Magnetic and transport properties of i-$R$-Cd icosahedral quasicrystals $(R=\text{Y},\text{Gd-Tm})$

We present a detailed characterization of the recently discovered $\text{i-}R\text{-Cd}$ $(R=\mathrm{Y},\text{Gd-Tm})$ binary quasicrystals by means of x-ray diffraction, temperature-dependent dc and ac magnetization, temperature-dependent resistance, and temperature-dependent specific heat measurements. Structurally, the broadening of x-ray diffraction peaks found for $\text{i-}R\text{-Cd}$ is dominated by frozen-in phason strain, which is essentially independent of $R$. i-Y-Cd is weakly diamagnetic and manifests a temperature-independent susceptibility. i-Gd-Cd can be characterized as a spin glass below 4.6 K via dc magnetization cusp, a third order nonlinear magnetic susceptibility peak, a frequency-dependent freezing temperature, and a broad maximum in the specific heat. $\text{i-}R\text{-Cd}$ $(R=\text{Ho-Tm})$ is similar to i-Gd-Cd in terms of features observed in thermodynamic measurements. i-Tb-Cd and i-Dy-Cd do not show a clear cusp in their zero-field-cooled dc magnetization data, but instead show a more rounded, broad local maximum. The resistivity for $\text{i-}R\text{-Cd}$ is of order $300\mu \Omega$ cm and weakly temperature dependent. The characteristic freezing temperatures for $\text{i-}R\text{-Cd}$ $(R=\text{Gd-Tm})$ deviate from the de Gennes scaling, in a manner consistent with crystal electric field splitting induced local moment anisotropy.

Figure 1

(a) Generalized $R\text{-Cd}$ binary phase diagram around the Cd concentrated region. The inset shows a single grain of i-Gd-Cd on a millimeter grid paper. (b) The front and back sides of a larger grain of i-Tb-Cd on a millimeter grid paper.

Figure 2

High-energy x-ray diffraction pattern of the i-Tb-Cd quasicrystal shown in Fig. 1. The recorded reciprocal plane is perpendicular to the twofold direction of the icosahedral quasicrystal. The logarithmic intensity scale emphasizes weak signals relative to the strongest Bragg peaks with maximum counts up to 146 000.

Figure 3

Powder diffraction patterns from all of the $\text{i-}R\text{-Cd}$ quasicrystals under investigation. The patterns are normalized to the strongest diffraction peak and offset for clarity. All peaks can be indexed to either the icosahedral phase or residual Cd flux. Stars indicate major diffraction peaks that come from Cd flux. The arrow indicates the (211111) peak. The inset shows the 6D quasilattice parameter $a_{6\mathrm{D}}$ as a function of atomic number $Z$, of rare earth $R$.

Figure 4

Systematics of diffraction peak broadening in i-Gd-Cd and i-Tm-Cd which represent the extremes in the range of $R$ concen-tration. Panels (a) and (b) plot the diffraction peak widths for each compound vs $G_{\parallel }$, and panels (c) and (d) plot the diffraction peak widths for each compound vs $G_{\perp }$ as described in the text. The dashed lines represent the best fit straight lines to the data.

Figure 5

Temperature-dependent dc magnetic susceptibility of i-Y-Cd and ${\mathrm{YCd}}_6$ measured at 10 kOe. The inset shows the field-dependent magnetization of i-Y-Cd measured at 2 K.

Figure 6

Irreversibility of dc magnetization measured at 50 Oe. Different colors indicate different field-cool temperatures (see text). The inset shows temperature-dependent inverse magnetic susceptibility of i-Gd-Cd measured at 10 kOe. The gray line represents Curie-Weiss behavior that is extrapolated from its high-temperature paramagnetic state.

Figure 7

The field dependence of $T_{\mathrm{irr}}$ for i-Gd-Cd. Fits according to Eq. (1) are shown with $b$ = 2.5 and $\alpha =3.3\times {10}^4$ Oe. The inset shows representative ZFC and FC measurements under different applied magnetic fields. Arrows indicate $T_{\mathrm{irr}}$ for different fields.

Figure 8

Third order magnetic susceptibility term ${\chi }_3$ normalized in temperature and peak height. For i-Gd-Cd, ${\chi }_3$ was measured at 333.3 Hz (black dots). Red and blue dashed lines present the ${\chi }_3$ data, obtained from Refs. [26, 36], for ${\mathrm{Y}}_{0.7}$${\mathrm{Tb}}_{0.3}$${\mathrm{Ni}}_2$${\mathrm{Ge}}_2$ and Tb-Mg-Zn.

Figure 9

Temperature-dependent dc magnetization measured at 50 Oe for $\text{i-}R\text{-Cd}$ $(R=\mathrm{Tb}$, Dy). Different colors indicate different FC temperatures. Gray lines represent Curie-Weiss behavior that was extrapolated from the high-temperature paramagnetic state.

Figure 10

Temperature-dependent dc magnetization measured at 50 Oe for $\text{i-}R\text{-Cd}$ $(R=\text{Ho-Tm})$. Data were acquired using a QD iHelium3 system. Gray lines represent Curie-Weiss behavior that is extrapolated from the high-temperature paramagnetic state.

Figure 11

Temperature-dependent specific heat for i-Y-Cd using a stoichiometry of ${\mathrm{YCd}}_{7.48}$. The inset shows $C_p/T$ versus $T^2$ up to 10 K.

Figure 12

(a) Temperature-dependent specific heat of i-Gd-Cd. The gray solid line represents the nonmagnetic part of the specific heat. The red solid line shows the magnetic specific heat. The inset shows the magnetic entropy with gray error bars (see text). (b) Low-temperature magnetic specific heat (red) on the right scale and low-temperature ZFC dc magnetization (black) on the left scale.

Figure 13

(a) Temperature-dependent specific heat of i-Tb-Cd. The red solid line shows the magnetic specific heat. The inset show the magnetic entropy with error bars. (b) Low-temperature magnetic specific heat (red) on the right scale and low-temperature ZFC dc magnetization (black) on the left scale.

Figure 14

(a) Temperature-dependent specific heat of i-Dy-Cd. The red solid line shows the magnetic specific heat. The inset show the magnetic entropy with error bars. (b) Low-temperature magnetic specific heat (red) on the right scale and low-temperature ZFC dc magnetization (black) on the left scale.

Figure 15

(a) Temperature-dependent specific heat of i-Ho-Cd. The red solid line shows the magnetic specific heat. The inset shows the magnetic entropy with error bars. (b) Low-temperature magnetic specific heat (red) on the right scale and low-temperature ZFC dc magnetization (black) on the left scale.

Figure 16

(a) Temperature-dependent specific heat of i-Er-Cd. The red solid line shows the magnetic specific heat. The inset shows the magnetic entropy with error bars. (b) Low-temperature magnetic specific heat (red) on the right scale and low-temperature ZFC dc magnetization (black) on the left scale.

Figure 17

(a) Temperature-dependent specific heat of i-Tm-Cd. The red solid line shows the magnetic specific heat. The inset shows the magnetic entropy with error bars. (b) Low-temperature magnetic specific heat (red) on the right scale and low-temperature ZFC dc magnetization (black) on the left scale.

Figure 18

(a),(b) Changes of $\Theta /T_{\max }$ as a function of the de Gennes factor: ${(g_J-1)}^{2}J(J+1)$. (c) Changes of $T_{\max }$ as a function of $\Theta$. Data for $\text{i-}R$-Mg-Zn, $\text{i-}R$-Mg-Cd, and i-Gd-Ag-In are obtained from Refs. [26, 37, 43, 44]. Dashed lines are guides to the eyes.

Figure 19

(a) Zero-field, normalized temperature-dependent resistance for i-Tb-Cd: as-grown sample (green triangle); polished and heat treated sample (black square). (b) Normalized temperature-dependent resistance of elemental Cd (polished and heat treated i-Tb-Cd sample in the inset) measured at zero field (black) and at 90 kOe (red).

Figure 20

Normalized temperature-dependent resistance for $\text{i-}R\text{-Cd}$ $(R=\mathrm{Y},\text{Gd-Tm})$ at zero field (black) and at 90 kOe (red). The value of resistivity is about $300\mu \Omega$ cm at room temperature.