1. Introduction
Multifunctional materials, especially with magnetoelectric and multiferroic properties, have attracted great attention in the past decade because of their potential multipurpose applications [
1,
2]. Rare-earth orthoferrites (
RFeO
3) and orthochromites (
RCrO
3), the latter in particular, have been reported to exhibit multiferroic properties due to the local structural inhomogeneity or exchange striction between the rare-earth element and the transition metal ion. In fact, almost a decade ago, Sahu et al. found that rare-earth orthochromites with the formula
RCrO
3 (
R = Ho, Er, Yb, Lu, or Y) exhibit rich and varying physical properties, including octahedral distortions, relaxor-like behaviour, spin-phonon coupling, ferroelectric and multiferroic properties [
3,
4,
5,
6]. The presence of two magnetic ions and rare-earth magnetic ions’ ability to control the orientation of transition metals’ magnetic moments originates complex magnetic phases that reflect on their magnetic, optical, and elastic properties. Their complex magnetic structures give rise to interesting magnetic phenomena, such as spin reorientation, a large magnetocaloric effect, and temperature-induced magnetisation reversal.
These materials crystallise in an orthorhombically distorted perovskite-like structure with four distorted perovskite units in the crystallographic cell (space group
Pbnm)—which forbids ferroeletric ordering, where the strong exchange interaction within the transition metal 3
d, Cr
3+-Cr
3+ subsystems is predominantly antiferromagnetic (G type-AFM) and usually orders at higher temperatures (several hundreds of Kelvin) than that of rare-earth 4
f, R
3+-R
3+ subsystems—but are also less anisotropic compared to the rare-earth ions. Two other types of anti-ferromagnetic (AFM) exchange couplings can be found in these systems, Cr
3+-R
3+ and R
3+-R
3+, which account for the numerous fascinating magnetic phenomena present below the Néel temperature. In fact, the coupling plays a decisive role in determining the different magnetic phases in orthochromites due to spin reorientation transitions, wherein the weak ferromagnetic component becomes parallel to the direction of the applied magnetic field. These several important differences make orthochromites, such as erbium orthochromite ErCrO
3, more suitable for the study of phase transitions (magnetic, electric or structural) depending on external stimuli—e.g., temperature, pressure, and applied magnetic fields [
7,
8,
9]. In reality, only a few papers have reported some of its properties. As far as ErCrO
3 is concerned, it presents a magnetic transition in the 113–140 K range and initially was believed to be multiferroic with a claimed ferroelectric (FE) transition in the 472–516 K temperature range, following the condensation of an octahedral tilting mode, which could have a geometric, electronic, and/or magnetic origin [
10]. More recently, the works from Meher et al. and Zhu et al. state that a net electric polarisation is observed in ErCrO
3 but only below
. Furthermore, they show that the paramagnetic nature of the paramagnetic rare-earth site is not necessary to the appearance of ferroelectricity in this system, as was initially believed [
11,
12].
Clearly, there is a need for further investigations to fully understand the multiferroic and magnetoelectric properties of many chromites. In particular, the origin (or even existence) of the ferroelectric order in these perovskite oxides continues to be shrouded with debate; among such papers is ErCrO3. Given the ErCrO3 complex’s nature, where several kinds of order parameters coexist and therefore, are likely to offer new kinds of functionalities, it is worthwhile to study at a local scale the structural, magnetic, and electric properties in order to better grasp the origins of these properties. In this work, we present the results of structural DC magnetisation measurements and perturbed angular correlation for polycrystalline ErCrO3.
2. Materials and Methods
Polycrystalline samples of ErCrO
3 were prepared by solid-state reaction of mixed stoichiometric quantities of Er
2O
3 (99.99%, Sigma-Aldrich, Burlington, MA, USA) and Cr
2O
3 (99.9%, Sigma-Aldrich). The mixture was pressed into pellet form, followed by a 15 h heat treatment at 1073 K. Two more grinding and consecutive heating steps were performed at 1573 K (48 h). Phase purity was confirmed by Rietveld refinement of the X-ray powder diffraction data collected with a Panalytical X’Pert Pro diffractometer and analysed with the Fullprof software package [
13,
14]. The magnetic properties were probed by performing isofield magnetisation curves with a commercial (MPMS Quantum Design) Superconducting Quantum Interference Device (SQUID) magnetometer. See previous work by the authors in reference [
14] for further details.
Then, γ − γ perturbed angular correlation (PAC) spectroscopy [
15] was applied to study, at the atomic scale, the structural, electrical, and magnetic properties of this compound. To perform γ − γ perturbed angular correlation (PAC) spectroscopy [
15], individual ~0.5 mm
3 samples from the same batch of material were first implanted with
111mCd ions (
111mCd →
111Cd,
t½ = 48 min) with a small dose of 10
11 atoms/cm
2 (dose lower than 1 ppm of the Er/Cr concentration) with 30 keV energy at the ISOLDE-CERN facility (Geneva, Switzerland). Complementary measurements with
111In ions (
111In →
111Cd,
t½ = 2.8 days) introduced into the sample by diffusion process were performed at the Faculty of Sciences of the University of Lisbon. Thermal annealing was performed on all samples, to recover from
111mCd implantation remaining point defects (for 20 minutes at 973 K) or to promote
111In diffusion (for 48 h at 1273 K), both in an air atmosphere. The crystalline quality of the sample post-implantation annealing process was later rechecked by X-ray diffraction (XRD). A study was performed as a function of temperature (723 K > T > 27 K,
111In), and from (673 K > T > 125 K,
111mCd), temperature ranges that span over the interesting magnetic phase transitions.
The short lifetime of the parent
111mCd probe requires that every temperature point is performed after a new implantation-annealing-measurement ~4 h cycling. In the case of the
111In probe, the same is not required, allowing the acquisition of multiple temperature data points with a single diffusion. Each temperature measurement took ~3 h of acquisition time using a 6—BaF
2 detector spectrometer [
16] at ISOLDE or in a 4—BaF
2 detector spectrometer at Lisbon equipped with a dedicated closed-cycle refrigerator or with a special high-temperature furnace. Both
111In and
111mCd decay to the same PAC probe nuclear excited state
111Cd, with
I = 5/2 and
Q = 0.664(7) [
17], by the emission of two consecutive γ rays. The angular correlation between the two γ rays can be perturbed by the EFG and existent magnetic hyperfine fields (
Bhf). Both the EFG and
Bhf couple to the nuclear electric quadrupole
Q and the magnetic dipole (
) moments of the intermediate nuclear state. The Hamiltonian for such static interactions, in the proper reference frame of the EFG tensor
Vij, with |
Vzz| > |
Vyy| > |
Vxx|, read:
where
ω0 = 3
eQVzz/[2
I(2
I − 1)ℏ] is the fundamental precession frequency,
I represents the nuclear spin of the probe intermediate state,
η = (
Vxx −
Vyy)/
Vzz is the EFG asymmetry parameter, and
Bhf is the magnetic hyperfine field [
15,
18,
19]. Below the antiferromagnetic transition (134 K) of ErCrO
3, in the presence of the two fields, we applied combined interaction theory to obtain the
Bhf and EFG parameters; above
TN, pure static electric quadrupole interactions were considered [
20,
21,
22].
In the case of a static electric quadrupole interaction, the time-dependent perturbation factor on the observable gamma-ray angular anisotropy of the decay cascade
Gkk(
t),
for polycrystalline samples, can be described as a sum of periodic terms, where
t is the time spent by the nucleus in the intermediate probing state. In the presence of EFG distributions, the periodic terms are attenuated, here represented by a Lorentzian attenuation function characterised by its relative width
δ:
The observable
frequencies relate to the energy splitting of the hyperfine levels created when a nuclear state interacts with the external EFG (in the case of
111Cd, the intermediate level is characterised by nuclear spin momentum of
I = 5/2). The quadrupole interaction splits this level into three (+/− degenerated) sub-levels, which is reason why there is a triplet of frequencies observed in the respective Fourier transform (FT)(
,
,
, where
) for each non-vanishing EFG distribution present in the system. The experimental
function can be described, for a static EFG interaction, by
, where
are the angular correlation coefficients of the nuclear decay cascade and
contains the perturbation terms of the angular correlation. (Further experimental details can be seen in references [
18,
23]).
3. Results and Discussion
Figure 1a presents the graphical output of the Rietveld refinement performed on the acquired XRD pattern of the ErCrO
3 sample after the final heat treatment.
All the diffraction peaks were indexed within the orthorhombic perovskite structure (single phase pattern) belonging to the space group
. The obtained values (
,
, and
) are in good agreement with those reported in the literature, evidencing the good quality of the sample [
4].
Figure 1b presents the isofield [M(T)] curve for ErCrO
3 taken from 5 to 350 K with an applied field of 0.1 kOe (in zero-field cooling—ZFC—and field cooling—FC—modes). The ErCrO
3 sample presented an expected behaviour: we observed the Cr
3+ spins ordering antiferromagnetically below
= 134 K (Cr
3+-Cr
3+-exchange interaction dominates), followed by a spin reorientation at 22 K (Γ
4 → Γ
1) (the Cr
3+-Er
3+ interaction becomes increasingly important), and finally below, [6–10] K, we observed the ordering of the second magnetic sub-lattice (
, Er
3+), where the Er
3+-Er
3+ interaction enters into consideration. One should point out that the two spin lattices present in the system can be coupled or not. In the case of a zero-field cooled mode, the Cr
3+ and Er
3+ substructures are uncoupled and experience the same external applied field, and thus contribute independently to the total magnetisation. In the FC measuring mode, when the Cr
3+ sub-lattice moments order at
, a local field will be imposed over the Er
3+ moments. Hence, the Er
3+ sub-lattice experiences a local field, which is the sum of the internal field due to the Cr
3+ sub-lattice and the external field. The resulting magnetisation depends on the relative contributions of the sub-lattices and their temperature-dependent magnetic behaviours, hence the difference between the ZFC and FC curves observed in
Figure 1b. In the inset, the temperature dependence of the reciprocal magnetic susceptibility data with a linear fit to the paramagnetic region is presented. The Curie-Weiss temperature was found to be Θ
p = −39(2) K and, also taken from the linear part of the reciprocal susceptibility, an effective paramagnetic moment of 10.4
μB was obtained [
7,
24]. The estimated effective magnetic moment is
μ = 10.23
μB for ErCrO
3 which is close to the theoretical value
μeff(ErCrO
3) = 10.35
μB the calculated from the free ion values 9.59
μB for Er
3+ and 3.87
μB for Cr
3+ (spin only values) moments added assuming their total randomness in paramagnetic phase, i.e.,
μ(ErCrO
3) =
. A weak ferromagnetic moment also arises due to the canting of the Cr
3+ atoms (for further details on the crystallographic and magnetic characterisation, see reference [
25]).
Figure 2a depicts the experimental
R(
t) anisotropy function (left) together with the Fourier transform (right) obtained in the ErCrO
3 system using the diffused
111In probe. The global fits to the
R(
t) functions are shown by the continuous pink lines (thicker ones) in the spectra. Additionally, together with the
R(
t) spectra are represented lines corresponding to the individual fractions used to perform the fits.
Figure 2b shows the same information but for the
111mCd PAC probe, but with the representation inverted: left to right and right to left (
R(
t)s and Fts).
The EFG parameters were probed as a function of temperature, T, within the 723 K > T > 27 K interval, which covers the reportedly relevant transition temperatures: ferroelectric transition, the magnetic ordering of the Cr sublattice, and the spin reorientation.
The spectrum obtained at 723 K revealed an EFG characterised by a fundamental frequency of
= 136(1) Mrad/s (
= 77(1) V/Å
2) and an asymmetry parameter
= 014(5), which are in good agreement with similar systems [
26]. A second EFG was used to improve the global fit, characterised by a higher fundamental frequency,
= 174(4) Mrad/s (
= 88(4) V/Å
2), and an asymmetry parameter
= 0.56(9).
In the literature, the works of Junqueira et al., Dogra et al., and Carbonari et al. present similar results to ours. In LaCoO
3 and La(Cr, Fe)O
3, where the
111In →
111Cd probe was introduced in the samples by a chemical process, two EFG interactions are observed and associated with two non-equivalent crystallographic sites, one associated with the rare-earth site (R) and the other to the Cr and Fe site. Rearick et al. reported that for perovskite systems with heavier R ions, the
111mCd probe primarily substitutes itself into the rare-earth sites, whereas in systems with lighter R (larger ionic radius), it can be substituted into both the B(Fe, Cr) and the rare-earth sites [
27]. Similar findings were obtained in the work of Dogra et al., were only the R site substitution was observed in LaCoO
3, whereas for LaCoO
3 and (La, Lu, Ho, Eu, Y, Yb)FeO
3, both sites were possible [
27,
28].
Sobolev et al. and Belik et al. also observed similar results—two EFGs, however, in their case. In these works, similar values of
and
were observed in systems with different rare-earth atoms [
28,
29,
30,
31]. In our results we cannot observe any EFG corresponding to probes at the Cr site. We believe that the chemical process used by those authors for introducing the
111In into the samples allows a distribution of the probes by the two lattice sites, whereas by implantation or by diffusion, this does not happen. Furthermore, results of the ab initio calculations show that we should expect a greater
Vzz value for the rare-earth site and a smaller one for the Cr site (
~4
), whereas in the case of the asymmetry parameter, a lower value (low distortion from axial symmetry) should be expected for the R site and a larger value (lack of axial symmetry) for the case of the Cr site. Additionally, we could argue that the presence of the second EFG was indicative of a partial cation inversion between Cr and In sites, as observed in some examples of indium-based 3d-transition metal perovskites [
26,
32,
33,
34], if not for the fact that the study of the dependence of the EFG parameters and probe distribution as a function of annealing temperature and time showed that the post-implantation/diffusion annealing improves with more time, higher temperatures, and slower cooling (with very slow cooling, the second EFG diminishes drastically, and in some situations even disappears). Thus, we were able to identify that the second EFG observed in this work was due to the post-implantation/diffusion annealing conditions, which is explained in detail in reference [
26] and does not have an impact on the results presented here. Thus, it will not be further discussed.
Below T = 473 K the spectra were fitted with the same EFG but with a slighter lower asymmetry parameter: . When decreasing the temperature even more, below 250 K, in order to be able to perform reasonable fits, we had to consider the scenario where the probes interact now with a magnetic hyperfine field in addition to the EFG. Accordingly, the fits were performed considering a magnetic hyperfine field (combined interactions (EFG+MHF)), even if a weak one. At 250 K, the MHF parameters associated with EFG are characterised by a Larmor frequency Mrad/s ( T) and orientated at an angle of with EFG principal component . These values increase only marginally as the temperature decreases, and at 125 K we have Mrad/s ( T) with the same . Only well below does the strength of the magnetic interaction become considerable. In this way, at the lowest temperatures measured, 27 and 75 K, the spectra fit were performed accordingly. EFG is thus characterised by a fundamental frequency of Mrad/s ( V/Å) and an asymmetry parameter of . The MHF parameters associated with EFG are characterised by a Larmor frequency of 44 Mrad/s ( T) and orientated at with EFG principal component (for both temperatures). The data below 250 K, i.e., the presence of an MHF above the magnetic order transition, are rather in line with our magnetisation measurements, as a relatively strong coercive field was observed in this sample well above the Cr3+ sub-lattice ordering temperature.
The PAC results using the 111mCd probe show similar EFGs to those using the 111In parent probe. Above T = 473 K, the spectra were fitted with the same EFG but with a higher attenuation parameter. Thus, the parameters obtained were Mrad/s ( V/Å) and an asymmetry parameter . In the region between and the reported ferroelectric transition (), the observed EFG is characterised by Mrad/s ( V/Å) and an asymmetry parameter of .
Below , the spectrum shows strong damping. The final fit solutions were obtained after carefully considering the different tested models and choosing the one that gave the best and consistent temperature dependence tendency. In the end, the adopted model was the one considering that the probes interact now with a magnetic hyperfine field in addition to the EFG. Accordingly, the fits were performed considering a magnetic hyperfine field below (combined interactions (EFG+MHF)). Therefore, at 125 K, the spectrum obtained revealed an EFG characterised by a fundamental frequency of Mrad/s ( V/Å), an asymmetry parameter , and a magnetic component Mrad/s ( T).
The magnetic hyperfine field, measured with
111In or with
111mCd, is very small. This was not unexpected because we were probing the rare-earth site above its ordering temperature. PAC on similar chromium perovskites (e.g., (Gd, Nd)CrO
3) also sustain this observation in the literature [
30]. In the cases of GdCrO
3 and NdCrO
3, both Gd
3+ and Nd
3+ ions have incomplete 4
f shells and in principle should contribute to the hyperfine magnetic field. However, in GdCrO
3 and NdCrO
3 perovskites measured with
181Ta, the observed
Bhf values are similar but much smaller than the corresponding value for LaCrO
3, where La
3+ has no 4
f-electrons [
28,
31]. The difference in values observed for these systems may be understood by considering the local magnetic moments of Cr
3+ and rare-earth ions both contributing to hyperfine fields in these compounds.
Let us consider the spin-only value for Cr3+ (3d3, μeff = 3.87 μB) for the purpose of illustration as the orbital contribution is expected to be largely quenched. In the cases of RCrO3, where Er3+ has a zero magnetic moment, only Cr3+ moments contribute to the hyperfine field. However, in the case of RCrO3 where R is Nd, Gd, Yb, Er, or Sm, the net effective moment has contributions from the rare-earth moments in addition to the Cr3+ moment, and these must be properly taken in to account. The effective moments in these compounds are, however, considerably reduced because Cr3+ moments are oriented anti-parallel to those of Er3+, resulting in lower hyperfine fields. It is therefore important to consider the relative importance of Cr3+-R interactions in addition to Cr3+-Cr3+ interactions in determining the hyperfine fields in these compounds. The Er3+-Er3+ interactions are important only at very low temperatures.
The thermal dependence of the EFGs main parameters (
Vzz and
η) obtained using
111In and
111mCd probes is depicted in
Figure 3a and
Figure 3b, respectively.
The EFG attributed to probes substituting
sites in the lattice measured with
111mCd and
111In shows a slight monotonic increase in the EFG principal component (
) when decreasing the temperature down to
. Distinct trends of experimental data on EFG(T) exist; however, the most common is the increase in
with decreasing temperature. Although no general description is available, there are several contributions to the temperature dependence of
, and their relative magnitude depends strongly on the details of the studied system. Nevertheless, a model proposed by Christiansen et al. [
35] shows that in most non-cubic materials, the temperature dependence of the EFG follows the so-called
law:
, which also fits well in this system. The obtained coefficient for the rare-earth site when fitting
is
K
and is associated with thermal lattice expansion and atomic vibrations (see solid line in
Figure 3a). However, in this temperature span, the asymmetry parameter associated with EFG
seems to present three distinct regimes, the first one above the
with
; a second between this
temperature and 293 K, where an apparent decrease in the value is present (
); and a third region where a monotonic increase is present down to the lowest measured temperature. No evident change was observed in the
trend when crossing
.
The EFG temperature evolution study on ErCrO3 showed two clear signals of local environment changes, one at the reported and the other just below 250 K. At the claimed ferroelectric phase transition, the EFG changes from a slightly distorted axial symmetry to an EFG with axial symmetry. Naturally, we cannot appoint these changes to a macroscopic crystallographic phase transition or even correlate them with a ferroelectric phase transition, but certainly they provide microscopic evidence that the local point-symmetry of the crystal might have changed. At temperatures around 250 K, we observed the development of an MHF and a change in the EFG to an axial slightly distorted one. These observations are rather in line with our magnetisation measurements, as a relative strong coercive field was observed well above the Cr sub-lattice ordering temperature.