Multifunctional behaviour in B-site disordered double perovskite EuPrCoMnO₆

The double perovskite structures have been derived out of simple perovskite structure of general formula ABO₃ (ideally cubic structure with space group Pm-3m), where exactly half of B site cations is replaced by another B' cation, and a rock salt ordering between these two is achieved [27]. The parent perovskite system ABO₃ is much interesting and a slight structural variation via different doping may lead significant effect on the various physical properties as all the physical and chemical properties are based on the crystal structure of materials. The magnetic properties of the double perovskites are much affected by the way of distribution of B-sites atoms. For example, in R₂CoMnO₆ double perovskites, Co²⁺–O^2-–Mn⁴⁺ interaction cause antiferromagnetic ordering whereas Co²⁺–O^2-–Co²⁺ and Mn⁴⁺–O^2-–Mn⁴⁺ interaction causes antiferromagnetic ordering. The substitution of B' for B, where B and B' have different charges/or sizes gives solid solution AB_1−x B'_x O₃. The substitution of B' for B, where B and B' have different charges/or sizes gives solid solution AB_1−x B'_x O₃. For the case, x = 0.5 the ordering of B-site cations may occur and it can be modified as A₂BB'O₆ double perovskite structure [27]. Thus, the main difference between the single and double perovskite is that half of B site cations of perovskite are replaced by another B' cation giving rise to double perovskite. The different elemental substitutions on the A and B-sites have been carried out to optimize their technological applications. Such substation of B' on B site may change the lattice structure depending on the ionic radii of B' and B cations. There are different arrangements of B-site cations like random, rock salt, and layered. A detailed survey on the arrangements of B-site cations can be found in the report of Anderson et al [27]. Earlier, much theoretical and computational effort has been carried out to approximate the possible structures of DPs [28]. They checked many DPs and found different structures like cubic, hexagonal, monoclinic, orthorhombic, tetragonal, trigonal, etc which are compatible with different DPs. We can assess the structural stability of the DP (AA')BB'O₆ using Goldschmidt tolerance factor (t), given by [29],

$$\begin{align}t = \frac{{\dfrac{{{r_{\text{A}}} + {r_{{\text{A}^{\prime}}}}}}{2} + {r_{\text{O}}}}}{{\sqrt 2 \left( {\dfrac{{{r_{\text{B}}} + {r_{{\text{B}^{\prime}}}}}}{2} + {r_{\text{O}}}} \right)}} = 0.822\end{align} \tag{ 1 }$$

where r stand for ionic radii and subscripts denotes corresponding elements. Ideally, case t = 1 corresponds to a perfect cubic geometry and the deviation of t from 1 causes a structural transition from the ideal cube to some lower symmetric phase. The larger difference in ionic radii of A (r_A – r_A') and B (r_B – r_B') elements cause lower values of tolerance factor and hence larger octahedral distortion. Moreover, the ordering of the B-site cations matter much in determining the exact space symmetry of double perovskites. In the perfect ordered state, B and B' cations are distributed regularly at their sites. However, according to Valasa et al, disordering among cations take place due to two reasons [30]: (a) ASD, which arises by means of interchange of B and B'-site cations and (b) anti-phase boundary, where at the boundaries of two ordered domains, the B/B'-sites occupancies are reversed. It has been observed that smaller difference in oxidation state (ΔZ_B) of B and B' favours disordered stacking as in this case both cations have similar chemical activity and will try to occupy both sites interchangeably [28]. This statement can also be understood with the help of thermodynamic law according to which for similar B and B' cations, the system will try to maximize its entropy and thus become disordered. While for the large (ΔZ_B) values, highly charged cations favour less charged cations at their neighbouring site to reduce Coulomb energy, thus leading to an ordered state [30, 31]. Other than this, the smaller difference in ionic radii (Δr_B) of B/B' atoms favours the disordered structure of double perovskites and larger Δr_B favours ordered structure assisted by induced strain [31, 32]. It has been concluded that a system with, ΔZ_B = 4 and Δr_B ⩾ 0.1 Å favours an ordered state whereas ΔZ_B = 0 and Δr_B ⩽ 0.1 Å favours a disordered.

Trusting the above-mentioned trends, we realized that our system EPCMO (t ∼ 0.82, ΔZ_B ∼ 2 and Δr_B = 0.215 Å) may have an ordered arrangement [33]. However, in some DPs (like Co/Mn-based DP) with ΔZ_B = 2, it has been found that ordered and disordered phases coexist due to Coulombic and thermodynamic competitions. Another problem with Co–Mn DPs is the existence of mixed valency (Co²⁺/Co³⁺ and Mn³⁺/Mn⁴⁺) due to similar redox potentials of Co²⁺−Mn⁴⁺ and Co³⁺−Mn³⁺ couples as it leads to random distributions of cations [34]. Moreover, the structural ordering present in the system depends on synthesis conditions [34, 35]. Thus, the EPCMO could exhibit both ordered and disordered arrangements and it is difficult to reveal exact atomic ordering at B-site when the cations have similar mean scattering factors. For case, if a double perovskite has been fitted to an orthorhombic phase (with space group Pnma), then the B-site cations are randomly distributed on their crystallographic sites. In this case, there is a 50% possibility of finding B/B' cation at each B-site (sometimes they are also treated as single perovskite). Thus, the systems are denoted as B-site disordered double perovskite in this case. However, if B and B' atoms are distributed in a perfectly ordered manner (for example monoclinic phase with space group P21/n) then the system is known as doubly ordered perovskite or simply double perovskites. The XRD pattern of the double perovskite may be similar to perovskite materials due to the similar scattering factor of B and B' cations. The XRD pattern of EPCMO is shown in figure 1. This XRD pattern of powdered EPCMO was best refined in a disordered orthorhombic phase with space group Pnma [36]. Thus, EPCMO can be considered as a B-site disordered double perovskite. The inset of figure 1 consists of a 3D structure of EPCMO showing the distribution of atoms over its site, visualized using VESTA [37]. The crystallographic data of EPCMO have been tabularized in table 1.

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Figure 2(a) shows the temperature-dependent ZFC and FC induced magnetization (M) of EPCMO at 100 Oe field. Magnetization varies very slowly down to 160 K. However below 160 K, M(T) increases and shows two successive magnetic transitions in the vicinity of T_C1 ∼ 146 K and T_C2 ∼ 138 K as the dM/dT curve exhibits inflection at these transition temperatures (as shown in the inset of figure 2(a)). It is well known that the magnetic properties of DPs are strongly influenced by the ASD and the mixed-valence states of Co and Mn elements owing to the change of B–O–B' exchange interaction [13, 34]. Similar to EPCMO, many researchers have already observed two successive magnetic transitions, where the first magnetic transition was attributed to the FM ordering of Co²⁺–O^2-–Mn⁴⁺ super-exchange interactions whereas the second FM transition emerges owing to the introduction of Co³⁺–O^2-–Mn³⁺ interaction [13, 34]. Moreover, J Krishna Murthy et al reported that the 2nd magnetic transition arises owing to Co³⁺–O^2-–Mn⁴⁺ super-exchange interactions [38]. To probe the same, we have carried out x-ray photoemission (XPS) measurements of Co2p and Mn2p core levels (figure 3). From, the XPS spectra it has been observed that there are ∼61% Co²⁺ states, ∼39% Co³⁺ states, 26% Mn³⁺ states and 74% Mn⁴⁺ states respectively. Therefore, as mentioned earlier, it can be understood that the magnetic transition around ∼146 K in EPCMO is attributed to the FM ordering of Co²⁺–O^2-–Mn⁴⁺ super-exchange interactions while second transition ∼138 K arises either due to the Co³⁺–O^2-–Mn⁴⁺ super-exchange FM interactions or related to the presence of few of Co³⁺ and Mn³⁺ in the disordered phase along with the dominant FM interactions arising from the ordering of Co²⁺ and Mn⁴⁺ ions [13, 34, 38, 39]. FM transition temperature of EPCMO is in good agreement as it is higher than the parent system ECMO [26] and is less than that of PCMO [39], as the size of Pr³⁺ ion is higher than Eu³⁺ ion. The transition temperature of A₂CoMnO₆, increases linearly for different A (rare-earth ion) from 48 K for Lu₂CoMnO₆ to 204 K for La₂CoMnO₆, as their ionic size increases from Lu to La [40]. It is important to mention here that, even in an ordered system, few of the Co/Mn exchanges their crystallographic positions, thus leading to ASD. ASD activates supplementary AFM ordering through Co²⁺–O^2-–Co²⁺ and Mn⁴⁺–O^2-–Mn⁴⁺ super-exchange interactions [26, 39]. The decreasing nature of M in ZFC curves below ∼133 K (T_a) has been attributed to the multifarious relationship of magnetic interaction between rare earth and transition metal sub-lattices [7, 10]. The cusp temperature T_a is a point where local magnetic anisotropy energy and the external magneto-static energy acquire balanced. The huge bifurcation between ZFC and FC curves indicates a strong spin frustration/spin-glass state due to the presence of different competing spin correlations [26, 41].

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Moreover, in the vicinity of magnetic transition, the microscopic nature of magnetization is described by the universal scaling hypothesis, where M_S (spontaneous magnetization), ${\chi _0}$ (initial susceptibility), and magnetization at T_C(M(H)), diverges as [10, 25],

$$\begin{equation}{M_\text{S}}\left( {0,\,t} \right)\,\sim \,{\left( { - t} \right)^\beta },\,t < 0\end{equation} \tag{ 2 }$$

$$\begin{equation}\chi _0^{ - 1}\left( {0,\,t} \right)\,\sim \,{\left( t \right)^\gamma },\,t > 0\end{equation} \tag{ 3 }$$

$$\begin{equation}M\left( {H,0} \right) \sim {\left( H \right)^{1/\delta }},t = 0\end{equation} \tag{ 4 }$$

where $t = \left( {T - {T_{\text{C}}}} \right)/{T_{\text{C}}}$, and the exponents δ, γ and β are related with each other via the Widom scaling relation, given by:

$$\begin{equation}\delta = 1 + \gamma /\beta .\end{equation} \tag{ 5 }$$

To examine the critical exponents (β, γ, δ) associated with long-range magnetic transition, we have measured closely spaced isothermal magnetization around T_C (figure 4(a)). The above-described power-law fitting to M_S and $\chi _0^{ - 1}$ for ETCMO gives the value of β = 0.60 ± 0.07 and γ = 1.19 ± 0.03 for EPCMO. Using Widom scaling relation, the value of δ is calculated to be 2.98. The value of δ is 3.0 for Mean Field Model, 4.8 for 3D Heisenberg Model, 4.82 for 3D Ising Model, and 5 for the Tricritical mean-field model [25]. Thus, the estimated value of the critical parameters for EPCMO follows the conventional mean-field scaling hypothesis [25, 42, 43]. The critical behavior study in other related DPs shows that the critical exponents are close to other conventional scaling hypotheses like 3D Ising model and 3D Heisenberg model [44, 45].

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Further, the evolution of the ZFC/FC magnetization at the different higher applied magnetic fields has been shown in figure 2(b). The magnetic transition temperature T_C1 of EPCMO moves toward a higher temperature at a high magnetic field similar to parent ECMO [26]. This characteristic is attributed to increased spin-ordering of FM materials at a higher temperature under the influence of a high external magnetic field [26, 46]. The magnitude of bifurcation between the ZFC/FC curves initially increases on increasing applied field strength up to 10 kOe and then decreases at higher fields. The bifurcation between ZFC and FC M(T) curves is usual in most of the FM materials, which originates due to magnetic anisotropy. Thus, the bifurcation should appear at a lower temperature in a higher magnetic field, which has been observed in EPCMO (figure 2(b)) and ECMO [26] as well, due to the suppression of the magnetic anisotropy in the high field [46]. Additionally, the observed cusp in the ZFC-magnetization curve around T_a has suppressed on the increasing field, which is a typical signature of the existence of some AFM phases or anti-phase regions in the system [26, 41]. Other than this, a third magnetic transition has been observed in EPCMO at a high field below 40 K (T_C3). This magnetic anomaly has been better described with the help of the AC susceptibility spectrum, which is discussed later on.

From the figure 5, it has been observed that the inverse DC susceptibility (χ⁻¹) curve of EPCMO shows linear behavior above 168 K; confirming a pure paramagnetic state. This data could be fitted with the Curie–Weiss (CW) law given by equation ${{\chi }} = C/\left( {T - {T_{{\text{CW}}}}} \right)$. This fitting (for T > 200 K) gives CW temperature (T_CW) around +118.6 K, again supporting a leading ferromagnetic phase [26]. The large difference between T_C1 and T_CW, which cannot be assigned to quantum fluctuations rather occurs owing to frustration through FM and AFM competition within the system. Further, it has been observed that the χ⁻¹(T) shows a downturn deviation from the CW line just below ∼168 K (T_GP) similar to PCMO [13]. Generally, rare-earth elements develop multiple magnetic interactions in the system, thus causing inhomogeneous magnetic ground states, in the form of clustered or phase-separated states [8, 10]. One form of these clustered phases is well known as the 'Griffiths like' phase. The GP was originally proposed for randomly diluted Ising ferromagnets, where a few fractions of the crystallographic sites can be occupied with spins and rest sites are either vacant or occupied by some nonmagnetic elements [47]. The GP arises below a characteristic temperature, known as Griffith's temperature (T_GP) and in the region T_C1 < T < T_GP where the system exhibits an unusual magnetic state due to the formation of short-range FM clusters of different sizes in the paramagnetic region [10, 13, 26]. Thus, the downturn behaviour of χ⁻¹(T) of EPCMO might be due to the emergence of the GP or some other FM clustered phase. The observed downturn significantly was suppressed at the higher applied field, suggesting the observed clustered phase is GP. In the GP phase region, χ⁻¹(T) follows the power-law given by [10, 41],

$$\begin{equation}{\chi ^{ - 1}}\left( T \right) = A{\left[ {\frac{{T - T\,_{\text{C}}^{\text{R}}}}{{T\,_{\text{C}}^{\text{R}}}}} \right]^{1 - \lambda }}\end{equation} \tag{ 6 }$$

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where A is the constant $T\,_{\text{C}}^{\text{R}}$ is the reduced random critical temperature of randomly distributed FM cluster and λ is the DC magnetic susceptibility exponent which should lie within 0 and 1 for $T\,_{\text{C}}^{\text{R}}$ < T < T_GP [41]. The value of $T\,_{\text{C}}^{\text{R}}$ should be chosen in such a way so that equation (1) yields value of λ close to zero in the PM region for T > T_GP [48]. Thus, the value of $T\,_{\text{C}}^{\text{R}}$ will be almost equal to CW-temperature which was determined using CW equation fitting in high temperature PM region. From the slope of the line fitted in the GP region (as shown in the inset of figure 5), the value of λ for EPCMO was found to be around 0.88.

The isothermal magnetization of EPCMO has been collected at 5 K and 300 K, which is presented in figure 6. From the figure, we can see that the EPCMO has strong FM type hysteresis at 5 K, which did not reach complete saturation even up to 70 kOe applied magnetic field. At 300 K, M(H) curve is completely linear over the whole cycle with almost negligible hysteresis, thus the system is a pure paramagnet at room temperature. Interestingly, we also observe clear steps in the isothermal magnetization curve (i.e. MMT) at 5 K in the third quadrant (around −5 kOe and −10 kOe) and a mirror image was observed in the fourth quadrant (around 5 kOe and 10 kOe), which has been demonstrated in the inset of figure 6. Jumps in magnetization occur only while forward field sweep direction i.e. for 0 to −70 kOe and are absent in decreasing field from −70 to 0 kOe owing to slow spin relaxation and again re-appear in subsequent forward field direction i.e. for 0–70 kOe; followed by large hysteresis. However, unlike ECMO [26], EPCMO has a larger step size (ΔM) at the high field side (∼10 kOe) than the step size at the low field side (∼5 kOe). Thus, observed MMT in EPCMO are purely field-induced due to transition to a FM state from uncompensated AFM states [49]. In Ca₃CoMnO₆, it has been investigated that the spin flop transition from E*-type magnetic structure (↑↑↓↓) to the ↑↑↑↓ Mn⁴⁺ (high spin S = 3/2) at the first jump and to ↑↑↑↑ with Co²⁺ (low spin S = 1/2) spin flop at second jump is the possible reason behind sharp step [50]. However, for EPCMO, step size (ΔM) is much smaller, thus, the possibility of field-induced spin flop behind the origin of MMT can be ruled out. Additionally, a close view of the M(H) curve shows that the loop is asymmetric around the origin, indicative of the presence of spontaneous EB [39, 51], as M(H) loop was recorded in ZFC mode, in EPCMO at low temperature. The magnitude of EB field is given as, H_EB = (H_C1 + H_C2)/2 [51], where H_C1 and H_C2 are the magnitudes of magnetic fields at which magnetization becomes zero, which is found to be around 1.17 kOe for EPCMO. The EB mainly appears due to interacting interfaces between FM–AFM magnetic states [39, 51].

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The bifurcation in ZFC and FC curves is attributed to the existence of superparamagnetic (SPM) state or spin-glass (SG) or cluster-spin-glass (CSG). This is generally observed only in those systems of spin clusters where the FC-magnetization curve displays a cusp around T_a [52]. The branching in ZFC-FC M(T) starts ∼133 K at a low field (100 Oe) showing the existence of high-temperature spin ordering in EPCMO. To explore such dynamics of spin, we have carried out AC susceptibility measurements elaborately. Both, the real part (χ') and the imaginary part (χ'') of AC susceptibility for EPCMO shows clear frequency-independent peaks near the first magnetic transition T_C1, which is attributed to the commencement of long-rang magnetic ordering (inset of figures 7(a) and (b)). However, near T_C2, AC susceptibility shows strong peaks and these peaks show minor shifts towards higher temperature at higher frequencies. Such behaviour in the magnetic systems having miscellaneous interactions is categorized by arbitrary and cooperative freezing of spins around a defined temperature i.e. the glass temperature (T_g). Beneath T_g, the system enters a region where spin gets frozen with an irregular long-range magnetic ordered state, which is eventually a SG state [53]. As already mentioned, the most important component of spin glass is the presence of different competing exchange interactions and ASD. The calculated value of the parameter p ∼ 0.002, where p is defined in terms of peak temperature T_f at frequency f as [39],

$$\begin{equation}p = \frac{{\Delta {T_{\text{f}}}}}{{{T_{\text{f}}}\Delta {\text{lo}}{{\text{g}}_{10}}\left( \,f \, \right)}}\end{equation} \tag{ 7 }$$

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where p has values between 0.005 and 0.08 for SG or CSG, while for SPM, it should be greater than 0.2 [39]. A rather small value of p for our system might be due to weak freezing of spins and the observed peaks are associated with long rang magnetic transition around T_C2, as peak shifting is much smaller. It can be mentioned here that the higher temperature spin ordering is disturbed by thermal fluctuations, i.e. the spins are effectively independent of each other [53]. However, at lower temperature, the spins start communications and form locally frozen units/clusters/droplets/domains. In EPCMO, another broad peak in χ''(T) curves at lower temperatures below 40 K has been observed (figure 8(a)). It is the temperature (T_C3) where higher field ZFC-M curves show third anomalous magnetic transition. These peaks show a significant shift towards higher temperatures at a higher frequency. For these peaks, the value of the p was found to be around 0.02. Thus, suggesting a re-entrant glassy state in the system [6, 54]. Moreover, under the application of the DC magnetic field (∼1000 Oe) these peaks grow up (figure 8(b)). Interestingly, the anomaly in DC-magnetization also was observed at higher fields (figure 2(b)). Moreover, as already been described ferromagnetic characteristics exist at lower temperatures. So the emergence of a glassy state must be correlated to the FM state. Thus, it can be said that there are clusters of spins in a glassy state, forming due to short-range FM ordering within the cluster. FM cluster-glass phase has also been seen in other systems [55, 56].

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