Physical properties of quaternary compounds Gd₂CoAl₄T₂ (T = Si, Ge) single crystals

Abstract

We have synthesized and investigated physical properties of two new quaternary compounds Gd₂CoAl₄T₂ (T = Si, Ge) single crystals, which are isostructural to Tb₂NiAl₄Ge₂ and Er₂CoAl₄Ge₂. The most important structural feature of these materials is the anti-CaF₂-type CoAl₄T₂ slabs. These materials show metallic behavior below 300 K and there is a long-range antiferromagnetic (AFM) transition appearing at 20 and 27 K for Gd₂CoAl₄Ge₂ and Gd₂CoAl₄Si₂, respectively. Resistivity and heat capacity measurements also confirm these bulk AFM transitions. Further analysis indicates that this long-range antiferromagnetism should result from the magnetic interaction between local moments of Gd³⁺ ions.

Graphical abstract

Keywords

magnetic materials / rare earth compounds / single crystal growth

1 Introduction

High-temperature metal solutions as flux are indispensable methods to grow single crystals with diverse exotic physical properties [1, 2]. Among a variety of metal flux, Al flux has some unique features. For example, it can dissolve a large number of elements, especially boron. Thus, Al flux is an important method to grow metal borides single crystals, such as transition metal and rare earth borides [3, 4]. Furthermore, Al can be dissolved readily not only in non-oxidizing acids but also in bases. This property is very important to synthesis single crystals that are easy to decompose in acids but not in bases. In addition, Al flux can also be used as a reaction flux to grow complex (ternary or quaternary) aluminides, especially alumosilicides and alumogermanides, because the phase diagrams of the Al-Si and Al-Ge show low eutectic points without forming any binary phases. A large amount of intermetallic alumosilicides and alumogermanides have been prepared from liquid Al, such as RENiAl₄Ge₂ (RE = Sm, Tb, Y) [5], Sm₂Ni(Ni, Si)Al₄Si₆ [6], and RE₈Ru₁₂Al₄₉Si₉ (Al_xSi_12-x) (RE = Sm, Pr) etc [7].

In this work, we discovered two new quaternary compounds Gd₂CoAl₄T₂ (T = Si, Ge) using Al flux. They are isostructural to Tb₂NiAl₄Ge₂ and Er₂CoAl₄Ge₂ [8, 9]. Detailed study on physical properties shows that these materials are metals with long-range antiferromagnetic (AFM) transition at low temperature. These AFM orderings can be mainly ascribed to the magnetic interaction of local moments of Gd³⁺ ions.

2 Experiment

Gd₂CoAl₄T₂ (T = Si, Ge) single crystals were grown by the Al flux method. Gd chunks (99.99%), Co lumps (99.99%), Al grains (99.99%) and Si or Ge granular (99.9999%) were mixed together in a molar ratio of \text{Gd}:\text{Co}:\text{Al}:\text{T}=2:1:2:18 and placed in an alumina crucible. Then, the crucible was sealed in the quartz ampoule under partial argon atmosphere. The sealed quartz ampoule was heated up to 1323 K for 12 h and then kept at that temperature for 4 h. Finally the ampoule was cooled down slowly to 1023 K with 5 K/h. At this temperature, the ampoule was decanted with a centrifuge to extract single crystals from the Al flux. X-ray diffraction (XRD) patterns were collected using a Bruker D8 X-ray diffractometer with Cu K_{\alpha } radiation (\lambda =0.15418 nm) at room temperature. The elemental analysis was performed using energy-dispersive X-ray spectroscopy (EDX) analyses. Electrical transport measurements were carried out in a Quantum Design physical property measurement system (PPMS-14). The electrical resistivity was measured using a four-probe method on rectangular-shaped single crystals. The current flows in the ab plane of the crystal. Magnetization measurements were performed in a Quantum Design magnetic property measurement system (MPMS3).

3 Results and discussion

Figure 1(a) shows the powder XRD pattern of ground Gd₂CoAl₄Ge₂ single crystals. It can be fitted well by using the structure of Er₂CoAl₄Ge₂ with the space group I4/mmm (No. 139). The fitted a- and c-axial lattice parameters are 4.1392(3) Å and 19.543(2) Å for Gd₂CoAl₄Ge₂ (also shown in Table 1), which are larger than those in Er₂CoAl₄Ge₂ (a=4.0971 Å and c=19.331 Å) [9]. It can be ascribed to the larger ionic radius of Gd than Er. On the other hand, when exploring the Gd-Co-Al-Si system we found that the powder XRD pattern of ground single crystals can also be fitted using above structure. The obtained lattice parameters from fitting give a=4.1099(1) Å and c=19.4146(8) Å for Gd₂CoAl₄Si₂, which are smaller than those in Gd₂CoAl₄Ge₂, because of smaller ionic radius of Si when compared to Ge. Correspondingly, the volume of unit cell V for Gd₂CoAl₄Si₂ is also smaller than that for Gd₂CoAl₄Ge₂ (Table 1). The composition analysis further confirms the formation of Gd₂CoAl₄Si₂. The atomic ratio of \text{Gd}:\text{Co}:\text{Al}:\text{Si} determined from the EDX measurement is 2:1.02:3.82:2.09 when setting Gd as 2, close to the chemical formula of Gd₂CoAl₄Si₂. Figures 1(c) and (d) show the XRD patterns of Gd₂CoAl₄T₂ single crystals. There are only the (00l) diffraction peaks appearing, indicating that the crystal surface is parallel to the ab-plane and the diffraction peaks of Gd₂CoAl₄Ge₂ shift to lower angles compared to the Gd₂CoAl₄Si₂ single crystal, consistent with the larger c axial lattice parameter of the former. The thick plate-like shapes of crystals [insets of Figs. 1(c) and (d)] are consistent with the crystal orientation and the layered structure of Gd₂CoAl₄T₂ mentioned below.

As shown in Fig. 2(a), the structure of Gd₂CoAl₄T₂ is built up by stacking CoAl₄T₂ slabs and bilayer of Gd atoms alternatively along the c axis. Similar to the NiAl₄Ge₂ unit in Tb₂NiAl₄Ge₂ [8], the CoAl₄T₂ slab has an antiflourite (anti-CaF₂) structure type, where T and Co occupy the site of Ca and F is replaced by Al. Thus, each Al atom is coordinated by two T and two Ni atoms, forming a tetrahedron. Two layers of these AlCo₂T₂ tetrahedra connect each other via edge sharing and form a two-dimensional {\left[{\text{CoAl}}_{\text{4}}{\text{T}}_2\right]}_{2D}^{\infty } slab [Fig. 2(b)]. On the other hand, the local structure of CoAl₄T₂ slab can also be described as following [8]. Each Co atom is surrounded by eight Al atoms, consisting of a slightly distorted CoAl₈ cube. These distorted CoAl₈ cubes connect each other by edge sharing and form an infinite layer with one half of the cubes filled with a Co center. The T atoms then are located above and below the Al₈ cubes which are not centered by Co atoms [Fig. 2(c)]. The fitted atomic positions for Gd, Co, Al and T are shown in Table 1. The values are close to those in Tb₂NiAl₄Ge₂ and Er₂CoAl₄Ge₂ [9, 8]. As shown in Table 1, the d_{\text{Gd}-\text{Gd}}, d_{\text{Si}/\text{Ge}-\text{Al}} and d_{\text{Al}-\text{Al}} (in the ab plane) for Gd₂CoAl₄Si₂ are slightly smaller than those for Gd₂CoAl₄Ge₂which can be ascribed to the smaller lattice parameters of the former. But the d_{\text{Co}-\text{Al}} and d_{\text{Al}-\text{Al}} (out of ab plane) for the former are abnormally larger than those for the latter. It suggests that the distorted CoAl₈ cubes in Gd₂CoAl₄Si₂ expand along the c axis and one of possible explanation is that the stronger bonding strength of Si-Al weakens those of Co-Al and Al-Al because of larger electronegativity of Si than Ge.

Figure 3(a) shows the temperature dependence of magnetic susceptibility \chi (T) of the Gd₂CoAl₄Ge₂ single crystal at H=1 kOe along the ab plane and the c axis with zero-field-cooling (ZFC) and field-cooling (FC) modes. There are sharp drops below 20 K in both ZFC and FC curves, and it can be ascribed to the onset of long-range AFM ordering. The Weiss temperature T_N determined from the peak of d(\chi T)/dT(T) curves with ZFC mode is 20.1 and 20.0 K for H//ab and H//c [inset of Fig. 3(a)] [10]. These values are close to that in Tb₂NiAl₄Ge₂ [8]. The decrease of {\chi }_{ab}(T) below T_N is more obvious than {\chi }_c(T), strongly suggesting that the spin is ordered antiferromagnetically in the ab-plane (easy plane of magnetization). When T>T_N, the \chi (T) decrease with increasing temperature for both field directions and they can be fitted very well using the Curie–Weiss (CW) law \chi (T)=C/(T-\theta ), where C is Curie constant and θ is the CW temperature. The linear fits for the curves of 1/\chi (T) vs. T between 50 and 300 K with ZFC mode (solid lines in Fig. 3(c)) give C=0.027110(6) emu·g^-1·Oe^-1·K and \theta =-30.93(5) K for H//ab, and C=0.029280(8) emu·g^-1·Oe^-1·K and \theta =-34.24(6) K for H//c. The negative values of θ indicate the AFM interaction in this material, consistent with the AFM ordering below T_N. The values of C correspond to the effective moment {\mu }_{\text{eff}}=8.2433(9) and 8.567(1) μ_B/Gd for H//ab and H//c. These values are close to the theoretical value of free Gd³⁺ ion (7.94 μ_B/Gd). It suggests that Co ions may not have local moments in Gd₂CoAl₄Ge₂ as in the case in Tb₂NiAl₄Ge₂ and other rare earth-cobalt-aluminum compounds [8, 11]. For Gd₂CoAl₄Si₂, there is also a drop in the \chi (T) curve at low temperature [Fig. 3(b)], corresponding to the AFM transition. The determined T_N from the peak of d(χT)/dT(T) curves is 26.4 and 26.8 K for H//ab and H//c [inset of Fig. 3(b)], slightly higher than those in Gd₂CoAl₄Ge₂. It could be due to the smaller d_{\text{Gd}-\text{Gd}} in the former. The easy plane of magnetization in Gd₂CoAl₄Si₂ is also the ab-plane because of the faster drop of {\chi }_{ab}(T) than {\chi }_c(T). From the linear fits of 1/\chi (T) curves [solid lines in Fig. 3(c)], the obtained C and θ are 0.031690(7) emu·g^-1·Oe^-1·K and -21.29(5) K for H//ab, when C=0.030280(9) emu·g^-1·Oe^-1·K and \theta =-24.74(6) K for H//c. Again, the negative values of θ indicate that the dominant magnetic interaction at high temperature is AFM, which evolves into the long-range AFM ordering below T_N. On the other hand, the corresponding {\mu }_{\text{eff}} is 8.255(9) and 8.069(1) μ_B/Gd for H//ab and H//c, respectively, comparable with those values in Gd₂CoAl₄Ge₂ and theoretical value of Gd³⁺ ions. In addition, the nearly perfect overlapping between the ZFC and FC \chi (T) curves indicate the absence of magnetic glassy state in these compounds. Figure 3(d) shows the M(H) loops at 2 K for both field directions. For Gd₂CoAl₄Ge₂, the M(H) loops exhibit the linear field dependence without the trend of saturation and hysteresis, irrespective of the field directions. It is consistent with the AFM orders in these materials. For Gd₂CoAl₄Si₂, the M(H) loop also shows similar linear field dependence when H//c. Interestingly, the M(H) curve exhibits a sharp jump at H ~ 29 kOe when H//ab, implying that there is a spin-flop transition, i.e., the spin directions are almost perpendicular to the field direction and nearly antiparallel to each other [12-14].

Figure 4 shows the temperature dependence of the in-plane resistivity {\rho }_{ab}(T) of Gd₂CoAl₄T₂ single crystals. These compounds exhibit metallic behavior in the whole temperatures range. The most notable feature of {\rho }_{ab}(T) is a sharp drop at low temperature. The determined temperature T_{\text{k}} from the peak of dρ_ab/dT curve [Inset (a) of Fig. 4] is 20.0 and 25.3 K for Gd₂CoAl₄Ge₂ and Gd₂CoAl₄Si₂, respectively, consistent with the transition temperature observed in the magnetization and heat capacity data (shown as below). The drop in the {\rho }_{ab}(T) curve originates from the rapid decrease in the spin disorder scattering below AFM transition. when taking into account the scattering of conduction electrons by phonons and antiferromagnetic magnons, the temperature dependence of {\rho }_{ab}(T) for can be expressed by [15, 16]

\begin{array}{}\text{(1)}& \begin{array}{ll}{\rho }_{ab}(T)=\hfill & {\rho }_0+A{T}^5+B{\text{Δ}}^2\sqrt{\frac{k_{B}T}{\text{Δ}}}{\text{e}}^{-\text{Δ}/(k_{B}T)}\hfill \\ \hfill & \times \left[1+\frac{3\text{Δ}}{2k_{B}T}+\frac{2}{15}{\left(\frac{\text{Δ}}{k_{B}T}\right)}^2\right]\mathrm{,}\hfill \end{array}\end{array}

where {\rho }_0 is residual resistivity, A and B is the constants of the electron-phonon and electron-magnon scattering term at low temperature, respectively, k_B is Boltzmann constant, Δ is the magnon gap energy. Both ρ_ab curves can be fitted very well [Inset (b) of Fig. 4] and the obtained {\rho }_0, A, B, and Δ is 35.3(2) μΩ·cm, 0.0107(2) nΩ·cm·K^-5, 0.148(2) μΩ·cm·K^-2, and 20.2(3) K for Gd₂CoAl₄Ge₂, and 22.9(1) μΩ·cm, 0.00211(5) nΩ·cm·K^-5, 0.0720(7) μΩ·cm·K^-2, and 25.3(3) K for and Gd₂CoAl₄Si₂, respectively. The fitted values of Δ are close to their AFM ordering temperature.

Figure 5 shows the temperature dependence of heat capacity C_p(T) for Gd₂CoAl₄Ge₂ single crystal. There is a λ-type anomaly with the peak position located at 19.95 K. It is the evidence of bulk long-range AFM ordering and the transition temperature is also consistent with that temperature obtained from d\chi (T)/dT curve [inset of Fig. 3(a)]. Moreover, at H=50 kOe the C_p(T) curve is perfectly overlapped with that at zero field, indicating that that the field of 50 kOe has a negligible influence on the AFM transition of Gd₂CoAl₄Ge₂. Assuming that the total heat capacity consists of electronic (C_e), lattice (C_{ph}) and magnetic (C_m) components, C_m can be estimated by the subtraction of C_e and C_{ph}. Because the absence of non-magnetic counterpart of this material, we fitted the heat capacity data in the high-temperature range (T\ge 35 K) well away from T_N when only considering C_e and C_{ph} and then extrapolated to 2 K. Using the Debye function, it has

\begin{array}{}\text{(2)}& \begin{array}{ll}{C}_p(T)\hfill & =C_e+C_{ph}\hfill \\ \hfill & =\gamma T+9RC{\left(\frac{T}{{\text{Θ}}_D}\right)}^3{\displaystyle {\int }_0^{{\text{Θ}}_D/T}}\frac{x^4{\text{e}}^x}{{({\text{e}}^x-1)}^2}\text{d}x\mathrm{,}\hfill \end{array}\end{array}

where γ is the Sommerfeld coefficient, R is the gas constant (R=8.314 J·mol^-1·K^-1), {\text{Θ}}_D is Debye temperature, C is a fitting parameter. The fitted γ and {\text{Θ}}_D is 355(2) J·mol^-1·Gd K^-2 and 321.9(6) K, respectively. The fitted curve is shown in Fig. 5(a) (red solid line) and after subtracting the electronic and lattice contributions from C_p(T), we obtain the C_m(T) curve [Fig. 5(b)]. Then, the magnetic entropy S_m(T) can be calculated using the integral S_m(T)={\displaystyle {\int }_0^T}{C}_m/T\text{d}T. As shown in Fig. 5(b), the S_m(T) increases gradually when increasing temperature and then tends to saturate above T_N. The obtained S_m up to 40 K is about 10.8 J·mol^-1·Gd K^-1, which is about 62% of theoretical value [Rln(2J + 1) = 17.3 J·mol-¹·Gd K^-1 for Gd³⁺ ions with J=7/2]. This discrepancy may originate from an overestimation of the electronic and lattice contributions which may cause a reduction in S_m(T). Similar to Gd₂CoAl₄Ge₂, there is also a peak at 26.97 K for Gd₂CoAl₄Si₂ at zero field [Fig. 4(c)], consistent with the results of magnetization measurement. In contrast to Gd₂CoAl₄Ge₂, at high field (H=50 kOe), the peak of C_p(T) shifts to lower temperature slightly (T_N=26.45 K), implying the suppression of AFM order by field. This could be related to the metamagnetic transition in Gd₂CoAl₄Si₂. After subtracting the electronic and lattice contributions from C_p(T), the obtained C_m(T) is shown in Fig. 4(d) and it exhibits similar behavior as in Gd₂CoAl₄Ge₂. The estimated S_m up to 40 K is 8.9 J·mol^-1·Gd K^-1, which is about 51% of theoretical value for Gd³⁺ ions. Again, this discrepancy may also be due to the overestimation of the C_e and C_{ph}.

4 Conclusion

In summary, we report the physical properties of two new quaternary compounds Gd₂CoAl₄T₂ (T = Si, Ge) single crystals grown by using Al flux. Gd₂CoAl₄T₂ belong to the tetragonal space group I4/mmm and the fitted a- and c-axial lattice parameters are 4.1392(3) Å and 19.543(2) Å for Gd₂CoAl₄Ge₂ and 4.1099(1) Å and 19.4146(8) Å for Gd₂CoAl₄Si₂. The crystal structure consists of layers of CoAl₄T₂ slab separated by bilayers Gd atoms. Both compounds are AFM metals and the T_N is about 20 and 27 K for Gd₂CoAl₄Ge₂ and Gd₂CoAl₄Si₂, respectively. Heat capacity measurements confirm the bulk feature of these AFM transitions. The long-range antiferromagnetism in these materials may solely originate from the magnetic interaction between Gd³⁺ ions and the Co ions should have negligible local moments. Moreover, the Gd₂CoAl₄Ge₂ exhibits metamagnetic transition when the field is along the ab plane and larger than 29 kOe.

References

[1] P. C. Canfield and Z. Fisk, Growth of single crystals from metallic fluxes, Philos. Mag. B 65, 1117 (1992)

[2] M. G. Kanatzidis, R. Pöttgen, and W. Jeitschko, The metal flux: A preparative tool for the exploration of intermetallic compounds, Angew. Chem. Int. Ed. 44(43), 6996 (2005)

[3] S. Okada, Y. Yu, T. Lundström, K. Kudou, and T. Tanaka, Crystal growth and some properties of LuB₄, LuAlB₄, and Lu₂AlB₆, Jpn. J. Appl. Phys. 35(Part 1, No. 9A), 4718 (1996)

[4] S. Okada, K. Kudou, K. Iizumi, K. Kudaka, I. Higashi, and T. Lundström, Single-crystal growth and properties of CrB, Cr₃B₄, Cr₂B₃ and CrB₂ from high-temperature aluminum solutions, J. Cryst. Growth 166(1–4), 429 (1996)

[5] B. Sieve, X. Z. Chen, J. A. Cowen, P. Larson, S. D. Mahanti, and M. G. Kanatzidis, Multinary intermetallics from molten Al. Synthesis of SmNiAl₄Ge₂ and YNiAl₄Ge₂. Possible spin frustration in separated triangular Sm³⁺ layers, Chem. Mater. 11(9), 2451 (1999)

[6] X. Z. Chen, S. Sportouch, B. Sieve, P. Brazis, C. R. Kannewurf, J. A. Cowen, R. Patschke, and M. G. Kanatzidis, Exploratory synthesis with molten aluminum as a solvent and routes to multinary aluminum silicides. Sm₂Ni(Ni_xSi_1-x)Al₄Si₆ (x=0.18-0.27): A new silicide with a ferromagnetic transition at 17.5 K, Chem. Mater. 10(10), 3202 (1998)

[7] B. Sieve, X. Z. Chen, R. Henning, P. Brazis, C. R. Kannewurf, J. A. Schultz, and M. G. Kanatzidis, Cubic aluminum silicides RE₈Ru₁₂Al₄₉Si₉ (Al_xSi_12-x) (RE = Pr, Sm) from liquid aluminum. Empty (Si,Al)₁₂ cuboctahedral clusters and assignment of the Al/Si distribution with neutron diffraction, J. Am. Chem. Soc. 123(29), 7040 (2001)

[8] B. Sieve, P. N. Trikalitis, and M. G. Kanatzidis, Quaternary germanides formed in molten aluminum: Tb₂NiAl₄Ge₂ and Ce₂NiAl_6-xGe_4-y (x~0.24, y~1.34), Z. Anorg. Allg. Chem. 628(7), 1568 (2002)

[9] G. Demchenko, J. Kónczyk, P. Demchenko, R. Gladyshevskii, W. Majzner, and L. Muratova, Quaternary alumogermanides in the Er-{Co,Ni}-Al-Ge systems, Chem. Met. Alloys 1, 254 (2008)

[10] M. E. Fisher, Relation between the specific heat and susceptibility of an antiferromagnet, Philos. Mag. 7(82), 1731 (1962)

[11] F. Canepa, M. Napoletano, M. L. Fornasini, and F. Merlo, Structure and magnetism of Gd₂Co₂Ga, Gd₂Co₂Al and Gd₁₄Co₃In_2.7, J. Alloys Compd. 345(1–2), 42 (2002)

[12] F. B. Anderson and H. B. Callen, Statistical mechanics and field-induced phase transitions of the Heisenberg antiferromagnet, Phys. Rev. 136(4A), A1068 (1964)

[13] Y. Shapira and S. Foner, Magnetic phase diagram of MnF₂ from ultrasonic and differential magnetization measurements, Phys. Rev. B 1(7), 3083 (1970)

[14] F. Keffer and H. Chow, Dynamics of the antiferromagnetic spin-flop transition, Phys. Rev. Lett. 31(17), 1061 (1973)

[15] S. N. de Medeiros, M. A. Continentino, M. T. D. Orlando, M. B. Fontes, E. M. Baggio-Saitovitch, A. Rosch, and A. Eichler, Quantum critical point in CeCo(Ge_1-xSi_x)₃, Physica B 281–282, 340 (2000)

[16] M. B. Fontes, J. C. Trochez, B. Giordanengo, S. L. Budko, D. R. Sanchez, E. M. Baggio-Saitovitch, and M. A. Continentino, Electron-magnon interaction in RNiBC (R=Er, Ho, Dy, Tb, and Gd) series of compounds based on magnetoresistance measurements, Phys. Rev. B 60(9), 6781 (1999)

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