Magnetoelectric, dielectric, and magnetic investigations of multiferroic

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Introduction
Multiferroic materials exhibit two or more ferroic orders.They are of special interest because of their potential applications as e.g.memories, spintronic, sensors, and in biomedical purposes [1,2].Recently, Zi et al. [3] have reported on a low-frequency communication device based on the magnetoelectric effect.Coupling between ferro-/ferrimagnetism and ferroelectricity results in the co-called magnetoelectric (ME) effect in which the electrical polarization is affected by a magnetic field and vice versa.Most of the single-phase ME compounds (e. g.TbMn 2 O 5 , BiMnO 3 ) show a small ME effect and/or it appears at low temperatures [4,5].However, Veena et al. [6] have recently reported on large magnetoelectric coupling at room temperature in Sr 2 FeNbO 6 .On the other hand, composite materials with separate ferro-/ferrimagnetic and ferroelectric phases often show a strong magnetoelectric response at room temperature, which is essential for technical applications [7,8].Furthermore, in magnetoelectric composite materials, the ME effect can be tuned by changing the stoichiometry of each single phase and by varying the molar ratio between the ferro-/ferrimagnetic and ferroelectric phase [912].The coupling between those two phases is mediated by their interfaces and the magnetoelectric effect can be understood as a product property between those ferroic orders [13].The two different phases in the composite material can be arranged in e.g.0-3 (particles surrounded by a matrix), 2-2 (layers), and 1-3 (pillars in a matrix) dimensionality [14].Lead-free 0-3 magnetoelectric composites based on BaTiO 3 and MFe 2 O 4 have been extensively investigated [9,1522].In comparison, composites with the relaxor ferroelectric Sr y Ba 1y Nb 2 O 6 (0.25  y  0.75) have been only rarely studied [2331].In contrast to composites with BaTiO 3 , the ferroelectric phase of Sr y Ba 1y Nb 2 O 6 in composites is stable even after sintering at high temperatures [3234].Ferroelectric Sr y Ba 1y Nb 2 O 6 crystallized in the open tungsten-bronze structure and shows a diffuse phase transition (DPT) between roughly 313473 K, depending on y [3539].The piezoelectric coefficient also depends on the Sr/Ba ratio (y) [40].The influence of the stoichiometry of the ferroelectric and ferro-/ferrimagnetic phases on the magnetoelectric output is less well studied [41,42].
The aim of this work is to investigate the influence of the cation stoichiometry of the ferrimagnetic and the ferroelectric phases of (Ni x Co 1x Fe 2 O 4 ) 0.3 (Sr y Ba 1y Nb 2 O 6 ) 0.7 composites on the magnetoelectric output.The samples were synthesized by the conventional mixed-oxide method.Phase evolution and microstructure of the composite ceramics were monitored by XRD, SEM, and EDX.The magnetoelectric behavior was investigated depending on H DC , frequency of H AC and composition.The Curie temperatures were determined by thermomagnetometric measurements.Moreover, the samples were characterized by impedance spectroscopy and magnetic measurements.The composites were synthesized by a classical mixed oxide synthesis as described in our previous paper [31].The oxides and carbonates were mixed in a planetary mill for 4 h using

Characterization
X-ray powder diffraction were carried out on a Bruker D8-Advance diffractometer at room temperature, equipped with a one-dimensional silicon strip detector (LynxEye) using Cu-K  radiation and a counting time of 1 s per data point.Scanning electron microscope images were collected with a Phenom ProX SEM in backscattered electron mode (BSE).Thermal analyses were performed with a heating-/cooling rate of 10 K min 1 in flowing nitrogen (75 ml min 1 ) using a TA Instruments TGA 550 thermobalance (weighing precision 0.01%).To determine the magnet transition temperature (Curie point), a bar magnet was placed underneath the balance [43].A Quantum Design PPMS9 system was used for magnetic and magnetoelectric measurements.Magnetic hysteresis loops were taken at 300 K with magnetic DC field cycling between 90 kOe.For magnetoelectric and impedance measurements, ceramic samples were sputtered on both sides with 100 nm thick gold electrodes using a Cressington Sputter Coater 108auto.For magnetoelectric measurements the samples were electrically poled along the thickness direction for 18 h at room temperature applying an electric field of about 7 kV cm 1 with a current limit of 0.1 mA.Magnetoelectric measurements were performed using a selfmade setup [9] with the magnetic DC field parallel to the electrical polarization and a small AC driving field of about 8 Oe was superimposed collinear to the static field by a solenoid.
The in-phase voltage (U ME ) was recorded by a lock-in technique.The magnetoelectric coefficient ( ME ) was calculated as The thickness of the ceramic samples was between 0.95 and 1.02 mm.The magnetoelectric performance was investigated at 300 K in a DC field cycling between 15 kOe at (H AC ) = 900 Hz.Frequency-dependent measurements were done at the DC field at which the maximum of  ME was found.An Impedance Analyzer 4192A (Hewlett Packard) was used for impedance measurements.After pressing to pellets, the composite powders were sintered in static air at 1373 K for 1 h (heating-/ cooling rate: 5 K min 1 ).The bulk densities of the black ceramic bodies were calculated from their weight and geometric dimension and the relative bulk densities were related to 5.37 g cm 3 , calculated from the single crystal densities of Sr 0.5 Ba 0.5 Nb 2 O 6 and Ni x Co 1x Fe 2 O 4 considering their nominal molar fractions [44].The (Ni x Co 1x Fe 2 O 4 ) 0.3 -(Sr 0.5 Ba 0.5 Nb 2 O 6 ) 0.7 ceramic bodies reveal an increase in density with increasing cobalt content (Fig. 1), e.g. for x = 1 a relative density of 71(1) % was achieved, whereas composites with x = 0 reached 83(1) %.         investigations by Shafer [53].In contrast samples with a Fe/M ratio lower than 2 show lower M s values in both cases [54].This effect is more pronounced for CoFe 2 O 4 samples and reflects the M s development between the composites and pure Ni x Co 1x Fe 2 O 4 ceramics (Fig. 5).These findings suggest an iron deficiency (Fe/M < 2) of the ferrite phase in the composites.shows a diffuse phase transition around 373423 K (Curie-range [45,66]).In contrast to ceramics of pure Sr 0.5 Ba 0.5 Nb 2 O 6 , for which a broad maximum of the permittivity occurs (see also Fig. S7, supporting information) no such maximum were found for the composite ceramic samples.However, the permittivity curves reveal a weak shoulder or at least a significant change in the slope at around 373 K, which is more visible by plotting  r  1 vs. temperature (Fig. S8, supporting information) Rising tan  values at high temperatures (inset in Fig. 7) are most likely due to a decreasing resistivity of the samples.Because of the low conductivities of the samples at room temperature ( DC << 10 7 S cm 1 ), the high-temperature impedance data were fitted by an equivalent circuit consisting of one resistance-capacitor (RC) element including a constant phase-shift element.The specific complex impedance (Z * spec ) for a single RC element is described by [67]:

Magnetoelectric properties
The  As seen in Fig. 10,  MEmax growths with increasing nickel content from 40(2) µV cm 1 Oe 1 (x = 0) to 180 (10) µV cm 1 Oe 1 (x = 1).Analogous tendencies were also reported in magnetoelectric composites consisting of Ni/Co-ferrites and BaTiO 3 , Pb(Zr/Ti)O 3 , or PbFe 0.5 Nb 0.5 O 3 [41,6870].The value of the magnetoelectric coefficient is influenced by resistivity, density, and grain size of the ceramics, as well as by the magnetostrictive-/ piezoelectric output of the individual composite phases.In generally, considerably decreasing resistivities (at least one order of magnitude) of the samples can reduced the magnetoelectric effect [30,31,71,72].However, the resistivity values of the samples are in the same order of magnitude and also the grain sizes are in a comparable range.The density of the ceramics decreases with nickel substitution, but this would rather degrade the magnetoelectric coupling.
Therefore, we conclude that the magnetoelectric output of the samples is mainly determined by the magnetostrictive behaviour of the Ni
However, the significantly lower  MEmax values for y = 0.6 and especially for 0.7 is unexpected.The resistivities of the samples (inset in Fig. 12), which also influenced the magnetoelectric output, differ only slightly from each other (1.64.510 3 kcm) and can therefore not explain the reduced  MEmax values for y > 0.5.We suppose that the reason for the decline of  MEmax lie in the microstructure and the formation of non-ferroelectric SrNb 2 O 6 [78] for y = 0.7.Due to the higher calcining temperatures necessary for the formation of phase-pure Sr y Ba 1y Nb 2 O 6 (y = 0.6, 0.7) the ferroelectric phase in the resulting composites reveal considerably larger grain sizes.For example, after sintering at 1373 K, the size of the Sr y Ba 1y Nb 2 O 6 grains are between 16 µm (y = 0.3, 0.5), 112 µm (y = 0.6), and 233 µm (y = 0.7), whereas the size of the NiFe 2 O 4 grains (0.53 µm) do not differ significantly with y (Fig. S12, supporting information).We suppose that the large grain size of the ferroelectric phase for y > 0.5 leads to a poorer contact between the ferrimagnetic and ferroelectric grains.
The strong reduction of  ME for composites with y = 0.The highest magnetoelectric coefficient was found for y = 0.5, whereas Sr y Ba 1y Nb 2 O 6 with significantly higher strontium content are less suitable as ferroelectric components for 03 magnetoelectric composite ceramics.Additionally, during the sintering process, composites with a Sr y Ba 1y Nb 2 O 6 composition near the limit of the ferroelectric range (y = 0.3, 0.7), tend to segregate into barium-and strontium-rich phases, respectively.µV Oe 1 cm 1 (@ 900 Hz).The development of  ME,max with x is similar to the evolution of

Fig
Fig. 2 shows the XRD patterns after sintering of compacted

Fig. 3
Fig. 3 shows the microstructure of selected composite ceramics.Due to the BSE mode of the

Fig. 4
Fig. 4 Magnetization at 300 K for (Ni x Co 1x Fe 2 O 4 ) 0.3 -(Sr 0.5 Ba 0.5 Nb 2 O 6 ) 0.7 composite ceramics sintered at 1373 K for 1 h.The inset shows M versus H in a small field range.The magnetization values are given with respect to the nominal Ni x Co 1x Fe 2 O 4 content.

Fig. 5
Fig. 5 Dependence of M s on the nickel content (x) of (Ni x Co 1x Fe 2 O 4 ) 0.3 -(Sr 0.5 Ba 0.5 Nb 2 O 6 ) 0.7 composites and Ni x Co 1x Fe 2 O 4 ceramic samples sintered at 1373 K for 1 h.

Fig. 7
Fig. 7 Dependence of the real part of  r  and tan  (inset) on temperature at 1 kHz for (Ni x Co 1x Fe 2 O 4 ) 0.3 -(Sr 0.5 Ba 0.5 Nb 2 O 6 ) 0.7 ceramic bodies sintered at 1373 K for 1 h.For the sake of clarity every 4 th data point is represented by a symbol.

Fig. 8
Fig. 8 Development of the specific DC resistivity with composition of (Ni x Co 1x Fe 2 O 4 ) 0.3 -(Sr 0.5 Ba 0.5 Nb 2 O 6 ) 0.7 ceramic sintered at 1373 K for 1 h.The uncertainties of the data are smaller than the symbol size.The inset shows the Cole-Cole plots of the samples.

Fig. 9
Fig. 9 Magnetoelectric coefficient (α ME ) vs. magnetic DC field for (Ni x Co 1x Fe 2 O 4 ) 0.3 -(Sr 0.5 Ba 0.5 Nb 2 O 6 ) 0.7 composites sintered at 1373 K for 1 h.The inset shows the frequency dependence (H AC ) of α ME at H DC( α max).For the sake of clarity, in the inset every 10 th data point is represented by a symbol.

x from 5 . 4 [ 70 ,
0 to 1.0 kOe (Fig. 10) as a result of the change in the magnetostrictive behaviour of Ni x Co 1x Fe 2 O 4 .The magnetoelectric effect in composites is widely accepted as a product property between a magnetostrictive (Ni x Co 1x Fe 2 O 4 ) and a piezoelectric material (Sr 0.5 Ba 0.5 Nb 2 O 6 ) [76,77].Therefore, the field-dependence development of the magnetoelectric coefficient reflects the magnetostriction evolution of Ni x Co 1x Fe 2 O 4 .The maximum slop of the magnetostriction (strain derivative) and the maximum of the piezomagnetic coefficient of NiFe 2 O 4 appears at a lower H DC field in contrast to CoFe 2 O 75].

Fig. 10
Fig. 10 Maximum of the magnetoelectric coefficient (α ME,max ) and the H DC field at which the maximum of α ME appeared (H DC( α max) ) depending on the composition x for (Ni x Co 1x Fe 2 O 4 ) 0.3 -(Sr 0.5 Ba 0.5 Nb 2 O 6 ) 0.7 .
, supporting information) show reflections of Sr y Ba 1y Nb 2 O 6 , NiFe 2 O 4 and small amounts (24 wt%) of orthorhombic or tetragonal (Ni,Fe)Nb 2 O 6 [JCPDS #01-077-1290/ #01-076-2355] as secondary phase [31], as aforementioned.Additionally, for the sintered composites with y = 0.7 reflections at 17.6, 22.9, 28.2, 29.1, and 31.8° in the XRD pattern indicate the formation of SrNb 2 O 6 (JCPDS #01-072-2088) with a fraction of about 20 wt%.Sintering at 1423 K leads in the case of composites with y = 0.3 to the formation of small amounts (ca.6 wt%) of Ba 3 (Fe,Ni)Nb 6 O 21 (JCPDS #01-079-0074, #01-079-0075), as confirmed by EDX analysis.The phase composition for y = 0.5, 0.6 and 0.7 does not change after firing at 1423 K.However, in all samples, the orthorhombic (NiFe)Nb 2 O 6 phase completely transforms to the tetragonal one with rutile structure [31] (Fig. S10, supporting information) after sintering above 1373 K.The saturation magnetization values, related to the nominal NiFe 2 O 4 content, are between 46.1(2)  47.0(2) emu g 1 for composites sintered at 1373 K and thus independent on the strontium content (y) as expected.The same is true for other sintering temperatures (Fig. S11, supporting information).As mentioned above, these values are slightly lower than the M s values of pure NiFe 2 O 4 .The evolution of the permittivity with temperature at 1 kHz depending on the Sr content (y) is depicted in Fig.12.All samples show increasing permittivity values with rising temperatures and a decrease of  r  above 473 K.The permittivity curves of the ceramic bodies do not show a clear maximum reflecting the transition from the ferroelectric to the paraelectric state.In contrast, measurements on phase-pure Sr y Ba 1y Nb 2 O 6 ceramics show dielectric maxima at 324(2), 353(2), 375(2), and 506(2) K (Fig.S7, supporting information), in accordance with literature data[36,39].As shown in the inset of Fig.12, the DC resistivity values, calculated from the impedance data, of the (NiFe 2 O 4 ) 0.3 (Sr y Ba 1y Nb 2 O 6 ) 0.7 composites lie in the same order of magnitude.Composites with y = 0.5 and 0.6 reveal only slightly lower DC resistivity values than samples with y = 0.3 and 0.7.

Fig. 12
Fig. 12 Dielectric behavior ( r /closed symbols, tan /open symbols) at 1 kHz for (NiFe 2 O 4 ) 0.3 -(Sr y Ba 1y Nb 2 O 6 ) 0.7 ceramic bodies sintered at 1373 K for 1 h.For the sake of clarity every 4 th data point is represented by a symbol.The inset shows the specific DC resistivity in dependence of the strontium content (y).The uncertainties of the data are smaller than the symbol size.
7 may additionally caused by the formation of considerable amounts of SrNb 2 O 6 of about 21 vol%, which appears as cuboidlike grains (14 µm) near the Sr 0.7 Ba 0.3 Nb 2 O 6 grains and hinders an effective mechanical coupling between nickel ferrite and strontium barium niobate grains (Fig. S13, supporting information).The complete development of  ME depending on H DC for all (NiFe 2 O 4 ) 0.3 (Sr y Ba 1y Nb 2 O 6 ) 0.7 samples is shown in Fig. S14 (supporting information).

Fig. S3 :
Fig. S3: Magnetization at 300 K for (Ni x Co 1x Fe 2 O 4 ) 0.3 -(Sr 0.5 Ba 0.5 Nb 2 O 6 ) 0.7 composite ceramics sintered at 1373 K for 1 h.The magnetization values are given with respect to the sample mass.

Fig. S7 :
Fig. S7: Dependence of the real part of the permittivity ( r ) on temperature at 1 kHz for various Sr y Ba 1y Nb 2 O 6 ceramic bodies sintered between 1473 and 1703 K for 1 h.For the sake of clarity every second data point is represented by a symbol.The inset shows the specific DC resistivity ( DC ) depending in the strontium content (y) of the Sr y Ba 1y Nb 2 O 6 ceramics.The DC resistivity values were calculated by fitting the impedance data by an equivalent circuit consisting of one resistance-capacitor (RC) element including a constant phase-shift element.The uncertainties of the data are smaller than the symbol size.

Fig. S11 :
Fig. S11: Magnetization at 300 K for (NiFe 2 O 4 ) 0.3 -(Sr y Ba 1y Nb 2 O 6 ) 0.7 composite ceramics sintered at 1373 K (a) and 1423 K (b) for 1 h.The magnetization values are given with respect to the nominal NiFe 2 O 4 content.In the inset the magnetization values are given with respect to the sample mass.

R. Köferstein, M.-S. Wartmann, S.G. Ebbinghaus, Magnetoelectric, dielectric, and magnetic investigations of multiferroic Ni x Co 1−x Fe 2 O 4 −Sr y Ba 1−y Nb 2 O 6 composites, Mater. Res. Bull. 177 (2024) 112860 (Open Access, DOI: 10.1016/j.materresbull.2024.112860).
, supporting information).Composite powders were prepared by mixing Ni x Co 1x Fe 2 O 4 and Sr y Ba 1-y Nb 2 O 6 powders to get the target composition of (Ni x Co 1x Fe 2 O 4 ) 0.3 (Sr y Ba 1y Nb 2 O 6 ) 0.7 .The resulting composite powders were mixed with 10 wt% of a saturated aqueous polyvinyl alcohol (PVA) magnetoelectric coefficient ( ME ) dependence on the static magnetic field (H DC ) at 300 K for (Ni x Co 1x Fe 2 O 4 ) 0.3 -(Sr 0.5 Ba 0.5 Nb 2 O 6 ) 0.7 composite ceramics sintered at 1373 K is shown in Fig.9.The evolution of  ME reveals a hysteretic behavior with coercive fields smaller than 100 Oe.  ME increases with rising H DC field up to a maximum/minimum ( MEmax ) and then continuously decreases to zero at higher fields.
[70,75] reduced from CoFe 2 O 4 to NiFe 2 O 4 which would expected lower  ME values for composite samples with increasing nickel content[73,74].However, to measure the magnetoelectric performance, an alternating magnetic field (H AC ) is superimposed to the H DC field.As pointed out by Aubert et al.[70,75],the applied H AC field leads to a dynamic deformation (piezomagnetic effect) of the ferrite grains.The resulting dynamic magnetostriction coefficient of CoFe 2 O 4 is lower than the one of NiFe 2 O 4 for low H AC fields [70,75], which explains the observed  ME evolution of our (Ni x Co 1x Fe 2 O 4 ) 0.3 -(Sr 0.5 Ba 0.5 Nb 2 O 6 ) 0.7 composites.Higher  ME values for composites with NiFe 2 O 4 compared to CoFe 2 O 4 were also found for other sintering temperatures (Fig. 11).The NiFe 2 O 4 based composites always show higher  ME values, although the density of the CoFe 2 O 4 -Sr 0.5 Ba 0.5 Nb 2 O 6 ceramics is higher which should lead to a better connectivity x Co 1-x Fe 2 O 4 phase.On the other hand, the magnetostriction induced by a static magnetic field (H between the ferroelectric and ferromagnetic grains.After sintering at 1473 K in both composite samples  ME drops down because of a considerable increase in conductivity of more than one order of magnitude[31].The H DC field at which  ME reaches its maximum (H DC(  max) ) almost linearity decreases with