Structural, magnetic and electrical properties of a new double-perovskite LaNaMnMoO6 material

Structural, magnetic, magnetocaloric, electrical and magnetoresistance properties of an LaNaMnMoO6 powder sample have been investigated by X-ray diffraction (XRD), magnetic and electrical measurements. Our sample has been synthesized using the ceramic method. Rietveld refinements of the XRD patterns show that our sample is single phase and it crystallizes in the orthorhombic structure with Pnma space group. Magnetization versus temperature in a magnetic applied field of 0.05 T shows that our sample exhibits a paramagnetic–ferromagnetic transition with decreasing temperature. The Curie temperature TC is found to be 320 K. Arrott plots show that all our double-perovskite oxides exhibit a second-order magnetic phase transition. From the measured magnetization data of an LaNaMnMoO6 sample as a function of the magnetic applied field, the associated magnetic entropy change |−ΔSM| and the relative cooling power (RCP) have been determined. In the vicinity of TC, |−ΔSM| reached, in a magnetic applied field of 8 T, a maximum value of ∼4 J kg−1 K−1. Our sample undergoes a large magnetocaloric effect at near-room temperature. Resistivity measurements reveal the presence of an insulating-metal transition at Tρ = 180 K. A magnetoresistance of 30% has been observed at room temperature for 6 T, significantly larger than that reported for the A2FeMoO6 (A = Sr, Ba) double-perovskite system.

Structural, magnetic, magnetocaloric, electrical and magnetoresistance properties of an LaNaMnMoO 6 powder sample have been investigated by X-ray diffraction (XRD), magnetic and electrical measurements. Our sample has been synthesized using the ceramic method. Rietveld refinements of the XRD patterns show that our sample is single phase and it crystallizes in the orthorhombic structure with Pnma space group. Magnetization versus temperature in a magnetic applied field of 0.05 T shows that our sample exhibits a paramagnetic-ferromagnetic transition with decreasing temperature. The Curie temperature T C is found to be 320 K. Arrott plots show that all our double-perovskite oxides exhibit a second-order magnetic phase transition. From the measured magnetization data of an LaNaMnMoO 6 sample as a function of the magnetic applied field, the associated magnetic entropy change |− SM| and the relative cooling power (RCP) have been determined. In the vicinity of T C , |− SM| reached, in a magnetic applied field of 8 T, a maximum value of ∼4 J kg −1 K −1 . Our sample undergoes a large magnetocaloric effect at near-room temperature. Resistivity measurements reveal the presence of an insulating-metal transition at Tρ = 180 K. A magnetoresistance of 30% has been observed at room temperature for 6 T, significantly larger than that reported for the A 2 FeMoO 6 (A = Sr, Ba) double-perovskite system.       [25]. Moreover, our samples present a ratio c/a < √ 2 (table 1) characteristic of a cooperative Jahn-Teller deformation. The strong orthorhombic distortion of the LaNaMnMoO 6 structure is because of the cooperative coupling of the MnO 6 and MoO 6 Jahn-Teller distorted octahedral B sites. Figure 1c shows the orthorhombic structure of LaNaMnMoO 6 projected along the (101) direction, where the (Mn/Mo)O 6 octahedra are apparent. A typical feature of the crystal structure of these doubleperovskite oxides is the presence of a superlattice owing to the ordered arrangement of the cations in the oxygen octahedral nodes (B sites). The superlattice formation owing to displacement of the anions from their ideal sites may be also considered as another cause.
The SEM image of the LaNaMnMoO 6 ceramic is presented in figure 1d. A larger grain (≈3.5 µm) with well-defined boundaries, which coexist with smaller ones, was noted for the LaNaMnMoO 6 ceramic. The average crystallite size can be evaluated from the width of diffraction peaks using Scherrer formula [28]: where K is the grain shape factor, λ is the X-ray wave length, and θ and β are the Bragg angle and the width at half maximum of the XRD peak, respectively. The C XRD of LaNaMnMoO 6 powder is found to be 41.57 nm. Obviously, the grain sizes observed by SEM are several times larger than those calculated by XRD, which indicates that each grain observed by SEM is composed of several crystallites. The ideal structure of the double perovskites is based on the adapted tolerance factor t of the single perovskite [29]. In general, for double perovskites A 2 B B O 6 , the tolerance factor can be written as [30] follows: where r A , r B and r O are the average ionic radii of the A site, B site and oxygen, respectively. The closer to t = 1, the more the structure corresponds to ideal cubic. Therefore, except in rare cases, one can consider the following rule for the double-perovskite family: for 1.05 > t > 1.00, a cubic structure is adopted within the space group; for 1.00 > t > 0.97, the most likely structure corresponds to the I 4/m tetragonal space group and if t < 0.97, the compound becomes either monoclinic (P21/n) or orthorhombic [31]. Table 3 shows the evolution of the tolerance factor of our sample LaNaMnMoO 6 and of its homologous double-perovskite oxide LaNaB B O 6 /A 2 MnMoO 6 with different symmetry. These values are in good agreement with those mentioned below. Our crystallographic data were used to also calculate this tolerance factor for LaNaMnMoO 6 such as  Fm-3 m 1.009 [32] .

Magnetic properties
A previous study shows that LaKMnMoO 6 compound exhibits an FM behaviour at low temperature. The Curie temperature T C is 180 K [34]. Magnetization versus temperature for the LaNaMnMoO 6 sample are plotted in figure 2. Our synthesized sample LaNaMnMoO 6 exhibits a PM to FM transition at T C = 320 K with decreasing temperature. T C has been determined from the peak position of the dM/dT curve, as shown in figure 2. Changing potassium content to sodium does not destroy the FM behaviour observed in LaKMnMoO 6 compound at low temperature; however, it induces an increase in the Curie temperature T C from 180 K for LaKMnMoO 6 to 320 K for LaNaMnMoO 6 . This result can be explained by the decrease of the average ionic radius r A of the A cation site of A A MnMoO 6 double-perovskite samples and/or the distortion of the octahedral MnO 6 and MoO 6 as observed in the Pr 0.7 Ba 0.3−x MnO 3 perovskite sample [36]. The FM behaviour increases with decreasing the average ionic radius r A from 1.500 Å with T C = 180 K for the LaKMnMoO 6 double-perovskite sample to 1.375 Å with T C = 320 K for LaNaMnMoO 6 . Our oxide is FM at low temperature. Such FM behaviour has not been observed in this homologous Sr 2 MnMoO 6 sample [24].
FM-PM transition of LaNaMnMoO 6 was modelled using a phenomenological model given by Hamad [37]. The dependence of magnetization on the variation of temperature is written by     In order to confirm the FM behaviour at low temperatures of our sample, we performed magnetization versus magnetic applied field up to 8 T at several temperatures. We plot in figure 4 the M (μ 0 H) curves for LaNaMnMoO 6 compound. The magnetization rises sharply for low magnetic applied field and then saturates for µ 0 H higher than 1 T. The saturation magnetization at 10 K and 5 T, deduced from the M (μ 0 H) curve, is 2.1 µ B /mole. The LaNaMnMoO 6 compound reaches approximately 50% of the theoretical saturation of Mn3+ (4 µB for S = 2).
The M (μ 0 H) curves can be simulated by the law-approach to saturation (figure 5) in the term [38]:             respectively. We have obtained a best fit between experimental and theoretical study. Parameters fit are listed in table 6. The effective magnetic moment (μ exp eff ) can be estimated using simple Curie Weiss formula:   Table 7. Parameters fit for the LaNaMnMoO 6 sample in 1 T, 2 T and 3 T applied magnetic field of (− S M (T)) curves.

Magnetocaloric characterizations
A giant field-induced entropy change is one of the important criteria for magnetocaloric materials. In fact, the isothermal measurements of magnetization allow us to determine the magnetic entropy change of the sample under an applied magnetic field, according to the classical thermodynamic theory based on Maxwell's relations using the following equation: M i and M i+1 are the experimental values of the magnetization measured at temperatures T i and T i+1 , respectively, under an applied magnetic field H. The magnetic entropy change can be measured through either the adiabatic change of temperature by the application of a magnetic field, or through the measurements of classical M(H) isotherms at different temperatures [42]. In our work, we have used the second method based on magnetization measurements versus magnetic field. Figure 9a shows the behaviour of the magnetic entropy change as a function of temperature under several values of external magnetic field for our double-perovskite sample.
According to the phenomenological model [43], the magnetic entropy change of a magnetic system under adiabatic magnetic field variation from 0 to final value H max is available by     Under an applied magnetic field of 2 T, the absolute value of S of the LaNaMnMoO 6 sample is 1.5 J kg −1 K −1 around T C , and it reaches 3.99 J kg −1 K −1 under a magnetic field change of 8 T. Although the S values in our compound are smaller than that observed in Gd ( S = 4.2 J kg −1 K −1 ) for H = 2 T [41] considered as the best magnetic refrigerant, the LaNaMnMoO 6 sample can be considered as a potential candidate for magnetic refrigeration.
In order to confirm the important MCE of our specimens, it is interesting to consider the relative cooling power (RCP) which can be determined from the following relation: δ FWHM is full width at half maximum of S(T) curve [45]. The RCP value is 41.99 J kg −1 under an applied magnetic field of 8 T. These results are interesting, compared with those of materials considered as good for applications in magnetic refrigerators. Our sample undergoes a large MCE above room temperature. The magnetic field dependence of the magnetic entropy change of materials with a second-order phase transition can be expressed as [46]: where n depends on the magnetic state of the sample and it is obtained from the fit plot of S Max M versus µ 0 H via equation (3.8) (figure 10). The value of n deduced from the fitting is equal to 0.66(5) (inset of figure 10). This value is different from the calculated using the relation; [47] (n = 0.29 (8)). This difference shows the signature of magnetic inhomogeneities in our sample.  Figure 11a shows the temperature dependence of heat capacity C p under different field variations in our sample calculated from the S M data using the following relation: C p presents positive values above T C and negative ones below T C . The maximum/minimum values of C p , observed at 323/317 K are 52.261/−68.839 J kg −1 K −1 and 78.630/−150.178 J kg −1 K −1 under 1 T and 2 T, respectively. Figure 11b shows the calculated C p as a function of temperature at 1 T and 2 T, using equation (3.11) below:

Electrical properties
The temperature dependence of the resistivity ρ(T) without and for an applied magnetic field of 3T and 6 T are plotted in figure 12. The electrical resistivity of LaNaMnMoO 6 powder attains 1533 Ω cm at 70 K. Then it passes a maximum at T ρ = 180 K and drops down to 1018.93 Ω cm at room temperature. The magnitude of resistivity is markedly higher than found for Ba 2 YIrO 6 single crystal (ρ (300 K) = 40 mΩ cm) [48].
For comparison, our compound shows that it is metallic at low temperatures (T < T ρ ), whereas his homologous Sr 2 MnMoO 6 sample is an insulator [24].
It should be noted here that there is a large difference between the electric (T ρ = 180 K) and magnetic (T C = 320 K) transition temperature values. The significant difference between T ρ and T C values may be owing to several factors: (i) smaller crystallite size of sample than that measured using XRD, (ii) influence of extrinsic contributions such as a large number of grain boundaries, and (iii) spin-polarized tunnelling between FM grains through an insulating grain boundary layer, and so on. The discrepancy of the grain size may be that the size measured using SEM is for grains consisting of more than one crystallite [49].
To understand the transport mechanism in the whole temperature range, we used the phenomenological percolation model [50,51], which is based on the phase segregation of FM and PM semiconductor regions.
Following this model, we carried out a quantitative analysis of the resistivity temperature dependence data for our sample. According to Li [51], the resistivity for the entire temperature range may then be  Based on the phase segregation mechanism (percolation model), the total resistance of the system could be visualized as the sum of the resistivity of the phase separated FM-metallic and PM-insulator: ρ = ρ FM * f + ρ PM * (1 − f ); f = (1/(1 + exp(−U 0 (1 − T/T mod C )/k B T))) is the volume concentration of the FM phase, and (1 − f ) is the volume concentration of the PM phase.
In order to see the correlation between the magnetic and electrical properties in our sample LaNaMnMoO 6 , we have fitted the experimental resistivity data (figure 12) using the above equation. It can be seen that the results calculated from equation (3.14) agree with the experimental data. Then, we found that the percolation model describes well enough the resistivity behaviour in a wide temperature range including the region of phase transition, whatever the external magnetic field. The best-fit parameters are given in table 9. The temperature dependence on the volume concentration of the FM phase f is shown in figure 13. It is clear that f (T) remains equal to 1 below the metal-semiconductor transition temperature, which confirms the strong dominance of the FM fraction in this range. The coexistence of ferromagnetism and metallic conductivity at low temperatures provides evidence of the existence of magnetoresistance MR. Defining the MR at a given temperature as MR = ρ/ρ = ((ρ(0) − ρ(H))/ρ(0))*100; where ρ(H) and ρ(0) are the resistivity in a magnetic applied field H and in a zero field, respectively. The magnetoresistance evolution versus temperature at the applied magnetic field (6 T) is illustrated in figure 14. The MR increases with decreasing temperature for the LaNaMnMoO 6 double-perovskite sample. It is found to be approximately 30% at room temperature and approximately 50% at 70 K at 6 T for our synthesized sample. We thus obtain a large magnetoresistance in the LaNaMnMoO 6 sample as that observed in the Sr 2 FeMoO 6 compound by Yuan et al. [19]. This result (large MR at room temperature and at low magnetic field) is explained by the effect of grain boundaries. This phenomenon was observed in the Sr 2 FeMoO 6 compound by Kobayashi et al. [18].

Conclusion
We have investigated structural, magnetic, magnetocaloric, electrical and magnetoresistance properties of an LaNaMnMoO 6 double-perovskite sample. Structure analysis reveals that our sample crystallizes according to the orthorhombic structure with Pnma space group. Magnetic measurements show a PM-FM transition with decreasing temperature. This new double perovskite exhibits an MCE and a large magnetoresistance near room temperature. A combination of both MCE and large MR in LaNaMnMoO 6 material makes the appropriate substance for magnetic refrigeration applications at room temperature.
Data accessibility. This article has no supporting data. Authors' contributions. S.M.B. carried out the experiments and designed the study, analysed the data and wrote the manuscript. W.C.-R.K. and M.M. helped to analyse the data and helped draft the manuscript. All authors gave their final approval for publication.