The stoichiometric amounts of high purity α-Fe₂O₃ and Cr₂O₃ were mixed for the preparation of Cr_1.4Fe_0.6O₃compound. The initial colours of α-Fe₂O₃ and Cr₂O₃ were red and green, respectively. The mixture of Fe₂O₃ and Cr₂O₃ was ground using agate mortar and pestle for nearly two hours in atmospheric conditions. The ground powder was mechanical alloyed using Fritsch planetary mono mill (pulverisette 7). The material and balls (combination of 10 mm Silicon Nitride and 5 mm Tungsten Carbide) mass ratio was maintained to 1:7. The mechanical alloying was carried out in atmospheric condition up to 84 hours in a silicon nitride (Si₃N₄) bowl with rotational speed 300 rpm. The non-magnetic balls and bowl (Silicon Nitride and Tungsten Carbide) were selected to avoid the magnetic contamination during the milling process. The milling process was intermediately stopped to monitor the uniform alloying of the mixture and to minimize the local heat generation that might occur during continuous milling. A small quantity of alloyed sample after 24 hours and 48 hours was taken out to check the structural phase evolution. The alloyed samples with different milling hours were made into pellets. The pellets of 84 hours milled sample were placed in alumina crucibles and annealed at 700°C in atmospheric conditions. After annealing for 1 hour, 3 hours and 17 hours, individual pellet was directly air quenched to room temperature. The mechanical alloyed samples was denoted as MAh, where h = 0, 24, 48 and 84 for alloying time 0, 24 hours, 48 hours and 84 hours, respectively. The samples annealed at 700°C were denoted as SNt, where t = 1, 3 and 17 for annealing time 1 hour, 3 hours and 17 hours, respectively.

Fig. 1 shows the XRD spectrum of mechanical alloyed and subsequent annealed samples. The MA0 sample (before milling) shows a mixed pattern of Fe₂O₃ and Cr₂O₃ phases. The peaks of Fe₂O₃ and Cr₂O₃ phases are well separated before mechanical alloying. As the alloying process continued by increasing the milling time, the individual peaks of Fe₂O₃ and Cr₂O₃ phases are merging to each other. The intensity of peaks is decreasing as the milling time increases up to 84 hours. At the same time broadness and symmetry in the shape of the peaks are increasing. Subsequent annealing of MA84 sample at 700°C, again, increases the peak intensity, along with increasing sharpness, with the increase of annealing time up to 17 hours. The undergoing phase evolution during the mechanical alloying and annealing process is clearly demonstrated in Fig. 2 for (104) and (110) peak positions. In the (MA0) mixed sample, the peaks position of Cr₂O₃ sample are at higher 2θ value with respect to Fe₂O₃ sample. The notable feature is that peaks of Fe₂O₃ sample disappear with the increase of milling time and the XRD pattern of alloyed compound is tending to achieve the character of Cr₂O₃. This indicates the diffusion of Fe atoms into the lattice sites of Cr atoms to form a solid solution of Cr_1.4Fe_0.6O₃.

Now, we understand the grain size refinement process. We have determined the grain size of alloyed samples from the prominent (012), (104), (110) and (116) XRD peaks using Debye-Scherrer formula: 〈d〉=0.089*180*λ3.14*β*cos⁡θcnm MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaamaaamaabaGaemizaqgacaGLPmIaayPkJaGaeyypa0tcfa4aaSaaaeaacqaIWaamcqGGUaGlcqaIWaamcqaI4aaocqaI5aqocqGGQaGkcqaIXaqmcqaI4aaocqaIWaamcqGGQaGkcqaH7oaBaeaacqaIZaWmcqGGUaGlcqaIXaqmcqaI0aancqGGQaGkcqaHYoGycqGGQaGkcyGGJbWycqGGVbWBcqGGZbWCcqaH4oqCdaWgaaqaaiabdogaJbqabaaaaOGaemOBa4MaemyBa0gaaa@4BF5@, where 2θ_C is the position of peak center, λ is the wavelength of X-ray radiation (1.54056 Å), β is the full width at the half maximum of peak height (in degrees). The 2θ_C and β values were calculated by fitting the XRD peak profile to Lorentzian shape. The average grain size of the alloyed compound is found to be in nanometer range, which suggested the nanocrystalline structure of the material. The grain size of the alloyed compound slowly decreases with the increase of milling time (i.e., <d> ~ 26 nm for MA24, 22 nm for MA48, and 15 nm for MA84 sample). The thermal annealing of MA84 (lowest grain size) sample at 700°C activates the increase of grain size (i.e., <d> ~ 19 nm, 21 nm and 22 nm for annealing time 1 hour, 3 hours and 17 hours, respectively). However, a finite amount of instrumental broadening and lattice strain may affect the XRD peak broadening in mechanical alloyed samples and hence, the grain size estimation based on the Debye-Scherrer formula may be far from good accuracy. To check these two factors, Williamson-Hall plot 19 was used. The Williamson-Hall equation is β_eff cosθ_C = Kλ/<d> + 2ε sinθ_C, where K is Scherrer constant (0.89), ε is the lattice strain and β_eff² = β² - β₀². In this case, the 2θ_C and β values were calculated by fitting the XRD peak profile to Voigt shape and β₀ is the full width at half maximum of standard Silicon powder. Finally, seven prominent XRD peaks were used for the β_eff cosθ_C vs. 2sinθ_C plot. The linear extrapolation of this plot to β_eff cosθ_C axis gives Kλ/<d> (and hence, grain size <d>) and the slope gives the lattice strain (ε). The calculated values of grain size and lattice strain are shown in Table 1. It is observed that the grain size calculated using Willimson-Hall plot is larger than that obtained from simple Debye-Scherrer formula, although the nature of the variation of grain size with milling time and annealing time is identical in both the cases. It is also observed that lattice strain of the alloyed compound increases with milling time and thermal annealing at 700°C reduces the lattice strain of the alloy. Similar effects were observed in other mechanical alloyed compound 20. The lattice parameter of the samples (shown in Table 1) was calculated by matching the XRD peaks into rhombohedral structure with R3C space group. The lattice parameters (a and c) and cell volume of the alloyed compound were increasing with the milling time. But, the lattice parameters of the annealed samples showed decreasing values with the increase of annealing time at 700°C. The finite amount of mechanical milling induced lattice strain and its release by thermal annealing may have some effect on the variation of lattice parameters of the samples. However, the understanding of the variation of cell parameters is more appropriate from the fact that lattice parameters of bulk Cr₂O₃ sample (a = 4.9510 Ǻ, c = 13.5996Ǻ, cell volume = 288.69Ǻ³) is smaller than that for bulk α-Fe₂O₃ sample (a = 5.0386Ǻ, c = 13.7498Ǻ, cell volume = 302.3Ǻ³). The calculated lattice parameters for both bulk samples are consistent with literature values 45. The continuous increase of lattice parameters and cell volume with milling time indicates the kinetic diffusion of larger size (0.67 Ǻ) Fe³⁺ ions into the boundary of smaller size (0.65 Ǻ) Cr³⁺ ions 2421. On the other hand, the decrease of cell parameters with the increase of annealing time indicated that the alloying process is, still, continued to attain the crystal structure of Cr₂O₃ dominated phase, because atomic ratio of Cr and Fe is 7:3. Here, it is pointed out that thermal heating plays a major role for obtaining the Cr₂O₃ dominated phase. It is believed that the variation of cell parameters is not significantly affected by the nano-sized grains in comparison with the undergoing change during alloying and annealing process. The cell parameters and grain size of the MA0 sample were not calculated, as the pattern is not due to single phase XRD spectrum.

The surface morphology (SEM picture) and chemical composition (EDX spectrum) can be studied for selected (MA0, MA48, MA84 and SN17) samples. The selected zone (~80 μm × 80 μm) of the samples, along with SEM picture and EDX spectrum, are shown in Fig. 3. The SEM picture of MA0 sample (Fig. 3a) suggests the heterogeneous mixed character of α-Fe₂O₃ and Cr₂O₃ particles. The mechanical alloying between α-Fe₂O₃ and Cr₂O₃ particles can be understood from the SEM picture of MA84 sample (Fig. 3b), where nanoparticles are distributed with a little bit agglomeration. A better uniformity in the particle size distribution is observed from the SEM picture (Fig. 3c) of thermal activated (SN17) sample. The elemental composition of the samples is determined from the point and shoots microanalysis at 10 selected points over a selected zone. The elements are found to be Cr, Fe and O. The atomic percentage of the elements is estimated from the EDX spectrum of the samples and Fig. 3d represents the spectrum for MA84 sample. The composition of Cr and Fe varies from 0.33 to 1.34 and 1.64 to 0.57, respectively, with respect to O composition 3 in MA0 sample. This suggests a random mixing of Fe₂O₃ and Cr₂O₃ oxides (i.e., an inhomogeneous distribution of elements) in MA0 sample. We obtained the atomic % of Fe (12.12), Cr (27.88) and O (60) (i.e., elemental composition Cr_1.38Fe_0.6O_2.97) for MA84 sample; atomic % of Fe (11.96), Cr (27.06), O (60.17) (i.e., elemental composition Cr_1.36Fe_0.6O_3.01) for SN17 sample. Therefore, elemental composition of the alloyed as well as annealed samples is close to the expected composition (Cr_1.4Fe_0.6O₃). The distribution of Cr, Fe and O atoms in the alloyed samples are cross checked from elemental mapping over a selected zone, as shown in Fig. 4 for MA48 sample. The mapping (Fig. 4c–e) suggests a uniform distribution of Cr, Fe, O atoms over the zone. The particle size (~500 nm) of MA48 sample estimated from the SEM picture (Fig. 4b) is much larger than that obtained from XRD data (~46 nm using Williamson-Hall method). This means the SEM picture indicates the size of polycrystalline particles. Achieving some basic knowledge of the structural properties (i.e., size, shape, composition, and crystal structure) of the samples, attempt has made below to understand the magnetic properties of the samples.

Fig. 5 shows the temperature dependence of ZFC and FC magnetization curve of different samples. The zero field cooled magnetization (MZFC), measured at 1 kOe field, does not change significantly (plateau like behaviour) in the temperature range 300 K to 600 K. The MZFC increases rapidly above 650 K to show a peak at about T_m ~ 810 K and then, MZFC rapidly decreases to indicate weak temperature dependence above 870 K. On the other hand, field cooled magnetization (MFC) at 1 kOe separates out from MZFC (i.e., onset of magnetic irreversibility) below the irreversibility temperature T_irr ~ 860 K. The separation between MFC and MZFC continued to increase with the decrease of temperature down to 300 K. The above features of MZFC and MFC are seen in the bulk α-Fe₂O₃ sample, as well as in the alloyed Cr_1.4Fe_0.6O₃ samples, except some typical changes in the shape of the curves. The continuous increase of MFC with down curvature is observed in both bulk α-Fe₂O₃ and alloyed samples (e.g., MA48 and MA84). Interestingly, the shape of MFC curves of the annealed samples (e.g., SN3) has transformed into up curvature as an effect of thermal heating. The magnetization of bulk α-Fe₂O₃ sample decreases in the alloyed samples. The decrease is, further, accelerated by subsequent annealing of MA84 sample at 700°C. The decrease of magnetization is also reflected in the suppression of peak magnetization at T_m, when the sample changes from bulk α-Fe₂O₃ to SN17. We noted that the position of MZFC maximum at T_m is highly sensitive to the magnitude of measurement field. This is confirmed from the decrease of T_m ~ 810 K (at 1 kOe) to 750 K (at 2 kOe) in MA48 sample (Fig. 4b). The paramagnetic to canted ferromagnetic ordering temperature T_N ~ 950 K of bulk α-Fe₂O₃ (hematite) sample [reported in Ref. 4] is higher than T_m ~ 810 K at 1 kOe (in the present work). The field dependence of T_m (~940 K at 100 Oe and ~845 K at 200 Oe) has already reported in bulk α-Fe₂O₃ (hematite) sample 2223. The present work showed that T_irr (~860 K) is higher than T_m (~810 K) and T_m decreases with the increase of measurement field. Based on these facts, we suggest that T_m does not represent a paramagnetic to canted ferromagnetic ordering temperature of the samples. Rather, T_m can be attributed as the temperature below which magnetic domains are blocked along the local anisotropy axes, where anisotropy energy might be higher than the measurement field 242526. The interesting point is that magnetic phase of α-Fe₂O₃ is, still, dominating in the alloyed compound, of course with diminished magnitude with milling time. This can be attributed to the presence of larger atomic moment of Fe³⁺ ions (~5 μ_B) in comparison with Cr³⁺ ions (~3 μ_B). The effect of α-Fe₂O₃ phase is becoming weak in the annealed samples, as seen from the weak magnetic irreversibility and upward curvature in the MFC curve of SN3 sample. The results clearly showed that Cr₂O₃ dominated typical antiferromagnetic phase in the alloyed compound is yet to achieve at 700°C. The diffusion of Fe atoms into the Cr lattices either still continues, although the XRD data indicated the stabilization of alloyed Cr_1.4Fe_0.6 O₃ close to the pattern of Cr₂O₃ sample. The appearance of a different kind of magnetic behaviour in the annealed samples may also be attributed to a modulated magnetic ordering at the interface of nano-sized grains.

The existence of possible modulated magnetic phase in the samples is investigated from the field dependence of dc magnetization. The magnetization (M) with the variation of field (H) at room temperature is shown in Fig 6. The M(H) data of bulk Fe₂O₃ and Cr₂O₃ are shown in Fig. 6a to compare the magnetic change in alloyed compound. Bulk Cr₂O₃ sample does not show any noticeable hysteresis loop, whereas Fe₂O₃ sample has shown a well defined loop. The mixture of Fe₂O₃ and Cr₂O₃, i.e., MA0 sample (Fig. 6b), shows a clear loop, but the magnitude of loop of MA0 sample is less in comparison with Fe₂O₃. This is due to the effect of Cr₂O₃ coexisting with Fe₂O₃. As the alloying process continued by increasing the milling time, the loop area gradually decreases, but noticeable, as shown for MA48 sample in the inset of Fig. 6c. It is interesting to note that the nature of M(H) curves of annealed samples (Fig. 6e–f) drastically differ in comparison with the mechanical alloyed samples. The extrapolation of high field M (positive H side) data (shown by dotted line in Fig. 6f) intersects the M axis to negative value and the negative magnetization confirmed the field induced magnetic behaviour in the annealed samples. We would like to mention that neither bulk Fe₂O₃ nor bulk Cr₂O₃ sample exhibited such induced magnetization. Recently, similar field induced magnetization has been observed in the Cr₂O₃ nanoparticles 27, originating from the competitive spin ordering at the core-shell interface 28. Viewing the absence of such field induced magnetic ordering in mechanical alloyed (with out heat treatment) samples, although grain size is in nanometer range, we believe that the field induced magnetic behaviour in our annealed samples is not solely due to particle size effect, but can be attributed to a modulated magnetic ordering due to diffusion of two different magnetic elements 29. The induced magnetic behaviour in annealed samples is also reflected in the field dependence of differential magnetization (dM/dH) curves (Fig. 7). The differential susceptibility (dM/dH) increases to exhibit a maximum for mechanical alloyed samples when the applied field approaches to zero value, whereas dM/dH exhibits a minimum near to the zero field value for the annealed samples. The observation of induced magnetism confirms an experimental evidence of modulated spin structure in this compound, which was suggested from Neutron diffraction study 8. To get the insight of modulated magnetic ordering, we analyze the M(H) data in terms of a general power series of H, i.e., the combination of liner and non-linear components in the equation

M(H) = χ₁H + χ₂H² + χ₃H³ + (rest of the terms)

In the above equation, we have assumed that magnetic susceptibility is not a scalar quantity, rather a tensor with directional property in the material. The coefficients χ₁ and χ₃ are assumed to be symmetric with field (H), where as χ₂ is antisymmetry to preserve the vector nature of magnetization (M). The validity of equation (1) is tested from Fig. 8. The M vs. H² data (in Fig. 8a) indicate that magnetization of all the samples are symmetric about the H² axis, irrespective of alloyed or annealed samples, and the change of magnetic direction is taken care by χ₂, i.e., χ₂(-H) = -χ₂(H). It is really interesting to note that M vs. H³ plot (Fig. 8b) represents a ferromagnetic like appearance, irrespective of the samples and confirms the symmetric nature of χ₃, where the change of magnetization direction is taken care by H. The investigation of non-linear components (specially the second-harmonic generation) in antiferromagnetic material may be one of the important technological aspects of the present material.

Now, look at the magnetic parameters. The remanent magnetization (M_R) and coercive field (H_C) of the samples were calculated using M(H) data. The variation of M_R and H_C of the alloyed compound with milling time and annealing time is shown in Fig. 9. We noted that both H_C (~1620 Oe) and M_R (~172 memu/g) of α-Fe₂O₃ sample are reduced by nearly 2.5 times in MA0 sample (H_C ~ 700 Oe and M_R ~ 66.3 memu/g), although Cr₂O₃ is not showing any hysteresis loop. This feature suggests that properties of magnetic particles, irrespective of bulk (present work) or nanosize (reported work 30), are strongly influenced by the surrounding matrix. The H_C of MA0 sample is continued to decrease with milling time (e.g., H_C ~ 120 Oe for MA24). On the other hand, H_C has shown a significant increase by annealing MA84 sample at 700°C up to 3 hours, followed by a slight decrease at 17 hours annealed sample (SN17). The M_R of MA0 sample also decreases to attain an almost constant value ~3.4 memu/g for MA24 and MA48 samples, followed by a slow increase (~4.4 memu/g) for MA84 sample and continued for (~5.3 memu/g) SN1 sample. The M_R value, again, starts to decrease at higher annealing time, e.g. ~3.9 memu/g for SN17 sample. The decrease of both remanent magnetization and coercivity at higher annealing time indicates that the alloyed compound is approaching to the magnetic state dominated by non-hysteretic Cr₂O₃ sample or a different kind of magnetic ordering that is already indicated earlier. The fact is that mechanical alloying has introduced a certain amount of lattice strain (and defects) in the material. However, we did not find the increase of coercivity with increasing milling time (and associated increasing strain), rather the coercivity decreases. Hence, the effect of strain and associated defects is minor on the magnetic properties of the present alloyed compound and such effect can be included in the combined contribution of grain boundary spins.