1 Introduction

Perovskite A1−x B x MnO3 manganites (where A is a rare earth element as La3+, Nd3+, etc., and B is a divalent cation as Sr2+, Ca2+, Ba2+, etc.) draw a lot of attention because of its properties. Its importance does not refer only to its elastic [1], structural, electronic and magnetic transition [2] properties, but also to the fascinating colossal magnetoresistance (CMR) property, which makes them an important material for applications [3, 4]. These properties can be controlled by several factors as the preparation method, the divalent ion content and size. CMR was explained on the basis of double exchange (DE) interaction, super-exchange interaction, charge localization via Jahn–Teller distortion with polaron formation, phase separation and site disorder; however, there are some complexities in the theoretical explanation. Among these materials, La1−x Sr x MnO3 is the most interested compounds, especially La0.7Sr0.3MnO3 due to its large ferromagnetic ordering temperature (T c) [5], besides to the exploration of x = 0.1–0.3 series as solid oxides fuel cell materials [6, 7].

Moreover, substitution of Mn ion by other transition metals such as Ni, Fe or Co is an interesting topic that attracts researchers to study [8, 9]. This substitution results in a disturbance in Mn3+–O–Mn4+ chains, leading to a change in Mn3+/Mn4+ ratio and destroying its coupling. This appears as a weakness in ferromagnetism, a change in transport properties [10], an increase in CMR effect [11] and a decrease in semiconductor–metal transition temperature (T ms) (but it depends on the doping element) [12]. Ni2+ is an interesting transition metal for Mn-site substitution, where the combination of Ni2+ with Mn4+ is favorable [13, 14]; but from the previous works, it weakens ferromagnetism [15, 16], which has a relation with DE reduction [17]. Nickel manganites oxides are considered as very good negative temperature coefficient (NTC) thermistors [18], and during the magnetoresistance (MR) it can be useful in magnetic applications. But for applications, in general, high MR values in small applied magnetic fields over a wide range of temperature are desirable [19], known as low field magnetoresistance (LFMR). Thus, the aim of this work is to investigate the structural, electrical and magnetoresistive properties of the polycrystalline La0.7Sr0.3Mn1−x Ni x O3 for LFMR applications.

2 Experimental

The La0.7Sr0.3Mn1−x Ni x O3 ceramics with x = 0, 0.025, 0.050 and 0.075 were prepared by the conventional solid-state reaction method. The starting raw La2O3, SrCO3, MnCO3 and NiO were mixed in stoichiometric proportions; La2O3 was dehydrated at 600 °C for 6 h. The mixture was ground for 6 h to ensure homogeneity and pressed into pellets under 490 MPa. The pellets were calcined in air at 900 °C for 10 h, and then they were reground for 5 h and pressed again under higher pressure of 980 MPa. They were sintered at 1100 °C for 20 h and left to cool gradually to room temperature. The electrical measurements were carried out by the standard four-point Van der Pauw technique in the temperature range of 80–290 K and at magnetic field of 0 and 0.5 T. All samples were examined by X-ray diffraction (XRD) with Cu Kα and wavelength of 0.15406 nm in angle range (2θ) of 18.00°–99.99°. The crystal structure and the lattice parameters were refined by Rietveld method using FULLPROF program.

3 Results and discussion

3.1 Structure

The XRD patterns in Fig. 1 show that all samples possess single phase with some additional diffraction peaks of La2O3 around 2θ = 27° disappearing with doping. The same peaks were also observed by Wandekar et al. [20, 21] in Co- and Ni-doped La–Sr–Mn–O systems. These peaks can be observed in La1−x Sr x MnO3 system at x ≥ 0.3 [22] because of the incomplete reaction between elements. Thus, Ni2+ addition may enhance the reaction between elements due to its bigger ionic size compared with Mn and decrease La2O3 peak’s intensity. Rietveld refinement of the patterns shows that the parent La0.7Sr0.3MnO3 (LSMO) crystallizes in the R-3C rhombohedral structure and gradually distorts to the orthorhombic structure with Ni2+ content up to x = 0.050, while for x = 0.075 it has a complete orthorhombic (Pbnm) structure (Table 1). The orthorhombic symmetry and structural transition were reported previously by Joshi and Hu et al. [23, 24], respectively. Mn/Ni atoms were refined at (0, 0, 0) site, and the agreement factors of refinement are shown in Table 1 as Bragg factor (R B) and goodness of fitting (χ 2). The average particle size was calculated from XRD using Laue–Scherrer’s formula and is presented in Table 1, which decreases with Ni2+ content increasing.

Fig. 1
figure 1

a Rietveld-based calculated profile of La0.7Sr0.3Mn0.925Ni0.075O3 at room temperature and b XRD patterns of La0.7Sr0.3Mn1−x Ni x O3 (x = 0, 0.025, 0.050 and 0.075)

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Table 1 Phase symmetry, lattice parameters, cell volume, average particle size by XRD and agreement factors of La0.7Sr0.3Mn1−x Ni x O3 compounds
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The structural transition proves the success of Ni2+ in the substitution process, which can be emphasized by the relative change in both lattice parameters and cell volume with Ni2+ content (Table 1). In spite of the larger ionic size of Ni2+ compared with Mn3+ [21] and Mn4+ (Ni2+, 0.069 nm; Mn3+, 0.066 nm; Mn4+, 0.060 nm), lattice parameters (a, b, c) and cell volume decrease with Ni2+ content, which is in agreement with the results in Refs. [25–27], and this decrease is large for x = 0.075. This suggests that either oxygen vacancies are created or charge balance by converting Mn3+ to Mn4+ may occur with Ni2+ content. But, in the later case, cell parameters are not expected to change much. So, it is more probable that oxygen vacancies were created and resulted in the reduction of cell volume [20, 25].

3.2 Electrical properties

Figure 2 shows the curves of temperature (T) dependence of resistivity (ρ) where an increase in resistivity and a decrease in T ms are observed with doping. The metallic state below T ms can be described on the basis of the DE mechanism (Mn3+–O–Mn4+) [5] that will be used to understand the increase in resistivity and the decrease in T ms (Table 2). As Mn ions are partially substituted by Ni2+, the change in Mn3+/Mn4+ ratio produces a decrease in DE, demonstrating the decrease in T ms. In other words, Ni2+ doping suppresses DE because of its non-participation in this mechanism (Mn3+–O–Ni2+). This can be clarified by considering that many bonds may form as the ferromagnetic Mn4+–O–Ni2+ bonds that can increase ferromagnetism and so T ms. But, as we can see from Fig. 2 and Table 2, there is a decrease in metallic region and T ms, which means the impossibility of these bonds formation [28]. But Ni2+ may be surrounded by the same ions consisting Ni2+–O–Ni2+ bonds and so Mn4+ consisting Mn4+–O–Mn4+ bonds, coupling antiferromagnetically and weakening DE [26, 28–30]. These antiferromagnetic bonds may increase in number with Ni2+ content, and this is a logical scenario, explaining T ms decreases and resistivity increases.

Fig. 2
figure 2

Temperature dependence of resistivity, ρ (T), of La0.7Sr0.3Mn1−x Ni x O3 compounds

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Table 2 T ms at magnetic field of 0 and 0.5 T, Debye temperature, θ D, phonon frequency, υ ph, E ρ , N(E F), W H and W D of La0.7Sr0.3Mn1−x Ni x O3 compounds
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With DE decreasing, the eg band electron of Mn encounters a difficulty in wandering that results in the increase of resistivity (Fig. 2). As shown in Fig. 2, the parent compound LSMO has a smaller resistivity compared with the doped samples, which is in agreement with the result in Ref. [25]. This increase in resistivity with Ni2+ ratio increasing can be explained also in terms of the change in Mn ions angle. Mn–O–Mn angle (θ) plays an important role in the eg electron mobility, where deviation from 180° increases distortion, decreases the transfer integral (t), t = t 0cos(θ/2) (where t 0 is the maximum value of t), decreases the DE [31] between Mn ions and increases resistivity. Thus, it is easy for conduction electron to move in the rhombohedral structure rather than the orthorhombic structure that has high bond distortion, resulting in localized carriers and higher resistivity. This may be clear from our results that during the gradual increase in resistivity with the gradual orthorhombic distortion with doping (up to x = 0.050), and the abrupt increase in resistivity associated with the complete orthorhombic distortion in x = 0.075, this abrupt increase in resistivity agrees with the orthorhombic phase of La0.7Sr0.3Mn1−x Fe x O3 [32].

The thermal variation of resistivity measured in applied magnetic field (H) of 0.5 T is presented in Fig. 3. For each sample, the isothermal resistivity values measured in H = 0.5 T are lower than that measured in H = 0 T. In addition, T ms values do not change under the effect of magnetic field except in x = 0.075 where there is a slight increase in its value (Table 2). This decrease in resistivity is due to the oriented spins by the applied magnetic field that eliminates charge carrier scattering during hopping process. Note that T ms values tabulated in Table 2 are far below room temperature, which can be attributed to the small particle size [33] that can decrease bond angle and increase its length [34], leading to a decrease in the transfer integral which in turn decreases T ms and increases resistivity.

Fig. 3
figure 3

Thermal variation of resistivity in H = 0 T and H = 0.5 T of La0.7Sr0.3Mn1−x Ni x O3 compounds: a x = 0, b x = 0.025, c x = 0.050, and d x = 0.075

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3.3 Magnetoresistance (MR)

Magnetoresistance was calculated from [ρ(H) − ρ(0)]/ρ(0), where ρ(H) is the resistivity measured in H = 0.5 T and ρ(0) is the resistivity measured in H = 0 T. Figure 4 shows the temperature dependence of MR. The negative values of MR indicate that the resistivity is affected by the applied magnetic field. The highest MR values are observed at low temperatures, which may be due to the spin dependent transport at grain boundaries [35–37]. With temperature elevating, MR decreases passing through broad hump at T > T ms except x = 0.075. At hump, MR increases in x = 0.025 and then decreases with further doping. For the first two doping samples, x = 0.025 and x = 0.050, the MR broad hump is enhanced and has a larger value compared with the parent LSMO compound.

Fig. 4
figure 4

Temperature dependence of MR of La0.7Sr0.3Mn1−x Ni x O3 compounds

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The MR values at room temperature (290 K) for samples are shown in Fig. 5, the highest value is observed for x = 0.025 and decreases at higher doping contents of x = 0.050 and 0.075. The room temperature MR values for all samples are −0.13 %, −4.26 %, −0.86 % and −0.73 % for x = 0, 0.025, 0.050 and 0.075, respectively; thus, Ni2+ doping can help electron transition rather than LSMO. This promotion in MR was observed in polycrystalline materials [38] and correlated to the spin dependant tunneling and the scattering process at grain boundaries. At grain boundaries, magnetization in grains is no longer oriented or connected, so carriers have to cross grains in tunneling. So, MR enhancement is related to the improvement of oriented states at grain boundaries. Consequently, we can expect that, at low doping level, the number of oriented states at grain boundaries is greater than that in LSMO. While, at high doping level, the disoriented states become higher and the thickness of grain boundaries may make the electron tunneling more difficult [27], which may decrease MR.

Fig. 5
figure 5

MR versus Ni2+ content (x) at room temperature (290 K)

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3.4 Conduction mechanisms above and below T ms

In the semiconducting region (T > T ms), a lot of works discussed the existence of variable range hopping (VRH) [39–41] as the only mechanism that governs the variation of electrical resistivity with temperature. But many articles proved the presence of polaron in the same region [42, 43]. Resistivity data at T > T ms are well fitted with Mott and Davis small polaron hopping (SPH) model [44] above T > θ D/2 with the following expression:

$$\rho /T = \rho_{\alpha } \exp \left( {E_{\rho } /k_{\text{B}} T} \right)$$
(1)
$$\rho_{\alpha } = \left[ {k_{\text{B}} /\upsilon_{\text{ph}} Ne^{2} R^{2} C\left( {1 - C} \right) \, \exp \left( {2\alpha R} \right)} \right]$$
(2)

where θ D/2 is the deviation temperature of linearity, θ D is Debye temperature, and Fig. 6a is SPH example of LSMO, k B is the Boltzmann constant, T is the absolute temperature, N is the number of ion sites per unit volume, R is the average inter-site spacing, C is the fraction of sites occupied by a polaron, α is the electron wave function decay constant, υ ph is the optical phonon frequency (estimated from hυ ph = k B θ D relation) and E ρ is the sum of the activation energy required to create free carriers (disorder energy) and the energy that activates carriers for hopping.

$$E_{\rho } = \left\{ \begin{aligned} & W_{\text{H}} + W_{\text{D}} /2 \, \quad {\text{for}}\;T > \theta_{\text{D}} /2 \hfill \\ & W_{\text{D}} \quad {\text{for}}\;T < \theta_{\text{D}} /4 \, \hfill \\ \end{aligned} \right.$$
(3)

where W D is the disorder energy and W H is the polaron hopping energy which is the difference between the electric activation energy (E ρ ) and the thermoelectric activation energy (E s ) (W H = E ρ  − E s ) [8].

Fig. 6
figure 6

a SPH and b VRH models of parent LSMO in H = 0 T, solid line representing the best fitted points with these models

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The values of θ D, E ρ , N(E F), υ ph, W H and W D were calculated and are tabulated in Table 2. Generally, all of these parameters increase with Ni2+ content (except x = 0.075) due to eg electron localization, while W D increases even in x = 0.075. The increase in E ρ can be explained by the electron–phonon interaction that results in carrier’s localization. So the energy required to create free carriers increases. For more accuracy, small polaron coupling interaction (γ ph), which is a measurement of electron–phonon interaction, was calculated from the following relation [43] as shown in Table 3:

$$\gamma_{\text{ph}} = 2W_{\text{H}} /h\upsilon_{\text{ph}}$$
(4)

where γ ph increases with Ni2+ content, asserting the previous explanation. According to Austin and Mott [45], the strong electron–phonon interaction can occur as the value of γ ph goes up to 4 (γ ph > 4), which is in a good agreement with the present results (Table 3). Also, the polaron mass (m p) and the effective rigid mass of lattice (m*) are related in the relation:

Table 3 P, J, γ ph, exp (γ ph) and W H/3 parameters of La 0.7Sr0.3Mn1−x Ni x O3 compounds at (290 K)
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$$m_{\text{p}} = m^{*} \exp \left( {\gamma_{\text{ph}} } \right)$$
(5)

where exp(γ ph) in Table 3 has high values, confirming the strong electron–phonon interaction [46].

As stated before, only VRH cannot describe the whole semiconducting range, but it is dominant in part of it. ρ (T) curves are found to be fitted well with VRH model in the temperature range of T ms < T < θ D/2 [47], as shown in Fig. 6b for LSMO as an example, obeying the following expression [8]:

$$\sigma = \sigma_{0} \exp \, \left( { - T_{0} /T} \right)^{1/4}$$
(6)

where T 0 is a constant (Mott characteristic temperature):

$$T_{0} = 18/k_{\text{B}} N(E_{\text{F}} )a^{3}$$
(7)

where N(E F) is the density of states near Fermi level (E F) and a is the localization length equals to 0.45 nm reported by Viret et al. [48]. The observed decrease in N(E F) with Ni2+ content in Table 2 may refer to the carriers’ localization and the increase in resistivity.

To determine whether the polaron hopping conduction is adiabatic or non-adiabatic process, Holstein conditions were used [49]. According to these criteria, polaron band width (J) should satisfy one of these conditions: J > P for adiabatic condition; J < P for non-adiabatic condition

$$J\left( T \right) \, \approx \, 0.67h\upsilon_{\text{ph}} (T/\theta_{\text{D}} )^{1/4}$$
(8)
$$P\left( T \right) = \left( {2k_{\text{B}} TW_{\text{H}} /\uppi } \right)^{1/4} \left( {h\upsilon_{\text{ph}} /\uppi } \right)^{1/2}$$
(9)

Results in Table 3 prove the small polaron formation since it can be formed under the condition of J < W H/3 [49], confirming SPH conduction at high temperatures. For LSMO, J > P means that the system is in the adiabatic state, but with Ni2+ doping content up to x = 0.050, the system converts to the non-adiabatic state (J < P). However, with Ni2+doping content further increasing (x = 0.075), the system returns back to the adiabatic state (Table 3). The important conclusion drawn is that a small amount of Ni2+ (up to 0.050) can convert LSMO system from adiabatic to non-adiabatic state.

Resistivity data below T ms were examined by empirical equations to know the nature of conduction at low temperatures.

$$\rho = \rho_{0} + \rho_{2} T^{2}$$
(10)
$$\rho = \rho_{0} + \rho_{2.5} T^{2.5}$$
(11)
$$\rho = \rho_{0} + \, \rho_{2} T^{2} + \rho_{4.5} T^{4.5}$$
(12)
$$\rho = \rho_{0} + \rho_{2} T^{2} + \rho_{4.5} T^{4.5} + \rho_{5} T^{5}$$
(13)

where ρ 0 is the resistivity term arising due to domains, grain boundaries and temperature independent process [50], ρ 2 T 2 term is due to electron–electron interaction, ρ 2.5 T 2.5 term is due to electron–magnon interaction, ρ 4.5 T 4.5 term is due to spin wave scattering process in the ferromagnetic region and ρ 5 T 5 term is the resistivity due to electron–phonon interaction.

The square of linear correlation coefficient (R 2) values were calculated for each equation and are listed in Table 4. Equation (13) is the most satisfied one in all samples (Table 4), and Fig. 7 shows the fitting of resistivity below T ms with Eq. (13) for x = 0.075 as an example. Equation (13) emphasizes the presence of grain boundaries, electron–electron interaction, spin wave scattering and electron–phonon interaction, which play an essential role in conduction mechanism in the metallic region, and their coefficients generally increase with doping (Table 5), leading to an increase in resistivity. The large increase observed in all coefficients of x = 0.075 may be attributed to the completely orthorhombic transition that has high lattice distortion, and such high values were reported previously in Refs. [32, 51] for higher concentrations in the orthorhombic distortion.

Table 4 Square of linear correlation coefficient (R 2) values for equations in ferromagnetic region
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Fig. 7
figure 7

Temperature-dependent resistivity of x = 0.075 below T ms, solid line representing the best fitting with Eq. (13)

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Table 5 Best-fitting parameters obtained from Eq. (13)
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4 Conclusion

In this work, structural, magnetoresistive and electrical properties of LSMO doped with Ni2+ (x = 0, 0.025, 0.050 and 0.075) were investigated. This results in a decrease in the DE mechanism, which in turn decreases T ms and increases resistivity with Ni2+ doping. The MR is enhanced with low doping of Ni2+ and decreases for high doping level.