As a representative of the strongly correlated systems, double perovskite Sr₂FeMoO₆ (SFMO) has been paid a great deal of attention. Because it has a considerable high low-field magnetoresistance (LFMR) behavior, a half-metal nature with 100% spin-polarization, and a high T_C well above room temperature.^[1–4] Those functional properties will make FeMo-based double perovskites systems (A₂FeMoO₆, A: Ca/Sr/Ba) become promising candidates from both fundamental investigations and potential technological applications in spintronics and magnetic storage devices operated at room temperature.^[1,2,5]

In an ideal A₂FeMoO₆ (A: Ca/Sr/Ba) structure, the electron configuration can be originally addressed as the localized spin-up electrons of the 3d⁵ (Fe³⁺) and the itinerant spin-down electron of the 4d¹ (Mo⁵⁺) shared by the Fe³⁺(t_2g ↓ )−O(2p)−Mo⁵⁺(t_2g ↓) subband.^[5,6] Localized five electrons of Fe³⁺ (3d⁵, S = 5/2) antiferromagnetically couple with one electron contributed by Mo⁵⁺ (4d¹, S = 1/2), resulting in a net magnetization of 4μ_B/f.u.^[7,8] However, a much lower magnetization is commonly reported in the experiments since the inevitable Fe/Mo anti-site defects (ASD) occurs, i.e., Fe occupies Mo positions wrongly and vice versa.^[7,9–11] ASD has a close correlation with magnetization. Additionally, theoretical works predicate that ASD significantly influences the electron spin polarization near Fermi level and even can destroy the half-metal property when exceeding a certain concentration.^[12,13] Hence, controlling ASD content is crucial for investigating the physical property in FeMo-based double perovskites. The itinerant electron at conduction band is suggested to mediate the ferromagnetic interaction between neighbor Fe cations by a double-exchange-like mechanism.^[14–16] Indeed, substituting the divalent A²⁺ ions in A₂FeMoO₆ (A: Sr²⁺/Ba²⁺) with the trivalent ions (such as La³⁺, Nd³⁺), a significantly improved T_C can be observed due to the increased electron density.^[6,17–20] Although these observations did disclose a positive correlation between ferromagnetic couplings strength and the carrier density near Fermi level, it cannot show the unique contribution of the band filling effect. In those electron-doped systems, the ionic sizes of the Sr²⁺/Ba²⁺ (1.26/1.42 Å) strongly differ from the substituting cations La³⁺/Nd³⁺ (1.16/1.109 Å), electron dopings not only provide the carrier into the conduction band but also trigger a rotation of (Fe, Mo)O₆ octahedra.^[6,17–19] The rotation will change the Fe–O–Mo band angle, even reduce the crystal symmetry and consequently modify the carrier density at the Fermi level.^[6,17–19] In order to provide a relatively clean research environment, we select Nd^0.3Ca^1.7FeMoO₆ as the research object because of the well-matched ionic sizes of Nd³⁺ (1.109 Å) and Ca²⁺ (1.12 Å), which can avoid the steric effects effect as far as possible. Through the above analysis, both the band filling effect caused by the electron doping and ASD significantly function on the physical properties of the FeMo-based double perovskites. Therefore, it is interesting to comparatively investigate two effects on physical properties.

In this work, three groups of single-phased pristine Ca₂FeMoO₆ (CFMO) and Nd^0.3Ca^1.7FeMoO₆ (NCFMO) ceramics were prepared at various sintering temperature (1050 °C, 1200 °C, and 1300 °C). The corresponding crystal structure, magnetization, resistivity, magnetoresistance, and the T_C were systematically and comparatively investigated.

The normalized XRD patterns of all samples are shown in Fig. 1(a). It can be clearly seen that all the diffraction peaks are well consistent with double perovskite structure with a monoclinic phase and a space group of P2₁/n and no second phase is detectable,^[21–25] which means that the C1–C6 samples are single-phased. The superstructure diffracted peaks of {110} resulting from the ordered arrangement of Fe and Mo cations at the B-sites are particularly sensitive to Fe/Mo ordering degree.^[25] Similar to the Fe/Mo ordering degree in SFMO, the Fe/Mo ordering degree in CFMO can be expressed by the relative intensity ratio of I{110} /{I(020) + I(112)} qualitatively.^[8] The variance of I{110} /{I(020) + I(112)} of C1–C6 as a function of the sintering temperature are plotted in Fig. 1(b). One can see clearly that, either maternal CFMO (C1, C3, C5) or NCFMO (C2, C4, C6), I{110} /{I(020) + I(112)} relative ratio improve with increasing sintering temperature. The experimental observation is consistent with data reported in FeMo-based double perovskites,^[7,26] confirming that manipulating the sintering temperature is a facile and efficient strategy to control the Fe/Mo ordering degree (contrary to Fe/Mo ASD). Interestingly, for each sintering temperature, I{110} /{I(020) + I(112)} relative ratio of the NCFMO (C2, C4, C6) ceramics is slightly less than that of the CFMO (C1, C3, C5), respectively. It indicates that Nd-substitution in CFMO has no obvious decrease of the Fe/Mo ordering degree. This is vastly different from the La-doped Sr₂FeMoO₆ systems, where, the Fe/Mo ordering degree shows a remarkable decrease upon the increase of La-doping content.^[6,18,27] The difference between them may attribute to the close ion sizes of Nd/Ca cations. The ordering degree of Fe/Mo (Fe/Mo ASD) has a close correlation with the magnetization, which will be discussed in the Fig. 2 in detail.

Fig. 1.

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	Fig. 1. (color online) (a) All the XRD patterns of C1–C6 samples. (b) The ratio of the I{110} /{I(020) + I(112)} as a function of the sintering temperature.

Fig. 2.

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	Fig. 2. (color online) Magnetic hysteresis loops (M–H) at 50 K for (a) C1, C2; (b) C3, C4, and (c) C5, C6. (d) The saturated magnetization (Ms) curves as a function of the sintering temperature for all the samples.

The M–H curves of C1–C6 ceramics measured at 50 K are present in Figs. 2(a)–2(c). It can be distinctly observed that all the samples show well-saturated hysteresis loops with a small coercive field, indicating a typical soft ferromagnetic behavior.^[28–30] The saturated magnetization (M_s) as a function of the sintering temperature curve is showed in Fig. 2(d). By comparing the Fig. 1(b) and Fig. 2(d), the varied trend of M_s with the sintering temperature is in accordance with that of the relative ratio of the I{110} /{I(020) + I(112)}, manifesting the main contribution of the Fe/Mo ordering degree to the magnetization. The reasons lie in that, once Fe/Mo ASD occurs, giving rise to antiferromagnetic –Fe–O–Fe–O– patches and paramagnetic –Mo–O–Mo–O– patches between ordering ferromagnetic domains.^[7,31] Actually, a great deal of experimental results confirmed that both patches can greatly weaken the magnetization in FeMo-based double perovskites.^[7,9,30] As for the origin of the less M_s of (C2, C4, C6) than (C1, C3, C5), there are two possible reasons: one is Nd-substitution will bring about intrinsic Fe/Mo defect in spite of close ion sizes of Nd/Ca cations; the other is the band filling effect caused by the electron injection at conduction band. Based on the above analysis, the magnetization is mainly controlled by the Fe/Mo ASD, whereas we cannot completely conclude the minor negative contribution of the band filling effect.

Generally, prepared process drastically affect the macroscopic structures of the ceramics, such as grain sizes, grain density, the connectivity between grains, grain boundary numbers, grain boundary strength and so on, which can strongly influence on the electrical transport, magnetoresistance, chemical states and other physical properties. Hence, the surface structures of C1–C6 are analyzed by SEM images as shown in Figs. 3(a)–3(f). As for maternal CFMO ceramics (Figs. 3(a)–3(c)), both the grains sizes and connectivity of (C1, C3, C5) improve significantly with increasing sintering temperature. The similar experimental phenomenon can be observed for Nd-doped CFMO (C2, C4, C6). The possible reasons may lie in that, high sintering temperature favors for promoting grain growth and improving connectivity between nearby grains. So the microstructures variance of all the ceramics is reasonable. Additionally, based on previous experimental data, the ceramic formed with a larger grain size and more close connectivity will show a reduced resistivity,^[30] which will be discussed as below.

Fig. 3.

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	Fig. 3. (color online) (a)–(c) Typical SEM images of (C1, C3, C5) and (d)–(f) (C2, C4, C6) ceramics.

The temperature-dependent resistivity (ρ–T) without and with a magnetic field of 2 T, and the temperature-dependent magnetoresistance (MR-T) curves for all the ceramics are shown in Figs. 4(a)–4(f), respectively. The resistivity of maternal CFMO ceramics (C1, C3, C5) decrease gradually with increasing the sintering temperature, and the similar tendency can be observed in Nd-doped CFMO ceramics (C2, C4, C6), which may be contributed by different macroscopic structures as displayed in Fig. 3. The negative magnetoresistance (MR) effect is a decrease of the electrical resistance in response to an applied magnetic field. In FeMo-based on double perovskites, it is confirmed that the MR effect is dominantly controlled by the grain boundary strength (GBs), which can be qualitatively expressed by the macroscopic resistivity.^[32–34] Generally, the GBs are contributed by the energy barrier Δ and the width s of the GB insulating barriers, the macroscopic physical parameters of GB, such as the connectivity, number, grain size, structural defects and local density of states can be included in parameters of s and Δ. The relation between resistivity and GB strength can be expressed as , where γ is a constant parameter. In general, for a given composition, the ceramic with a larger resistivity will display higher MR at the same measured conditions.^[26,33–35] It is interesting to find that the resistivity of C1 shows a sharp decrease under an external magnetic field of H = 2 T. Such a changed magnitude weakens gradually with increasing measured temperature, indicating a strong correlation of negative MR behavior with the temperature (the right y axis). The MR effect of maternal CFMO ceramics (C1, C3, C5) are suppressed by the increasing sintering temperature. For example, the MR% of C1, C3, and C5 at 50 K are −27.5%, −13.7%, and −8.17%, respectively. The diminished resistivity values of (C1, C3, C5) predicate the decreased grain boundary strength, leading to a suppressed MR effect as shown in Figs. 4(a)–4(c). Actually, the similar MR behavior can be found in (C2, C4, C6) ceramics.

Fig. 4.

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	Fig. 4. (color online) Temperature-dependent resistivity (ρ–T, the left y axis) without and with a magnetic field of 2 T, temperature-dependent MR curves (the right y axis) of C1–C6.

The temperature-dependent MR behaviors under a magnetic field of 2 T have been investigated in Fig. 4. The response of the MR to the varied magnetic field is also important for practical applications. Therefore, the MR of C1–C6 as a dependence of the magnetic field (MR–H) curves obtained at 50 K and 300 K are plotted in Fig. 5 and Fig. 6, respectively. Here, The MR% is defined as: MR% =( ρ_H − ρ₀) × 100%/ρ₀, where ρ_H and ρ₀ are the resistivity with and without the external field. From Figs. 5(a)–5(c), mainly three aspects of MR with respect to H can be expressed. The first is that all the samples show a typical characteristic of the LFMR behavior,^[1,35] i.e., negative MR increases deeply at low field (H ⩽ 1 T), whereas increases relatively smoothly at high field (H > 1 T). Moreover, such an LFMR property of C5 and C6 deteriorates drastically. The second is that, both (C1, C3, C5) and (C2, C4, C6) ceramics display a weakened LFMR effect with improved sintering temperature (Fig. 5(d)). The temperature-dependent LFMR behavior is contrary to the magnetization response as discussed in Fig. 2, whereas consistent with the tendency of resistivity with the sintering temperature. The sharp contrast indicates that LFMR in the research objects is dominantly controlled by the grain boundary effect not by ASD content. Additionally, the observed temperature-dependent LFMR nature convincingly predicates that lowering the sintering temperature is an efficient experimental strategy of optimizing the MR performance. A considerable LFMR (H = 1 T) of −22.5% can be obtained in C1, which is much larger than the reported approximately −12.5% in maternal CFMO ceramics.^[23] The third, LFMR values of (C1, C3, C5) are superior to that of the Nd-doped CFMO (C2, C4, C6) ceramics at the same sintering temperature. This result is in accordance with the similar electron-doped FeMo-based double perovskites.^[8,23,36] The possible reasons lie in that, the band filling effect contributed by Nd-substitution will bring about the injection of the electron at conduction band, and resulting in the decreased spin polarization of electron near Fermi level, and then a decreased MR property.^[8,36] Actually, MR property of C1–C6 measured at 300 K exhibit a similar behavior (Fig. 6).

Fig. 5.

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	Fig. 5. (color online) Magnetoresistance as a function of the magnetic field (MR–H) curves at 50 K for (a) C1, C2; (b) C3, C4, and (c) C5, C6. (d) LFMR% at 1 T for C1–C6 as a function of the sintering temperature.

Fig. 6.

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	Fig. 6. (color online) MR–H curves of (a) C1, C2; (b) C3, C4, and (c) C5, C6 at 300 K. (d) LFMR% at 1 T for C1–C6 as a function of the sintering temperature.

The field-cooling (200 Oe, 1 Oe = 79.5775 A·m⁻¹) magnetization-temperature (M–T) curves of C1–C6 are shown in Figs. 7(a)–7(c). All the ceramics transited from a paramagnetic state to a ferromagnetic state with decreasing the temperature.^[29] The T_C, indicated by an abrupt drop in the magnetization to zero, which can be estimated from the inflection point of M–T curves.^[6,29] One can clearly see that, all the ceramics exhibit a well-above room temperature T_C values (Fig. 7(d)), and the T_C values of Nd-doped C2, C4, and C6 are higher than that of C1, C3, and C5, respectively. The observation is contrary to the magnetization response, manifesting minor role of the Fe/Mo ASD on the T_C values. Although the spin polarization of electron at Fermi level decrease because of the band filling effect, giving rise to the increased carrier density near the Fermi level, which is proposed to has a positive ferromagnetic coupling strength.^{[6,18,19,23,30]} The carrier density of the Nd-doped C2, C4, and C6 is higher than that of maternal CFMO ceramics (C1, C3, C5), then resulting in an improved ferromagnetic interaction strength and an optimized T_C values.

Fig. 7.

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	Fig. 7. (color online) Temperature-dependent magnetization (M–T) curves for (a) C1, C2; (b) C3, C4, and (c) C5, C6. (d) Evolution of the Curie temperature (TC) as a dependence of the sintering temperature.

Two series of CFMO (C1, C3, C5) and NCFMO (C2, C4, C6) ceramics sintered at (1050 °C, 1200 °C, 1300 °C) have been specially designed to comparatively investigate the band-filling effect and Fe/Mo ASD on the physical properties of CFMO. The x-ray diffraction indicates that Fe/Mo ASD can be effectively tuned by controlling the sintering temperature. A consistent varied trend of the M_s with the Fe/Mo ASD manifests that the magnetization behavior is mainly controlled by the Fe/Mo ASD not by the band filling effect. Interestingly, magnetoresistance (MR) property of a given composition is dominantly contributed by the grain boundary strength, which can be expressed by the macroscopic resistivity values. However, the band filling effect caused by the Nd-substitution can decrease the spin polarization, and thus suppress MR performance fundamentally. Compared to the maternal CFMO ceramics, a considerable improved T_C can be observed in NCFMO ceramics since the band filling effect can increase the carrier density near Fermi level, which is responsible for the ferromagnetic coupling interaction strength. Maybe, our work can provoke further investigations interest into the correlation of the band-filling effects and Fe/Mo disorder with the physical properties of other Fe/Mo-based double perovskites.