Core and surface structure and magnetic properties of mechano-synthesized LaFeO₃ nanoparticles and their Eu³⁺-doped and Eu³⁺/Cr³⁺-co-doped variants

Abstract

The core and surface structure and magnetic properties of mechano synthesized LaFeO₃ nanoparticles (30–40 nm), their Eu³⁺-doped (La_0.70Eu_0.30FeO₃), and Eu³⁺/Cr³⁺ co-doped (La_0.70Eu_0.30Fe_0.95Cr_0.05O₃) variants are reported. Doping results in a transition from the O′-type to the O-type distorted structure. Traces of reactants, intermediate phases, and a small amount of Eu²⁺ ions were detected on the surfaces of the nanoparticles. The nanoparticles consist of antiferromagnetic cores flanked by ferromagnetic shells. The Eu³⁺ dopant ions enhance the magnetization values relative to those of the pristine nanoparticles and result in magnetic susceptibilities compatible with the presence of Eu³⁺ van Vleck paramagnetism of spin–orbit coupling constant (λ = 363 cm⁻¹) and a low temperature Curie–Weiss like behavior associated with the minority Eu²⁺ ions. Anomalous temperature-dependent magnetic hardening due to competing magnetic anisotropy and magnetoelectric coupling effects together with a temperature-dependent dopant-sensitive exchange bias, caused by thermally activated spin reversals at the core of the nanoparticles, were observed.

Introduction

The orthorhombically distorted perovskite-related rare-earth orthoferrite materials of the composition (RE)FeO₃, where RE is a rare earth ion, are technologically attractive due to their physicochemical properties that render them of potential usage in a host of applications^{1,2,3,4,5,6,7}. One such a material is lanthanum orthoferrite, LaFeO₃, that crystallizes in the space group Pbnm (# 62) with lattice constants a = 5.556 Å, b = 5.565 Å and c = 7.862 Å⁵. The La³⁺ and Fe³⁺ ions, respectively, occupy the so-called A sites and the six O²⁻ coordinated octahedral B sites (BO₆). Unlike cubic perovskites, where the A sites are 12 O²⁻-coordinated cuboctahedra (AO₁₂), the orthorhombically distorted (RE)FeO₃ (RE = from Pr to Lu) compounds possess 8 O²⁻-coordinated A sites (AO₈). However, in bulk LaFeO₃, Marezio et al.⁸ have shown that the difference between the distances of the La³⁺ ion to its eighth and ninth nearest O²⁻ neighbors, namely, 2.805 Å and 3.041 Å, respectively, is insignificant. Hence, the A sites in LaFeO₃ are considered AO₉ polyhedra. The magnetic ordering of the high-spin Fe³⁺ cations in LaFeO₃ results in G-type antiferromagnetism (AFM) which is accompanied by a weak canted ferromagnetic (FM) component. The high Néel temperature (T_N) of ~ 740 K reported for the material is a consequence of the strong Fe³⁺–O²⁻–Fe³⁺ superexchange coupling^1,9. The other inherent properties of LaFeO₃, which are important from an applied viewpoint, include thermal, electrical, magneto-optical, and high chemical stability, in addition to multiferroicity^2,4,5,10.

To extend the technological utilization of LaFeO₃, some researchers have attempted to modify its properties by producing it either in the form of nanoparticles or by introducing substituents for La³⁺ and/or Fe³⁺ cations^2,3,4. In this respect, novel magnetic properties, such as magnetic exchange bias (EB), superparamagnetism, and spin glass behavior, have been reported for LaFeO₃ nanoparticles of sizes in the 10–60 nm range^2,3,9,10,11. Such properties, which are of interest for various applications, including magnetic sensors, spintronics, and data storage devices^1,4,6, could be further tuned by single-site cation doping. In connection with this, we note that when soft chemistry methods were used to introduce Na⁺, Zn²⁺, Sb³⁺ or Ce⁴⁺ as sole substituents for La³⁺ in LaFeO₃ nanoparticles, the coercivity (H_c) was found to depend on the dopant concentration^3,5,11. Doping with single cations such as Na⁺ and Zn²⁺ has affected the superparamagnetic behavior of the nanoparticles, as both the blocking and relaxation temperatures were found to decrease^3,9. Of interest to us in this paper is the work of Hosseini et al. who reported the use of the sol–gel route to form Eu³⁺-doped LaFeO₃ nanoparticles of the composition La_1−xEu_xFeO₃ (x ≤ 0.15) without elaborating on how Eu³⁺-doping affects their structural and magnetic properties¹². Similarly, the substitution of Fe³⁺ in LaFeO₃ nanoparticles with transition metal (TM) cations has been an active area of research^4,6,10. For instance, a spin-glass-like freezing temperature and cluster-spin behavior were reported when Mn³⁺ and Cr³⁺ were used as substituents for Fe³⁺ in LaFeO₃ nanoparticles^13,14. EB behavior has been reported to be barely noticeable when substituting La³⁺ cations with Zn²⁺ in LaFeO₃ nanoparticles^3,10. Ferromagnetically weak single-domain LaFeO₃ nanoparticles with particle size-dependent H_c were reported when Fe³⁺ ions were partially substituted⁴ by Ti⁴⁺. Recently, we have shown that Ru³⁺-doping modifies the properties of mechano-synthesized LaFe_1−xRu_xO₃ nanoparticles, resulting in Jahn–Teller-like distortion, a size-dependent hyperfine magnetic field, and a monotonic decrease in the optical band gap with increasing Ru³⁺ content⁶. In addition, the structure of the mechano-synthesized LaFe_1−xRu_xO₃ nanoparticles was found to index to the O′-type perovskite structure with the lattice parameters related according to c/$\sqrt 2$ < a < b as opposed to the O-type perovskite structure of bulk LaFeO₃ wherein a < c/$\sqrt 2$ < b⁶. These modifications are associated with the route of mechano-synthesis, which is known to form nanoparticles with a non-uniform core–shell structure in which the exchange interactions between the inner crystalline core and an outer disordered or amorphous shell often result in novel physical properties^15,16. To the best of our knowledge, few studies have been devoted to the case in which both La³⁺ and Fe³⁺ cations in LaFeO₃ nanoparticles are concurrently substituted^17,18,19. Such co-doping was found to lead to notable changes in the magnetic and ferroelectric properties, as was shown for the La_0.8Sr_0.2Fe_1−xCu_xO₃, La_0.9Dy_0.1Fe_0.9Ti_0.1O₃ and La_1−xDy_xFe_1−yMn_yO₃ nanoparticles. In a previous study on mechano-synthesized nanoparticles of the isostructural compound EuFeO₃, co-doped with Nd³⁺ and Cr³⁺ with the composition Nd_0.33Eu_0.67Fe_1−xCr_xO₃, we reported an unusual crystal distortion wherein Eu³⁺ and Fe³⁺ cations exchange their normal expected A and B sites and novel magnetic properties¹⁵.

In this paper, we report on the synthesis of LaFeO₃, La_0.7Eu_0.3FeO₃ and La_0.7Eu_0.3Fe_0.95Cr_0.05O₃ nanoparticles using a mechanical milling route. We then systematically study the effect of Eu³⁺-doping and Eu³⁺/Cr³⁺ co-doping on the structural and magnetic properties of the synthesized nanoparticles. Of special interest to us is studying the contribution of the majority Eu³⁺ and minority Eu²⁺ ions detected on the intrinsic magnetic properties of the nanoparticles. As the investigated compounds have AFM ground states, it is important to carefully synthesize them as single phases so as to eliminate any contribution of Fe or Fe-oxide impurities on these magnetic properties. The experimental techniques used include X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FT-IR) and ⁵⁷Fe Mӧssbauer spectroscopy, X-ray photoelectron spectroscopy (XPS) and vibrating sample (VSM) magnetometery.

Materials and methods

LaFeO₃, La_0.70Eu_0.30FeO₃ and La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles were prepared starting from stoichiometric mixtures of high-purity α-Fe₂O₃, La₂O₃, Eu₂O₃ and Cr₂O₃ that were subjected to mechanical milling for different times using a Fritch D-55743 P6 milling machine with tungsten carbide vial (250 mL) and balls. The milling speed was 300 rpm, and the ball-to-powder mass ratio was 15: 1. A Carbollite (HTF 1800) furnace was used to heat the pre-milled mixtures for 10 h at various temperatures to achieve single-phased final products. XRD measurements were performed using an X’Pert PRO PANanalytical diffractometer where the Cu-K_α radiation (λ = 1.5406 Å) was employed in the 2θ-range of 20.00–80.00° at the rate of 0.02° per second. The GSAS program was used to perform XRD Rietveld refinements²⁰. A JEM-1400-JEOL system, operating at 200 kV, was used to obtain high-resolution transmission electron microscopy (HRTEM) images. A PerkinElmer SpectraOne system was used to collect FT-IR spectra in the range 500–4000 cm⁻¹ with a signal resolution of 4 cm⁻¹ for 40 scans. ⁵⁷Fe Mössbauer measurements were done at 298 K and 78 K with a conventional constant acceleration spectrometer using the 14.4 keV gamma ray provided by a 50 mCi ⁵⁷Co/Rh source operating in transmission mode. The isomer shift values are quoted relative to α-Fe at 298 K. An Omicron NanoTechnology MXPS system (Scienta Omicron, Germany) employing the Al Kα radiation (hν = 1486.6 eV) was used to collect XPS spectra. The C 1s reference peak, at the binding energy of 284.6 eV, was used for binding energy calibration, and the data was fitted with the CasaXPS²¹. The VSM magnetometer option of a Quantum Design PPMS system was used to record the thermal dependence of magnetization. The measurements were carried out in both the field cooling (FC) and zero field cooling (ZFC) modes under an external magnetic field of 50 kOe in the 4–300 K temperature range. ZFC magnetic hysteresis loops were obtained at different temperatures and applied fields of up to 9 T.

Results and discussion

Mechano-synthesis and crystal structure

The XRD patterns shown in Fig. 1 indicate that the formation of single-phase LaFeO₃ and that of its Eu³⁺-doped LaFeO₃ and Eu³⁺/Cr³⁺ co-doped LaFeO₃ (La_0.70Eu_0.30Fe_0.95Cr_0.05O₃) variants are attained after heating the corresponding 80 h pre-milled reactants’ mixtures at 600 °C (10 h) and 700 °C (10 h), respectively. These temperatures are ca. 600–700 °C lower than the ones reported for the formation of LaFeO₃ and its cation-doped modifications using the conventional solid-state routes²². It is obvious from the TEM images shown in Fig. 2 that the three materials are composed of semi-spherical nanoparticles that tend to agglomerate. The LaFeO₃ sample exhibits the widest particle size distribution with the mean particle size of (40 ± 10) nm relative to both La_0.70Eu_0.30FeO₃ and La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ (30 ± 10) nm. The results of the XRD Rietveld refinements, where in the case of the doped samples a common position for the La³⁺ and Eu³⁺ ions was assumed and a temperature factor to account for their disorder was included, are also shown in Fig. 1, Tables 1 and 2. It follows that each nanomaterial is structurally indexable to an orthorhombic perovskite-related phase (space group Pbnm)^5,7. As the microstrain values for the doped LaFeO₃ samples (Table 2) are too small to be considered a factor contributing to the structural distortion associated with apparent broadened peaks relative the ones expected for the corresponding bulk samples, we attribute the broadening to lattice dislocations and surface disorder associated with crystallite size reduction to the nanometer scales²³. The relatively large values of the microstrain in the La_0.70Eu_0.30FeO₃ and La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ samples, relative to that of the LaFeO₃ sample, are obviously induced by cationic doping and co-doping. The data given in Tables 1 and 2 were used in combination with VESTA software²⁴ to draw the polyhedra of the crystal structure of LaFeO₃ with the ionic positions, bond lengths, and angles shown in Fig. 3.

Figure 1

Observed, calculated and difference of the XRD patterns for the (a) LaFeO₃, (b) La_0.70Eu_0.30FeO₃, and (c) La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ samples. The Miller indices of each peak are given in the form of (hkl) and the blue bars indicate the positions of Bragg’s reflection peaks. The inset shows the relative intensity reversal of the (220) and (024) peaks.

Figure 2

TEM images of the (a) LaFeO₃, (b) La_0.70Eu_0.30FeO₃, and (c) La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles. The insets are the histograms of the particle size distribution. The solid line is the fit to the log-normal size distribution.

Table 1 The structural parameters extracted from the Rietveld refinement of XRD data for the LaFeO₃, La_0.70Eu_0.30FeO₃ and La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles recorded at room temperature. Space group: Pbnm (62) and the R-Factors have their normal significance and relate to regions of the profile at which Bragg peaks contribute. R_p < 7.91%, R_wp < 7.99%, R_exp < 6.77%, χ² ~ 1.483.

Table 2 The fractional coordinates of the ions in the LaFeO₃, La_0.70Eu_0.30FeO₃ and La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles extracted from the Rietveld refinement of the XRD data obtained at room temperature.

Figure 3

The polyhedra of the LaFeO₃ nanoparticles as derived from the XRD Rietveld refinement. The large gray spheres represent La³⁺ ions in 8 O²⁻ coordinated sites, the orange spheres refer to Fe³⁺ ions in FeO₆ octahedra and the small green spheres represent O²⁻ ions. O1 and O2 refer to O²⁻ ions with two different environments.

For the LaFeO₃ nanoparticles, the difference between the distances of La³⁺ to its eighth and ninth nearest O²⁻ neighbors, 2.527 Å and 3.028 Å, is larger than that expected for bulk LaFeO₃ mentioned earlier^8,10. This, in turn, justifies the conclusion that the La³⁺ polyhedron at the A-site of the LaFeO₃ nanoparticles is LaO₈ rather than LaO₁₂ as expected for bulk LaFeO₃^8,10. This result indicates that the change in the La³⁺ coordination number is strongly instigated by the weakening of ionic exchange interactions at the surface of the nanoparticles. From Table 1, it can be seen that the Fe–O1 bond lengths vary coincidentally with the FeO₆-volumes. There was no cationic site exchange similar to that we previously reported for EuFe_xCr_1−xO₃ nanocrystalline particles using a similar mechano-synthesis regime²⁵. The fact that the lattice constants of the LaFeO₃ nanoparticles are slightly smaller than those of their bulk counterparts cited above²² may be attributed to the dislocations and disorder induced on the surface layers of the nanoparticles. The FeO₆ octahedra in the LaFeO₃ nanoparticles (Fig. 3) appeared to be severely distorted owing to variations in the intra-octahedral O1–Fe–O2 bond angles.

It is clear from the obtained lattice parameters of the LaFeO₃ nanoparticles that their distorted crystal structure is of the O′-type⁶. The diffraction peaks of the La_0.70Eu_0.30FeO₃ nanoparticles broadened and shifted toward larger angles (Fig. 1). Hence, their lattice constants decreased relative to those of the LaFeO₃ nanoparticles (Table 1). These changes entail the substitution of 8-coordinated La³⁺ ions (1.36 Å) with smaller 8-coordinated Eu³⁺ ions (1.066 Å) in the lattice structure of LaFeO₃²⁶. Generally, the influence of the Eu³⁺ dopant on the deformation of octahedral sites is justifiable in terms of the Goldsmith formalism⁷. In contrast to the LaFeO₃ nanoparticles, it can be seen from Table 1 that doping with Eu³⁺ affects the lattice constants of the La_0.70Eu_0.30FeO₃ nanoparticles, such that a < c/$\sqrt 2$ < b indicates that the orthorhombic distortion of the nanoparticles is O-type. We associate this crossover of the a and c/$\sqrt 2$ parameters with the significant difference between the O1-Fe-O2 angle in the Eu³⁺-doped LaFeO₃ nanoparticles and LaFeO₃ nanoparticles (Table 1) owing to the partial substitution of La³⁺ ions with smaller Eu³⁺ ions. Similar anomalous parameter crossovers have been reported for solid solutions of rare-earth orthoferrites and orthocobaltites, such as PrCo_1−xFe_xO₃ and EuCo_1−xFe_xO₃^27,28. To reflect more on the structural distortion resulting from Eu³⁺ doping, using Glazer's tilt system of perovskites²⁹, one notes that the variation in the lattice parameters of the La_0.70Eu_0.30FeO₃ nanoparticles corresponds to the first tilt type along the [010] direction. As shown in Table 1, partial substitution of La³⁺ with Eu³⁺ led to a single long Fe-O2 bond along the b-axis and a pair of Fe-O1 and Fe-O2 short bonds in the ac plane.

We now turn to La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles. As shown in Table 2, the Eu³⁺ and La³⁺ ions preferentially occupy a slightly distorted “average” A-site, whereas the Cr³⁺ ions are randomly distributed with Fe³⁺ ions in the B-sub-lattice.. It turns out that the introduction of 5% Cr³⁺ (0.615 Å) substituent ions for Fe³⁺ (0.645 Å)²⁶ resulted in a slight increase in the a lattice parameter and a concomitant decrease in the b and c lattice parameters relative to those of the La_0.70Eu_0.30FeO₃ nanoparticles. The estimated crystallite sizes for the three types of nanoparticles were within experimental error, consistent with the particle sizes deduced from the TEM measurements. This implies that the nanoparticles may generally be considered crystallites.

The FT-IR spectra of the mechano-synthesized LaFeO₃ nanoparticles and their Eu³⁺-doped and Eu³⁺/Cr³⁺-co-doped modifications in the range of 400–700 cm⁻¹ shown in Fig. 4 are typical of perovskite oxides that structurally index to the Pbnm space group^4,7. Theoretically, Pbnm phases have nine dipole-active optical phonon modes in the 400–700 cm⁻¹ range, of which those between 400 and 500 cm⁻¹ are O²⁻ octahedral bending vibrations, and those beyond 500 cm⁻¹ are O²⁻ stretching vibrations^7,30. However, some peaks are very difficult to detect because of the line broadening associated with the small particle sizes or the possible presence of O²⁻ vacancies on the surfaces. Evidently, the slight differences in the FT-IR spectra relative to the spectrum of the LaFeO₃ nanoparticles were a consequence of cationic doping. On the basis of the ionic interactions present, the vibrational bands would contribute intrinsic Lorentzian shapes to the FT-IR spectrum. Temperature-dependent effects, instrumental effects, and/or sample characteristics cause the background signals to experience Gaussian broadening^31,32. Hence, we opted to fit the FT-IR spectra shown in Fig. 4 with the Voigt functions. The spectral broadband at ~ 588 cm⁻¹, for the LaFeO₃ nanoparticles was assigned to the antisymmetric stretching vibrational modes of the FeO₆ octahedra⁷. The relatively asymmetric peak may be related to the non-uniform cationic distribution in the shells of the nanoparticles, which leads to cluster-glass-like features¹⁴. Peak broadening reflects the wide size distribution observed in the TEM image (Fig. 2). The weak band at ca. 505 cm⁻¹ owing to the out-of-phase stretching vibrations of the BO₆ octahedra, as has been observed for some orthochromites and orthomanganites³², is closely associated with a Jahn–Teller-like distortion³⁰. For Eu³⁺-and Eu³⁺/Cr³⁺-doped LaFeO₃ nanoparticles, the notable enhancement in the symmetry of the stretching vibrational modes and their narrowing are indicative of a more uniform cationic distribution and limited particle size range relative to those of the LaFeO₃ nanoparticles. The substitution of the lighter La³⁺ ions (138.904 amu) by heavier Eu³⁺ ions (151.962 amu) in the La_0.70Eu_0.30FeO₃ nanoparticles shifted the absorption band of the FeO₆ stretching vibrations from 583 to 574 cm⁻¹, which is expected, as the wavenumber is inversely proportional to the ionic mass^18,33. The small concentration of Cr³⁺ ions in the La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles was not sufficient to cause an observable shift for the same band relative to that of the La_0.70Eu_0.30FeO₃ nanoparticles. The small shoulder at 505 cm⁻¹, associated with the O′-type structural mode of LaFeO₃ does not exist in the Eu³⁺-doped and Eu³⁺/Cr³⁺-co-doped nanoparticles, presumably because of the O-type structural distortion. We now turn to The shifts in the bending vibrational mode at 426 cm⁻¹ in the FT-IR spectrum of the LaFeO₃ nanoparticles to 432 cm⁻¹ and 431 cm⁻¹ in the spectra of La_0.70Eu_0.30FeO₃ and La_0.70Eu_0.30Fe_0.95Cr_0.05O₃, respectively. These shifts are consistent with the increased bending of the Fe–O2–Fe angle revealed by the XRD refinement of the La_0.70Eu_0.30FeO₃ nanoparticles and the subsequent decrease in the electronegativity of Cr³⁺–O²⁻ compared with Fe³⁺–O²⁻ in the La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles. Hence, the FT-IR spectra further confirmed that LaFeO₃ nanoparticles and their Eu³⁺-doped and Eu³⁺/Cr³⁺ co-doped modifications were formed.

Figure 4

FT-IR spectra of the (a) LaFeO₃, (b) La_0.70Eu_0.30FeO₃, and (c) La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles in the range of 400–700 cm⁻¹ at 298 K.

Mössbauer characterization

The zero-field ⁵⁷Fe Mössbauer spectra of LaFeO₃, La_0.70Eu_0.30FeO₃ and La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles, recorded at 298 K and 78 K, are shown in Fig. 5, and the corresponding fitted hyperfine parameters are given in Table 3. All spectra show pure magnetic six-line patterns with broadened absorption lines, which reflect both the particle size distribution and varied cationic environments for the doped samples around the ⁵⁷Fe nuclei. It is pertinent to note that Fujii et al.¹ reported Mössbauer spectra for LaFeO₃ nanoparticles with an average particle size of ca. 13 nm, which are pure doublets. While the LaFeO₃ system is essentially AFM in character, the Mössbauer doublets were attributed to the superparamagnetic behavior of the FM nanoparticle shells that resulted from the uncompensated surface spins¹. The absence of such doublets in the Mössbauer spectra of the present nanoparticles rules out the presence of any superparamagnetic behavior, which is consistent with their relatively larger average particle sizes relative to 13 nm^1,14. The Mössbauer spectrum of the LaFeO₃ nanoparticles at either 298 or 78 K was best fitted to a single sextet with a typical isomer shift value of the Fe³⁺ state^11,34. The isomer shift values at 298 K (0.37–0.41 mm/s) indicate the high-spin nature of the Fe³⁺ ions in all nanoparticles⁶. The increase in the isomer shift values at 78 K relative to their values at 298 K is explicable in terms of the second-order Doppler shift³⁴. The small negative quadrupole shift values at both temperatures are indicative of the distorted crystal structures, as discussed earlier^6,11. We associate the relatively high value of the hyperfine magnetic field of the LaFeO₃ sample at 298 K (51.5 T), which is typical for nanoparticles exhibiting AFM ordering with strong Fe–Fe coupling, with Fe nuclei at the nanoparticle cores^1,6. The tangible increase in the hyperfine field value as the temperature is decreased to 78 K (Table 3) is associated with the removal of the thermal vibrations and subsequent spin alignment, especially in the shells of the nanoparticles^1,13,15,34. As shown in Fig. 5 and Table 3, doping the LaFeO₃ nanoparticles with Eu³⁺ and co-doping them with Eu³⁺/Cr³⁺ broadened the Mössbauer absorption lines. The best fit of the spectra of both doped nanoparticles was attained using two superimposed magnetic subspectra, S1 and S2. S1, with smaller isomer shifts and larger effective hyperfine magnetic fields, are associated with Fe³⁺ environments similar to those in undoped LaFeO₃ or with poor Eu³⁺ (in La_0.70Eu_0.30FeO₃) and Eu³⁺/Cr³⁺ (in La_0.70Eu_0.30Fe_0.95Cr_0.05O₃) environments. The slight decrease in the hyperfine field values of sextet S1 at both temperatures for both types of doped nanoparticles relative to those of the LaFeO₃ nanoparticles is attributed to their relatively smaller average particle size, as revealed by the TEM images. Slight differences existed between the isomer shift values of the undoped LaFeO₃ nanoparticles and those of the S1 sextet. This may be related to the different electronic configurations of the dopant ions that, in turn, lead to slightly different electric fields at the sites of ⁵⁷Fe nuclei³⁴. Sextet S2, whose hyperfine magnetic fields are notably smaller than those of the LaFeO₃ nanoparticles, is associated with Fe³⁺ environments where the Fe–O–Fe of the magnetic superexchange interaction of pristine LaFeO₃ is weakened by the presence of Eu³⁺ or Eu³⁺/Cr³⁺ nearest neighbors in La_0.70Eu_0.30FeO₃ or La_0.70Eu_0.30Fe_0.95Cr_0.05O₃, respectively. This is supported by the larger linewidth of S2 for the La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles, which, in turn, suggests a random distribution in the numbers of Eu³⁺ and Cr³⁺ cationic neighbors of the Fe³⁺ ions at the A and B sites, respectively^6,34. The weakening of the S1 and S2 hyperfine magnetic fields in the spectra of the La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles implies weakened exchange interactions between Fe³⁺ ions because of the negative super-transferred hyperfine field produced by the half-filled d-orbitals of the Cr³⁺ ions at the sites of the ⁵⁷Fe nuclei³⁵. The fact that the spectral intensities at 298 K and 78 K for both sextets, S1 and S2, are the same supports their assignments to the Fe³⁺ environments, as described above.

Figure 5

The ⁵⁷Fe Mӧssbauer spectra recorded from the (a) LaFeO₃, (b) La_0.70Eu_0.30FeO₃, and (c) La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles at (a) 298 K and (b) 78 K.

Table 3 The hyperfine parameters derived from fitting the Mӧssbauer spectra recorded at 298 K and 78 K (between brackets and in italics) for the LaFeO₃, La_0.70Eu_0.30FeO₃ and La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles.

Surface composition: XPS spectral analysis

The La 3d, Eu 3d, Fe 2p and O1s XPS spectra of the LaFeO₃ nanoparticles and their Eu³⁺-doped and Eu³⁺/Cr³⁺ co-doped modifications are shown in Fig. 6. The C 1s XPS peak at 284.6 eV was taken as a reference for all charge shift corrections. The La 3d_3/2 and La 3d_5/2 peaks of the LaFeO₃ sample at the binding energies (BE) 850.4 eV and 833.6 eV (Fig. 6a) are similar to those reported for sol–gel processed LaFeO₃ nanoparticles^7,36. Satellite peaks at BE values 854.4 eV and 837.3 eV correspond to the shake-up of the La 3d_3/2 and La 3d_5/2 states, respectively, due to electron transfer from the O 2p valence band to empty La 4f states³⁶. As these BE values have been reported for both La₂O₃ and LaFeO₃^7,37, the existence of some unreacted La₂O₃ components on the surface of these mechano-synthesized LaFeO₃ nanoparticles could not be ruled out. Additionally, these BE values may be partly associated with the very small amounts of Fe-doped La₂O₃³⁸ and/or La-doped α-Fe₂O₃³⁹ intermediate phases that develop during the reaction, leading to the LaFeO₃ phase. The BE values of the La 3d_3/2 and La 3d_5/2 spectra for the La_0.70Eu_0.30FeO₃ nanoparticles, 850.8 eV and 834.0 eV, and those of the La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles, 849.9 eV and 833.1 eV, are slightly higher than those of the LaFeO₃ nanoparticles. This implies that introducing the more electronegative Eu³⁺ (1.2) for the less electronegative La³⁺ (1.1) shifts the La 3d spectral peaks towards higher BE values because of the lowering of the electron densities⁴⁰. Similarly, the lower BE values for the La 3d spectral peaks of the La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles relative to those of the La_0.70Eu_0.30FeO₃ nanoparticles may be attributed to doping with the less electronegative Cr³⁺(1.66) for the more electronegative Fe³⁺ (1.83), which increases the La³⁺ and O²⁻ electron densities and consequently lowers the BE values⁴⁰.

Figure 6

The (a) Fe 2p, (b) La 3d, (c) Eu 3d, and (d) O 1s core-level XPS spectra recorded from the (i) LaFeO₃, (ii) La_0.70Eu_0.30FeO₃, and (iii) La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles. The solid lines represent the best fitting of the experimental data. The estimated error for the binding energy values is ± 0.01 eV.

Figure 6b shows the Fe 2p XPS spectra of all the nanoparticles. The asymmetrical Fe 2p_3/2 peak of the LaFeO₃ nanoparticles could be decomposed into distinct peaks at BE of 709.5 eV and 711.3 eV corresponding, respectively, to surface Fe²⁺- and Fe³⁺-containing species^7,41. Previously, we reported a similar reduction of Fe³⁺ to Fe²⁺ on the surface of mechano-synthesized Nd_0.33Eu_0.67Cr_xFe_1−xO₃ nanoparticles¹⁵. In addition, the presence of surface Fe²⁺ ions has been reported for other REFeO₃ compounds in the form of bulk or nanoparticles, such as PrFeO₃⁴², ErFeO₃⁴³ and Ir-doped YbFeO₃⁴⁴. In fact, the shake-up satellite peak at a BE value of 717.8 eV, which is located at + 8.3 eV from the Fe 2p_3/2 peak at 709.5 eV, is typical of satellite signals of ferrous species⁴¹. The presence of these Fe²⁺ impurities suggests the existence of O²⁻ vacancies as balancing defects. Together, these results imply the formation of an O²⁻ defective perovskite phase of LaFeO_3-δ at the surface of the nanoparticles⁴⁵. Hence, we associate the Fe 2p_3/2 peak at the BE of 709.5 eV to this surface LaFeO_3-δ component. The sub-spectral peak at 711.3 eV is almost similar to that of Fe³⁺ ions in α-Fe₂O₃ (711.2 eV). Hence, we associate the 711.3 eV peak with the La-doped α-Fe₂O₃ intermediate phase implied above by the La 3d XPS spectrum³⁹. The Fe 2p_1/2 spectral component was fitted with two peaks centered at the BE values of 723.2 eV and 725.8 eV which are assigned, respectively, to LaFeO_3-δ and either or both of LaFeO₃ and La-doped α-Fe₂O₃^7,36,39. As is seen in Fig. 6b, the binding energies of the Fe 2p_3/2 peaks increase for the La_0.70Eu_0.30FeO₃ nanoparticles (710.0, 711.7 eV) relative to the corresponding values of the LaFeO₃ nanoparticles. This is suggestive that the incorporation of Eu³⁺ in LaFeO₃ results in lesser O²⁻ vacancies hence more Fe³⁺ ions and, consequently, stronger Fe–O bonds. However, for the La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles the binding energies of Fe 2p core-level spectra tend to decrease on the Cr³⁺ substitution. The reason for this is apparently the same as that we argued above for the similar trend in the La 3d spectra following the Cr³⁺ substitution.

Each of the Eu 3d core-level XPS spectra of the Eu³⁺-doped and Eu³⁺/Cr³⁺-co-doped LaFeO₃ nanoparticles, shown in Fig. 6c, is composed of five peaks. For the La_0.70Eu_0.30FeO₃ sample, the peaks were assigned as follows. The Eu³⁺ doublet at the BE values of 1134.3 eV (Eu 3d_5/2) and 1163.6 eV (Eu 3d_3/2) is attributed to a surface Eu³⁺-doped α-Fe₂O₃, as is reported elsewhere⁴⁶. The weak Eu²⁺ doublet at the BE values 1124.4 eV (Eu 3d_5/2) and 1154.7 eV (Eu 3d_3/2), which is consistent with those reported before for other Eu-containing systems⁴⁷, merits special attention as it appears to influence the nanoparticles’ low temperature magnetic behavior to be discussed in the next section. The presence of Eu²⁺ ions, in systems like the present ones, is attributed to an intermediate valence between the electronic configurations of Eu³⁺ and Eu²⁺ ions⁴⁸. This reduction of Eu³⁺ to Eu²⁺ is implicative of the presence of balancing O²⁻ vacancies on the surface of nanoparticles. Hence, we associate the Eu²⁺ doublet with the weak La_0.7Eu_0.3FeO_3-δ surface component. The fifth fitted peak in the Eu 3d core level spectrum, at the BE value 1128.1 eV was not, to our knowledge, reported before for any Eu-containing solid. Hence, we assume that it is due to the investigated La_0.70Eu_0.30FeO₃ nanoparticles. Such an assignment appears logical as the Eu 3d core level XPS spectral peak at the close BE value of 1129.0 eV was assigned before to Nd_0.33Eu_0.67FeO₃ nanoparticles¹⁵.

As is clear from Fig. 6c, the presence of Cr³⁺ in the La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles slightly shifts the Eu 3d doublet relative to that of the La_0.70Eu_0.30FeO₃, to the BE values of 1133.8 eV and 1163.5 eV. These values are consistent with those reported for EuCrO₃ doublets, suggesting the possibility that traces of EuCrO₃ are present on the surface of La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles²⁵. In similar lines to those given above, we attribute the Eu 3d core-level XPS peak at the BE value 1123.9 eV and the shake-down satellite at 1154.9 eV, in the spectrum of the La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles, to an Eu²⁺-containing surface component that could be La_0.7Eu_0.3FeO_3-δ and/or La_0.70Eu_0.30Fe_0.95Cr_0.05O_3-δ⁴⁷. The fifth peak in the Eu 3d spectrum of the same sample, at the BE value of 1127.6 eV, is negatively shifted and enhanced in intensity relative to the corresponding one in the spectrum of La_0.70Eu_0.30FeO₃. Taken together, these results imply that even a low concentration of the less electronegative Cr³⁺ relative to the substituted Fe³⁺ may significantly influence the surface composition of the mechano-synthesized La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles, with the possibility of having surface traces of pure and/or Cr³⁺-doped La_0.70Eu_0.30FeO_3-δ as well as EuCrO₃²⁵.

The O 1s XPS spectra of the nanoparticles are shown in Fig. 6d. As we have, previously, done with similarly mechano-synthesized rare earth orthoferrites¹⁵, we resolve the O 1s peak for the LaFeO₃ nanoparticles into three overlapping peaks. In agreement with the La 3d spectra, the first component of the O 1s peak (I) at a BE value of 528.2 eV is related to perovskite-related LaFeO₃ and/or moderately Fe-doped La₂O₃^7,36,38. The second component (II) at 529.9 eV is assigned to the α-Fe₂O₃ and/or La-doped α-Fe₂O₃, both of which are implicated by the Fe 2p spectra discussed above^15,39,41. The LaFeO_3-δ phase, whose presence was inferred from the Fe 2p spectra, is associated with the minor third component of O 1s (III) at the BE value of 532.5 eV^15,41,45. With Eu³⁺ doping, the BE of the components of the O 1s peak increased to 529.0 eV (I) and 530.4 (II) eV which, in line with the above analysis, we ascribe to La_0.70Eu_0.30FeO₃ and Eu³⁺-doped α-Fe₂O₃, respectively⁴⁶. The positive shift of O 1s, in the XPS La_0.70Eu_0.30FeO₃ spectrum, is possibly due to the decrease in the distance between the O²⁻ ion and their doped Eu³⁺ neighbors due to the higher electronegativity of Eu³⁺ relative to that of La³⁺⁴⁰. The absence of the third component (III) in the O 1s XPS spectrum of the La_0.70Eu_0.30FeO₃ sample suggests that doping with Eu³⁺ results in the elimination of the Fe²⁺-containing LaFeO_3-δ surface component. With the inclusion of the Cr³⁺ ion, the BE values of the three O 1s XPS peaks decrease slightly to 528.0 eV (I), 529.6 eV (II) and 532.7 eV (III) relative to those of the La_0.70Eu_0.30FeO₃ nanoparticles. Such a reduction is attributed to the lower electronegativity⁴⁰ of Cr³⁺ over Fe³⁺. Based on previous work, and in line with above analysis, the BE values of these O 1s XPS spectral peaks are assigned, respectively to EuCrO₃, Eu³⁺-doped α-Fe₂O₃ and pure and/or Cr³⁺-doped La_0.70Eu_0.30FeO_3-δ surface components²⁵. To summarize, the above XPS data analysis has shown mechano-synthesized Eu³⁺-doped and Eu³⁺/Cr³⁺-co-doped LaFeO₃ nanoparticles to have complex surface structures, that contain pure and Eu³⁺/Cr³⁺ doped and co-doped LaFeO₃ phases, O²-deficient undoped and Eu³⁺/Cr³⁺-doped LaFeO₃ phases, traces of undoped or doped initial reactants. Such complexity is expected on the surfaces of nanoparticles prepared by mechanical milling and subsequent sintering^15,25.

The magnetic properties

Figure 7 shows the temperature dependence of the FC and ZFC magnetization in the range of 2–300 K under an applied field of 50 kOe for LaFeO₃, Eu³⁺-doped, and Eu³⁺/Cr³⁺-co-doped LaFeO₃ nanoparticles. As expected for a magnetically ordered system, the FC magnetization curves for all samples exhibited similar temperature dependencies to their Mössbauer magnetic hyperfine fields, decreasing with increasing temperature. The wider bifurcation observed for the LaFeO₃ nanoparticles reveals stronger thermomagnetic irreversibility in comparison to the Eu³⁺-doped and Eu³⁺/Cr³⁺-co-doped nanoparticles¹³. The ZFC magnetization of the LaFeO₃ nanoparticles initially decreased with decreasing temperature to a minimum and then increased without exhibiting a clear maximum below the bifurcation point⁴⁹. Based on the Mössbauer data, this could be explained in terms of the core/shell model, as was done by other^1,13,16,49 researchers. While the core is AFM in nature, the spins of the glass-like shells assume an FM ordering owing to the AFM spin canting at the cores in addition to the field applied during the measurement. The magnetization enhancement to values similar to those previously reported for LaFeO₃ nanoparticles at very low temperatures could result from a local spin order that develops at the interface between the canted AFM cores and FM shells as a result of strong spin coupling^9,13,50. With a gradual increase in temperature, the interfacial exchange coupling weakens, while the core spins resist alignment even by a field as high as 50 kOe⁵⁰. Thus, the core–shell AFM-FM coupling requires higher thermal agitation and/or a higher applied field to be weakened, as manifested by the development of the spin-glass-like behavior at ~ 75 K (Fig. 7). This may explain why spin-glass-like behavior was not detected by zero-field Mössbauer measurements at 78 K. At temperatures higher than 75 K, the spins of the FM shell start to reverse their orientation in the direction of the applied field, and concomitantly, the AFM coupling at the cores starts to decay. Consequently, the ZFC magnetization increased with a further increase in temperature, as observed^9,10. Similar behavior was not observed in the FC curve of the same sample because the surface spins were readily aligned in the field direction, resulting in an apparently higher magnetization relative to that obtained in the ZFC case (Fig. 7).

Figure 7

The temperature dependence of the FC and ZFC magnetization of the (a) LaFeO₃, (b) La_0.70Eu_0.30FeO₃, and (c) La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles under an applied field of 50 kOe.

As shown in Fig. 7, with decreasing temperature, the ZFC and FC magnetization values for the La_0.70Eu_0.30FeO₃ and La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles increased throughout the scanned temperature range. The higher magnetization values for both materials relative to those of the pristine LaFeO₃ sample are evidently linked to the introduction of paramagnetic Eu ions as partial substituents for diamagnetic La³⁺. A comparison of the FC molar susceptibility (χ_m) values of the three materials, as depicted in Fig. 8, reveals that the magnetic contribution of the Fe³⁺ ions is barely detectable in LaFeO₃ compared to that of the Eu ions in the other two compounds. To determine the contribution of Eu³⁺ and XPS-detected minority surface Eu²⁺ ions to the total susceptibility of both the Eu-doped samples, hereafter referred to as χ_m(Eu), we subtracted χ_m of the LaFeO₃ from that of either. The rationale here is to exclude the magnetic effect of the Fe³⁺ sublattice, which is similar in all three compounds. Each of the obtained χ_m(Eu) curves, shown in Fig. 9a (La_0.70Eu_0.30FeO₃) and 9-b (La_0.70Eu_0.30Fe_0.95Cr_0.05O₃), may be divided into two temperature regions, viz. 2–20 K and 20–300 K. In the first low temperature region, the observed upward ascending trend of χ_m(Eu) below 20 K is implicative of a Curie–Weiss type paramagnetism that is solely associated with the minority Eu²⁺ ions having an electronic configuration of [Xe] 4f⁷ and a theoretical effective magnetic moment μ_eff of 7.94 μ_B similar⁴⁸ to that of Gd³⁺. In the second region, the behavior of χ_m(Eu) was attributed mainly to the van Vleck paramagnetism of the Eu³⁺ excited states⁴⁸. According to the Russell–Saunders formalism, Eu³⁺ ([Xe] 4f⁶) has a total angular momentum (J) of zero and, hence, a nonmagnetic ground state (⁷F₀)⁵³. Nevertheless, Eu³⁺ has a spin–orbit interaction given by (λL.S) with L and S orbital and spin angular momenta, respectively, and (λ) is the spin–orbit coupling constant^47,48,50. In the framework of the van Vleck theory, the fact that the differences between the ground state and the low-lying excited states ⁷F_J of the Eu³⁺ ion are of the order of k_BT at room temperature (207 cm⁻¹) results in the Eu³⁺ ions contributing a temperature-dependent term ($\chi$) to the paramagnetic susceptibility, whose value depends on λ⁴⁸. For instance, while for insufficiently large values of λ relative to (207 cm⁻¹), a non-negligible magnetic moment might be observed at low temperatures, the Eu³⁺ ions contribute a minute van Vleck temperature-independent paramagnetic term ($\chi_{0}$) that is linked to the ⁷F₀ state⁴⁸. Based on the above, the χ_m(Eu) curves in Fig. 9a,b were not amenable to satisfactory fits by separately applying a Curie–Weiss type equation to the low-temperature data and a van Vleck type equation fit to the data in the ~ 20–300 K temperature range. However, the best fits of each of the χ_m(Eu) curves in the entire temperature range of 2–300 K were obtained by considering both the temperature-independent and-dependent Eu³⁺ van Vleck terms in addition to the Eu²⁺ Curie–Weiss type paramagnetic term using the following equation⁴⁸:

$$ \chi_{m } (Eu) = \chi_{o} + n\chi_{m } (Eu^{2 + } ) + (1 - n)\chi_{m } (Eu^{3 + } ) $$

(1)

where n is the relative Eu²⁺ contribution to the total χ_m(Eu) in the temperature range of the measurement. By limiting ourselves to the first three excited states of Eu³⁺, Eq. (1) can be rewritten as follows:

$$ \begin{aligned} \chi_{m} (Eu) & = \chi_{0} + n \times \frac{C}{{T - \theta_{W} }} + (1 - n) \times \frac{{N_{A} \mu_{B}^{2} }}{{3k_{B} T}} \\ & \quad \times \frac{{(24/a) + (13.5 - 1.5)e^{ - a} + (67.5 - 2.5)e^{ - 3a} + (189 - 3.5)e^{ - 6a} }}{{1 + 3e^{ - a} + 5e^{ - 3a} + 7e^{ - 6a} }} \\ \end{aligned} $$

(2)

where N_A is Avogadro’s constant, θ_W is the Weiss temperature, a = λ/k_BT. The other symbols have the usual meanings. This has yielded for the La_0.70Eu_0.30FeO₃ nanoparticles the values of μ_eff = 0.72μ_B, θ_W ~ − 14 K, n = 0.58, λ = 363 cm⁻¹ and $\chi_{0}$ = 5.3 × 10⁻⁵ emu/Oe. mol. Similar values were obtained for the La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ except for n and θ_W, which were found to be = 0.70 and ~ − 11 K, respectively. Starting with the low-temperature upturn in χ_m(Eu) that we ascribed to Eu²⁺ spins, it is evident that the negative values of θ_W imply the presence of AFM interactions among the Eu²⁺ spins. However, the obtained θ_W values for both compounds reflect the nature of this weak AFM interaction. The value of μ_eff = 0.72μ_B/Eu²⁺ is very small when compared to the corresponding theoretical value for a free Eu²⁺ ion (7.94 µB)⁵⁰. This could possibly reflect the fact that the Eu ions in both materials were in a valence fluctuation state with no localized magnetic moments. We now turn to the remaining part of the scanned temperature range, where the obtained value of λ suggests that the energy interval between the ground state (⁷F₀) and first excited (⁷F₁) state for Eu³⁺ (4f⁶) ions, in both compounds, primarily influences the paramagnetic susceptibility above 521 K. This, in turn, explains the weak relative contribution of the Eu³⁺ van Vleck temperature-dependent susceptibility to the total χ_m(Eu), viz. 0.42 (La_0.70Eu_0.30FeO₃) and 0.30 (La_0.70Eu_0.30Fe_0.95Cr_0.05O₃) in the 20–300 K temperature range. The fact that these results are slightly different from those reported for other Eu-containing oxide systems⁴⁸ could possibly be ascribed to the high applied field (H = 50 kOe), crystal field anisotropy of the distorted crystal structure, and screening effect, as indicated by the increase in the Mössbauer isomer shift of the S2 sextet (Table 3).

Figure 8

Temperature dependence of magnetic molar susceptibility for the LaFeO₃, La_0.70Eu_0.30FeO₃ and La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles under an applied field of 50 kOe.

Figure 9

Temperature dependence of the FC Eu-related molar susceptibility $\chi_{m}$ (Eu) for the (a) La_0.70Eu_0.30FeO₃ and (b) La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles, obtained by subtracting the molar susceptibility contribution of the LaFeO₃ nanoparticles from that of the La_0.70Eu_0.30FeO₃ and La_0.70Eu_0.30FeO₃ ones, respectively, measured in an applied field of 50 kOe. The solid line represents the best fitting line based on Eqs. (1) and (2).

Figure 10 shows that the magnetization values of the La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles were lower than those of the La_0.70Eu_0.30FeO₃ nanoparticles. This is presumably due to the substitution of the weaker magnetic Cr³⁺ ion (µ = 3 µ_B) for the stronger Fe³⁺ ion (µ = 5 µ_B), which weakens the AFM coupling relative to that of the La_0.70Eu_0.30FeO₃ nanoparticles^13,51. The slight increase in the bifurcation of the La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles relative to that of the La_0.70Eu_0.30FeO₃ nanoparticles can be attributed to an increased interface anisotropy caused by co-doping with both Eu³⁺ and Cr³⁺ ions. Considering the limited temperature range used for the FC and ZFC scans, we conclude this section by qualitatively commenting on the irreversibility temperature (T_irr) of the nanoparticles (Fig. 7). The value of T_irr for La_0.70Eu_0.30FeO₃, ~ 287 K, is lower than the corresponding values for the undoped and Eu³⁺/Cr³⁺-co-doped LaFeO₃ counterparts, both of which could not be determined firmly in the scanned temperature range. The reduction in T_irr for the La_0.70Eu_0.30FeO₃ sample relative to that of the LaFeO₃ sample can be explained using the argument given above for the enhancement of the ZFC magnetization values to approach those of the FC magnetization owing to doping with Eu³⁺. Similarly, the higher T_irr of the La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles relative to that of the La_0.70Eu_0.30FeO₃ nanoparticles is associated with the diminution of the ZFC magnetization values relative to those of the FC, following the introduction of Cr³⁺ ions.

Figure 10

The hysteresis loops (M–H curves) of the LaFeO₃, La_0.70Eu_0.30FeO₃, and La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles at (a) 300 K and (b) 4 K. The inset shows a zoom-in image of the same loops to display the non-zero values of both coercivity and remnant magnetization at 2 K.

A final comment in this part goes for the high applied field of 50 kOe used in the FC and ZFC measurements of Fig. 7 and the discussion that followed. This is exactly the same applied field value, deemed necessary to saturate the canted ferromagnetic moments of Fe³⁺, by Ahmadvand et al.⁴⁹ in investigating the exchange bias effect in the pristine LaFeO₃. This is why it was easy to exclude the contribution of the Fe³⁺ moments in the above calculations of molar susceptibility. This spin canting arises from the disturbing effect of the crystalline field on the much stronger exchange field, as evidenced by hysteresis loops. Fitting the thermal-dependent magnetization at high field (1.5 kOe ≤ H ≤ 50 kOe) and low temperatures with the Curie–Weiss law, the saturation magnetization almost exclusively represents the rare earth moment, as found in⁵².

To gain insight into the static features of the magnetic behavior in the three samples, temperature-dependent DC magnetization was performed under an applied field of 100 Oe, as shown in Fig. S1. One notices two distinct glassy states to emerge at ~ 93 K and ~ 90 K for the LaFeO₃ nanoparticles, that shift slightly to ~ 92 K and ~ 84 K for both the Eu³⁺ doped and Eu³⁺/Cr³⁺ co-doped variants. This behavior may be linked to the magnetic anisotropy associated with the formation of short-range ordered ferromagnetic clusters and/or a strain-related spin reorientation process for the surface Fe³⁺ cations⁵³.

The ZFC hysteresis loops of the LaFeO₃, La_0.70Eu_0.30FeO₃ and La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles were measured at 300 K, 200 K, 100 K and 4 K under an applied field (H) varying between − 9 T and 9 T. Only the loops measured at 300 K and 4 K are shown in Fig. 10. Generally, the loops exhibit a superposition of a dominant contribution ascribed to the AFM core and an FM contribution stemming from both the uncompensated spin-glass shell and canted AFM spins at the core^{2,11,13,16,19}. The values inferred from Fig. 10 for some of the magnetic parameters are listed in Table 4². The fact that a field as high as 9 T is not sufficient to saturate M at all temperatures indicates the dominant AFM behavior of the cores. Moreover, the hysteresis loops of the Eu-containing nanoparticles at 4 K, as compared to the pristine sample, exhibit a linear non-compensated paramagnetic contribution as well as a weak ferromagnetic behavior, as shown in the inset of Fig. 10b. The paramagnetic behavior is obviously due to the Curie Weiss-like behavior that was attributed to the surface Eu²⁺ ions at low temperatures in the preceding section. The small remnant magnetization (FM contribution) is due to the canted tendency of the FeO₆ octahedra, which affects the superexchange of neighboring Fe t_2g electrons through Dzyaloshinskii–Moriya (DM) interactions^19,50. The values of the instantaneous magnetization in the different M-H isotherms follow similar trends to those obtained for the FC magnetization of the nanoparticles (Fig. 8), such that La_0.70Eu_0.30FeO₃ has the highest M values and LaFeO₃ has the lowest magnetoelectric coupling in these multiferroic nanoparticles, which reduces the effective magnetic anisotropy⁵⁴.

Table 4 The maximum magnetization (M_max), coercivity (H_c), and exchange bias (EB) of the mechano-synthesized LaFeO₃, La_0.70Eu_0.30FeO₃ and La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles at 300 K, 200 K, 100 K and 4 K. Estimated errors are given in parentheses.

While the values of M_max for the doped nanoparticles decreased with increasing temperature, as expected (Fig. 11a), for the LaFeO₃ nanoparticles, M_max was almost constant in all hysteresis isotherms. This is explicable in terms of the weakening of the exchange coupling of the spins at the AFM/FM core/shell interface, as suggested above, to enhance the ZFC magnetization of the same nanoparticles with temperature. Consequently, under the same maximum applied field (9 T), M_max was expected to be constant. The values derived from Fig. 10 for the coercivity H_c (= (H_c1 − H_c2)/2), where H_c1 and H_c2 are the coercive fields to the right and left of H = 0 values, are given in Table 4. Clearly, the doped samples had smaller H_c values relative to the LaFeO₃ nanoparticles. This may be partly explained in terms of the Stoner-Wohlfarth model, which relates the reduction in H_c to a corresponding reduction in magnetocrystalline anisotropy⁵⁵. The smaller average particle sizes of the doped nanoparticles relative to those of the LaFeO₃ ones enhance the influence of the uncompensated surface spins that become susceptible to easy flipping by the applied field, thereby reducing H_c. It is interesting to note from the temperature dependence of H_c in Fig. 11b that, rather than becoming magnetically harder with decreasing temperature, the mechano-synthesized LaFeO₃ and La_0.70Eu_0.30FeO₃ nanoparticles softened as the temperature decreased from 200 to 4 K. For the La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles, this range extends to 300–4 K. Such an unusual thermal dependence of H_c has been reported before for sol–gel prepared LaFeO₃ nanoparticles, where the coercivity was found to decrease by ca. 15% upon cooling from 220 to 5 K⁴⁹. In the present case, H_c for the LaFeO₃ and La_0.70Eu_0.30FeO₃ has been significantly reduced by ca. 70% and 90%, respectively, between 200 and 4 K. For the La_0.70Eu_0.30Fe_0.95Cr_0.05O₃, it has dropped by ~ 95% as the temperature was changed from 300 to 4 K. This anomalous magnetic softening may be attributed to the competition between the magnetic anisotropy and magnetoelectric coupling in these multiferroic nanoparticles, which reduces the effective magnetic anisotropy⁵⁶.

Figure 11

The thermal variation of (a) the maximum magnetization (M_max), (b) coercivity (H_c) and (c) exchange bias field (EB) for the LaFeO₃, La_0.70Eu_0.30FeO₃ and La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles. The symbols in all figures are as shown in the legend of (c).

The negative H_c shifts in the M-H loops for all the samples (Fig. 10) imply the presence of an exchange bias (EB) anisotropy. This is further evidence that the nanoparticles are composed of AFM cores and FM-like shells because EB is known to develop owing to the competition between the exchange and Zeeman energies at the interface of both magnetic structures⁴⁹. The values of the EB fields, EB (= (H_c1 + H_c2)/2), for the different nanoparticles are listed in Table 4, and their thermal variation is depicted in Fig. 11c. It can be observed that the EB fields increased, reaching a maximum value at 100 K, and then decreased with increasing temperature. The temperature dependence of the EB fields can be related to the thermal activation of the spin reversal in the AFM cores of the particles, which plays a significant role in inducing EB anisotropy in the FM/AFM interfaces of the nanoparticles^13,52. Initially, the applied field induced a preferred spin alignment in some nanoparticles. When the field direction is reversed, the spins in some nanoparticles, particularly those with large volumes, may not gain sufficient thermal energy to reverse direction. Consequently, the core spins of these nanoparticles did not contribute to the hysteresis loop during the entire cycle, thereby inducing spontaneous EB anisotropy¹³. This may explain why the LaFeO₃ nanoparticles, which had the largest particle size and size distribution, as shown in Fig. 2, had the highest EB fields relative to the doped nanoparticles. Throughout the temperature range investigated, the lowest EB values were recorded for La_0.70Eu_0.30FeO₃ nanoparticles. As the EB field values in Fig. 11c reflect the strength of the exchange magnetic coupling, it is evident that doping with Eu³⁺ ions weakens the coupling in the AFM cores. The sharp suppression of EB in the doped nanoparticles at 4 K may demonstrate the robust low-temperature impact of the relatively small amount of surface Eu²⁺ ions, as indicated by the susceptibility analysis above. The slight increase in the EB field values for the La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles relative to those of La_0.70Eu_0.30FeO₃ may be attributed to the distribution of the dopant Cr³⁺ ions in the La_0.70Eu_0.30FeO₃ ionic matrix, where the formation of the Cr³⁺–O²⁻–Cr³⁺ AFM superexchange interaction is more favorable¹³ than that of Fe³⁺–O²⁻–Cr³⁺. This in turn strengthens the overall exchange coupling within the AFM cores. As a final comment in this section, we note that the present mechano-synthesized LaFeO₃ nanoparticles show higher EB fields than those of similar sizes prepared using other synthesis routes. For example, at 300 K, the EB value was ~ 217 Oe relative to 139 Oe for LaFeO₃ nanoparticles prepared via the sol–gel route⁵⁷ and ~ 8.523 kOe (4 K) relative to 1.205 kOe (5 K)⁴⁹. Apparently, this is related to the complex surface composition induced by the mechano-synthesis route, as discussed in section “Surface composition: XPS spectral analysis”, which has no counterpart in the case of LaFeO₃ nanoparticles prepared using other techniques.

Conclusion

Single-phase perovskite-related LaFeO₃, La_0.70Eu_0.30FeO₃ and La_0.70Eu_0.3Fe_0.95Cr_0.05O₃ nanoparticles (20–50 nm) were mechano-synthesized at 600 °C (10 h) for the pure and 700 °C (10 h) for the two variants. These temperatures are substantially lower by ~ 600–700 °C than those at which the corresponding bulk materials are traditionally synthesized using solid-state methods. Upon Eu³⁺ doping and Eu³⁺/Cr³⁺ co-doping, the perovskite-related orthorhombic LaFeO₃ structure undergoes a transition from the usual O′-type distorted orthorhombic structure of orthoferrites to the O-type structure. Eu³⁺ ions preferentially occupy the A-sites in the crystal structure of LaFeO₃, whereas Cr³⁺ ions are randomly distributed over the octahedral B-sites, and the bond angles and lengths are sensitive to doping and co-doping. Both ⁵⁷Fe Mӧssbauer and magnetic measurements suggested that the nanoparticles were composed of dominant canted AFM cores and FM shells because of uncompensated surface spins, and no superparamagnetism was observed. The increase in ZFC magnetization of the LaFeO₃ nanoparticles at relatively low temperatures is attributed to the resistance of the core spins; hence, the local spin order that develops at the interface between the canted AFM cores and FM shells is to be aligned by the applied magnetic field. The magnetization of the nanoparticles was sensitive to the presence of Eu³⁺ and Cr³⁺ ions. The La_0.70Eu_0.30FeO₃ and La_0.70Eu_0.30Fe_0.95Cr_0.05O₃ nanoparticles were found to display Eu³⁺ van-Vleck-type paramagnetic molar susceptibility with a spin–orbit coupling constant of 363 cm⁻¹ in the ~ 20–300 K range and a Curie–Weiss like behavior below 20 K due to the minority of the surface Eu²⁺ ions. The θ_W and μ_eff values obtained at low temperatures for the Eu-doped nanoparticles suggest a weak AFM interaction between the Eu²⁺ ions and the Eu²⁺/Eu³⁺ valence state fluctuations, hence the absence of localized Eu magnetic moments. All nanoparticles exhibited anomalous magnetic softening with decreasing temperature, which is referred to as the competition between magnetic anisotropy and magnetoelectric coupling. The nanoparticles reveal temperature-dependent dopant-sensitive exchange bias fields that manifest their AFM/FM core–shell nature, reflecting the thermal activation of the spin reversal at their cores.