{20}$ ($R=\text{Nd}$ and Sm) as a function of temperature.

Figure 8

(Color online) Temperature-dependent specific heat for $R{\text{Co}}_2{\text{Zn}}_{20}$ ($R=\text{Nd}$, Sm, and Y).

Figure 9

(Color online) Temperature-dependent magnetization of $R{\text{Co}}_2{\text{Zn}}_{20}$ $\left(R=\text{Gd-Yb}\right)$ compounds divided by applied field $H=1000\text{Oe}$.

Figure 10

(Color online) Applied field $\left(H=10000\text{Oe}\right)$ divided by the magnetizations of $R{\text{Co}}_2{\text{Zn}}_{20}$ $\left(R=\text{Gd-Yb}\right)$ as a function of temperature.

Figure 11

(Color online) Temperature-dependent specific heat for $R{\text{Co}}_2{\text{Zn}}_{20}$ ($R=\text{Gd-Tm}$, Y, and Lu), as well as ${\text{Tb}}_{0.5}{\text{Y}}_{0.5}{\text{Co}}_2{\text{Zn}}_{20}$. Inset: temperature-dependent magnetic entropy for ${\text{TbCo}}_2{\text{Zn}}_{20}$. The dashed line presents the entropy of the full Hund’s ground state of ${\text{Tb}}^{+3}$.

Figure 12

(Color online) Normalized magnetic part of entropy for $R{\text{Co}}_2{\text{Zn}}_{20}$ $\left(R=\text{Dy-Tm}\right)$ as well as for ${\text{Tb}}_{0.5}{\text{Y}}_{0.5}{\text{Co}}_2{\text{Zn}}_{20}$ (in units of per mole $R^{3+}$). The error bars were estimated from the $\pm 1\%$ of the total entropy.

Figure 13

(Color online) Magnetic part of specific heat for $R{\text{Co}}_2{\text{Zn}}_{20}$. The solid and dashed line present the experimental and calculated results, respectively.

Figure 14

(Color online) Temperature-dependent magnetization of $R{\text{Fe}}_2{\text{Zn}}_{20}$ $\left(R=\text{Gd-Tm}\right)$ divided by applied field $H=1000\text{Oe}$.

Figure 15

(Color online) Applied field $\left(H=1000\text{Oe}\right)$ divided by the magnetizations of $R{\text{Fe}}_2{\text{Zn}}_{20}$ $\left(R=\text{Gd-Tm}\right)$ as a function of temperature.

Figure 16

(a) $C_p$ for ${\text{TbFe}}_2{\text{Zn}}_{20}$; (b) $\rho$ and $d\rho /dT$. Left inset: magnetic part of $C_p$; right inset: magnetic entropy $S_M$.

Figure 17

(Color online) Field-dependent magnetization of ${\text{TbFe}}_2{\text{Zn}}_{20}$ along the three principle axes at 2 K. The three lines represent the calculated results based on molecular field approximation (all being clustered near $9{\mu }_B$ and appearing as a single line). Inset: Arrott plot of magnetic isotherms for ${\text{TbFe}}_2{\text{Zn}}_{20}$.

Figure 18

(a) $C_p$ for ${\text{DyFe}}_2{\text{Zn}}_{20}$; (b) $\rho$ and $d\rho /dT$. Left inset: magnetic part of $C_p$; right inset: magnetic entropy $S_M$.

Figure 19

(Color online) Field-dependent magnetization of ${\text{DyFe}}_2{\text{Zn}}_{20}$ at 2 K along the three principle axes. The solid lines represent the calculated result. Inset: Arrott plot of magnetic isotherms for ${\text{DyFe}}_2{\text{Zn}}_{20}$.

Figure 20

(a) $C_p$ for ${\text{HoFe}}_2{\text{Zn}}_{20}$; (b) $\rho$ and $d\rho /dT$. Left inset: magnetic part of $C_p$; right inset: magnetic entropy $S_M$.

Figure 21

(Color online) Field-dependent magnetization of ${\text{HoFe}}_2{\text{Zn}}_{20}$ at 2 K along the three principle axes. The solid lines represent the calculated result. Inset: Arrott plot of magnetic isotherms for ${\text{HoFe}}_2{\text{Zn}}_{20}$.

Figure 22

(a) $C_p$ for ${\text{ErFe}}_2{\text{Zn}}_{20}$; (b) $\rho$ and $d\rho /dT$. Left inset: magnetic part of $C_p$; right inset: magnetic entropy $S_M$.

Figure 23

(Color online) Field-dependent magnetization of ${\text{ErFe}}_2{\text{Zn}}_{20}$ at 2 K along the three principle axes. The solid lines represent the calculated result. Inset: Arrott plot of magnetic isotherms for ${\text{ErFe}}_2{\text{Zn}}_{20}$.

Figure 24

(a) $C_p$ for ${\text{TmFe}}_2{\text{Zn}}_{20}$; (b) $\rho$ and $d\rho /dT$. Left inset: magnetic part of $C_p$; right inset: magnetic entropy $S_M$.

Figure 25

(Color online) Field-dependent magnetization of ${\text{TmFe}}_2{\text{Zn}}_{20}$ at 2 K. The solid lines represent the calculated result. Inset: Arrott plot of magnetic isotherms for ${\text{TmFe}}_2{\text{Zn}}_{20}$.

Figure 26

(Color online) (a) Temperature-dependent $M/H$ and (b) resistivity for ${\text{YbFe}}_2{\text{Zn}}_{20}$ and ${\text{YbCo}}_2{\text{Zn}}_{20}$ $\left(H=1000\text{Oe}\right)$.

Figure 27

(Color online) (a) $T_{\text{C}}$ and ${\theta }_{\text{C}}$, the maximum value on $\Delta \rho$ (b) with respect to the de Gennes factor for $R{\text{Fe}}_2{\text{Zn}}_{20}$ $\left(R=\text{Gd-Tm}\right)$.

Figure 28

(Color online) Magnetic part of specific heat versus $T/T_{\text{C}}$ for $R{\text{Fe}}_2{\text{Zn}}_{20}$ $\left(R=\text{Gd-Tm}\right)$.

Figure 29

(Color online) Single-ion CEF splitting energy levels for $R{\text{Co}}_2{\text{Zn}}_{20}$ $\left(R=\text{Tb-Tm}\right)$. The arrows present the $T_{\text{C}}$ values for $R{\text{Fe}}_2{\text{Zn}}_{20}$ with respective $R$.

Figure 30

(Color online) (a) $\rho$ versus $T$, (b) $\Delta \rho$ versus $T$, and (c) $\Delta \rho$ versus $T/T_{\text{C}}$ for $R{\text{Fe}}_2{\text{Zn}}_{20}$ $\left(R=\text{Gd-Tm}\right)$. Inset: the blow-up $\Delta \rho$ data for ${\text{TmFe}}_2{\text{Zn}}_{20}$. The arrow presents the FM ordering temperature.

Figure 31

(Color online) (a) Temperature-dependent $M/H$ for ${\text{TbFe}}_2{\text{Zn}}_{20}\left(H=1000\text{Oe}\right)$ from different initial growth molar ratio of starting elements; (b) temperature-dependent $\rho$ in zero applied field.

Figure 32

$T_{\text{C}}$ values for different growth of $R{\text{Fe}}_2{\text{Zn}}_{20}$ $\left(R=\text{Gd-Tm}\right)$ samples with respect to the de Gennes factor.