Elucidating the lack of magnetic order in the heavy-fermion ${\mathrm{CeCu}}_2\mathrm{Mg}$

Magnetic, transport, and thermal properties of ${\mathrm{CeCu}}_2\mathrm{Mg}$ are investigated to elucidate the lack of magnetic order in this heavy-fermion compound with a specific heat value, $C_{\mathrm{mag}}{/T|}_{T\to 0}\approx 1.2$ J/mol ${\mathrm{K}}^2$ and robust effective magnetic moments (${\mu }_{\mathrm{eff}}\approx 2.46{\mu }_{\mathrm{B}}$). The lack of magnetic order is attributed to magnetic frustration favored by the hexagonal configuration of the Ce sublattice. In fact, the effect of magnetic field on $C_{\mathrm{mag}}/T$ and residual resistivity ${\rho }_0$ does not correspond to that of a Fermi liquid (FL) because a broad anomaly appears at $T_{\max }\approx 1.2$ K in $C_{\mathrm{mag}}\left(T\right)/T$, without changing its position up to ${\mu }_{0}H=7.5$ T. However, the flattening of $C_{\mathrm{mag}}{/T|}_{T\to 0}$ and its magnetic susceptibility ${\chi }_{T\to 0}$, together with the $T^2$ dependence of $\rho \left(T\right)$, reveal a FL behavior for $T\le 2$ K which is also supported by Wilson and Kadowaki-Woods ratios. The unusual coexistence of FL and frustration phenomena can be understood by placing paramagnetic ${\mathrm{CeCu}}_2\mathrm{Mg}$ in an intermediate section of a frustration-Kondo model. The entropy, $S_{\mathrm{mag}}$, reaches $0.87\mathrm{R}ln6$ at $T\simeq 100$ K, with a tendency to approach the expected value $S_{\mathrm{mag}}=\mathrm{R}ln6$ of the $J=5/2$ ground state of ${\mathrm{Ce}}^{3+}$.

Figure 1

(a) Crystal structure of ${\mathrm{CeCu}}_2\mathrm{Mg}$. Cerium (blue), copper (gray), and magnesium (orange). (b) Ce layers in the $ab$ plane. The hexagonal lattice of Ce atoms is sketched for a Ce atom having six first neighbors.

Figure 2

(a) Low temperature ($T<25$ K) thermal dependence of the magnetic susceptibility in a semilogarithmic representation. Inset: temperature dependent inverse magnetic susceptibility, with a Curie-Weiss fit, Eq. (1), shown as solid line. (b) Field dependent isothermal magnetization at temperatures as labeled. Inset: high field magnetization data measured up to 60 T at 1.6 K.

Figure 3

(a) Thermal dependence of the electrical resistivity, $\rho \left(T\right)$, measured at various external fields as labeled. Inset: corresponding $\rho \left(T\right)$ vs $T^2$ dependence. (b) Field dependent, relative isothermal magnetoresistivity $\left[\rho \right(H)-\rho (H=0\left)\right]/\rho (H=0)$ measured at various temperatures as labeled.

Figure 4

(a) High temperature specific heat up to 130 K, showing the total contribution, $C_P/T$, compared with the ${\mathrm{LaCu}}_2\mathrm{Mg}$ reference for phonon subtraction to obtain the magnetic contribution $C_{\mathrm{mag}}/T$. (b) Analysis of $C_{\mathrm{CEF}}$, the CEF Schottky contribution to the total magnetic contribution $C_{\mathrm{mag}}$, using a set of Schottky anomalies (see text).

Figure 5

Temperature dependence of $C_{\mathrm{mag}}/T$ in a semi-$logT$ representation; solid line: ground state contribution $C_{\mathrm{GS}}/T$ computed by subtracting the $C_{\mathrm{CEF}}/T$ from $C_{\mathrm{mag}}/T$. Inset: effect of applied magnetic fields upon $C_{\mathrm{mag}}/T$ vs $T$ at low temperature.

Figure 6

Thermal increase of the entropy normalized to the entropy of a doublet (i.e., $\mathrm{R}ln2$). The continuous curve is the entropy evaluation from the fit of the specific heat performed in Fig. 5 that extrapolates towards $S=\mathrm{R}ln6$. Inset: comparison of low temperature $M/H\equiv \chi$ (outer left axis) and $C_{\mathrm{mag}}\left(T\right)/T={\gamma }_T$ (right axis). The continuous curve indicates the Wilson-like ratio for the low temperature range (inner left axis).