Evolution from 4f-electron antiferromagnetic to ferromagnetic order in the CeCu(⁠$Ge1−xSnx$⁠) alloy series (⁠$≤x≤1$⁠)

The compounds RTX (R = f - electron, T = d - electron, X = p - electron) cystallize in different crystal structures and order magnetically in a wide temperature range.¹ Large amount of experimental research was devoted to the compounds CeCuGe^2,3 and CeCuSn^4,5 probing their magnetic and electronic properties. Both compounds were found to crystallize in structures derived from the hexagonal $AlB2$ - type with Ce atoms located on the Al site.

The compound CeCuGe has been reported to order ferromagnetically at T_C = 10 K.^4,6 In the paramagnetic state it exhibits Curie-Weiss behavior with an effective magnetic moment (⁠$μeff$⁠) per Ce of 2.50 $μB$ that is close to the value of 2.54 expected for free Ce ion.³ The resistivity data of this compound follows the T² - power law in the temperature range 10 - 30 K, consistent with the appearance of spin fluctuations above T_C.³ In the ordered state, the resistivity behavior can interpreted in terms of scattering conduction electrons on magnons. The heat capacity of CeCuGe shows a Schottky - type anomaly around 68 K associated with crystalline electric field (CEF) effects.⁶ 

The CeCuSn compound has been reported to order below 8.6 K with a complex AFM - type structure.⁴ In the ordered state, the heat capacity exhibits a maximum near 7.4 K, signalling a rearrangement of the AFM structure.⁷ Two structural modifications of CeCuSn were synthesized by Sebastian et al.⁸ The high-temperature $β−CeCuSn$ phase crystallizes with the hexagonal NdPtSb-type structure, while the low-temperature $α−CeCuSn$ phase adopts the hexagonal structure of the ZrBeSi-type.

In view of the different magnetic states in CeCuGe and CeCuSn, we found it interesting to investigate a solid solution of the two compounds $CeCu(Ge1−xSnx)$⁠. Here, we report the results of magnetic and heat capacity measurements of this alloy series.

Polycrystalline samples of $CeCu(Ge1−xSnx)$ were prepared by arc - melting stoichiometric amounts of the elements (purities in at %) Ce (99.98), Cu (99.995) Ge and Sn (99.999) under ultra - high purity argon atmosphere. The samples were overturned and remelted three times to promote homogeneity. The weight losses after final melting were always less than 1 wt.%. Subsequently, the sample ingots were wrapped in tantalum foil, encapsulated in evacuated quartz tubes, and annealed at 850⁰C for two weeks.

The products were checked by powder X - ray diffraction using a Bruker D8 ADVANCE diffractometer with CuKα radiation (⁠$λ=1.5406Å$⁠). The X - ray diffraction spectra were analyzed using the cell and intensity least - squares (CAILS) - Pawley refinement method from TOPAS ACADEMIC.

Temperature- and magnetic field-dependent properties of the prepared alloys were measured using commercial equipment, namely a Quantum Design Physical Property Measurement System (PPMS) and a Magnetic Property Measurement System (MPMS).

X - ray diffraction obtained for the two end compounds as well as two other compositions in the series together with the CAILS refinement fits to the data, are shown in Fig. 1. The space group setting used in the CAILS - Pawley refinement was P6₃/mmc hexagonal ZrBeSi - type structure. The results of the refinements are shown by black solid lines through the measured data and the Sn content (x) dependence of the lattice parameters (a and c) and unit cell volume (V) are shown in the insets of Fig. 1. It is observed that V and a increase linearly with x. The linear increase in V is consistent with Vegard’s law which suggests the stability of the Ce valence across the series as well as no change in the number of conduction electrons, which ensures metallic bonding of the alloy system.

The inverse magnetic susceptibility, $χ−1(T)$ of the $CeCu(Ge1−xSnx)$ alloys, measured in a field of 0.1 T in the temperature range $1.7≤T≤400$ K, are shown in Fig. 2. At temperatures above 100 K, $χ−1(T)$ exhibits Curie - Weiss (CW) behaviour:

where all the parameters have their usual meaning. Least squares fits (LSQ) against the experimental data are shown as solid lines in Fig. 2. Parameters obtained from these fits are gathered in Table I. At lower temperature, $χ−1(T)$ data deviate from CW linear behaviour and this may be attributed to the onset of magnetic ordering or CEF effect. The obtained $μeff$ values are reasonably close to that predicted within a Russel - Saunders coupling scenario for the trivalent Ce - ion (2.54 $μB$⁠). This finding indicates fairly stable 4f electronic state of the cerium atoms. For all compositions, the Weiss temperature was found negative. The negative values of $θp$ for FM compositions indicate that regardless the FM ordering, also these systems are dominated by AFM exchange interactions. The low temperatures, $χ(T)$ data measured in field of 0.1 T are shown in Fig. 3 for selected compositions in the AFM and FM region. For compositions in the range $0.7≤x≤1$⁠, $χ(T)$ data show a kink associated to PM - AFM transition at T_N as indicated by arrows in Fig. 3a. Below T_N, an abrupt rise of $χ(T)$ data is observed which may be associated to coexistence of AFM and FM exchange interactions or canting of the AFM structure. As shown in Figs. 3b–3d, $χ(T)$ data of the compositions with $x≤0.6$ exhibits a FM - like behaviour. The PM - FM transition around T_C was estimated from the minimum value of $dχ(T)/dT$ curves (right axis) for each composition as indicated by arrows in the figures. The estimated values of T_N and T_C from $χ(T)$ data are listed in Table I. The obtained values of T_N and T_C for the two end compounds are in good agreement with previously reported values of T_C = 10 K^4,6 for CeCuGe and T_N = 8.6 K for CeCuSn.⁷ 

The field-dependent magnetization was measured in fields up to 5 T at T = 1.7 K. $M(μ0H)$ for compositions with $x≥0.7$ (inset Fig. 3a), initially increases linearly up to a critical field, then deviate from linearity at high field. This deviation is associated to field - induced magnetic transition occurring in these alloys, at the critical field. Small hysteresis was observed for these compositions in the process of increasing and decreasing field. As shown in the insets of Figs. 3b–3d, $M(μ0H)$ of compositions with $0≤x≤0.6$ exhibits a FM - like behaviour characterized by an abrupt rise of $M(μ0H)$ upon application of weak magnetic field, followed by a tendency towards saturation in high fields. For all compositions, the magnetization measured in 5 T at 1.7 K is less than 1.1 $μB$⁠, which is approximately half the theoretical value for free $Ce3+$ ion (g_JJ = 2.14 $μB$⁠). The difference can be attributed to the CEF effects.

The 4f - electron contribution to the specific heat, C_4f(T), of selected compositions is presented in Fig. 4. The data was obtained by subtracting from the measured C_p(T) curves the phonon contribution resulting from the fits of the conventional equation for the specific heat of a metal at temperature well above T_C and T_N: $CP(T)/T=γconv+βT2$ (see insets of Fig. 5). The magnetic phase transitions in these compositions manifest themselves as clear maxima in the C_p(T)/T curves (see insets of Fig. 4). The so-derived values of T_C and T_N, listed in Table I, are close to those obtained from the $χ(T)$ data. A second anomaly below T_C and T_N at T_t1 = 4.6 K and 3.2 for compositions with x = 0.4 and 0.8 respectively is observed. These anomalies may be associated with spin reorientation or rearrangement of the FM or AFM structure also observed previously in CeCuSn.⁷ In the case of x = 0.4, another anomaly is observed above T_C at T_t2 = 11.3 K. Below T_C, C_4f(T) data can be described assuming magnon excitations, with an energy gap $ΔC$ in the FM spin - waves spectrum (solid red curves in Fig. 4). Applying the formula

where $γ$ is the Sommerfeld coefficient and A a constant, one obtained by LSQ fitting the parameters gathered in Table II. The values of $Δc$ and A obtained for x = 0.2 are of the same order of magnitude as those reported before for CeCuGe.⁶ As can be inferred from Table II, $ΔC$ and A decrease with increasing the Sn content x.

Fig. 5 displays the entropy S(T) calculated from the C_p(T) data as $S(T)=∫0T[Cp(T′)T′]dT′$⁠. For all the measured compositions, S(T) reaches a value of Rln2 expected for doublet ground state somewhat above the respective transition temperature (Black dashed lines Fig. 5).

Magnetic and heat capacity measurements of $CeCu(Ge1−xSnx)$ indicate that FM ordering extends up to 60% Sn substitution. For compositions with $x≥0.7$⁠, AFM ordering is observed with a kind of spin - reorientation in the ordered region. C_p(T) data below T_C can be well described assuming spin - waves excitations.

Support is acknowledged from the SA-NRF (81296). The Research Development of UWC for financial support. AMS and BMS thanks the SA-NRF (93549), the SA-Thuthuka (99231) and the Faculty of Science and URC of UJ for financial assistance.