Magnetic Transition and Magnetocaloric Effect of Gd_1−xNd_xMn₂Ge₂ (x = 0.3 and 0.4) Compounds

Abstract

Gd_1−xNd_xMn₂Ge₂ compounds with x = 0.3 and 0.4 were prepared by arc melting and crystallized in the ThCr₂Si₂-type structure with the space group I4/mmm based on X-ray powder diffraction (XRD) results. Magnetic transition and magnetocaloric effect (MCE) of the Gd_1−xNd_xMn₂Ge₂ compounds were investigated by magnetic measurements on a physical property measurement system (PPMS). Gd_0.7Nd_0.3Mn₂Ge₂ compound exhibits complicated magnetic transitions at around 63 K (T_comp), 86 K (T₁), 136 K (T_C), 260 K ($T_{\mathrm {N}}^{\text {inter}}$), and 347 K ($T_{\mathrm {C}}^{\text {inter}}$), respectively, while Gd_0.6Nd_0.4Mn₂Ge₂ compound shows a spin re-orientation transition at about 52 K. Combined with isothermal magnetization curves and the Maxwell relation, the maximum magnetic entropy changes of Gd_0.7Nd_0.3Mn₂Ge₂ and Gd_0.6Nd_0.4Mn₂Ge₂ were calculated to be 4.31 and 5.15 J kg^− 1 K^− 1 under the applied magnetic field changing from 0 to 5 T, respectively.

1 Introduction

Ternary intermetallic compounds containing rare earth (RE) elements, transition metals, and third element Ge and/or Si (e.g., REMn₂Ge₂ and REMn₂Si₂) have been studied extensively due to their interesting physical properties [1,2,3,4,5,6,7,8]. REMn₂Ge₂ compounds with the body-centered tetragonal ThCr₂Si₂-type structure manifest complex magnetic transitions due to the interplay between 3d and 4f magnetism and the strong dependence of the magnitude of the Mn moment and the magnetic state of the Mn sublattice on the Mn–Mn interatomic distance [9,10,11]. Magnetic transitions and magnetic properties of REMn₂Ge₂ compounds are strongly dependent on the Mn–Mn intraplanar and interplanar exchange interactions, which affects the Mn–Mn interatomic distance in the ab plane (d Mn-Mna) governed by the lattice parameter (a) [12,13,14,15,16,17,18,19,20,21,22,23]. The critical distance of d Mn-Mna and lattice parameter (a) is 2.870 and 4.060 Å, respectively, based on the reported experimental results [12,13,14,15,16,17,18,19,20,21]. If d Mn-Mna > 2.870 Å (a > 4.060 Å), the intralayer (in-plane) Mn–Mn coupling is antiferromagnetic, while the interlayer (along the c-axis) Mn–Mn coupling is ferromagnetic. In the case of 2.840 Å < dMn-Mna < 2.870 Å (4.020 Å < a < 4.060 Å), the intralayer and interlayer Mn–Mn couplings are antiferromagnetic. When d Mn-Mna < 2.840 Å (a < 4.020 Å), there is no intralayer in-plane spin component and the interlayer Mn–Mn coupling is collinear ferromagnetic or antiferromagnetic along the c-axis [13,14,15,16,17,18,19,20,21].

Among these REMn₂Ge₂ compounds, magnetic transitions of Nd_1−xY_xMn₂Ge₂ [24], Nd_1−xEr_xMn₂Ge₂ [25], Gd_0.925La_0.075Mn₂Ge₂ [26], and Nd_1−xGd_xMn₂Ge₂ [27] compounds were investigated experimentally. Nd_1−xGd_xMn₂Ge₂ (x ≤ 0.6) compounds show the ferromagnetic transition with a spin re-orientation at low temperature, while Nd_1−xGd_xMn₂Ge₂ (0.7 ≤ x < 1) compounds exhibit the ferromagnetic behavior with the compensation point and re-entrant ferrimagnetism [27]. In addition, magnetocaloric effect (MCE) of REMn₂Ge₂ compounds, e.g., Gd_1−xSm_xMn₂Ge₂ [28], Pr_1−xY_xMn₂Ge₂ [29], Nd(Mn_1−xFe_x)₂Ge₂ [30], and Nd_0.2Gd_0.8Mn₂Ge₂ [31], were studied experimentally. The maximum magnetic entropy change of Gd_0.8Nd_0.2Mn₂Ge₂ under a magnetic field change of 1 T was negative (− 0.812 J kg^− 1 K^− 1) at the re-entrant ferromagnetic transition temperature, while it was positive (0.682 J kg^− 1 K^− 1) at the antiferro-ferromagnetic transition temperature [31].

In order to better understand the effect of substitution of Nd for Gd on magnetic properties of GdMn₂Ge₂ compound, the crystal structure, magnetic transitions, and magnetocaloric properties of Gd_1−xNd_xMn₂Ge₂ (x = 0.3 and 0.4) compounds were investigated experimentally in this work.

2 Experiment

Gd_1−xNd_xMn₂Ge₂ (x = 0.3 and 0.4) compounds were prepared in an arc furnace by arc-melting pure elements (99.99% purity) using a non-consumable tungsten electrode under an inert argon atmosphere. To compensate the weight loss during the melting and annealing procedure, 3% excess of Mn was added. Ingots with the mass of about 3 g were melted four times to achieve good homogeneity. The ingots were annealed in an evacuated quartz tube at 1173 K for 240 h and then quenched in ice water.

The crystal structure and phase identification of the samples were determined by X-ray powder diffraction (XRD, PLXcel 3D) using Cu Kα radiation in the range from 20^∘ to 120^∘ with 0.2626 step sizes at 45 kV and 40 mA at room temperature. The crystal structure was refined by the Rietveld technique using the GSAS software. Magnetization measurements were carried out using a physical property measurement system (PPMS-9, Quantum Design) in the temperature range of 10 ∼ 380 K under applying magnetic field of 200 Oe. The temperature dependence of magnetization was recorded following zero-field-cooled (ZFC) and field-cooled (FC) measurement protocols. The samples were cooled in the absence of a field (ZFC) or in the presence of a field (FC), and then the magnetization was measured during warming. Isothermal magnetization of the samples was measured by PPMS at different temperatures under the applied magnetic field of up to 5 T.

3 Results and Discussion

3.1 Phase Analysis

Figure 1 is the Rietveld refinement results of the XRD patterns of Gd_1−xNd_xMn₂Ge₂ (x = 0.3 and 0.4) compounds at room temperature. The refinement results confirm that the compounds are single phase crystallizing in the ThCr₂Si₂-type structure with the space group I4/mmm. The lattice parameters of Gd_0.7Nd_0.3Mn₂Ge₂ and Gd_0.6Nd_0.4Mn₂Ge₂ derived from the Rietveld refinements are a = 4.055(6) Å, c = 10.890(7) Å and a = 4.060(6) Å, c = 10.893(8) Å, respectively, which are consistent with the reported data (a = 4.054 Å, c = 10.884 Å and a = 4.061 Å, c = 10.888 Å) [27].

Fig. 1

The Rietveld refinement results of XRD patterns of a Gd_0.7Nd_0.3Mn₂Ge₂ and b Gd_0.6Nd_0.4Mn₂Ge₂. The red points and the solid lines are the experimental and calculated XRD patterns, respectively. The green lines are the differences between the experimental and calculated intensities, while the vertical bars indicate the position of Bragg refractions

3.2 Magnetic Transitions

Figure 2 shows the temperature dependence of magnetization of Gd_1−xNd_xMn₂Ge₂ (x = 0.3 and 0.4) compounds in the temperature range of 10–380 K in a magnetic field of 200 Oe. In Fig. 2a, Gd_0.7Nd_0.3Mn₂Ge₂ compound exhibits a re-entrant ferromagnetism accompanied with a sequence of magnetic transitions from antiferromagnetic to ferromagnetic, antiferromagnetic, and ferromagnetic states according to the experimental results [32, 33], which is similar with the magnetic behavior of SmMn₂Ge₂ [34]. A transition occurs from the intralayer antiferromagnetic (AFl) state to the canted ferromagnetic (Fmc) state at 347 K (${\mathrm {T}}_{\mathrm {C}}^{~~\text {inter}}$). ${\mathrm {T}}_{\mathrm {C}}^{~~\text {inter}}$ corresponds to the minimum of dM/dT of the FC curve. With decreasing temperature, a transition from canted ferromagnetic (Fmc) state to an interlayer antiferromagnetic (AFmc) state at 260 K (${\mathrm {T}}_{\mathrm {N}}^{~~\text {inter}})$ is found. ${\mathrm {T}}_{\mathrm {N}}^{~~\text {inter}}$ corresponds to the maximum of dM/dT of the FC curve. The AFmc state is stable until about 136 K (T_C(RE)). It shows a re-entrant ferromagnetism below T_C(RE) because of the long-range ordering of Gd moment coupling ferromagnetically with ferromagnetic component of the Mn sublattice. At the lower temperature, the compensation temperature (T_comp) was found at 63 K. The magnetic moment of the RE sublattice increased more rapidly with the decreasing temperature than that of the Mn sublattice, yielding the compensation point at 63 K. On the other hand, in Fig. 2b, the ZFC and FC magnetizations of Gd_0.6Nd_0.4Mn₂Ge₂ compound show two magnetic transitions temperatures (T_SR and ${\mathrm {T}}_{\mathrm {C}}^{~~\text {inter}}$). According to the experimental results [27], the spin re-orientation behavior is observed below ${\mathrm {T}}_{\mathrm {C}}^{~~\text {inter}}$. The spin re-orientation temperature (T_SR) was determined to be 52 K by the cusp maximum of the magnetization FC curve, which corresponds to a re-arrangement of the Mn order from a canted ferromagnetic structure (Fmc) to a conical ferromagnetic structure (Fmi) with the ferromagnetic order perpendicular to the tetragonal c-axis, resulting in a stronger ferromagnetic component.

Fig. 2

Temperature dependence of magnetization of a Gd_0.7Nd_0.3Mn₂Ge₂ and b Gd_0.6Nd_0.4Mn₂Ge₂ measured in the applied magnetic field of 200 Oe

As can be seen in Fig. 2, Gd_0.7Nd_0.3Mn₂Ge₂ compound exhibits multiple magnetic transitions in the temperature range of 10–380 K, while Gd_0.6Nd_0.4Mn₂Ge₂ compound has two magnetic transitions in the same temperature region. Since the atomic radius of Nd is larger than that of Gd, the substitution of Nd for Gd results in an increase of the Mn–Mn bond lengths. The d Mn-Mna (2.8677 Å) of Gd_0.7Nd_0.3Mn₂Ge₂ compound is slightly less than the critical distance (2.870 Å). The interlayer and intralayer Mn–Mn exchange couplings in Gd_0.7Nd_0.3Mn₂Ge₂ compound are antiferromagnetic, which leads to the formation of the AFmc-type antiferromagnetic structure below $\mathrm {T}_{\mathrm {N}}^{~~\text {inter}}$ [12,13,14,15,16,17,18,19,20]. Meanwhile, the d Mn-Mna (2.8713 Å) of Gd_0.6Nd_0.4Mn₂Ge₂ compound is slightly larger than the critical distance (2.870 Å). The interlayer Mn–Mn exchange coupling in Gd_0.6Nd_0.4Mn₂Ge₂ compound is ferromagnetic, and the intralayer Mn–Mn exchange coupling is antiferromagnetic, resulting in the formation of the canted Fmc-type ferromagnetic structure [12,13,14,15,16,17,18,19,20]. It confirms that the interlayer and intralayer Mn–Mn exchange interactions are very sensitive to the intralayer distance (d Mn-Mna), resulting in the ferromagnetic or antiferromagnetic ordering of the Mn–Mn coupling.

In addition, the ZFC and FC curves of Gd_0.6Nd_0.4Mn₂Ge₂ compound split below ${\mathrm {T}}_{\mathrm {C}}^{~~\text {inter}}$ in Fig. 2b. During the FC process, the ferromagnetic component of Mn moment has a preferred orientation in an external field [32, 34], while that is pinned randomly during ZFC process and therefore the overall magnetization of the compound in the ZFC curve is smaller than that in the FC curve [33, 34]. It is worth noting that both the FC and ZFC magnetizations tend to have very low values below T_SR.

3.3 Magnetocaloric Effect

Figure 3 shows the isothermal magnetization of Gd_1−xNd_xMn₂Ge₂ (x = 0.3 and 0.4) compounds measured in the vicinity of the transition temperature (${\mathrm {T}}_{\mathrm {C}}^{~~\text {inter}})$ with the magnetic field change from 0 to 5 T. As manifested in Fig. 3a, the magnetization of Gd_0.7Nd_0.3Mn₂Ge₂ compound increases rapidly under low fields and slowly under the high fields below ${\mathrm {T}}_{\mathrm {C}}^{~~\text {inter}}$, indicating the possibility of some antiferromagnetic components in this temperature range, whereas the magnetization of the compound shows antiferromagnetic behavior at high temperature (above ${\mathrm {T}}_{\mathrm {C}}^{~~\text {inter}}$). In Fig. 3b, Gd_0.6Nd_0.4Mn₂Ge₂ compound has the ferromagnetic behavior at low temperature (below ${\mathrm {T}}_{\mathrm {C}}^{~~\text {inter}}$), while it shows antiferromagnetic behavior at high temperature (above ${\mathrm {T}}_{\mathrm {C}}^{~~\text {inter}}$). Moreover, the magnetization of Gd_0.6Nd_0.4Mn₂Ge₂ compound increases more rapidly at low magnetic field than that of Gd_0.7Nd_0.3Mn₂Ge₂ compound and shows a tendency to approach the saturation with increasing applied magnetic field.

Fig. 3

Isothermal magnetization curves of a Gd_0.7Nd_0.3Mn₂Ge₂ and b Gd_0.6Nd_0.4Mn₂Ge₂ measured at different temperatures close to ${\mathrm {T}}_{\mathrm {C}}^{~~\text {inter}}$

In general, Arrott plots are used to determine the type of the phase transition of a compound near ${\mathrm {T}}_{\mathrm {C}}^{~~\text {inter}}$ according to the Inoue-Shimizu model [35]. This model involves a Landau expansion of the magnetic free energy (F) of up to the sixth power of the total magnetization (M).

$$ F = \frac{C_{1} (T)}{2} M^{2} + \frac{C_{3} (T)}{4} M^{4} + \frac{C_{5} (T)}{6} M^{6}-\mu_{0} MH $$

(1)

It has been pointed out that the order of a transition is closely related to the sign of the Landau coefficient C₃(T) at the Curie temperature [36]. The transition is of the first order if C₃(T_C) is negative, while it is of the second order for positive C₃(T_C). The sign of C₃(T_C) could be determined by means of Arrott plots [37]. If the Arrott plot is S-shape near the transition temperature, C₃(T_C) is negative, otherwise it is positive. Figure 4 is the Arrott plots of Gd_1−xNd_xMn₂Ge₂ (x = 0.3 and 0.4) compounds at different temperatures. As shown in Fig. 4a, b, no S-shaped curve is shown near ${\mathrm {T}}_{\mathrm {C}}^{~~\text {inter}}$. Therefore, the magnetic transition of Gd_1−xNd_xMn₂Ge₂ (x = 0.3 and 0.4) compounds at 347 and 349 K (${\mathrm {T}}_{\mathrm {C}}^{~~\text {inter}}$) is a second-order transition.

Fig. 4

Arrott plots of a Gd_0.7Nd_0.3Mn₂Ge₂ and b Gd_0.6Nd_0.4Mn₂Ge₂ at different temperatures close to ${\mathrm {T}}_{\mathrm {C}}^{~~\text {inter}}$(Mn)

The magnetic entropy change (ΔS) was calculated using Maxwell’s thermodynamic relation, $\left (\frac {\partial S}{\partial H}\right )T = \left (\frac {\partial M}{\partial T}\right )H$. The magnetic entropy change is given by:

$$ {\Delta} S(T,H) = S(T,H)-S(T,0) = - {{\int}_{0}^{H}} \left( \frac{\partial M}{\partial T}\right) \mathrm{d}H $$

(2)

where ΔS, M, H, and T are the magnetic entropy change, magnetization, applied magnetic field, and the temperature of the system, respectively. Equation (2) can be approximated by the following expression [38]:

$$ {\Delta} S = - {\sum}_{i} {\frac{1}{T_{i + 1} -T_{i}} (M_{i + 1} - M_{i})_{H} {\Delta} H_{i}} $$

(3)

where M_i and M_i+ 1 are the magnetization values measured in a field H at the temperatures T_i and T_i+ 1, respectively.

Using equation (3) and the isothermal magnetization curves, the temperature dependence of the magnetic entropy change were derived for Gd_0.7Nd_0.3Mn₂Ge₂ and Gd_0.6Nd_0.4Mn₂Ge₂ compounds (seen in Fig. 5). As can be seen, the magnetic ΔS increases gradually near the transition temperature. In this work, the maximum magnetic ΔS of Gd_1−xNd_xMn₂Ge₂ (x = 0.3 and 0.4) compounds for a magnetic field change of 5 T close to the transition temperature ${\mathrm {T}}_{\mathrm {C}}^{~~\text {inter}}$(Mn) were calculated to be 4.31 and 5.15 J kg^− 1 K^− 1, respectively. Under the similar magnetic transition temperature range and same applied magnetic field change, the maximum values of the magnetic ΔS are 2.35 and 1.84 J kg^− 1 K^− 1 for Nd(Mn_1−xFe_x)₂Ge₂ (x = 0.1 and 0.2) [30], − 1.0 and − 1.1 J kg^− 1 K^− 1 for Gd_1−xSm_xMn₂Ge₂ (x = 0.4 and 0.6) [28], and 2.94 and 3.47 J kg^− 1 K^− 1 for Pr_1−xY_xMn₂Ge₂ (x = 0.2 and 0.5) [29].

Fig. 5

Temperature dependence of magnetic entropy changes of a Gd_0.7Nd_0.3Mn₂Ge₂ and b Gd_0.6Nd_0.4Mn₂Ge₂ under different applied magnetic fields

4 Conclusions

In this work, the crystal structure, magnetic transitions, and magnetocaloric properties of the Gd_1−xNd_xMn₂Ge₂ (x = 0.3 and 0.4) compounds were investigated experimentally by XRD and magnetic measurements. The following conclusions were drawn:

• (1) XRD results confirm that the crystal structure of Gd_1−xNd_xMn₂Ge₂ (x = 0.3 and 0.4) compounds is the ThCr₂Si₂-type structure with the space group I4/mmm. The Rietveld refinement results show that the lattice parameters of these two compounds are well consistent with the reported experimental data.

• (2) The magnetization measurements reveal that Gd_0.7Nd_0.3Mn₂Ge₂ compound shows complex magnetic states with multiple magnetic transitions, including AFl-type antiferromagnetism, Fmc-type canted ferromagnetism, AFmc-type antiferromagnetism, and the re-entrant ferrimagnetism, while Gd_0.6Nd_0.4Mn₂Ge₂ compound exhibits a spin re-orientation transition with the AFl-type antiferromagnetism and the Fmc-type canted ferromagnetism.

• (3) Using the Maxwell relation, magnetic entropy changes of Gd_1−xNd_xMn₂Ge₂ (x = 0.3 and 0.4) compounds are calculated from isothermal magnetization curves measured at different temperatures. Under the magnetic field change of 5 T, the maximum magnetic entropy changes of Gd_0.7Nd_0.3Mn₂Ge₂ and Gd_0.6Nd_0.4Mn₂Ge₂ compounds are 4.31 and 5.15 J kg^− 1 K^− 1, respectively.