The 𝐿α𝑀n_1−𝑥𝐴𝑂₃ (𝐴=𝐶o,𝑁i) magnetite samples were analyzed by examining strain effects obtained from different substitutions of B-site with magnetite. To correlate the observed effects of the strain tests on the samples, an analysis of their electric and magnetic responses was performed. An analysis of the behavior of the 𝐿α𝑀n_1−𝑥Co_x𝑂₃ sample was performed first and an analysis of the 𝐿α𝑀n₁₋𝑥Ni_x𝑂₃ sample second.

The 𝐿α𝑀n_1−𝑥(𝐶o/𝑁i)_𝑥𝑂₃ samples were prepared using the sol-gel technique using a solution of lanthanum nitrate 𝐿α(𝑁𝑂₃)₃ (0.1𝑀),, manganese nitrite 𝑀n(𝑁𝑂₃)₂ (0.1𝑀), cobalt nitrite 𝐶o(𝑁𝑂₃)₂ (0.1𝑀), a stoichiometric ratio of nickel nitrate and citric acid 𝐶₆𝐻₈𝑂₇ (0.2𝑀).. The obtained solution was jellified and heated to 100 °C and finally the obtained foam was heated at 600 °C for 4 hours.

Fig. 5 depicts the X-ray spectrum for different concentrations of cobalt where an orthorhombic structure with 62 space group pbmn can be observed. In such samples the chemical composition and morphology were determined by EDX and SEM, respectively. The inhomogeneity of the compositions is lower than 5%.

Figure 5 Source: The Authors.

Furthermore, several measurements of ac-susceptibility were taken using a Lake Shore 7000 susceptometer with a frequency of 20 Hz and a magnetic field strength of 800 A/m, with a range of temperatures between 80° K and 300° K.

The real and imaginary part of the susceptibility as a function of temperature for different concentrations of cobalt is shown in Figs. 7a and 7b. The paramagnetic-ferromagnetic/anti-ferromagnetic transition and Curie temperature (T _c ) were obtained using the derivative of dX´/dT. Notably, the temperature T _c increases when the concentration of cobalt is increased, which can be related to the increased interaction of double-exchange. The observed peaks of susceptibility suggest that they can be understood as a spin-glass behavior related to competition between the ferromagnetic and anti-ferromagnetic interactions [24].

Table 3

Source: The Authors.

Figure 6 Source: The Authors.

Figure 7 Source: The Authors.

Fig. 8 shows the resistivity as a function of temperature for different concentrations of cobalt. A metal-insulator transition can be observed where, at specific temperatures, the change in resistivity is abrupt and is denoted by T _t and determined by the maximum derivative of the resistivity vs. temperature (dρ/dT).

Figure 8 Source: The Authors.

Table 4 lays out the assigned temperature for different levels of samples doped with cobalt. The increase in resistivity is closely related to the observed rise in activation energy and T _t , which can be attributed to an increase in electron hopping among the different sites of Mn. In this respect, T _t rises to higher temperatures when the concentration of cobalt increases, exhibiting a clear correlation between these occurances. However, the values of T _c and T _t do not coincide which can be attributed to the samples’ magnetic inhomogeneity. This type of inhomogeneity is attributed to the multiple peaks that cross over into the imaginary part of the measured susceptibility.

Table 4

Source: The Authors.

In contrast, it is well known that there are remarkable differences in the magnetotransport properties for thin films and bulk materials which have been mainly been ascribed to biaxial strain induced by the substrate on the structure of the thin films owing to the differences in the lattice location (Lattice mismatch) between the film and substrate. In the case of magnetite samples with CMR, the coupling electron lattice plays a key role in understanding their electric and magnetic properties. The Jahn-Teller effect describes this coupling which is caused by biaxial distortions that allow the degeneracy levels of 𝑒𝑔 from the 𝑀n of a crystalline medium to be surpassed.

Table 4 indicates how the increase in the effects of strain produces a rise in the resistivity of the sample, i.e., the change in the constant lattice parameter can be explained by the small size of the cobalt ion in comparison to the Mn^3+/4+ ion. In addition, a double peak structure is observed in the susceptibility measurements which is produced by a high concentration of cobalt which, in turn, could be related to the strain effects and domain wall motion.

As depicted in Fig. 9, the increase in Co concentration in LaMn_1-xCo_xO₃ samples produced an increment of the biaxial strain ε _bi , which shifts Tc to higher temperatures. Such shifts can be explained by the substitution of Mn (B-sites) with Co ions, which are smaller (radius of Co³⁺ = 0.54 Å , radius of Ni³⁺ = 0.56 Å, radius of Mn³⁺ =0.58 Å).

Figure 9 Source: The Authors.

The behavior of LaMn _1-x Ni _x O ₃ samples at 0.1 < x < 0.5, in both magnetic and electric parts, was determined by taking magnetic susceptibility measurements (real and imaginary parts) and taking measurements of the resistivity as a function of temperature using the conventional four probe method.

All samples were characterized by taking measurements of X-ray diffraction (see Fig. 10), which shows an orthorhombic structure pbnm categorized within the 62 space group. The lattice constants a,b,c and the unit cell volume (V) were determined by Powder Cell software (see Table 5). As depicted in Fig 11, the lattice parameters decrease when exposed to the concentration of 𝑁𝑖, which can be explained by the lower ionic radius of nickel (ionic radius of Ni = 0.60, ionic radius of Mn= 0.80)

Figure 10 Source: The Authors.

Table 5

Source: The Authors.

Figure 11 Source: The Authors.

The spectrum from X-ray diffraction obtained exhibits a single-phase system; impure phases were not observed according to the equipment’s indications.

Furthermore, the observed shifts are related to the different ion sizes of 𝑁𝑖. Using EDX spectroscopy, the analysis of chemical composition shows variations from the stoichiometry < 5 % and the concentration of 0₂ was not substantially affected (variations of less than 2%) by the heat treatments to which the samples were subject.

As depicted in Fig. 12, the real (a) and imaginary (b) parts of normalized ac-susceptibility are shown (X/X _0, and X/X ₀ respectively) as a function of temperature for different concentrations of nickel.

Figure 12 Source: The Authors.

The Nickel-doped samples exhibit a remarkable behavior-which can be attributed to their spin-glass state-that can be observed as a peak in ac-susceptibility measurements. This behavior could be explained as the result of the competition between the antiferro and ferromagnetic regimes. Similar situations have been observed in different compounds [25]. It is well known that the orbital antiferromagnetic state of 𝐿αMn0₃ is easily destroyed, resulting in a ferromagnetic state. Nevertheless, such ferromagnetic behavior could be the result of many other mechanisms that depend on the nature of substituted cations and substitutional levels [26].

The observed peaks that cross into the susceptibility measurements (X´/X´) have been attributed to double-exchange interactions of 𝑀n³⁺−𝑂₂ ²−−𝑀n⁴⁺,, which gradually vanish due to the interaction of an antiferromagnetic superexchange of the kind 𝑀n⁴⁺−𝑂₂ ²−−𝑀n⁴⁺ and 𝑁i⁴⁺−𝑂₂ ²−−𝑁i⁴⁺ [27].

Table 6 shows the transition temperatures of the insulated metal (T _t ) and the magnetic transition (T _c ) of the processes mentioned above. Although the transition temperature values do not explain any coincidence between the non-monotonic behavior and the concentration of Ni, all samples indicate a correlation between electric and magnetic phenomena. The general trend of different transition temperatures increases depending on the concentration of Ni.

Table 6

Source: The Authors.

Figure 13 Source: The Authors.

The corresponding resistivity as a function of temperature for all nickel-doped samples is shown in Fig. 13. A metal-insulator transition was observed. The transition temperature T _t was determined by the maximum value of dR/dT vs. temperature. A significant increase in the resistivity as a function of the concentration of nickel was observed, and is depicted in the overlay of Fig. 10, which shows the resistivity of the sample that was a doped with 0.5.

The transition temperature (T _t ) does not monotonically change when nickel is present, which correlates appropriately with the magnetic measurements (see Table 6). Nevertheless, T _c and T _t do not exhibit the same values, which is attributed to magnetic inhomogeneity. The inhomogeneity of the samples is characterized by multiple peaks in the imaginary part of the susceptibility [25].

The pseudo-perovskite RO₃ at the A-site is available and the applied pressure produces an increase in the rigid octahedron rotation RO₆. In the perovskite, the A-ion inhibits a possible collapse and the applied pressure decreases the rotation using the decrease in ionic radius mismatch which shows a denser packing of the 0₂ ion surrounding the ion at the A-site. Several papers that have studied the effects of pressure on PrNi0 ₃ samples and the results of crystallography of neutrons have confirmed that the octahedron Ni0 ₆ rotates less when pressure is applied; θ tends to 180° and the Ni- 0 bond is compressed.

In contrast, the measurements of resistivity as a function of temperature (see Fig. 13) are the outcome of the notable increase in resistivity in the samples as a function of the concentration of either Co or Ni. In addition, the results of ρ vs. T with T>T _t (T _t denotes the metal-insulator transition temperature) can be explained accurately at lower doping levels (x ≤ 0.1) by means of mechanisms related to adiabatic and non-adiabatic polaron hopping. Nevertheless, increasing the concentration of either Co or Ni, the hopping mechanism of variable range can also explain the experimental results obtained here at certain temperatures more accurately. At high doping levels (x ≥ 0.5), the experimental results describe an overall range of temperatures that fit properly into a mechanism explained as hopping at variable range.

Figure 14 Source: The Authors.

In the case of LaMn0 ₃ perovskite, the Mn ions fill the B-sites, which are surrounded by 0₂ octahedrons, meeting at the corners to form a tridimensional lattice, while the Lα ions fill the A-sites between these octahedrons. Electronic conduction involves the movement of charge between orbitals d in Mn and p in 0 ₂ ; the p - d orbital overlap is very sensitive to geometrical changes (angles and bond lengths) generated by variations of ion size at A-sites or external applied pressure.