The Magnetic/Electrical Phase Diagram of Cr-Doped Antiperovskite Compounds GaCFe_3−𝑥Cr_𝑥 (0≤𝑥≤0.9)

Abstract

We report the effect of Cr doping on the structural, magnetic, and electrical transport properties in Cr-doped antiperovskite compounds GaCFe_3−𝑥Cr_𝑥 (0≤𝑥≤0.9). With increasing the Cr content 𝑥, the lattice constant increases while both the Curie temperature and the saturated magnetization decrease gradually. The electrical resistivity shows different behaviors as a function of 𝑥. For 𝑥≤0.6, there exists a semiconductor-like behavior below a certain temperature which decreases with increasing 𝑥. In contrast, for 0.7≤𝑥≤0.9, the resistivity shows a metallic behavior in the whole temperature measured (2–350?K). In particular, the Fermi-liquid behavior is obtained below 70?K. Finally, based on the magnetic and electrical properties of GaCFe_3−𝑥Cr_𝑥 (0≤𝑥≤0.9) a magnetic/electrical phase diagram was plotted.

1. Introduction

Since MgCNi₃ was firstly reported as a new superconductor with the antiperovskite structure [1], the antiperovskite compounds AXM₃ (A = Ga, Al, Sn, Zn, Cu, In, Ge, Ag; X = C, N; M = Mn, Fe, Ni) have been extensively investigated [2–13]. Particularly, plenty of theoretical and experimental studies were performed for the Ni-based and Mn-based antiperovskite compounds [2–12]. Based on previous theoretical investigations [14, 15], the antiperovskite compounds AXM₃ have similar electrical band structure which determines the basical physical properties, indicating that all these antiperovskite compounds (e.g., Mn-, Fe-, or Ni-based) may exhibit similar physical properties.

Recently, considerable attention has been paid to the Fe-based antiperovskite compounds due to their interesting physical and mechanical properties, such as low temperature coefficient of resistance (LTCR) [16], magnetocaloric effect (MCE) [13, 17, 18], and good corrosion resistance [19, 20]. GaCFe₃ has been investigated for several decades as a typical Fe-based antiperovskite compound. It is a ferromagnetic (FM) material with the FM Curie temperature (𝑇_𝐶) of 510?K as reported previously [15]. Very recently, the studies of chemical doping at Ga site in GaCFe₃ have been reported, and some interesting physical properties such as extremely LTCR and large room-temperature MCE have been observed [13, 16, 17]. Based on the previous investigations of Mn- or Ni-based antiperovskite compounds, the chemical doping has been proved to be an effectual method to manipulate the basic physical properties [6, 10, 21–24]. As reported previously in antiperovskite compounds GaCMn_3−𝑥Ni_𝑥 [25], GaCMn_3−𝑥Ni_𝑥(orCrorCo)_𝑥 [26, 27], and SnCMn_3−𝑥Fe_𝑥 [28], the chemical doping at Mn site can affect the magnetic and electrical transport properties significantly. Similarly, the chemical doping at Fe site for GaCFe₃ may be performable. However, no report was found on the chemical substitutions for the Fe site of Fe-based antiperovskite compound GaCFe₃. As reported previously [14, 15], the density of states at the Fermi level 𝐸_𝐹 [𝑁(𝐸_𝐹)] is mainly from Fe 3d electrons in AXFe₃. As we know, the Cr (3d⁵4s¹) has one less 3d electron than Fe (3d⁶4s²) atom. Meanwhile, the Cr atom is bigger in size than that of Fe. The influences of hole doping and the change of lattice constant on the physical properties in GaCFe_3−𝑥Cr_𝑥 will be thus interesting.

In this paper, the structural, magnetic, and electrical evolutions with doping level 𝑥 in GaCFe_3−𝑥Cr_𝑥 (0≤𝑥≤0.9) were investigated. It is found that the lattice expands while both the Curie temperature and the saturated magnetization decrease gradually as 𝑥 increases. For GaCFe_3−𝑥Cr_𝑥 with 𝑥≤0.6, the electrical resistivity exhibits a semiconductor-like behavior at low temperature while displaying a metallic behavior at elevated temperature. As the doping level 𝑥 is above 0.7, the resistivity is metallic with a 𝑇² temperature dependence below 70?K. Finally, a magnetic/electrical phase diagram of GaCFe_3−𝑥Cr_𝑥 (0≤𝑥≤0.9) was presented.

2. Experimental Details

Polycrystalline samples GaCFe_3−𝑥Cr_𝑥 (0≤𝑥≤1.0) were prepared as described in our previous paper [13]. Powder X-ray diffraction (XRD) data was collected at room temperature using an X-ray diffractometer with Cu 𝐾_𝛼 radiation (PHILIPS, 𝜆=0.15406?nm). The data of XRD was refined using a standard Rietveld technique to determine the crystal structure parameter and the purity of phase. Magnetic measurements were performed on a superconducting quantum interference device magnetometer (SQUID 5T, Quantum Design) and on a vibrating sample magnetometer (VSM, Quantum Design). The electrical resistivity and specific heat were carried out on a physical property measurement system (PPMS 9T, Quantum Design). The electrical transport properties were measured by the standard four-probe method to eliminate the contact resistivity.

3. Results and Discussion

Figure 1(a) shows the room-temperature XRD patterns for the samples GaCFe_3−𝑥Cr_𝑥 (𝑥=0, 0.05, 0.1, 0.15, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0). Obviously, all GaCFe_3−𝑥Cr_𝑥 are single phase with a cubic antiperovskite structure (space group: Pm3m) except for a small amount of chromium (marked by open triangle) for 𝑥=1.0. Moreover, according to the vertical bars the central position of peak (200) of GaCFe_3−𝑥Cr_𝑥 shifts to lower angles with an increase of Cr content,suggesting that the lattice constant expands with increasing 𝑥. The Rietveld refinements of XRD patterns were performed for all samples to determine the lattice parameter. As shown in Figure 1(b), the refined lattice parameter increases with 𝑥, which is consistent with the shift of peak (200) in Figure 1(a). The expansion of lattice can be attributed to the larger atom radius of Cr than that of Fe.

(a)

(b)

Figure 1 

(Color online) (a) Room-temperature X-ray powder diffractions for GaCFe3−𝑥Cr𝑥 (0≤𝑥≤1); the green vertical dashed line is a guide to the eye and the open triangle stands for the peak of chromium. (b) The lattice parameter 𝑎 as a function of 𝑥 for GaCFe3−𝑥Cr𝑥 (0≤𝑥≤1).

Figure 2(a) presents temperature-dependent magnetization 𝑀(𝑇)/𝑀(5?K) curves for GaCFe_3−𝑥Cr_𝑥 (0≤𝑥≤0.9) at 100?Oe under zero-field-cooled (ZFC) process. Obviously, each 𝑀(𝑇) curve exhibits an FM-PM transition as reported in GaCFe₃ [15]. The Curie temperature (𝑇_𝐶) (determined by the minimal value of 𝑑𝑀/𝑑𝑇, shown in Figure 2(b)) is presented in Figure 2(d). It displays that the value of 𝑇_𝐶 decreases with increasing Cr content 𝑥. In order to investigate the magnetic ground state of GaCFe_3−𝑥Cr_𝑥, the isothermal 𝑀(𝐻) curves at 5?K are measured and plotted in Figure 2(c). Apparently, all the 𝑀(𝐻) curves display similar 𝐻-dependent behavior: with increasing the magnetic field, the magnetization increases initially and then tends to saturation above 10?kOe. Here, the value of saturated magnetization (𝑀_𝑆) is obtained by the extrapolation of the high field (10–45?kOe) 𝑀(𝐻) curve to 𝑀-axis, which is shown in Figure 2(c) (the green dash line). As shown in Figure 2(d), the 𝑀_𝑆 decreases with increasing 𝑥.

(a)

(b)

(c)

(d)

Figure 2 

(Color online) (a) Temperature-dependent magnetization 𝑀(𝑇)/𝑀(5 K) curves under ZFC process at 100 Oe for GaCFe3−𝑥Cr𝑥 (0≤𝑥≤0.9). (b) Temperature dependence of 𝑑𝑀/𝑑𝑇 for GaCFe3−𝑥Cr𝑥. (c) Magnetic field dependence of magnetization 𝑀(𝐻) curves for GaCFe3−𝑥Cr𝑥 at 5 K; inset shows the enlargement of 𝑀(𝐻) curves at positive 𝐻. (d) The 𝑥-dependent 𝑇𝐶 and 𝑀𝑆 for GaCFe3−𝑥Cr𝑥.

According to the previous theoretical studies [14, 15, 29], the density of states at the Fermi level 𝐸_𝐹 [𝑁(𝐸_𝐹)] is mainly from Fe 3d electrons in AXFe₃. Generally, the change of 𝑁(𝐸_𝐹) can be caused by many factors such as expansion/shrinkage of lattice, Fe/Cr 3d-C 2p hybridization effect, and band filling effect. In a conventional scheme, the expansion of lattice constant may give rise to the increasing of 𝑁(𝐸_𝐹) due to the decrease of bandwidth [13, 16]. However, another important factor is associated with the detailed electronic structure at Fermi level. In GaCFe₃, the calculation of band structure suggests that the position of 𝐸_𝐹 is located at the left hand of a sharp peak [14]. Considering the electronic structure of Cr (3d⁵4s¹) and Fe (3d⁶4s²), the Cr substitution for Fe can be considered as hole doping. Assuming a rigid band model, it will shift the 𝐸_𝐹 to lower energy side. As a result, the value of𝑁(𝐸_𝐹) in GaCFe_3−𝑥Cr_𝑥 is reduced with increasing 𝑥. Based on the Stoner model of itinerant ferromagnetism, the reduced 𝑁(𝐸_𝐹) will lead to a decrease in the magnetization [30]. Therefore, 𝑥-dependent 𝑀_𝑆 could be understood based on the above discussions. Now, how can the Cr-doping reduce the 𝑇_𝐶? In itinerant ferromagnetism the main contribution to the magnetism is the itinerant electrons. Here, in GaCFe₃ the itinerant electrons are mainly 3d electrons of transition element. With the Cr doping level increasing, the 3d electrons decrease, which leads to a decrease in the exchange integral 𝐽. Correspondingly, the value of 𝑇_𝐶 decreases with increasing 𝑥. In a word, the evolutions of 𝑇_𝐶 and 𝑀_𝑆 are mainly attributed to the cooperation of the lattice expansion and changes of electronic structure by chemical doping.

In order to investigate the type of magnetic transition for GaCFe_3−𝑥Cr_𝑥, we measured the 𝑀(𝐻) curves around the corresponding 𝑇_𝐶 for the selected samples. Figure 3(a) displays the isothermal magnetization 𝑀(𝐻) curves measured between 180 and 390?K with the magnetic fields up to 45?kOe for GaCFe_2.6Cr_0.4. The 𝑀(𝐻) curves were measured under the increasing/decreasing field processes around 𝑇_𝐶 (∼305?K). As shown in Figure 3(a), all the 𝑀(𝐻) curves around 𝑇_𝐶 are reversible during the increasing/decreasing field processes without any hysteresis, indicating a second-order magnetic transition [9]. In addition, the Arrott plots derived from 𝑀(𝐻) around 𝑇_𝐶 are presented in Figure 3(b). For GaCFe_2.6Cr_0.4, it is evident that the slope of 𝐻/𝑀 versus 𝑀² curve at high magnetic fields is positive for each temperature measured, confirming a second-order magnetic transition again [9, 23]. Analogously, for GaCFe_2.2Cr_0.8 (𝑇_𝐶∼165?K), the 𝑀(𝐻) curves and the Arrott plots in a temperature range of 100–250?K were shown in Figures 3(c) and 3(d), respectively, which confirm a second-order magnetic transition too. It is reasonable to conclude that the FM-PM transition is of second order for the left compositions in serial GaCFe_3−𝑥Cr_𝑥.

(a)

(b)

(c)

(d)

Figure 3 

(Color online) (a) Isotherm magnetization 𝑀(𝐻) curves for GaCFe2.6Cr0.4 between 180 and 390 K with external magnetic fields up to 45 kOe. (b) The Arrott plots deduced from 𝑀(𝐻) curves in (a). (c) Isotherm magnetization 𝑀(𝐻) curves for GaCFe2.2Cr0.8 between 100 and 250 K. (d) The Arrott plots deduced from 𝑀(𝐻) curves in (c).

Figures 4(a) and 4(b) illustrate the temperature dependence of resistivity 𝜌(𝑇) at zero magnetic field (2–350?K) for GaCFe_3−𝑥Cr_𝑥. All the magnitude of resistivity is comparable with other isostructural compounds [9, 22, 31, 32]. Figure 4(c) presents the temperature-dependent resistivity at both zero magnetic field and 5?T. Obviously, both curves are almost overlapped. The MR value (defined as (𝜌(𝐻)−𝜌(0𝑇))/𝜌(0𝑇)) is positive and very small (=1%) even at 5?T, suggesting that the magnetic field has little impact on the resistivity in GaCFe_3−𝑥Cr_𝑥. Figure 5(a) shows the normalized resistivity 𝜌(𝑇)/𝜌(350K) for GaCFe_3−𝑥Cr_𝑥 between 2 and 350?K. There exists a minimal resistivity (𝜌_min) and the corresponding temperature 𝑇_𝜌min decreases with increasing 𝑥 (to see Figure 5(b)) for low-doping samples. In high-doping samples (0.7≤𝑥≤0.9), the 𝜌_min disappears, which can be seen clearly in Figure 5(c). As shown in Figure 5(d), the low-𝑇 resistivity was well fitted by the formula 𝜌=𝜌₀+𝐴𝑇² (𝜌₀ and 𝐴 represent the residual resistivity and 𝑇²-term coefficient of the resistivity, resp.) up to about 70?K, indicating a Fermi-liquid behavior for GaCFe_3−𝑥Cr_𝑥 (0.7≤𝑥≤0.9) at lower temperatures. That is to say, the electron-electron scatterings are dominant at lower temperature (5–70?K) [5, 9]. Furthermore, the fitting parameter 𝐴 decreases with increasing 𝑥, which is shown in the left inset of Figure 5(d). However, at the elevated temperatures (100–270?K), 𝜌(𝑇) increases almost linearly with temperature for the samples with 0.7≤𝑥≤0.9 according to the fitting results (see the inset of Figure 5(c)), meaning that the contributions of electron-phonon scatterings exceed those of the electron-electron scatterings [9, 16]. In addition, the slope of linear part decreases with increasing 𝑥 as displayed in the right inset of Figure 5(d). The above results can be simply understood as follows: with increasing the temperature, the number of excited phonons increases quickly, resulting in the enhancement of the phonon scatterings [9].

(a)

(b)

(c)

Figure 4 

(Color online) (a)-(b) Temperature-dependent electrical resistivity at zero magnetic field in a temperature range of 2–350 K for GaCFe3−𝑥Cr𝑥 (0≤𝑥≤0.9). (c) The resistivity as a function of temperature at zero magnetic field and 5 T for GaCFe3.

(a)

(b)

(c)

(d)

Figure 5 

(Color online) (a) The normalized resistivity 𝜌(𝑇)/𝜌(350 K) dependence of temperature at zero field between 2 and 350 K for GaCFe3−𝑥Cr𝑥 (0≤𝑥≤0.9). (b) The temperature of minimal resistivity as a function of 𝑥 for GaCFe3−𝑥Cr𝑥 (0≤𝑥≤0.6). (c) Temperature dependence of resistivity at zero magnetic field for GaCFe3−𝑥Cr𝑥 (0.7≤𝑥≤0.9); inset displays the linear fits of 𝜌(𝑇) for the samples with 0.7≤𝑥≤0.9 between 100 and 270 K. (d) The lower-𝑇 𝜌(𝑇) data plotted as 𝜌(𝑇) versus 𝑇2 for the samples with 0.7≤𝑥≤0.9; the left and right insets show fitted parameters 𝐴 and 𝑘 as a function of 𝑥, respectively (see text for details).

Figures 6(a)–6(c) show the specific heat 𝐶_𝑃(𝑇) for GaCFe_3−𝑥Cr_𝑥 (0.7≤𝑥≤0.9) measured between 7 and 70?K at zero field. As shown in the inset of Figures 6(a)–6(c), the data below 20?K is plotted as 𝐶_𝑃(𝑇)/𝑇 versus 𝑇² which can be well expressed by using the following equation [5]: 𝐶_𝑃(𝑇)𝑇=𝛾+𝛽𝑇²+𝛿𝑇⁴, (1) where 𝛾 (Sommerfeld constant) is the electronic contribution, 𝛽 is the phonon contribution, and 𝛿 is deviations from the linear dispersion of the acoustic modes in extended temperature range. The fitted parameters 𝛾, 𝛽, and 𝛿 as a function of 𝑥 are shown in Figure 6(d) and the insets of Figure 6(d), respectively. With 𝑥 increasing, the 𝛾 and 𝛽increase while the 𝛿decreases. Accordingly, the Debye temperature Θ_𝐷=((𝑛×1.94×10⁶)/𝛽)^1/3 (where 𝑛 is the number of atoms in a unit cell and equal to 5 for GaCFe_3−𝑥Cr_𝑥 (0.7≤𝑥≤0.9)) is derived from the value of coefficient 𝛽. The detailed results of 𝜌₀, 𝐴, 𝛾, 𝛽, 𝛿, and Θ_𝐷 for GaCFe_3−𝑥Cr_𝑥 (0.7≤𝑥≤0.9) are summarized in Table 1. Generally, the value of Kadowaki-Woods (KW) ratio 𝐴/𝛾² is the well-known measure of electron-electron correlation [3, 16]. By taking the values of 𝐴 and 𝛾 listed in Table 1, the KW ratio was calculated for GaCFe_3−𝑥Cr_𝑥 (0.7≤𝑥≤0.9). For 𝑥=0.7, 0.8, and 0.9 the values of KW ratio are 2.70 × 10^-7?µO?cm/(mJ/mol?K)², 3.46 × 10^-7?µO?cm/(mJ/mol?K)², and 2.38 × 10^-7?µO?cm/(mJ/mol?K)², respectively, which are much less than the universal value 𝑎₀=10⁻⁵?µO?cm/(mJ/mol?K)² of for strong electron-electron system [3], meaning a weak electron-electron correlation.

Table 1 

The fitting parameters of 𝜌₀, 𝐴, 𝛾, 𝛽, 𝜎, and Θ_𝐷 for GaCFe_3−𝑥Cr_𝑥 (0.7≤𝑥≤0.9), respectively.

(a)

(b)

(c)

(d)

Figure 6 

(Color online) (a)–(c) Temperature-dependent heat capacity 𝐶𝑃(𝑇) at zero magnetic field for GaCFe3−𝑥Cr𝑥 (0.7≤𝑥≤0.9) between 6.7 and 70 K; inset shows the plots of 𝐶𝑃(𝑇)/𝑇 versus 𝑇2 below 20 K and the solid line represents the fitting results according to (1). (d) The fitting parameter 𝛾 as a function of 𝑥 for GaCFe3−𝑥Cr𝑥; the left and right insets show the parameters 𝛽and 𝛿 as a function of 𝑥, respectively.

Finally, based on the data of magnetic and electrical transport properties, the magnetic/electrical phase diagram for GaCFe_3−𝑥Cr_𝑥 (0≤𝑥≤0.9) is plotted in Figure 7. As for the magnetic phase diagram there are FM and PM regions; and the metallic, semiconducting, and Fermi-liquid areas are shown in electrical phase diagram.

Figure 7 

(Color online) The magnetic/electrical phase diagram for GaCFe3−𝑥Cr𝑥 (0≤𝑥≤0.9).

4. Conclusion

In summary, we present the magnetic/electrical phase diagram of GaCFe_3−𝑥Cr_𝑥 (0≤𝑥≤0.9). The influences of the Cr doping on the structure, magnetic, and electrical transport properties have been investigated systematically. With increasing the Cr content 𝑥, the lattice parameter increases while both the 𝑇_𝐶 and 𝑀_𝑆 decrease gradually. For the samples with 𝑥≤0.6, the resistivity curves show a semiconductor-like behavior below a certain temperature, which decreases as 𝑥 increases. On the contrary, for 𝑥≥0.7 the semiconductor-like behavior disappears, and the metallic behavior is dominant in the whole temperature range (2–350?K). Particularly, the samples with 𝑥≥0.7 show a Fermi-liquid behavior at low temperatures. In addition, we confirm that the FM-PM transition in the serial GaCFe_3−𝑥Cr_𝑥 is of second order.

Acknowledgments

This work was supported by the National Key Basic Research under Contract no. 2011CBA00111 and the National Natural Science Foundation of China under Contracts nos. 51001094, 51171177, 11174295, and 91222109.