Structural, Electrical and Magnetic Study in Nanocrystallite La2CuMnO6 Ceramics

Structural, dielectric and magnetic properties of nano-size polycrystalline, La 2 CuMnO 6 (LCM) samples were studied in the temperature range 80 K to 300 K. Orthorhombic single phase with space group 'Pnma' was confirmed by Rietveld refinement of XRD peaks. The small-polaron driven dielectric dispersion showed relaxation peaks in the vicinity of low-temperatures. The X-ray absorption spectroscopy (XAS) confirmed the charge states of Cu (2+) and Mn (4+) ions. DC-resistivity analysis supported the thermally activated conduction for high temperature and the variable range hoping (VRH) mechanism of conduction at low-temperature. The deviation of super-exchange angles between B-site cations from an ideal 180º value produced non-collinearity in the antiferromagnetic response of this ceramic and was confirmed canted antiferromagnetic behaviour. Positive Curie temperature along with finite coercivity indicated that the super-exchange interaction between Cu 2+ and Mn 4+ ions influenced the magnetic behaviour of this ceramics and showed a heterogenous magnetic response.


Introduction
The double perovskite materials of the form A2B'B"O6, coupled with any pair of transition metals at B-site, provide a large number of choices to explore a variety of multifunctional materials. Both B-site ions can be alternately arranged along the three crystalline axis, as found in the NaCl-type of arrangement. This ordering controls the fundamental properties of materials, like; magnetic, dielectric, vibrational and ionic conductivity, particularly in manganese-based double perovskite compounds. These compounds have been studied extensively; because of the wide variation in their physical properties like charge spin dependent magnetoelectric, magnetoresistance and multiferroicity. The presence of electro-magnetic coupling makes these compounds compatible with modern electronic devices. In these compounds, the presence of small conductivity, near and above room temperature, offered a new class of dielectric materials, known as leaky dielectric materials, used for microelectronic applications [1][2][3][4][5][6].
The double perovskites compounds of the form La2B′MnO6 (B′ = Ni, Co, or other transition elements) attracted lots of attention in the last decade due to their multifunctional properties [7][8][9][10]. The proper choice of 3d-elements as B-site cations, provides peculiar magnetic and electrical properties due to their complex nature of charge states [11]. The discovery of magneto-dielectrics in La2NiMnO6, accelerated the current pace of research activities [12], Lin et al. showed a relaxor-like dielectric behaviour occurred in La2NiMnO6 [13] and La2CoMnO6 [14]. In addition, ferroelectric and diffused ferroelectric properties were reported for different compositions of double perovskites [15][16][17][18][19][20]. Due to this substantial and promising dielectric response at high frequencies, double perovskites have been extensively studied [21][22][23][24]. Mir. et. al. studied the halfmetallicity properties of La2CuMnO6 and reported that La-O bond is ionic in nature, whereas Cu-O and Mn-O are covalent [23]. It was also reported that the Mn-d states along with notable contribution of Cu-d states are combinedly responsible for magnetic response in La2CuMnO6 ceramics [24].
Exploring the temperature dependent electrical and magnetic properties of such ceramics, will be very interesting for the fundamental physics as well as for the possible electronic device application point of view.
In our previous study, structural, morphological and high temperature dielectric properties of La2CuMnO6 (LCM) were reported [25]. The dielectric response of microstructured LCM crystals showed Maxwell-Wagner dielectric relaxation and non-Debye dielectric relaxation. Correlated Barrier Hopping (CBH) dependent conduction was observed in the micro-structured LCM crystals. However, the study was somewhat limited for micro size-grains and up to high-temperature electrical properties only. Therefore, investigation of below room temperature electrical and magnetic properties of this ceramic, will be fascinating.
In this work, a systematic study on the structural, electric and magnetic characteristics of nanostructured LCM ceramics and the effect of the nano-sized grains on the physical properties of this LCM ceramics were presented. An attempt to investigate the origin of non-collinearity in magnetic behaviour and to co-relate the low temperature dielectric anomalies with magnetic anomalies were made.

Experimental
LCM nano-sized polycrystalline samples were synthesized by the sol-gel reaction of stoichiometric quantities of highly pure reagents La(NO3)3*6H2O (by Loba chemicals), Mn(NO3)2*4H2O, Cu(NO3)2*2.5H2O and citric acid (by Merck). These chemicals were mixed in distilled water and this solution was stirred for 10 hours at 80 ℃ under uniform heat on a magnetic stirrer to obtain a thick gel. The thick gel was kept in the oven at 180 ºC for the next 10 hours and calcined it at 750 K for 6 hours. Several pellets prepared for various characterizations were sintered at 800 o C. Room temperature X-ray powder diffraction measurements were performed using Rigaku Ultima IV, Japan (Cu-Kα, λ = 1.54 Å) and Rietveld refinement of XRD data was performed by using FULLPROOF software.
The JSM-5410 scanning electron microscope (equipped with Si (Li) X-ray detector) was used to study the surface morphology of the nanostructured LCM polycrystalline ceramics.
The scanning electron images (SEIs) and backscattered electron images (BEIs) were taken at room temperature. The energy-dispersive spectrum (EDS) was recorded within the energy range of 0-10 keV. The transmission electron microscope (TEM) images were taken using JEM-100 CX II (with resolution 3 Å to 1.4 Å and accelerating voltage 20-100 kV in 20 kV steps). Soft X-ray absorption spectroscopy (XAS) at Mn, Cu L-edge were recorded at polarized light soft X-ray absorption beamline Indus-2 at RRCAT, Indore India. The sintered pellets' surface was polished and coated with high purity silver pest (Alfa Aesar) for electrical measurements. The temperature-dependent electric measurements were carried out using the Novo-Control GmbH set-up. Temperature-dependent DC-magnetization measurement was carried out using 7 Tesla SQUID-VSM (Quantum Design Inc., USA).

X-ray Diffraction Analysis
Room temperature X-ray diffraction (XRD) patterns of LCM are shown in Fig. 1 along with their Rietveld refinement patterns, where red-colored open circle curve represents the recorded XRD pattern, the black-colored solid-line curve represents the calculated patterns of XRD refinement data, the green vertical lines show Bragg's positions of XRD peaks and the blue-colored curve shows the difference between the observed and calculated XRD data. The Pseudo-Voigt function with 'Pnma' space group (for orthorhombic phase) is used to fit XRD patterns. The linear interpolation method is used for background data fitting. The scale factor, half-width parameters and isotropic thermal parameters (Biso) are kept varying throughout the refinement process.
The peak splitting in the vicinity of 32 o , whose hkl indices are (002) and (121) and dspacings are 2.7688 Å and 2.7570 Å, respectively, is an indication of the particular space group. Table 1 shows the results of XRD refinement, where the Biso values of Cu/Mn and Oxygen atoms are higher than La-atoms, indicating that the displacements of B-O bonds significantly affect the physical properties of this ceramic [26][27][28].
Scherrer's equation has been used to measure the average crystalline size of LCM, as given below: where D is average crystalline size, k is a constant (shape factor = 0.9), λ is the wavelength of the X-ray radiation used (λCu = 1.5406 Å), β is the full width half maximum (FWHM) and is the respective angle. The observed average crystal size is 38 ± 2 nm.
It is well known that the nano-sized crystals influence the spontaneous orthorhombic lattice strain. Therefore, in order to observe this effect, spontaneous lattice strain was measured by using equation (2): where a and c are the lattice parameters (for 'Pbnm' space group c replaces by b) and 'S' is the spontaneous lattice strain. The obtained spontaneous strain value (S) is 7.1 × 10 -3 , which is higher than micro-structured ceramics (6.7 × 10 -3 ). This small change in strain affects the bond angles between Mn-O-Mn, which in turn affects the physical properties of this ceramic. and fobs = 0.91, indicating that the symmetry of the compound is either monoclinic or orthorhombic [29][30][31][32].

Geometrical analysis
The deviation of tolerance factor from the ideal rock-salt structure may also introduce lattice strain [33]; therefore, to estimate the average crystal size and strain parameters, the given size-strain expression (equation-5) is employed [34][35][36][37][38]: where 'dhkl' represents the inter-planar spacing of particular planes and 'ε' represents the average strain of the lattice. 'β' represents FWHM of the corresponding peaks and 'D' represents the average crystalline size. 'k' is the Scherrer constant or shape constant (k = 0.9). Fig.3 shows the respective plot of equation (5). The estimated average size of the crystals is 45.3 ± 3 nm, consistent with the measured value using Sherrer's equation (1) (38 ± 2 nm). The evoked strain is estimated by extrapolating the fitting line and it is equal to 9.02 × 10 -3 .  This individual grain's measured size is larger than that of the average crystalline size, which was estimated using Scherrer's equation (38 ± 2 nm) and from the fitting of size-strain plot (47.3 ± 3 nm). We deduced from the high-resolution TEM that the grains consist of smaller crystallites with different orientations (Fig. 4 (a)).  Fig. 7 (a) shows the real part  of complex dielectric permittivity in the temperature range 80 K to 300 K and in the frequency range 3 kHz to 1 MHz. This plot shows two anomalies; (i) A steep-increasing behavior in the temperature range of 80 K to 120 K, indicating the orientation of local charge carriers or dipoles, which were not settle-down at low temperatures [40][41][42]. As the frequency increases, these anomalies are tending to higher temperatures, indicating dielectric-relaxation in this region. (ii) The plateau regions, with  ~500, in the temperature range 120 K to 200 K, indicating saturation of polarization of the local charge carriers or dipoles, were available at low temperatures. In addition, the values of dielectric dispersion decrease for higher field frequencies in the temperature range 200 K-250 K, which indicates the lack of polarization of the available dipoles in LCM [43][44][45][46][47].

Dielectric Analysis
Furthermore, the increase in dispersion values, reaching  ~ 10 3 -10 4 , near room temperature, indicates that the accumulation of local charge carriers and thermally generated new charge carriers at grain boundaries improve the dielectric dispersion features of LCM.
The crystalline size of the ceramics and conducting nature of the grain boundaries also play a significant role in the complex dielectric permittivity measurement [45,[47][48][49].
As the crystalline size of this ceramic is nanometric, the contribution of individual grains and grain boundary surface layers becomes more significant, leading to such a high dielectric response of LCM (~10 4 ). In our previous study [25], it was reported that the magnitude of dielectric permittivity of the order of ~10 2 for the micro-sized LCM.  Fig. 8 (a). These peaks indicated the occurrence of more than one type of relaxation process in this ceramic [45,[50][51][52][53][54]. The relaxation-peak frequency (fmax) was estimated by using equation (6): where = 2πfmax and is the most probable relaxation time. The characteristic relaxation time o can be determined by the modified Arrhenius equation given below: where τo is the characteristic relaxation time at infinitely high temperature, Ea is the activation energy involved in dielectric relaxation, kB is the Boltzmann constant and T is the temperature in Kelvin. The respective plot of equation (7), in the temperature range 85 K-110 K is shown in Fig. 8 (b).
The estimated activation energy values of Ea and the characteristic relaxation time τo, are 127 meV and 16 ps respectively, indicating that the relaxation process is driven by the nearest-neighbor-hopping (NNH) of small polarons [55][56][57].

Electric modulus analysis
We can elucidate the opacity resulting from grain/grain boundary effects during the analysis of the complex dielectric behavior of this sol-gel-derived nano-sized LCM ceramics by electric modulus analysis. The electric modulus plots were prepared using the following equations with the help of complex dielectric data [56]: The relaxation time-temperature-dependent plot is shown in Fig. 9 (c). The linear dependence of relaxation time with the reciprocal temperature allows us to apply Arrhenius law to fit experimenral data using equation (7). The estimated activation energy is 107. … (9) where Mmax is the peak value of the imaginary part of modulus and the fmax is the corresponding peak frequency, the corresponding plot at 80 K, is shown in Fig. 9 (d). We have chosen β = 0.7 to obtain the proper fitting of the curve, which indicates that the presence of non-Debye relaxation in the dielectric behaviour of this ceramic [56][57][58][59][60][61].  To study the conductivity behavior of LCM, we divided it into two parts; only the temperature dependent part and temperature and frequency dependent part of electrical conductivity. The first part of conductivity is related to the thermally drift of charge carriers and follows the Arrhenius relation:

Electrical conductivity analysis
where Ea is activation energy required for electrical conduction and 0 represents the preexponential factor. The plots of log vs. 1000/T for several applied frequencies are shown in the inset (Fig.b) of Fig. 10. The observed data points were fitted using equation (10) up to the reasonable linear limit for the lowest available frequencies. The average value of the estimated activation energy is 160 meV, which indicates the thermally generated small polaronic or electronic nature of electrical conduction [51,56].
We propose that the hopping of charge carriers between trapping centers available at interfacial states present in this material is one of the strong reasons for relaxation peaks in the lower range of temperatures. The presence of Cu 2+ -ions leads to the JT-distortion and breaks the degeneracy of 3d-orbital and produces vacant states, which function as additional hoping sites or trapping centers for charge carriers at low temperatures. The plot of peak relaxation times, τmax vs. reciprocal of the peak temperature, is shown in inset (Fig. b) of Fig.10. The estimated value of activation energy is 117 meV, which is consistent with the activation energy determined from M data (107.2 meV, see Fig. 9 (c)), suggesting that the phenomenon of electrical conduction dominated over dielectric relaxation, and both are driven by small polarons [63].
The power-law is employed to analyze the non-linear features of conductivity [64] as: where 0 is temperature-dependent pre-exponent of conductivity, n is the exponent parameter devoted to the deviation of the dielectric characteristics of this material from Debye behavior and it also highlights the inter-ionic coupling strength. It has been mentioned in the literature that the polaronic-conductance mechanism includes locally degenerated charge carriers, electronic dipole moments and elastic energy [65,66].
To study the effect of frequency on the conductivity behavior of LCM, we focused on the high frequency (> 50 kHz) data of this compound. Equation (11) is employed to fit the plots of log vs. log f (inset in Fig. 11) in the temperature range 120 K to 320 K. Fig. 11 shows the plot of exponent parameter n vs. T, obtained by the slope of the fitting of log vs. log f plots. The decreasing nature of n is followed by a saturation near 300 K, indicating that the conductivity characteristic of LCM is driven by the correlated barrier hopping mechanism associated with the overlapping of small-polaron tunneling mechanism. This characteristic influenced the dielectric behavior of this ceramic [34,[67][68][69][70].

DC resistivity analysis
To analyze the conductivity characteristic of LCM, more precisely, we studied its dc-resistivity, , behavior across a wide range of temperatures. Resistivity  vs. temperature plot in the temperature range 80 K to 490 K is shown in Fig. 12. The resistivity value decreases with increasing temperature from 7.3 × 10 4 to 9.3 × 10 -3 Ω m, supporting the negative coefficient of the temperature of resistivity. This temperature-dependent semiconducting nature of resistivity characteristic of LCM suppresses the appearance of the relaxation-peaks in the high-temperature dielectric response of LCM [71][72][73]. To study the effect of temperature, we divided its dc-resistivity behavior into three-parts: (i) Conduction due to drift of the thermally active charge carriers at the temperature above 350 K, which supported thermally activated conduction (TAC) mechanism of the conduction (equation (12)), (ii) Conduction due to the presence of small polarons in the temperature range 190 K to 280 K, accompanied the nearest-neighbor hopping (NNH) mechanism (equation (13) Here ETAC and ENNH are the activation energy related to TAC and NNH type of conduction and 0 is the pre-exponent parameter. kB is the Boltzmann constant, T is the absolute temperature. In equation (14), T0 is the Mott-temperature related to the available density of state near Fermi energy N(Ef) as: where 'α' is the tunneling probability [56].
The red-colored trace belongs to the region of the TAC mechanism and its corresponding Arrhenius fitting, by using equation (12) is shown in the inset (Fig. (a)) of which supported the short-range mobility of thermally generated charge carriers. In the temperature range, 190 K -280 K, the nearest neighbor interstitial sites serve as hopping sites for charge carriers. Charge carriers can jump between these sites either by absorbing the phonons or by releasing the phonons. The activation energy required for such an NNH process could be estimated using equation (13), where ENNH represents the required activation energy or potential fluctuation for defects level [77]. The estimated value of ENNH is equal to 132.5 meV with ρNNH = 9.8 × 10 -4 (Ω-m). We observed a non-linearity in the log  vs 1000/T plot as temperature goes below 190 K (see blue-colored incircle in the inset ( Fig.(a)) of Fig. 12), indicates that the hopping of charge carriers is possible only at the most prominent sites available at low temperatures. The VRH mechanism of the conduction can be used to analyze such drifting of charge carriers. Hence, the resistivity at low-temperature was analyzed by using equation (14). On considering the three-dimensional hopping condition, we have chosen the exponential value '1/4', and the corresponding plot is shown in the inset (Fig.(b)) of Fig. 12

DC magnetic field analysis
The dc-magnetic behavior provides charge exchange interaction between B-sites ions and Oxygen-ions. Fig. 13 (a) shows the Zero-Field Cooled (ZFC) and Field Cooled (FC) magnetization measurement at 100 Oe of LCM ceramics. It is evident from the magnetization behavior that the ZFC and FC cycles show a maximum at 18 K, below which the ZFC curve shows a sharp drop and FC curve gradually decreases down to 9 K (as shown in the inset of Fig. 13 (a)). These observations suggest that below 18 K, this compound has anti-ferromagnetc behavior. Moreover, a strong magnetic-irreversibility is observed in the M-T behavior of LCM, temperature above 18 K, indicating some additional magnetic coupling between B-site ions other than Mn 4+ -O 2--Mn 4+ networks. To probe the cause of such irreversibility, we have analyzed inverse susceptibility data with respect to temperature. Fig. 13   Oe, but for a collinear-antiferromagnetic system, one would expect a linear hysteresis behavior without any coercivity. Therefore, it appears that the present system has a noncollinear antiferromagnetic structure or canted antiferromagnetic structure. The positive value of the Curie temperature (31.4 K) supported this assumption as well. Moreover, at a lower temperature (below ~100 K), the magnetic moment was still unsaturated, even at 7 Tesla of the applied magnetic field and this feature again indicated the cantedantiferromagnetic nature of the sample. However, neutron diffraction study would be a promising approach to get a better idea of the magnetic structure, exchange interactions, and charge-states of such ceramics constituents. Overall, we can say that the magnetic response of LCM is canted-antiferromagnetic because of the super-exchange interaction between Cu 2+ -O 2--Mn 4+ , a similar nature was observed by Blasse [86].

Conclusion
The LCM sample was prepared using the traditional sol-gel reaction method. The

Acknowledgement
In addition to NIT Patna, the present work described in this paper is supported by NEHU Shillong, Officials from University of Silesia, Poland and center Director UGC-DAE-CSR Indore. We acknowledge D. M. Phase and R. Sah for utilization of SXAS beamline at RRCAT Indore.

Conflicts of interest
There are no conflicts of interest to declare. Figure 1 Rietveld re nement of the X-ray diffraction pattern carried out in the orthorhombic phase of La2CuMnO6 ceramics.  Size -strain plot of La2CuMnO6 for analysing the average crystalline size.    The variation of real part (a) and imaginary part (b) of dielectric permittivity with temperature of La2CuMnO6 at different frequencies ranging 3 kHz to 1 MHz.    Stretched exponent parameter 'n' variation with temperature of ac conductivity of La2CuMnO6 ceramics estimated from logσ vs frequency plot.

Figure 12
Dc-resistivity variation with temperature of La2CuMnO6 nano-ceramics, (a) plot of log ρ vs inverse of T tted by modi ed Arrhenius equations used for TAC and NNH mechanism of conductivity, (b) plot of ln ρ vs T-1/4 tted by Mott-VRH model.

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