Magnetic and Magnetocaloric Properties of SrRu_1−xFe_xO₃

Abstract

We have systematically investigated the crystalline and electronic structures, magnetic and magnetocaloric properties of polycrystalline SrRu_1−xFe_xO₃ (x = 0 and 0.1) samples fabricated by the solid-state reaction method. The X-ray diffraction analyses of the samples indicated single phase orthorhombic perovskite structure. A thorough analysis of X-ray-absorption-based electronic structure revealed that both Fe²⁺ and Fe³⁺ ions are present in x = 0.1, in which concentration of Fe³⁺ ions is higher than that of Fe²⁺ ions. More careful analyses on the isothermal magnetization data derived from the Banerjee’s criterion demonstrated that the ferromagnetic-paramagnetic phase transition in all samples belongs to the second-order phase transition type. These results were also confirmed by a recently proposed quantitative criterion, which considered an exponent n from the magnetic field and temperature dependences of the magnetic entropy change (ΔS_m). Especially, around T_C, we have found that the ΔS_m reaches the maximum values of 1.65 and 1.32 J.kg⁻¹.K⁻¹ for x = 0 and 0.1, respectively, for a field change of ΔH = 50 kOe. Magnetic-field dependences of the maximum magnetic-entropy change (ΔS_max) obey a power law of ΔS_max(H) ∝ Hⁿ, where the values of n = 0.92–0.94 are far from the mean-field-theory value (2/3), indicating short-range magnetic order existing in the samples.

Fig. 4 (a), (b) M(H) data, (c), (d) Arrott plots of M² vs. H/M, and (e), (f) −ΔS_m(T) curves at various ΔH values for SrRu_1−xFe_xO₃. Arrow lines indicate the direction of increasing H value.

1. Introduction

Currently, divalent alkaline-earth ruthenates with the general formula of ARuO₃ (A = Ca, Sr, Ba) are still sparking rigorous spotlight from the solid-state-physics community because of their peculiar electronic and magnetic properties relying upon the radius of the alkali metal ion.^1–8) For BaRuO₃, its ferromagnetic order is suppressed under pressure of 8 GPa, and fluctuations in the vicinity of the Curie temperature (T_C) increase as changing pressure.²⁾ While CaRuO₃ is a paramagnetic conductor, SrRuO₃ is a 4d ferromagnetic conductor with a Curie temperature T_C = 160 K, despite the fact that both compounds crystallize in the orthorhombic structure (Pbnm space group).³⁾ The magnetic-order difference in these compounds is ascribed to the effect of A²⁺ ion on the relative populations of the spin-up and spin-down bands and on the widths of the 4d bands of (RuO₃)²⁻.⁹⁾ The 4d bands in CaRuO₃ is narrower than those in SrRuO₃ because there are more covalent characters in the Ca–O bond than in the Sr–O bond. With a high chemical stability and rich variety of electronic and magnetic features, SrRuO₃ has been vastly explored fundamentally and practically.^{1,3,4,10–13)} Furthermore, it is previously pinpointed that at 125 kOe and 4.2 K, the magnetic moment of SrRuO₃ is about 1.55 μB/mol. The magnetization of this compound seems unsaturated even at high fields, indicating the very narrow 4d band; specifically when it is being compared to a 3d band of iron^3,9) and to a large magnetocrystalline anisotropy which was caused by a strong spin-orbit interaction.¹⁾ Ferromagnetism in SrRuO₃ is still regarded to have an obscure origin since the saturation moment is less than the magnetic moment (2 μB/mol) presumed for the localized t_2g low-spin configuration of Ru⁴⁺.^14,15) Earlier reports suggested that the ferromagnetism of SrRuO₃ is vagrant,¹⁰⁾ and also the compound itself can be viewed as a bad metal.¹⁶⁾ Moreover, SrRuO₃ thin film’s magnetic critical behavior is affiliated to the 3D Ising model, and it is in accordance with experimentally examined high uniaxial anisotropy which lingers above T_C.^11,17) The transport and magnetic properties of SrRuO₃ can be adjusted via partial substitutions at Sr and Ru sites with various cations. Interestingly, Mieville et al.¹⁸⁾ exposed that the chemical substitution on the two separate cation sites in SrRuO₃ could produce various results. The ferromagnetic behavior prevails with up to 65% substitution of Ca²⁺ for Sr²⁺ while this behavior was destroyed with 20% substitution of Ti⁴⁺ for Ru⁴⁺. Pi et al.¹⁹⁾ revealed that when Zn²⁺, Ni²⁺, Co²⁺ and Mn³⁺ were doped into the Ru site of SrRuO₃, T_C was notably decreased from 166 K down to 105 K. On the contrary, T_C was increased up to 188 K with the Cr³⁺ doping. Additionally, the resistivity of this group of oxides is altered due to the deviation of the oxygen stoichiometric ratio at the grain boundary. Biswas et al.¹⁰⁾ inspected the magnetic and electronic behaviors of SrRu_1−xIr_xO₃ (0 ≤ x ≤ 0.25) and found that all samples showed ferromagnetic order and a fully-metallic behavior, despite the increased resistivity and the decreased T_C. They concluded that the sample with x = 0.25 had gone through a metal-to-insulator transition at 75 K and a spin-glass-like behavior at 45 K along with the omission of ferromagnetic long-range ordering.

The Fe-doping effect on the transport and magnetic behaviors of SrRu_1−xFe_xO₃ was first reported by Gibb et al.²⁰⁾ For x values up to 0.2, a less significant influence on the magnetic and electronic properties was detected, despite the increasing level of oxygen deficiency. With further increasing of x up to 0.3, the structural transformation can be identified by the X-ray diffraction study. For x = 0.3, the sample is at an intermediate between a localized-electron system and a collective-electron system. The conflicting exchange mechanism in the system created intricate magnetic interactions. As x > 0.3, the decreased oxygen deficiency was generated from the oxidation of Ru⁴⁺ to Ru⁵⁺ states. Bansal et al.²¹⁾ also has thoroughly inspected the alteration in the transport and magnetic behaviors of (SrFe)_1+x(RuFe)_1+xO_3+δ by substituting Fe at both alkaline earth and transition-metal sites to reduce oxygen deficiency. They discovered that the conduction behavior had transformed from the metallic behavior (x ≤ 0.1) to the non-metallic one (x > 0.26). The minimum resistivity was observed as a function of temperature for 0.1 < x < 0.26. A transition of the ferromagnetic-to-paramagnetic state was observed as x ≥ 0.3. These results could be associated with the initial small mean free path of the system of this bad metal, and are also likely connected to the substitution of Fe³⁺ for Ru⁴⁺.

Apart from studying the magnetic and transport properties of 4d transition ferromagnets of pure and doped SrRuO₃, a very few reports on their magnetocaloric (MC) properties have also been found, with some anomalous characters. Zhang et al.¹²⁾ analyzed the MC effect of SrRuO₃ under an applied field of 65 kOe and acquired the magnetic entropy change (ΔS_m) of 2.5 J/kg K and the adiabatic temperature change (ΔT_ad) of 3.1 K at 160 K. Conversely, Sarkar et al.¹⁾ attained both normal and inverse MC effects in SrRuO₃ co-doped with Ba and Ti. They concluded that the paramagnetic-ferromagnetic transition along with the magnetization reversal are the reasons leading to this phenomenon. Furthermore, the large magnetocrystalline anisotropy, the coupling between local and itinerant moments, and the random orientation of easy axis are perceived as the key factors to inquire some of the intriguing magnetic and MC properties of this system. To gain more knowledge about this material system, in the present work, we show a systematical study on the structure, oxidation state of Fe, magnetization, and MC effect of polycrystalline SrRu_1−xFe_xO₃ (x = 0 and 0.1) compounds.

2. Experimental Details

Polycrystalline SrRu_1−xFexO₃ (x = 0 and 0.1) perovskite-type samples were prepared by the ceramic technique in air, using Sigma-Aldrich chemicals of SrCO₃, RuO₂ and Fe₂O₃ (purity: 99.9%) as starting materials. These well-mixed powders according to nominal masses of SrRu_1−xFe_xO₃ were pre-annealed at 850°C for 12 h. Following several times of intermediate grinding alongside the pre-annealing at temperatures below 1000°C, the pre-annealed samples were pressed into pellets and sintered at 1120°C for 12 h. After annealing, and cooling down to room temperature, the crystalline structure of the acquired samples was examined by an X-ray diffractometer (D8 Discover, Bruker) equipped with a Cu-K_α radiation source. The Rietveld refinement was also employed to analyze collected X-ray diffraction data. The oxidation number of Fe was analyzed by using X-ray absorption near edge structure (XANES) at the K-edge. The magnetic and MC properties were studied by means of a superconducting quantum interference device (SQUID) working in the temperature and magnetic-field ranges of T = 15–250 K and H = 0–50 kOe, respectively. Here, the samples in powder were used for magnetization measurements.

3. Results and Discussion

Figures 1(a), (b) present powder X-ray diffraction (XRD) patterns of SrRu_1−xFe_xO₃ (x = 0 and 0.1). The data analysis has revealed that both samples are single-phase and have crystalized in an orthorhombic perovskite-type structure (the space-group Pnma) with the unit-cell parameters of a ≈ c ≈ $a_{p}\sqrt{2} $ and b ≈ 2a_p (a_p is defined as the lattice parameter of a pseudo-cubic perovskite unit cell), as represented in Fig. 1(c). The refined values of the lattice parameters and unit-cell volume are a = 5.564(4) Å, b = 7.840(8) Å, c = 5.526(4) Å and V = 241.113 ų for x = 0, and a = 5.571(5) Å, b = 7.848(8) Å, c = 5.532(6) Å and V = 241.90 ų for x = 0.1. The observation of the Fe-doping induced lattice expansion of SrRuO₃ contrasts with the shrinkage of the lattice at the same Fe doping level previously reported by Fan et al.¹¹⁾ This discrepancy can be associated with different tendencies towards the occupation of the Fe ion. Indeed, Felner et al.²²⁾ observed that the Fe ions exhibit a preference to occupy in the Sr site instead of in the Ru site, resulting in the reduced lattice parameters because of the smaller size of Fe ion compared to the Sr²⁺ one. Therefore, in our case, the lattice expansion indicates the preferred occupation of Fe ions at the Ru site.

Fig. 1

XRD patterns of SrRu_1−xFe_xO₃ with (a) x = 0 and (b) x = 0.1 analyzed using the Rietveld refinement. Experimental points (red symbols) and refined curves (blue lines) are shown. Vertical blue ticks denote the diffraction reflections of the orthorhombic phase. A representation of the orthorhombic Pnma structure is graphed in (c).

Together with the XRD analysis, we have also based on the XANES spectra to identify the oxidation number of Fe in SrRu_1−xFe_xO₃ (x = 0.1). According to Teo,²³⁾ the absorption-edge position of an investigating sample in comparison with that of standard samples indicates the information about the oxidation number of an absorbing atom. Therefore, the XANES spectra of FeCl₂ and CaFeO_2.5 containing Fe²⁺ and Fe³⁺, respectively, have been recorded as the standard samples. The XANES spectra of all investigating samples shown in Fig. 2(a) indicate a rapid increase in the intensity at 7120∼7130 eV, which is associated with the Fe K-edge absorption. The middle points (E_mid) of the absorption edges are the maxima of the first derivative curves of the corresponding samples. Figure 2(b) shows that the E_mid values are about 7122.7, 7127.5 and 7128.8 eV for FeCl₂, SrRu_1−xFe_xO₃ and CaFeO_2.5, respectively. The E_mid value of SrRu_1−xFe_xO₃ occupies between the values of FeCl₂ and CaFeO_2.5, but close toward that of CaFeO_2.5. This proves that both Fe²⁺ and Fe³⁺ ions are present in SrRu_1−xFe_xO₃ (x = 0.1), and concentration of Fe³⁺ is higher than that of Fe²⁺ ions with an estimated Fe³⁺/Fe²⁺ value of 8/2. It is known that parent SrRuO₃ contains Ru⁴⁺ ions and the partial replacement of Fe³⁺ and Fe²⁺ for Ru⁴⁺ could lead to the appearance of Ru⁵⁺ due to charge disproportionation of Fe³⁺ + Ru⁴⁺ → Fe²⁺ + Ru⁵⁺. This observation is well consistent with a recent adjustment by Lei and co-workers²⁴⁾ that the combination of Fe³⁺ and Ru⁵⁺ ions is energetically favored over that of Fe⁴⁺ and Ru⁴⁺ ions. Such mixed valence state in SrRu_1−xFe_xO₃ influences magnetic and MC behaviors, as being shown below.

Fig. 2

(a) Fe K-edge XANES spectra and (b) their derivative curves of SrRu_1−xFe_xO₃ (x = 0.1) and standard samples FeCl₂ (Fe²⁺) and CaFeO_2.5 (Fe³⁺) in the energy range E = 7110∼7180 eV.

To investigate the magnetic properties of SrRu_1−xFe_xO₃, temperature dependences of zero-field-cooled (ZFC) and field-cooled (FC) magnetization, M_ZFC/_FC(T), at an applied field of 100 Oe were measured, in which the entire measurements were carried out according to the heating direction. The results are displayed in Figs. 3(a), (b). For the sample with x = 0, its M_ZFC(T) curve exhibits a sharp cusp at T = 160 K, and below 160 K, the magnetization is slowly decreased with decreasing T. This cusp could be connected to cluster spin-glass behavior at temperatures below 160 K, and the cusp peak is considered as the freezing temperature. Below this temperature, spins freeze in one of metastable states located in the system.²⁵⁾ This behavior was also observed in (Ba, Ca)_xSr_1−xFe_0.5Ru_0.5O₃,²⁵⁾ La_0.7Ca_0.3Mn_1−xSc_xO₃,²⁶⁾ and La_0.7Ca_0.3Mn_1−xZnO₃.²⁷⁾ Above 160 K, the magnetization is abruptly reduced to zero because the sample experiences a transition from the ferromagnetic (FM) to paramagnetic (PM) state. This phase transition occurs within a narrow temperature range. In contrast, for x = 0.1, in its M_ZFC(T) curve, no cusp was detected, and the M value decreases with increasing temperature, and the broadened FM-PM transition is observed. Notably, at T = 15 K, the M_ZFC(T) and M_FC(T) curves display a substantial divergence of about 10 and 7 emu/g for x = 0 and 0.1, respectively. This feature has also been found in many perovskite-type compounds, which is related to the irreversible magnetization contribution,^1,28) or to a large magnetic anisotropy induced by magnetic domains in the samples.¹¹⁾

Fig. 3

(a), (b) M_ZFC(T) and M_FC(T) curves of SrRu_1−xFe_xO₃ for H = 100 Oe; the insets in (a), (b) show the first derivative of dM_FC(T)/dT and (c) χ⁻¹(T) plots (open symbols) in the PM region; the solid lines are fitting curves to the Curie-Weiss law.

The value of T_C obtained from the maximum of the first order deviation with respect to temperature of an M_FC(T) curve (as shown in the inset of Figs. 3(a), (b)) are about 165 and 150 K for x = 0 and 0.1, respectively, indicating a decrease of T_C with increasing x. T_C of the un-doped sample is slightly higher than the T_C values reported by Fan et al.¹¹⁾ and Zhang et al.,¹²⁾ plausibly due to the discrepancies in sample preparation conditions, which could influence the oxidation number of Fe and oxygen deficiency. According to our XANES analysis, when Ru⁴⁺ in SrRuO₃ was partially replaced by Fe³⁺, some Ru⁴⁺ ions were altered into Ru⁵⁺ ions and a small amount of Fe²⁺ also appeared to balance the valence in the system. Super-exchange interactions between these ions strongly compete with the pre-existing FM coupling of Ru⁴⁺–Ru⁴⁺.¹¹⁾ Consequently, the FM-PM transition temperature has been reduced as observed.

Temperature dependences of the inverse magnetic susceptibility, χ⁻¹(T), are shown in Fig. 3(c) for all the investigated samples. The straight line in the PM part of each curve is fitted by the Curie-Weiss (CW) law of $\chi (T) = \frac{C}{T - \theta }$, where $\text{C} = \frac{N_{A}\mu_{\textit{eff}}^{2}}{3k_{B}}$ is the Curie constant, N_A is Avogadro’s constant, k_B is the Boltzmann constant, μ_eff is the effective magnetic moment, and θ is the CW temperature. The fit values obtained for $\mu_{\textit{eff}}^{\textit{exp}}$ and θ are 2.85μ_B and 164.7 K, respectively, for x = 0, and 4.29μ_B and 125 K, respectively, for x = 0.1. Additionally, the theoretically effective magnetic moment, $\mu_{\textit{eff}}^{\textit{cal}}$, of SrRu_1−xFe_xO₃ could be expressed as¹¹⁾ $\mu_{\textit{eff}}^{\textit{cal}} = \sqrt{ {(1 - 2x)\mu_{\textit{Ru}4 + }^{2} + x(0.8\mu_{\textit{Fe}3 + }^{2} + 0.2\mu_{\textit{Fe}2 + }^{2} - \mu_{\textit{Ru}5 + }^{2})}\mathstrut} $. Using the effective magnetic moments of Fe³⁺ (5.9μ_B), Fe²⁺ (4.9μ_B), Ru⁴⁺ (2.83μ_B) and Ru⁵⁺ (3.87μ_B), the calculated effective magnetic moment for x = 0 and 0.1 are 2.83μ_B and 2.86μ_B, respectively. It can be seen that T_C ≈ θ for x = 0 indicating that this sample obeys the Curie-Weiss law well. A large discrepancy between T_C and θ, $\mu_{\textit{eff}}^{\textit{exp}}$ and $\mu_{\textit{eff}}^{\textit{cal}}$ observed for x = 0.1 could be due to FM clusters in the PM region. Interestingly, for x = 0.1, there is a downturn deviation from the CW law in a temperature range from T_C to the Griffiths temperature T_G. As indicated by the arrow in Fig. 3(c), T_G is defined as the temperature that χ⁻¹(T) begins to drift from the linear behavior in the high-temperature PM state. This downturn in χ⁻¹(T) is characteristic of the Griffiths phase,²⁹⁾ and described by an expression $\chi^{ - 1} \propto (T - T_{C}^{\textit{rand}})^{1 - \lambda }$, where $T_{C}^{\textit{rand}}$ is the random transition temperature and λ is a non-universal exponent with 0 < λ < 1. Fitting the χ⁻¹(T) data above T_C to this equation, the acquired value of λ is 0.39 and $ T_{C}^{\textit{rand}}$ is about 156 K. In the temperature regime between $ T_{C}^{\textit{rand}}$ and T_G, the interaction between the FM and PM phases is dominant. This indicates that the system is not a perfect FM ordering or a complete PM behavior. Concerning the Griffiths behavior, its origin has been suggested to be from a quenched disorder owing to a structural distortion³⁰⁾ and/or arising from a mismatch of radius and valence states of doping ion to the A/Ru – site as a random dilution and/or a formation of FM clusters in the PM phase matrix.²⁹⁾ In this Fe doped sample, compared to x = 0 sample, there is a coexistence of FM and PM phase above T_C. This may be related to the interaction of Ru–O–Ru, Ru–O–Fe, and Fe–O–Fe due to complicated exchange interactions like double-exchange and super-exchange interactions. Sarkar et al.³¹⁾ also observed the Griffith phase in Sr_1−xBa_xRu_1−xTi_xO₃ as x ≥ 0.2, and assigned it to be associated with diamagnetic BaTiO₃. Meanwhile, Gupta et al.³²⁾ found the Griffith phase in SrRu_1−xTi_xO₃ as x > 0.3. They suggested a Griffith singularity occurring as a result of site dilution, and depicted the appearance of small-sized FM clusters above T_C. The cluster size decreases with increasing Ti content. The Griffith-phase signature has also been attested in Sr_1−xCa_xRuO₃.³³⁾ The authors explained that the Ca substitution suppressed the Ru–O–Ru angle bond, and diluted the FM interaction between Ru ions, leading to the Griffith-phase-like behavior.

The nature of FM-PM transition and the MC effect of SrRu_1−xFe_xO₃ have been studied from a set of isothermal magnetization curves, M(H), that were measured at temperatures near T_C with a 2 K interval. For all samples, typical curves are displayed in Figs. 4(a), (b). Prior to every magnetization measurement, the samples were initially heated to a room temperature and then cooled down to the targeted temperature without any applied field. This step is to ensure a perfect demagnetization. Further, each of the measured sample shows that the value of M monotonically decreases with increasing temperature at a given H; while at a given temperature, M increases with H. Notably, for all samples, even at H = 50 kOe, the magnetization saturation is still out of reach. This is because the lowest temperature has a value near the T_C and because of the coexistence of FM and PM phases. As T increases, the nonlinear dependences of M(H) in the FM region transform into the linear ones corresponding to the PM state. Through Arrott plot (i.e., the M² vs. H/M curves), we could assess the characteristic of the FM-PM phase transition,³⁴⁾ as presented in Figs. 4(c), (d). At high H values, the plots near T_C are not a series of parallel straight lines, and there is no straight line at T = T_C passing through the origin. These traits confirm short-range magnetic order, meaning that the magnetic interactions in the samples do not obey the mean-field theory proposed for long-range order. Based on Banerjee’s criteria,³⁵⁾ the particular traits of the FM-PM phase transition could be taken into account from the slope sign of the M² vs. H/M curves. The magnetic transition is a second-order phase transition (SOPT) when the entire slope of M² vs. H/M curves near T_C exudes a positive slope. Inversely, the magnetic transition is a first-order phase transition (FOPT) when the slopes show a negative sign. The results shown in Figs. 4(c), (d) indicate the Arrott-plot curves having positive slopes. This proves a SOPT taking place in the samples.

Fig. 4

(a), (b) M(H) data, (c), (d) Arrott plots of M² vs. H/M, and (e), (f) −ΔS_m(T) curves at various ΔH values for SrRu_1−xFe_xO₃. Arrow lines indicate the direction of increasing H value.

The MC effect in SrRu_1−xFe_xO₃ has been studied through magnetic entropy change (ΔS_m), which was assessed up to 50 kOe. The |ΔS_m| was determined from an indirect calculation using the thermodynamic Maxwell’s relation (with zero initial magnetic field).³⁶⁾   

\begin{equation} |\Delta S_{m}(T,H)| = \int_{0}^{H\textit{max}}\left(\frac{\partial M}{\partial T}\right)_{H}dH \end{equation} (1)

For point-to-point measurements, the above equation can be written as a summation of   

\begin{equation} |\Delta S_{m}| = \sum \frac{M_{i} - M_{i + 1}}{T_{i + 1} - T_{i}}H_{i} \end{equation} (2)

where M_i and M_i+1 are the M values measured at T_i and T_i+1 in a magnetic-field sweep of H_i, respectively. According to eq. (1), |ΔS_m| value is a $\frac{\partial M}{\partial T}$ slope-dependent, inferring that during an abrupt magnetic transition, a large |ΔS_m| could be obtained. Also, |ΔS_m| is maximized around T_C, where the rapid decays of the magnetization mostly occur.

The magnetic entropy change as a function of temperature for various applied field values can be seen in Figs. 4(e), (f). Because only one magnetic phase (PM-FM) transition is recorded in our samples, normal MC effect would be observed. Sarkar et al.¹⁾ reported that in SrRuO₃ codoped with Ba and Ti, both normal and inverse MC effects coexist, due to the two magnetic phase transitions, namely a second-order PM-FM transition and a first-order FM-antiferromagnetic transition. As shown in Figs. 4(e), (f), |ΔS_m| increases with increasing H and achieves the highest values near T_C, as presumed from eq. (1). The maximum |ΔS_m| values (denoted as |ΔS_max|) obtained for ΔH = 50 kOe are about 1.65 and 1.32 J.kg⁻¹.K⁻¹ for x = 0, and 0.1, respectively. This result indicates the suppressed the MC effect by Fe dopants, which is related to the dilution of Ru concentration. Here, the |ΔS_max| value of x = 0 is fairly consistent with previous report on the same compound,¹²⁾ implying that the current sample is of eminent quality. Specially, Fig. 6 shows broad |ΔS_m(T)| curves that results in a large relative cooling power (RCP), which is known as a one of the important parameters to evaluate the MC effect.²²⁾ It can be calculated by using an expression of RCP = |ΔS_m| × δT, where δT is the full-width-at-half-maximum of a |ΔS_m| curve.²²⁾ The obtained values are 114 J.kg⁻¹ for x = 0 and 150 J.kg⁻¹ for x = 0.1 under an applied field of ΔH = 50 kOe. Although the |ΔS_max| magnitude slightly decreased with increasing x, this disadvantage is offset by an increase in RCP values, which are increased by Fe doping. Having reviewed previous reports on typical (Sr, Ca)RuO₃-based materials, as shown in Table 1, one can see that the |ΔS_max| values obtained in this work are higher than those obtained from (Ba, Ti)-codoped SrRuO₃ and comparable to those from Bi_0.4Ca_0.6Mn_0.8Ru_0.2O₃.

Table 1 Experiment values of T_C, and MC-related parameters (|ΔS_max|, and RCP) for SrRu_1−xFe_xO₃ compounds compared with those for (Sr, Ca)RuO₃-based materials.

As considering magnetic-field dependences of |ΔS_max|, we have found these data follow a power function of |ΔS_max| ∝ Hⁿ, where H varies from 5 to 50 kOe, and n is an exponent affiliated to magnetic order, which is dependent on T and H.³⁶⁾ Fitting |ΔS_max| data to the power law, as shown in Fig. 5, yielded n values of approximately 0.97 and 0.92 for x = 0, and 0.1, respectively.

Fig. 5

Field dependences of ΔS_max for SrRu_1−xFe_xO₃. The data are fitted to the power law |ΔS_max| ∝ Hⁿ and the fittings are indicated by the solid lines.

A recent publication by Law et al.³⁶⁾ described a new quantitative criterion to determine the order of magnetic phase transition. This is done by computing n(T, H) associated with the magnetic entropy change as follows:   

\begin{equation} n(T,H) = \frac{d\,\mathit{ln}|S_{m}|}{d\,\mathit{ln}\,H} \end{equation} (3)

Using the mentioned criteria for magnetic materials, at temperatures well below T_C, n is supposed to be in the value tendency of 1, whereas n has the tendency of 2 when T has much higher value than T_C. Near the T_C, for materials with a FOPT, the peak is n > 2; while for materials with SOPT, these large values will be absent.³⁷⁾ These values of n should be acknowledged because the samples are in a multi-domain state in a small field. Thus, by employing eq. (3), the exponent n at an applied field above 10 kOe could be estimated, as seen in Fig. 6. Evidently, one can see a variation trend of 1 → minimum → 2 in the n(T) curves for all samples. The absent of large values n > 2 is the criterion to ascertain that the FM-PM transition in the samples is a SOPT type (according to the above quantitative criterion), in accordance with those obtained from Banerjee’s criteria. This corroborates the benefit of applying the quantitative criterion besides Banerjee’s criterion in determining the order of a phase transition. Moreover, the minimum n values at T_C under an applied field of H = 50 kOe are 0.61 and 0.54 for x = 0 and 0.1, respectively. These values are contrasting with the mean-field-theory value of n = 2/3. This difference is due to the absence of long-range magnetic order, meaning the presence of magnetic inhomogeneity in the samples. It is well known that the replacement of Ru by Fe leads to the presence of Ru–O and Fe–O bond lengths together with three types of network arrangements of Ru–O–Ru, Ru–O–Fe, and Fe–O–Fe in a crystal lattice. Long-range magnetic Ru–O–Ru and Fe–O–Fe networks are partially destroyed by short-range magnetic Ru–O–Fe. Also, the substitution of Fe³⁺ and Fe²⁺ for Ru⁴⁺ created Ru⁵⁺ and led to an addition of interactions between Fe³⁺, Fe²⁺, Ru⁴⁺ and Ru⁵⁺ ions. These interactions compete with the intrinsic FM coupling of Ru⁴⁺–Ru⁴⁺. Thus, it is possible to present some antiferromagnetism¹¹⁾ which results in the decrease of the T_C, and |ΔS_max| as increasing Fe doping concentration in SrRu_1−xFe_xO₃.

Fig. 6

n(T, H) curves of the SrRu_1−xFe_xO₃ samples for H = 10 and 50 kOe.

4. Conclusions

We studied the structural characterization, oxidation state of Fe, the magnetic and magnetocaloric properties of SrRu_1−xFe_xO₃ (x = 0, and 0.1). The Fe-doping induced lattice expansion of SrRuO₃ that is assigned to the appearance of Fe³⁺ and Fe²⁺ with estimated value of Fe³⁺/Fe²⁺ is about 8/2 replacing partially for Ru⁴⁺ ions, leading to the appearance of Ru⁵⁺. The anti-FM interactions associated with Fe³⁺/Fe²⁺–Ru⁴⁺/Ru⁵⁺ pairs compete with FM interactions associated with Ru⁴⁺–Ru⁴⁺ pairs cause short-range magnetic order, and hence reduce the T_C as increasing Fe doping concentration in SrRu_1−xFe_xO₃. Detailed inspections in connection to the CW law and Griffiths phase for the M(T) data disclosed the coexistence of FM, anti-ferromagnetic, and PM interactions at temperatures T_C < T < T_G in the Fe-doped sample. The analyses of the M(H) data using the Arrott plots and the quantitative criterion n(T) indicated that the SOPT occurs in the both samples. Investigations into the magnetocaloric effect indicated the Fe-doping caused the slightly reduced |ΔS_max|.

Acknowledgement

This research is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 103.02-2019.335, and the research at Korea was supported by the National Research Foundation of Korea Grant No. 2020R1A2C1008115.

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