1 Introduction

One of the promising areas of modern materials science is the development of synthesis methods, the study of the composition, structure, and possibilities of using nanosized materials with different functional properties [1,2,3,4,5,6]. Of greatest interest is bismuth ferrite BiFeO3 (BFO) which attracts the attention of researchers due to its electrical and magnetic properties. In addition, there are reports on the use of bismuth ferrite nanoparticles in medicine, since they possess antibacterial properties [7].

Out of the whole variety of multiferroics with a perovskite structure, bismuth ferrite is one of the most promising compounds due to the existence of ferroelectric and magnetic phases in it with high ordering temperatures (Tc = 1083 K, TN = 673 K [8,9,10,11]). This means manifestations of the magneto-electric effect are to be expected at temperatures convenient for practical applications (298 K and higher) and in relatively low fields. However, there are several problems that prevent the realization of the full potential of bismuth ferrite. First, it is quite difficult to obtain single-phase bismuth ferrite. The synthesized samples almost always contain Bi25FeO39 impurities with a sillenite structure and Bi2Fe4O9 with a mullite structure [12,13,14,15,16]. In [17,18,19], this is explained by thermodynamic reasons associated with the features of the stable existence of BFO, Bi25FeO39, and Bi2Fe4O9. In [20], thermodynamic analysis showed that the regions of stable existence of BFO are below 447 °C and above 767 °C, and, therefore, for the synthesis of pure bismuth ferrite, the process must be carried out in these temperature ranges.

Second, BFO is characterized by a spatially modulated spin structure, which is a cycloid with a period of 62 nm [21]. The spin cycloid is an obstacle to the manifestation of the magneto-electric effect by bismuth ferrite under normal conditions. The reason for the appearance of the cycloid is the inhomogeneous magneto-electric interaction, due to which spontaneous electric polarization induces spatial spin modulation. A change in the degree of polarization will lead to a change in the magnetoelectric interaction and a rearrangement of the spin structure. In the first approximation, the degree of rhombohedral distortion of the cell, c/a, can serve as a criterion for the degree of polarization. The destruction of antiferromagnetic cycloid requires changing the c/a ratio, thereby reducing the degree of electric polarization [22].

For BiFeO3, various methods of destruction of the spin cycloid are used: the application of a strong magnetic field, the replacement of bismuth ions with ions of rare-earth elements, iron, or other 3d-metals, the production of BiFeO3 thin films, and others. [22,23,24,25,26,27]. Rare earth elements as BFO dopants are attractive due to their electronic configuration and the presence of an unfilled 4f shell. In [28], using the example of R0.15Bi0.85Fe03 (R = La, Nd, Gd, Dy, Er) samples i,t was shown that even small concentrations of introduced rare-earth metal ions significantly changed the magnetic properties of bismuth ferrite. In [29, 30], the doping of BFO with 3d-metals with intrinsic magnetic moments led to an improvement in the magnetic and ferroelectric properties of bismuth ferrite, extended the interval for the formation of continuous solid solutions, and an increase in the thermal stability of BiFeO3. It was established in [31] that the doping of BFO with Ni2+ ions contributed to an increase in residual magnetisation by 16 times in comparison with undoped bismuth ferrite, which was associated with the superexchange interaction of Fe3+-O-Ni2+. It was found in [32] that for ceramics of BiFe0.75Co0.25O3 the composition B saturation magnetisation (Ms = 1.6 A m2/kg), residual magnetisation (Mr = 0.7 A m2/kg), and coercive force (Hc = 39 kA/m) increased significantly compared to undoped BiFeO3. For BFO nanopowders doped with cobalt ions, the specific magnetisation in a 1.27 MA/m field at a temperature of 100 K was 61.2 A m2/kg and decreased at a temperature of 300 K to 39.5 A m2/kg, nevertheless remaining significantly higher than that for undoped bismuth ferrite [33].

For BiFeO3 films with a thickness of 50–500 nm, a giant magneto-electric effect (~ 3.8 V/A) was observed at room temperature, exceeding the magneto-electric effects in other materials under the same conditions by several orders of magnitude [34].

In this study, we propose the synthesis of nanoscale BFO with simultaneous doping with ions of the f-block element Ho for the destruction of a spin cycloid (Fig. 1). It is assumed that the transfer of bismuth ferrite into the nanoscale state will entail a change in the ratio of the crystal lattice parameters c/a and, accordingly, a change in the spin structure. A phase size effect is possible, which will lead to a decrease in the content of the low-temperature impurity phase Bi25FeO39 and an increase in the proportion of the high-temperature phase BiFeO3. The difference between the magnetic moments and ionic radii of holmium and bismuth will have a significant effect on the exchange interaction energy and magnetic properties of BFO.

Fig. 1
figure 1

Proposed approaches to the synthesis of pure BiFeO3 and destruction of the spin cycloid

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The aim of this study was the synthesis of HoxBi1-xFeO3 nanopowders by spray pyrolysis method and determination of the effect of holmium concentration on the magnetic and electrical characteristics of the samples.

2 Experimental

2.1 Materials and methods

Bismuth ferrite samples doped with holmium HoxBi1-xFeO3 (where x = 0, 0.05, 0.10, 0.15) were synthesized by the spray pyrolysis method [35]. Crystalline hydrates of holmium nitrate (reagent grade CAS 14483–18-2), iron nitrate (analytical reagent grade TU 6–09-02–553-96), and bismuth nitrate (analytical reagent grade CAS 10035–06-0) in a stoichiometric ratio corresponding to the final composition of HoxBi1-xFeO3 (where x = 0, 0.05, 0.10, 0.15) were dissolved in nitric acid with the addition of tartaric acid C4H6O6. The solution was placed in the disperser of the BFO synthesis unit (Fig. 2).

Fig. 2
figure 2

Scheme of the installation for the synthesis of BiFeO3 using the spray pyrolysis method. 1 – compressor, 2 – disperser, 3 – nozzles, 4 – rubber stopper, 5 – reactor (quartz tube), 6 –MTP-2 M tube furnace, 7 – thermocouple, 8 – thermostat, 9 – glass tube with 90° turn, 10 – receiver for collecting nanopowder

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In the disperser (2), the solution was transferred to the aerosol state with a particle size of 0.8 to 2.0 μm. Then, the aerosol was transferred by air flow into the reaction chamber (5) and heated in the hottest part to 770 °C. At this temperature, nitrates decompose with the formation of bismuth ferrite. The flow rate was 9 l/min, the aerosol particles were in the reaction zone for about 0.6 s. The particles were collected by passing the gas through water (10). Then, the solution was filtered and the powder was dried in air for 24 h.

2.2 Characterization

The phase composition of the samples was studied using an Empyrean BV X-ray diffractometer with a Cu anode (λ = 1.54060 nm). The start angle was 2θ = 10º, the final angle was 2θ = 80º, and step = 0.02º. The database of the International Center for Diffraction Data (JCPDS) was used for the analysis of diffraction patterns (Cards: 73–0548, 46–0416, 72–1832, 77–2008, 83–0410, 74–2352, 77–2355, 82–1533, 84–0311, 83–0932).

Quantitative elemental analysis and determination of morphological features were carried out on a JSM-6380LV JEOL scanning electron microscope with an INCA 250 microanalysis system. The particle size distribution histogram was plotted using the "ImageJ” program, version 1.53 k.

The particle size was determined by transmission electron microscopy (TEM, transmission electron microscope CarlZeiss Libra-120).

The magnetic characteristics of the samples were measured using a LakeShore 7407 vibrating sample magnetometer in the magnetic fields up to 1.27 × 106 A/m. The powder with mass 20–40 mg was packed in the flat plastic bag. Magnetic moment was normalized to the mass of the samples, and saturation magnetization (Ms) was obtained after fitting of the high-field region of M(H) curve.

Flat disks with a diameter of 6.1 mm and a thickness of 0.8 mm were made from HoxBi1-xFeO3 samples for measurements of the magnetodielectric effect. The samples were prepared by pressing the initial powder in a mold with a force of 3 × 104 N. The thickness of the samples obtained was determined by the mass of the loaded powder. Electrodes made of the electrically conductive adhesive "Kontaktol" based on silver were applied on the samples and connected to AM-3016 RLC meter (AKTAKOM). The samples were placed between the poles of an electromagnet that created an external magnetic field in two orientations: along the disk plane and perpendicular to it. The values of the magnetic field were determined using an RSH1-10 magnetic induction meter.

3 Results and discussion

3.1 Phase composition of the synthesized samples

According to XRD data (Fig. 3), BiFeO3 and Ho0.05Bi0.95FeO3 samples synthesized by spray pyrolysis were almost single phase with an insignificant content of Bi25FeO39 and Bi2Fe4O9. Several reflections of ferrite with a mullite structure were clearly expressed on the diffraction pattern of the Ho0.15Bi0.85FeO3 sample, although they had low intensity. Thus, the nominal degree of doping x = 0.15 can be considered as the limiting boundary for the introduction of holmium ions into BFO when the content of Bi25FeO39 and Bi2Fe4O9 impurity phases becomes significant.

Fig. 3
figure 3

Diffraction patterns of powders synthesized by spray pyrolysis: 1- BiFeO3, 2—Ho0.05Bi0.95FeO3, 3—Ho0.15Bi0.85FeO3. The dashed line indicates the BiFeO3 standard (Card 73–548)

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For the assessment of the content of impurities in the samples (Table 1), a semi-quantitative analysis of diffraction patterns was carried out by the “corundum number” method [36] using the formula

Table 1 Composition of the synthesized bismuth ferrite samples calculated by the corundum number method
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$$w_{{\text{k}}} = \frac{{{\text{I}}_{{\text{k}}}^{{{\text{max}}}} /{\text{RIR}}_{{\text{k}}} }}{{\sum\limits_{{\text{i}}} {{\text{I}}_{{\text{i}}}^{{{\text{max}}}} /} {\text{RIR}}_{{\text{i}}} }},$$
(1)

where wk is the mass fraction of phase k, Ikmax is the intensity of the largest reflex of the phase k, RIRk—corundum number of phase k, Iimax are the intensities of the largest reflections of i phases, and RIRi are corundum numbers of i phases. The synthesized samples contain less impurities in comparison with the results of other authors [11].

When superimposing diffraction patterns (Fig. 3), a shift in the reflections of samples doped with holmium Ho0.05Bi0.95FeO3 and Ho0.15Bi0.85FeO3, relative to the dopant-free BiFeO3, toward higher values of 2θ angles was noted. This finding indicates the distortion of the crystal lattice due to the introduction of ions with other ionic radii. Based on the values of ionic radii (r(Bi3+) = 0.117 nm; r(Ho3+) = 0.104 nm; r(Fe3+) = 0.069 nm; r(O2−) = 0.138 nm;) [37] and data on the shift of peaks in the diffraction pattern, it can be concluded that holmium ions were incorporated in the positions of bismuth ions in the crystal lattice of bismuth ferrite.

EDX analysis confirmed the presence of holmium in the samples (Fig. 4 a, b). The average values of the weight percent and atomic percent of the Ho, Bi, Fe, and O elements are shown in Table 2, and the results were consistent with the expected chemical composition (Table 2).

Fig. 4
figure 4

Spectra of elemental composition of samples; a – BiFeO3, b – Ho0.15Bi0.85FeO3

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Table 2 EDX analysis of BiFeO3:Ho3+ nanosized powders
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The values of coherent scattering regions (CSR) of the particles of the synthesized samples (Table 3) were calculated using the Scherrer formula [38]:

Table 3 The average CSR of the synthesized samples
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$$\beta=\frac{m\lambda }{D\cos\theta},$$
(2)

where β is the physical broadening, rad; m = 1; λ is the wavelength of X-ray radiation, nm; and D is the particle diameter.

As can be seen from Table 3, the average CSR values practically coincided for the undoped BFO and Ho0.05Bi0.95FeO3 samples, taking into account the error. During the transition from Ho0.05Bi0.95FeO3 to Ho0.15Bi0.85FeO3, there was a tendency for a slight increase in CSR values, which may be due to the phase inhomogeneity of the sample due to the presence of Bi25FeO39 and Bi2Fe4O9 impurities in the amount more than 10 wt%.

The lattice parameters of the samples were calculated using the UnitCell program: The calculated data for hexagonal packing are shown in Table 4.

Table 4 Lattice parameters of BiFeO3:Ho3+ samples synthesized by spray pyrolysis
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It can be seen that the lattice parameters and its volume decreased with an increased concentration of dopant, which correlated with shift of diffraction angles toward larger values observed in the diffraction patterns of HoxBi1-xFeO3 samples. In general, these data confirmed the incorporation of an ion with a smaller ionic radius (i.e., holmium) in place of an ion with a larger ionic radius (i.e., bismuth). The dependence of the lattice parameters on the degree of doping is satisfactorily approximated by a linear function (Fig. 5).

Fig. 5
figure 5

Graph of the dependence of lattice parameter a (a) and lattice parameter c (b) versus doping degree

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For the evaluation of possible stoichiometric deviations of the synthesized samples from the nominal composition for the Ho0.15Bi0.85FeO3 sample, elemental analysis was performed and the real composition was established—Ho0.14Bi0.81FeO2.87. Deviation from the nominal composition can be associated both with the presence of impurities in the sample and with the volatility of bismuth oxide at high temperatures.

3.1.1 Morphological characteristics of particles

The synthesized bismuth ferrite powder is represented by predominantly spherical agglomerates with a size of 1–3 μm (Fig. 6a).

Fig. 6
figure 6

SEM images of the BiFeO3 nanopowder (a) and histogram of size distribution of agglomerates (b), TEM image of the BiFeO3 (c, d)

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According to TEM data (Fig. 6), agglomerates were formed by particles with a size of 50–170 nm. A significant difference from the CSR values, calculated using the Scherrer formula, was due to possible significant calculation errors.

3.2 Magnetic properties of samples

For all synthesized samples, hysteresis loops were measured at temperatures of 300 K and 100 K, according to the obtained dependences of the specific magnetic moment on the magnetic field strength (Fig. 7a, b). The measurements were carried out over a range of fields from − 1.27 × 106 A/m up to + 1.27 × 106 A/m. An external field was applied in the sample plane to minimize the effect of the demagnetising factor.

Fig. 7
figure 7

Hysteresis loops of samples at temperatures of 300 K (a) and 100 K (b)

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Undoped BiFeO3 demonstrated a close to linear dependence of the specific magnetic moment on the external field, typical for antiferromagnets, while samples doped with holmium were characterized not only by a higher value of the specific magnetic moment at the same fields, but also by a hysteresis field dependence, which is typical for ferrimagnets (Table 5).

Table 5 Results of measurements of magnetic properties of samples
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The specific residual magnetisation and specific saturation magnetisation of both pure bismuth ferrite and BiFeO3 samples, doped with holmium, decreased with an increase in temperature from 100 to 300 K. The coercive force of all samples also decreased with increase in temperature up to 300 K, since thermal fluctuations which “loosen” the spins increase with the increasing temperature and the magnetic order decreases. This type of field dependence of the specific magnetic moment is characteristic of ferrites doped with rare-earth elements [39, 40], as well as rare-earth metal ferrites [41, 42].

At a temperature of 100 K, the values of the specific residual magnetisation and specific saturation magnetisation of HoxBi1-xFeO3 samples naturally increased with an increase in dopant concentration. At 300 K, the trend toward an increase in these characteristics also remained; however, for a sample containing 15% holmium, a slight decrease in Ms compared to that for Ho0.1Bi0.9FeO3 was observed. The decrease in the coercive force with an increase in dopant concentration was clearly expressed; however, the Ho0.15Bi0.85FeO3 sample both at 100 and at 300 K showed a significant increase in Hc in comparison with undoped bismuth ferrite.

Temperature dependence of the specific magnetic moment in a 1.27 × 106 A/m field is shown in Fig. 8.

Fig. 8
figure 8

Temperature dependence of the specific magnetic moment of samples in a 1.27 × 106 A/m field

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For all samples, the specific magnetic moment decreased with an increase in temperature. In this case, with an increase in the holmium concentration to 10%, the curves of the temperature dependence were higher, while the curve of the temperature dependence of the specific magnetic moment for Ho0.15Bi0.85FeO3 sample was below that for Ho0.1Bi0.9FeO3.

All revealed dependences of the magnetic characteristics of HoxBi1-xFeO3 samples on the concentration of holmium ions were primarily associated with a change in the energy of the exchange interaction caused by a change in the parameters of crystal cells due to the difference in ionic radii and magnetic moments of the cations of the substituted bismuth and the substituting holmium. The general trend in the change in the magnetic characteristics of doped bismuth ferrite was impaired at the critical value of the concentration of holmium ions in the range from 10 to 15%. This was also confirmed by the high value of the specific magnetic moment of the Ho0.1Bi0.9FeO3 sample at all temperatures compared to that for Ho0.15Bi0.85FeO3 (Fig. 8).

ZFC and FC dependencies were measured in a 3.2 × 104 A/m field for the Ho0.15Bi0.85FeO3 sample (Fig. 9).

Fig. 9
figure 9

Temperature ZFC and FC dependences of the Ho0.15Bi0.85FeO3 sample in a 3.2 × 104 A/m field

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These dependences allowed calculating the average and maximum particle sizes of the sample using the Bean-Levenston formulas (3) [43], assuming, according to [44], that for bismuth ferrite \({K}={10}^{5}\frac{ {erg}}{{ {cm}}^{2}}\)

$$\langle K\rangle \langle V\rangle=K{T}_{f}$$
(3)
$$\langle K\rangle {V}_{max}=K{T}_{rev}$$
(4)

where \(\langle {K}\rangle\) is average value of the constant of magnetic crystallographic anisotropy, \(\langle {V}\rangle\) is the average value of the particle volume, K is the Boltzmann constant, Tf is freezing temperature (maximum of ZFC-curve), Vmax is the maximum value of the volume of particles, and Trev is the temperature at which the ZFC and FC curves begin to diverge (determined as the temperature at which the difference between the ZFC and FC curves exceeds 3%).

The obtained values of the average particle size of 6.8 ± 0.2 nm and the maximum particle size of 7.8 ± 0.3 nm differ significantly from the results of electron microscopy, which was probably due to the agglomeration of individual nanoparticles into micron objects.

3.2.1 Electrical properties of samples

For measurements of the magnetodielectric effect, the samples were made in the form of flat capacitors, as described above, and connected to an RLC meter to determine the electric capacitance. Using the known values of the electric capacitance and the thickness and area of the capacitor plates, the dielectric constant was calculated using formula (5):

$$\varepsilon = \frac{{C_{d} }}{{\varepsilon _{0} S}}$$
(5)

For HoxBi1-xFeO3 samples in the frequency range from 0 to 200 kHz, the dependence of the dielectric permittivity on frequency in a zero external magnetic field was practically absent (Fig. 10), which is consistent with the results of [45] and [46].

Fig. 10
figure 10

Dependence of the dielectric permittivity of the samples on the signal frequency

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Despite the fact, that dependence on the external magnetic field was revealed, it was comparable with the measurement error. At a frequency of 100 kHz at room temperature, the field dependences of the longitudinal and transverse magnetic capacitances of the samples were measured; the results for the maximum field are shown in Table 6.

Table 6 Magnetic capacitance values for holmium-substituted ferrites in a magnetic field of 0.4 MA/m at room temperature
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For this series of samples, the value of the magnetocapacitance was less than a tenth of a percent in any fields and for any orientation of the sample, which disagrees with the results of [47, 48], where the value of the magnetocapacitance was 1% in a field of 1.1 T for pure BiFeO3 and 1.6% in the field of 1.1 T for Bi0.95La0.05FeO3 and for Bi0.95Nd0.05FeO3. It should be noted that the values given in [47] and [48] were obtained for ceramic BiFeO3 samples, and therefore, the fact of a strong influence of particle dispersion on the dielectric properties was confirmed.

4 Conclusions

HoxBi1-xFeO3 nanopowders synthesized by spray pyrolysis, according to TEM and SEM, were spherical agglomerates with a size of 1.5–3 μm consisting of individual particles with a size of 50–170 nm. A decrease in the lattice parameters and unit cell volume of the HoxBi1-xFeO3 samples was shown, and EDX data indicate the inclusion of holmium ions in the positions of bismuth ions in the BiFeO3 lattice. Doping of nanoscale BFO with holmium led to a significant increase in the saturation magnetization and remanent magnetization, while the coercive force decreases. The magnetic properties of HoxBi1-xFeO3 were characterized by a strong temperature dependence, and the frequency dependence of the permittivity was not observed in the frequency range up to 200 kHz. The values of magnetic capacitance in fields up to 5 × 105 A/m were less than a tenth of a percent due to the high dispersion of particles.