Tunneling magnetoresistance in nanogranular La_1-xSr_xMnO₃ (x$∼$0.5)

Lot of the studies of Mn³⁺/Mn⁴⁺ mixed-valent manganites of La_1-xSr_xMnO₃ type have been devoted to the magnetoresistive effects that may become extremely large depending on the sample character, magnetic field strength, and temperature range, see, e.g., Ref. 1 and references therein. In these systems three types of magnetoresistance can be distinguished. First is the so-called collosal magnetoresistance (CMR), a kind of metamagnetic transition observed in magnetically inhomogeneous manganites in the vicinity of phase transitions between the AFM (less conducting) and FM (more conducting) phases. Second type is intrinsic to manganites of purely FM ground state. It is observed typically in single crystals and high-quality thin films, peaks in the vicinity of PM-FM transition and vanishes completely below ∼T_C/2.^2,3 Its source is both in the charge carrier scattering on magnons or critical spin fluctuations, and is thus an analogy to the giant magnetoresistance (GMR) known for the ferromagnet/normal-metal multilayers.⁴ Third, there is a spin-dependent transport characteristic for granular manganites, which is associated with tunneling of charge carriers across the barriers formed by grain boundaries. This tunneling magnetoresistance (TMR) depends on the magnetic and chemical nature of grain boundaries, and its extent increases with decreasing temperature and saturates for T→0. There is an analogy to the spin-dependent tunneling in magnetic tunnel junctions based on FM metals,⁵ the main distinction being the nearly complete spin polarization of electron carriers in FM manganite oxides.⁶ In contrast to the exhaustive magnetoresistance studies focused on La_1-xSr_xMnO₃ manganites with "optimum strontium doping" (x∼0.3 leading to highest T_C), the present study deals with the field-dependent effects in "more doped" systems in a narrow composition region around x∼0.5; i.e., between the FM ground state of half-metallic character and A-type AFM ground state of anisotropic 2-dim metallic character.^7,8 In this respect three samples have been investigated – the highly dense bulks of compositions x=0.45 and 0.55, both prepared by a classical ceramic sintering (CCS), and the granular FM/AFM composite fabricated by spark plasma sintering (SPS) of molten salt synthesized nanoparticles of composition x=0.47.

The highly dense La_1–xSr_xMnO₃ bulk samples of compositions x=0.45 and 0.55 with 88 and 94% theoretical density, denoted as CCS45 and CCS55, were prepared by classical ceramic sintering at 1520 and 1500 °C in air. The granular sample SPS47 of 68% theoretical density was prepared using crystallites of 40 nm size grown at ∼500 °C from respective nitrates in NaNO₂ flux. These crystallites are, however, featured by a certain radial distribution of La³⁺/Sr²⁺ cations and surface overoxygenation, the effects resulting in a two-phase magnetic composition, consisting of FM ordering in crystallite cores and A-type AFM ordering in shells.⁹ The sintering by spark plasma effectuated in four heating steps between 600 and 800 °C, each of 60 s duration, provided a nanogranular ceramics without a significant increase of the mean crystallite size (see electron micrographs of original nanoparticles and the nanogranular ceramics in Figure S1 of supplementary material). The SPS47 sample can be thus viewed as a two-phase composite where FM manganite granules making about 55% of sample volume are embedded in AFM manganite matrix.

The phase purity of all the products, their crystal structure, and mean size of crystallites in the case of SPS47 were analyzed based on X-ray diffraction (XRD) patterns recorded by a Bruker D8 diffractometer (⁠$CuKα$ radiation) and evaluated by Rietveld method (FULLPROF program). The magnetic characterization was carried out on a SQUID apparatus MPMS XL (Quantum Design) in the range 2–350 K. Electric and thermal transport properties were investigated using home-made apparatuses in a broad temperature range 3–1100 K, exhaustingly described in Refs.10, 11. The investigation of magnetoresistance was performed only below room temperature in the range 5–300 K using longitudinal geometry – the magnetic field H oriented parallel to electric current J. The isothermal field-dependent magnetoresistance scans were performed up to 5 kOe only because of interference between cryocooled cold head and magnet, respectively. Temperature scans at higher fields above 5 kOe appeared feasible by using “pre-cooled” sample space, which led to somewhat reduced range of experimental temperatures, e.g., 25–300 K for H = 40 kOe.

The structural and magnetic data, presented in supplementary material, show that the highly dense sample CCS45 is of rhombohedral perovskite structure. The sample undergoes FM ordering at T_C=343 K and the net magnetization at low temperatures reaches 3.61 μ_B per Mn, which is close to the theoretical spin-only value 3.55 μ_B for half-metallic La_0.55Sr_0.45MnO₃ with Mn³⁺(3d⁴)/Mn⁴⁺(3d³) mixture in the 0.55:0.45 ratio. On the other hand, the magnetic state in granular sample SPS47 is inhomogeneous, as evidenced by complex character of the temperature derivative of FC/ZFC susceptibility difference (see Figure S3 of supplementary material). The SPS sample is further characterized by more gradual FM ordering below T_C≈350 K, significantly reduced value of net magnetization ∼2.0 μ_B, and presence of high-field paraprocess, i.e., properties typical for magnetic nanoparticles.¹² Finally, the La_0.45Sr_0.55MnO₃ sample CCS55 is of tetragonal structure with lattice parameters close to cubic metrics. In agreement with published phase diagram, the sample undergoes a two-step magnetic transition - the FM ordering at T_C=265 K followed by a first order transition to A-type AFM state (T_N ∼ 204 and 208 K on cooling and heating, respectively).⁷ The magnetic states of the CCS45, SPS47, and CCS55 samples are further manifested in thermopower measurements. The data in Figure S5 of supplementary material show indeed important anomalies in Seebeck coefficient at T_C and T_N points.

The main issue of the present study is the zero-field resistance and magnetoresistance. The relevant data for the high-temperature sintered samples CCS45 and CCS55 are presented in Figure 1. The results for bulk ferromagnet CCS45 exhibit clear signs of the GMR-type magnetoresistance (see Introduction) in the vicinity of the FM transition at T_C =343 K. In addition there is a negative magnetoresistive effect that extends to low temperatures and steadily increases with increasing external field up to 40 kOe though the sample is magnetically saturated in external field of 5 kOe - see Figure S2 of supplementary material. The relative magnitude of this extrinsic effect, defined for given temperature as $(ρ0−ρ(40kOe))/ρ(40kOe)=(σ(40kOe)−σ0)/σ0$⁠, makes in the FM sample CCS45 a practically temperature independent value of ∼12%. The situation in sample CCS55 is more complex because of the FM/AFM crossover. Most importantly, in the low-temperature AFM phase there is a magnetoresistive effect that increases with applied field in a parabolic dependence with no or very little linear term, reaching the integral value of ∼6% for 0–40 kOe. The results for the nanogranular sample SPS47 are given in Figure 2. The sample shows a large magnetoresistance that consists of two distinct parts – the low-field component that correlates with the field dependence of the net magnetization in FM metallic phase, and the high-field part that is practically of a linear dependence on applied field. Detailed magnetoresistance data including the hysteretic isothermal behavior and temperature dependence of both low field magnetoresistance (LFMR) and high field magnetoresistance (HFMR) effects in the SPS47 sample are seen in Figures S6 and S7 of supplementary material.

The magnetoresistive data on the highly dense bulk samples CCS45 and CCS55 reveal properties that are characteristic for intrinsic behaviors of manganites in FM and A-type AFM ground states. In addition to GMR, the CCS45 sample exhibits certain extrinsic magnetoresistance, nearly independent of temperature below 300 K and persisting obviously to high fields. Our observation is coherent with previous reports on the high-temperature sintered ceramics La_1-xSr_xMnO₃ (x≤0.33) with large grains.^2,13 This high-field magnetoresistance suggests that there is a significant scattering of charge carriers on grain-boundary magnetic defects that, due to their strong AFM correlations, resist to saturation up to very high magnetic fields.

The CCS55 sample is a representative of the A-type (layered) AFM phase. Intrinsically, the electric conduction is metallic in FM planes of the A-type AFM structure and semiconducting in the perpendicular direction, i.e., along Mn chains with alternating +/− spins.⁸ As the observed magnetoresistance in present ceramics is concerned, two sources of the extrinsic contribution should be considered: the first one is the field-dependent transfer of charge carriers between domains of different orientations of the conducting FM layers, and the second one is associated with the growth of FM regions in expense of AFM component, i.e., a kind of metamagnetic transition that is at the root of CMR effect appearing at phase boundaries of manganites.

The predominantly ferromagnetic SPS47 nanogranular product is characterized by large tunneling magnetoresistance at low temperatures. The observed behavior with coexistence of the hysteretic LFMR and quasi-linear HFMR is typical for manganites where FM ground state is of the double exchange (DE) origin, and arises from a field-dependent transport of spin-polarized metallic carriers; i.e., the second-order tunneling via resonant Mn⁴⁺ states in the barrier between FM granules.^13,14 According to the theory applied for polycrystalline manganites by S. Lee et al.,¹⁴ each tunneling event is given by a product of two transmission probabilities, that depend on angle Θ_1,b between spin orientation of grain 1 and local spin orientation in the barrier state and angle Θ_b,2 between the local spin orientation and spin orientation of grain 2, respectively. The contribution to bulk conductivity is then given by an average over all tunneling links. By assuming that FM grains in nanogranular sample are nearly uniform and their superspin moments are magnetically non-correlated (except for action of external field), the averaging provides a rather simple formula for the normalized magnetoconductance, see supplementary material:

in which only the average angles with respect to the orientation of applied field are contained. In particular, ϑ refers to the orientation of superspin and $M=Ms⟨cosϑ⟩$ (M_s=3.53 μ_B per Mn for the sample SPS47) is the field induced magnetization of whole ensemble of FM granules, whereas $ϑb$ refers to the orientation of strongly AFM coupled localized spins in the tunneling barrier. For fields low enough but sufficient for complete magnetic polarization of FM granules, the mean values are $⟨cosϑb⟩≈0$ and $⟨cos2ϑb⟩=1/3$⁠, which gives a theoretical limit of 33% for total low-field magnetoconductance. For high fields where $M/Ms≈1$⁠, the resonant tunneling depends on magnetic polarization of the localized spins in intergranular space, that can be described through susceptibility $χp$ (⁠$χp$ reflects the paraprocess of intergranular AFM-correlated phase) by the expression

where M_b=3.0 μ_B for Mn⁴⁺. This gives rise to a magnetoconductance linearly dependent on H and extending up to several hundred kOe,¹⁵ with a possibility of much smaller quadratic contribution. In this respect the magnetoresistance behavior of present SPS47 sample is in accordance with these theoretical predictions – (i) the low-field contribution following essentially the $M2/Ms2$ dependence (see the magnetoconductance data shown in Figure 3) with maximum of 27% at 5 K and (ii) the unsaturated linear high-field contribution depicted in Figure 2. With increasing temperature, the low-field effect decreases because other conduction channels in the A-type AFM matrix between FM granules are employed. On the other hand, the high-field effect is somewhat less temperature dependent and its slope makes 10⁻⁵ Oe⁻¹ and 2⋅10⁻⁶ Oe⁻¹ at 5 and 300 K, respectively (see Figure S7 of supplementary material). According to Expr. (2), the slope observed at low temperature gives $χp$= 18⋅10⁻⁶ μ_B/Oe, which is significantly larger value when compared with the observed susceptibility of paraprocess in non-FM regions in the SPS sample, $χp$=6.7⋅10⁻⁶ μ_B/Oe, or susceptibility of pure A-type AFM phase of CCS55 sample, $χp$=4.0⋅10⁻⁶ μ_B/Oe (see Figure S2 of supplementary material). Still stronger AFM correlations are observed in purely Mn⁴⁺ archetypal compound CaMnO₃ as documented by $χp$=0.73⋅10⁻⁶ μ_B/Oe.¹⁶ Such apparent inconsistency between the slopes of magnetoconductivity and paraprocess of the SPS47 sample should mean that resonant tunneling actually occurs preferentially via Mn⁴⁺ states in the barrier that are much more polarizable by magnetic field than average.

Three La_1–xSr_xMnO₃ samples, close in composition but exhibiting different behaviors, have been prepared and studied – the high-temperature sintered ceramics x=0.45 and 0.55, used as examples typifying purely FM and purely A-type AFM magnetic phases, and the nanogranular sample x=0.47, prepared by spark plasma sintering of molten salt synthesized nanoparticles. The latter product can be viewed as an assembly of FM granules with ∼40 nm size, separated by the A-type AFM matrix of limited conductivity. This AFM phase together with the grain boundary forms a tunneling barrier for transmission of the spin-polarized e_g carriers. The field-dependent tunneling effects observed on this sample are theoretically treated in terms of the low- and high-field positive magnetoconductance. Based on a detailed analysis of these LFMC and HFMC contributions, related to the field-induced alignment of FM granules and the spin canting in AFM matrix, respectively, we conclude that the sample conductivity is governed by resonant tunneling, i.e., the second-order transmission via Mn⁴⁺ sites in the intergranular space. The experimental data on the nanogranular SPS sample confirm the theoretically predicted scaling of the LFMC effect with squared reduced magnetization, and provide a quantitative comparison between the linear coefficient of HFMC and the high-field paraprocess seen in the magnetization measurement.

See supplementary material for structural data and additional figures detailing magnetic behaviors and transport properties of studied samples. Further, more detailed comment on the theory of tunneling magnetoconductance is given.

The work was supported by Project No. 15-10088S of the Czech Science Foundation.