Abstract
A polycrystalline sample of Sr(Mn1/2Nb1/2)O3 (SMNO) was synthesised via the solid-state reaction method, confirming a single-phase perovskite structure. Room-temperature XRD analysis revealed a tetragonal crystal system. Micro-Raman spectroscopy exhibited broad peaks, suggesting the presence of a vibrational band and ferroelectric characteristics. Dielectric properties were investigated over a broad frequency (100–1 MHz) and temperature (24–360°C) range, revealing strong low-frequency dispersion, a very high dielectric constant and loss (∼6). A broad permittivity peak was observed at 280°C across all measured frequencies. The frequency and temperature dependence of the ac conductivity (σac) suggest a thermally activated relaxation mechanism. Impedance spectroscopy indicated that the dielectric and conductive properties of the material arise from the contributions of bulk, grain boundaries and electrode effects. Magnetic measurements identified an antiferromagnetic transition at 41 K, co-existing with a low-temperature ferromagnetic phase. The growing demand for miniaturised and versatile electronic components drives our strong interest in developing dielectric ceramics. These materials are critical for applications such as capacitors, sensors, actuators and transducers.
Introduction
There are several technical applications for oxides with complicated perovskite structures and high dielectric constants in microelectronics.1,2 Both memory storage devices and capacitors, which need materials with a high dielectric constant, frequently use these materials. For many real-world applications, this is a disadvantage since their dielectric characteristics tend to change dramatically with temperature. Since regulations restrict lead utilisation, the majority of dielectric materials with perovskite structures also include a significant quantity of lead, which raises environmental problems. As a result, dielectric materials with lower lead concentration or ceramics that are completely lead-free are becoming more and more necessary to solve these environmental issues.
Ceramics of perovskite structure (ABO3) have been showing rich and diverse physical properties, which are of immense potential for different industrial applications.3–9 This structure can accommodate two or more cations at both A-site and B-site, making it a complex perovskite of the form (A1, A2, A3…..)(B1, B2, B3…..)O3. In this complex perovskite, the material can be tailored with different cation substitutions to get the desired result. When the B-site cation has an empty d0 orbital, it produces Ferroelectricity (the material that possesses spontaneous electric polarisation, which an electric field can switch) like BaTiO3, Li NbO3, etc. When the B-site cation is occupied with a cation having a partially filled d orbital, it generally shows magnetic order. In the last several years, scientists have been substituting both d0 cation and dn cation at the B-site in complex perovskite structures to attain multifunctional materials. As a result, a very interesting material is formed, called a multiferroic material, where both Ferroelectricity and magnetic order are achieved in the same phase.10–16
These multiferroic materials have found tremendous applications in device fabrication, like memory storage devices, spintronics devices, sensors and actuators. One of the most studied complex perovskite multiferroics is Pb(Fe1/2Nb1/2)O3. 17 It shows very strong electric polarisation but weak magnetic behavior. Recently, Pb has been replaced by other cations like Ba, Ca, etc., to get rid of toxic Pb. In this study, we have replaced Pb by Sr at the A-site and Fe by Mn at the B-site to make single-phase Sr(Mn1/2Nb1/2)O3, which is expected to be a lead-free multiferroic with a complex perovskite structure.
The giant dielectric response of Sr(Fe₁/₂Nb₁/₂)O3 was reported by Raevski et al., 18 and its magnetic properties were examined by Tezuka et al. 19 However, until the recent study by Saha and Sinha, 20 there were few thorough investigations into its dielectric behavior over a wide range of temperatures and frequencies. The Maxwell-Wagner polarisation process was used in earlier studies 20 to explain the high dielectric constant of Sr(Fe₁/₂Nb₁/₂)O3 ceramics. However, more complicated behavior has been demonstrated by related compounds such as Ba(Fe₁/₂Nb₁/₂)O3 21 and Ba(Fe₁/₂Ta₁/₂)O3, 22 indicating that more investigation into the underlying physical sources of dielectric relaxation and the gigantic dielectric response in Sr(Fe₁/₂Nb₁/₂)O3 is still required.
In the present work, a dielectric study of the strontium iron niobate SrFe1/2Nb1/2O3 ceramic prepared by a solid-state reaction technique is presented. The introduction of transition metals at the B-site has been explored in previous literature; however, there is limited research on several regions, such as optical, electrical and dielectric, in some distinct regions. This gap has led to a wealth of scientific investigation and potential applications. In this article, we investigated the structural and micro-structural properties of the material. In addition, we have briefly studied dielectric, impedance and transport in a wide temperature range of 24–360°C and a frequency range of 100 Hz to 1 MHz. Also, the optical study, that is, UV and Raman spectroscopy, was conducted to obtain the bandgap and molecular vibrations of the material. The impact of weak ferromagnetism at low temperatures is apparent from the M–H loop.
Experiment
Sr(Mn1/2Nb1/2)O3 with polycrystalline structure were synthesised through the solid-state method 23 using AR-grade precursors: SrCO3 (98%, Loba Chemicals, India), Mn2O3 (98%, Alfa Aesar) and Nb2O5 (99%, Loba Chemicals, India).
The reactive powders were mixed mechanically in an appropriate stoichiometric ratio. The above powders were mixed completely under dry conditions for 1 h in an agate mortar, followed by a wet treatment (e.g., methanol) for 2 h to achieve a homogeneous mixture. Then the mixed powder in a platinum crucible was calcined at 1200°C for 6 h. The powder so obtained after calcination was cold pressed into pellets (dia. 10 mm) under an uniaxial pressure of 5 × 106 N/m2 using polyvinyl alcohol (PVA) as the binder. The pellets were then sintered at 1250°C for 6 h. The pellets were finally coated with silver paint, followed by drying at 150°C for 2 h prior to electrical measurements.
To know the compound formation, X-ray diffraction (XRD) studies were carried out (X-ray powder diffractometer (Rigaku, PANalytical X’Pert). The XRD pattern of the calcined powder was recorded at room temperature with CuKα radiation (λ = 1.5405 Å). An X-ray study was carried out in a wide range of Bragg angles (20° ≤ 2θ ≤ 80°) at a scan speed of 3°/min. Micro Raman spectroscopic behavior was studied via Renishaw invia Reflex (UK) spectrometer. Electrical analysis was carried out using a computer-controlled impedance analyser “HIOKI LCR METER” in the frequency range from 100 Hz to 1 MHz in a temperature range of 24‒360°C. The acquisition of data was monitored using frequency and temperature. The magnetic measurements are taken in SQUID-VSM.
Results and discussion
XRD study
Figure 1(a) depicts the SMNO X-ray diffraction pattern at ambient temperature. The acquired findings show that the samples have a tetragonal perovskite structure in a single phase without any additional impurity peaks. To substantiate these claims, the powder underwent Rietveld refining. The Fullprof software was used to carry out the structural refinement. After refinement of the samples, the numbers obtained from

(a) Room temperature XRD diffraction pattern, (b) Rietveld refinement, and (c) Unit Cell structure of SMNO compound.
The refined atomic positions (Wyckoff and occupancy) of SMNO sample.
The average crystallite size, calculated using the Debye-Scherrer formula (
Raman study
Figure 2 shows the micro Raman studies at room temperature of the prepared sample. Broad peaks are obtained at 304, 577, 694 and 818 cm−1. The peak at 304 cm−1 may be due to the LO2-TO3 phonon, which may arise from local symmetry breaking due to the tilting of the octahedral and distortions of the polar order. The peak at 577 cm−1 may be assigned to B-O displacement, while the peak at 694 cm−1 may be due to the symmetrical stretching of BO6 octahedra. The peak at 818 cm−1 may be a signature of ferroelectricity in the sample and may represent the vibrations of Mn+3 and Nb+5 ions. The broadening of peaks may be due to lattice disorder. 24 Raman spectroscopy revealed several key vibrational modes. The peaks at 694 and 304 cm−1 are characteristic of SrCO3, associated with its in-plane bending, symmetric stretching and lattice vibrations. 25 A peak at 818 cm−1, potentially linked to Mn3+ and Nb5+ vibrations, suggests the presence of ferroelectric properties. The observed peak broadening indicates lattice disorder within the material. 24

Room temperature Micro Raman spectra of Sr(Mn1/2Nb1/2)O3.
Dielectric and electrical properties
Frequency variation plays a crucial role in the performance and functionality of advanced photonic and electronic systems,26–27 such as two-channel whispering gallery mode (WGM) self-injection locking lasers and relaxor antiferroelectrics for neuromorphic computing.28–29 In the case of WGM self-injection locking lasers used in hybrid optically pumped atomic comagnetometers, precise frequency tuning enables enhanced laser stability, reduced linewidth and improved sensitivity to magnetic fields, which are essential for accurate atomic spin measurements. Frequency control between the two laser channels ensures proper synchronisation with atomic transitions, thereby boosting the overall precision and reliability of the comagnetometer. Similarly, in relaxor antiferroelectric materials, frequency-dependent dielectric responses are key to emulating synaptic behavior in neuromorphic systems. By applying variable frequencies, it becomes possible to modulate polarisation dynamics and achieve tunable resistive states, mimicking the adaptive learning processes of biological neurons. Together, these applications demonstrate how frequency variation is a powerful tool for optimising performance in cutting-edge technologies across both quantum sensing and brain-inspired computing. Here, we have studied the frequency variation of the dielectric constant and loss.
The frequency response of dielectric properties, that is, variation of relative permittivity (εr) and loss tangent (tan δ) with frequency at room temperature for SMNO (Figure 3) shows a marked dispersive characteristic in both the permittivity and loss tangent pattern. The value of relative permittivity attains a value of around 10,000 at a frequency of 100 Hz; at the same frequency, the loss tangent also attains a very high value of almost 3.5. This lossy behaviour of the sample may be attributed to the oxygen ion vacancies produced due to the fluctuation of oxidation states of Mn in the oxygen octahedra. Both εr and tan δ values decrease with increasing frequency up to 10 kHz, which is a typical behavior of dielectric and ferroelectric materials. With increasing frequency, some of the dynamic polarisation phenomena cease. However, beyond 10 kHz, while there is a plateau followed by a sharp fall of εr, the value of tanδ slowly increases with increasing frequency. So, the overall frequency response of the material in this observed frequency window may be attributed to low-frequency relaxation phenomena, deviation from Debye-type behavior and possible grain boundary barrier effect. 30

The frequency variation of relative permittivity (εr) and loss tangent (tan δ) of Sr(Mn1/2Nb1/2)O3 at different temperatures (50–300°C).
Figure 4(a) and (b) show respectively the variation of relative permittivity (εr) and the loss tangent tan δ with temperature at different frequencies, that is, 50 kHz, 100 kHz and 1 MHz. εr for the material shows very high values, that is, 5739, 5476 and 3353, respectively, for 50 kHz, 100 kHz and 1 MHz at 24°C, while the tanδ value lies below 0.6 for all frequencies at this temperature. Both εr and tanδ increase with temperature for all frequencies. An anomaly in the εr vs. temperature pattern is observed in the range 100‒250°C and finally, a diffused peak is observed at 280°C for all frequencies. The peak values of εr are 24,250, 21,600 and 17,390 for frequencies 50 kHz, 100 kHz and 1 MHz, respectively. The tanδ vs. temperature pattern also shows a rise of tan δ with increasing temperature and an anomaly in the temperature range 100‒200°C with a peak at 324 °C for frequency 1 MHz. In contrast, for lower frequencies, the value reaches the limiting value of the instrument.

(a) Variation of relative permittivity (εr) of Sr(Mn1/2Nb1/2)O3with temperature at different frequencies i.e., 50 kHz, 100 kHz and 1 MHz and (b): Variation of loss tangent tanδ of Sr(Mn1/2Nb1/2)O3with temperature at different frequencies i.e., 50 kHz, 100 kHz and 1 MHz.
An exceptionally high value of relative permittivity with tan δ lying below 1.0 up to a temperature of around 200°C is a remarkable feature for SMNO. The diffused peak at 280°C for all frequencies may be attributed to a possible ferroelectric transition of this material. Also, due to the comparable ionic radii of the B-site cations in the perovskite structure, the distribution of these cations may be random, which consequently may lead to an order-disorder phase transition. With a high value of tan δ, the material shows a lossy behaviour. This lossy behavior may be attributed to oxygen ion vacancies due to fluctuation of oxidation states of Mn in the oxygen octahedra.
The application of dielectric materials under electric fields has enabled significant advancements across various high-performance technologies. For instance, electric current-induced dislocation slip and grain boundary alignment demonstrate how dielectric behavior can influence microstructural evolution in conductive or semiconductive materials, enhancing their mechanical and functional properties. 31 In advanced layered structures such as alternating Ti3C₂Tx/Co multilayers, the integration of dielectric components and conductive phases, especially with engineered interfaces like Co “frosting,” improves electromagnetic wave absorption and infrared stealth capabilities by tailoring dielectric polarisation and impedance matching. 32 Additionally, in the domain of neuromorphic computing, core–shell nanowire memristors utilising quasi-2D filament confinement highlight how controlled dielectric properties enable reliable and scalable electronic synapses. 33 These developments underscore the importance of dielectric materials in directing charge transport, field-induced phenomena and overall device performance. A comparison study regarding the dielectric constant has been reported in Table 2.
Comparative values of the dielectric constant of different compounds.
Impedance study
Resistance has a significant impact on the overall impedance of an electrical circuit, particularly in alternating current (AC) systems. Impedance, which represents the total opposition to current flow, consists of both resistance (the real part) and reactance (the imaginary part from inductors and capacitors). 35
Figure 5 shows the variation of real (Z′) and imaginary parts of impedance (Z″) as a function of frequency at different temperatures. The pattern variation of real (Z′) impedance as a function of frequency shows a low-frequency dispersive region followed by a merger into a plateau region. Also, the value of Z′ decreases both with increasing temperature and frequency. The decrease of Z′ with rise of temperature is a typical semiconducting property with the negative temperature coefficient of resistance (i.e., NTCR type behavior), while the decrease of Z′ with increasing frequency and finally merging on a plateau irrespective of temperature shows a thermally activated ac conductivity and release of space charge. These results indicate a possibility of an increase in the ac conductivity of the material with a rise in temperature in the high frequency region, possibly due to the release of space charge as a result of a lowering in the barrier properties of the material.

Variation of real (Z′) and imaginary (Z″) part of impedance of Sr(Mn1/2Nb1/2)O3 with frequency (100 Hz–1 MHz) at different temperatures (50–300°C).
The loss spectrum (variation of imaginary impedance (Z″) with frequency) at different temperatures in Figure 5 shows the appearance of peaks at a characteristic frequency dependent on temperature. It can be related to the type and strength of the electrical relaxation phenomenon occurring in the material. A significant broadening of the peaks with a rise in temperature and their asymmetric nature suggests the presence of a temperature-dependent relaxation process with a spread of relaxation times.
Conductivity study
The conductivity spectra (i.e., the variation of a.c. conductivity [σac] as a function of frequency) at different temperatures (50–325°C) are shown in Figure 6. At almost all temperatures, the spectra show a low-frequency plateau region followed by high-frequency dispersion. The frequency-independent plateau in the low frequency range is associated with the dc conductivity σdc.

Variation of ac conductivity (σac) with frequency of Sr(Mn1/2Nb1/2)O3 at different temperatures with power law fitting at 150°C (inset).
This plateau region extends to higher frequencies with increasing temperature. This type of conductivity behavior is well explained by Jonscher's power law
36
given by the formula
A graph (Figure 7) is plotted between σdc and the inverse of absolute temperature (1000/T). The graph can be split into three different linear regions with three different slopes obeying the Arrhenius formula

Variation of dc conductivity (σac) with inverse of absolute temperature of Sr(Mn1/2Nb1/2)O3.
The activation energy (Ea) calculated from the slopes is 0.12 in the low temperature range (50−100°C), 0.21 in the mid temperature range (125−225°C) and 0.49 in the high temperature range (250−325°C).
The calculated values of activation energy in different temperature ranges show that the bulk conductivity at low temperature, grain boundary conductivity at the mid temperature and electrode response dominate at the high temperature region of conductivity. 16 Also, the value of conductivity increases by two or three orders with an increase in temperature. So, the material shows NTCR behaviour like that of a semiconductor. The overall dielectric response, along with the heterogeneous conduction process, indicates that the material might have a diffused ferroelectric transition near 280°C along with Maxwell-Wagner polarisation, oxygen ion vacancies (VO) induced dielectric relaxation and space charge polarisation.37,38
Nyquist plot study
To gain more insight into the electrical microstructure of the material, a complex impedance analysis was performed. Figure 8(a) and (b) shows the graph plotted between the imaginary (Z″) versus real (Z′) part of the complex impedance (Nyquist plot) at different temperatures. The semicircles appear to be stretched, indicating a distribution in time constant characteristics, which supports the diffused nature of the phase transition of the material and departure from Debye-like behavior. The Nyquist plots at higher temperatures (≥225°C) show an additional contribution due to the grain boundary effect to the electrical response of the material. The assignment of the two semi-circular arcs to electrical response due to grain interior and grain boundary can be expressed as an equivalent electrical circuit built up by cascading of two parallel resistance and capacitance (RC circuits) connected in series, each being responsible for a semicircle in the experimental electrical response and appear to be consistent with the ‘brick-layer model’ for a polycrystalline material. 39 Generally, to represent the departures from Debye-like ideality, a constant phase element, CPE, is also included with the parallel RC element. The equivalent circuit (inset) and a representative fitting curve (solid curve) according to this circuit with the experimental data at 250°C (scattered points) are shown in Figure 8(c).

The graph plotted between the imaginary (Z″) versus real (Z′) part of the complex impedance from (a) 50 to 200°C, (b) 225°C to 325°C (c) The equivalent circuit (inset) and a representative fitting curve (solid curve) according to this circuit with the experimental data at 250°C (scattered points).
All plots have been fitted as per the equivalent circuit mentioned above and the values of Bulk capacitance Cb at different temperatures are calculated. A graph is plotted between Cb and temperature, shown in Figure 9. The graph shows a broad peak near 280°C, which is further evidence of the fact that the diffused phase transition in the material near 280°C is not due to the extrinsic factors.

Variation of bulk capacitance (Cb) with temperature for Sr(Mn1/2Nb1/2)O3.
Magnetic properties
Magnetisation switching via electric field is an emerging technique that allows control of a material's magnetic state without the need for external magnetic fields or high current densities. This approach is highly desirable for low-power spintronic devices and next-generation memory technologies. By applying an electric field, the magnetic anisotropy or exchange interactions within certain multiferroic or magnetoelectric materials can be altered, leading to a reversal or reorientation of the magnetisation direction.40–42 This effect is particularly significant in systems where electric polarisation and magnetisation are strongly coupled, such as in magnetoelectric heterostructures or strain-mediated ferroelectric/ferromagnetic composites. Unlike conventional methods that rely on current-induced magnetic fields, electric field-driven switching offers energy efficiency, faster operation and scalability. As research advances, this mechanism holds great promise for developing ultra-low-power, non-volatile memory and logic devices.
Figure 10(a) shows magnetisation (M) in both zero-field-cooled (ZFC) and field-cooled (FC) modes measured at 0.05 T of the SMNO ceramic sample. Magnetisation increases gradually with the decrease in temperature below 300 K, and around 41 K, a kink is observed at both magnetic fields without any observable shift in the temperature. Further, there is no bifurcation in ZFC and FC magnetisation modes around this kink, indicating a thermodynamic transition. However, a bifurcation in ZFC and FC starts below 15 K, which is quite prominently visible when drawn in log scale, as shown in Figure 10(b). The kink at 41 K indicates a magnetic order transition. The magnetisation again increases continuously below this kink temperature, showing the existence of weak ferromagnetism.

(a) Magnetisation (M) versus temperature (T) graph in ZFC and FC mode at 0.05 T (b) M-T curve in log scale.
The effect of weak ferromagnetism at low temperature is evident from the nonlinearity in the M–H hysteresis loop with a small opening in the loop at 10 K shown in Figure 11. It has been established that the magnetic order in perovskites can show both antiferro and ferromagnetic components.43,44

Magnetisation (M) versus Field (H) at 300 K and 10 K of the sample.
This type of metastable magnetic state in the polycrystalline material is observed in systems when ferromagnetic interactions are introduced randomly in a predominantly antiferromagnetic matrix. 16 Here, Mn+3 is in a high-spin state, but the distributions of Nb+5 and Mn+3 are random at the B-site. Therefore, some of the superexchange interactions may give rise to the observed weak ferromagnetism and a random distribution of ferromagnetic interactions in the present system. Thus, it may be concluded that the distribution of Nb+5 and Mn+3 is actually random in our sample, which also has a significant effect on its dielectric properties. Nevertheless, this noteworthy low-temperature feature needs to be investigated in detail to ascertain its nature and origin and also its relation to the magnetoelectric coupling in this system. From a view of geometry, the antiferromagnetism is based on 180° of B-O-B′ bond angle, and the bending of the B-O-B′ bonding in the distorted perovskite would give additional magnetic interaction. By decreasing exchange interaction and increasing Dzyaloshinskii-Moriya interaction, week ferromagnetic order might be induced. The bifurcation in ZFC and FC mode in the M-T curve below 15 K needs further investigation to find a possible spin glass transition in the material.
Conclusion
A polycrystalline single-phase ceramic sample, SMNO, has been successfully prepared, which is confirmed through a room temperature XRD study. The micro Raman studies indicate a signature of ferroelectricity in the material. The diffused peak in the permittivity pattern at 280°C shows a possible ferroelectric transition in the material. The impedance data were analysed according to an equivalent circuit selected on the basis of conductivity spectra and the Nyquist plot. Analysis of the ac conductivity (σac) as a function of both frequency and temperature indicates the existence of a thermally activated relaxation process. The variation of bulk permittivity with temperature was compared with the temperature dependence of relative permittivity measured at constant frequencies. An order disorder phase transition, along with grain, grain boundary and electrode effects, contributes to the overall dielectric response of the material. A kink at 41 K and an increase in magnetisation in the M-T graph below this temperature show an antiferromagnetic transition with the onset of ferromagnetism below 41 K The nonlinear behavior of magnetisation as a function of a field with a finite opening in the M–H loop, at 10 K, gives further evidence of ferromagnetism. Our research is motivated by the miniaturisation and application flexibility in electronics, leading to a focus on the design and fabrication of innovative dielectric ceramics. These materials are essential for prevalent devices, including capacitors, transducers, sensors and actuators.
