Compare with BiFeO3, due to the substitution of Sm in BiFeO3, the intensity of secondary phases (Bi2Fe4O9 & Bi25FeO40) are diminished and the peak intensities of (1 0 4) plane is decreased compared to (1 1 0) plane indicating a slight structural distortion in R3c phase than BiFeO3 (\ref{803282}). As a result the volume of the unit cell slightly reduces. This trend is similar to the x- ray diffraction patterns observed by sati et al [\cite{Chandra_Sati_2014}].
Further, adding 5% of Holmium on Sm doped BiFeO3 eliminates the secondary phases arising from pristine BiFeO3 and shift the peak intensities to higher angles (Fig \ref{803282}). Similar results are reported in few of the modified A - site doped BiFeO3 ceramic[\cite{Chandra_Sati_2014}\cite{Kumar_2013}]. This shift in peak intensities conform the substitution effect of Ho3+ on Sm doped BiFeO3 and results in significant structural distortion on the crystal structure of Bi0.85Sm0.1Ho0.05FeO3.
The Goldschmidt tolerance factor is used to examine the structural stability of the compounds given by
\(t\ =\frac{<r_A>+r_0}{r_B+r_0}\) (1) Where <rA> is the average radius of Bi3+, Sm3+ and Ho3+ ions at A site and rB and r0 are the radius of Fe3+ and O2- ions respectively. The tolerance factor of BiFeO3, Bi0.9Sm0.1FeO3 and Bi0.85Sm0.1Ho0.05FeO3 are found to be 0.889, 0.884 and 0.881 respectively. Since the tolerance factor of Bi0.85Sm0.1Ho0.05FeO3 is comparatively minimum and less than unity, since the tolerance factor is minimum and less than unity in Bi0.85Ho0.05Sm0.1FeO3, it is expected that during co - doping, the influence of short range trivalent metal ions such as Ho3+ and Sm3+ are compensated by long range Bi3+ ions with minimum lattice strain. The shift in XRD peaks around 51°, 57° supports the substitution in Bi0.85Sm0.1Ho0.05FeO3.
Fig \ref{262685} & \ref{194306} shows the Rietveld refinement of the powder diffraction pattern using GSAS II (General Structure Analysis System II) with least square algorithms[\cite{Toby_2013}] . Bi0.85Sm0.1Ho0.05FeO3 is indexed well in R3c phase with the acceptable goodness of fit(GOF), R-structure factor(Rf), R-Bragg factor(Rb), R-pattern factor (Rp)and weight profile factor (WRp) values. The normal probability plots for the distribution of error in the experimental X-ray diffraction is calculated from error analysis using Bayesian fits and differences normalized by the corresponding values of the estimated standard deviations, ranges, slope and their intercepts[\cite{Gagin_2015}]. The Rietveld refined parameters of all the samples are listed in the Table \ref{960385} and are shown in Fig. \ref{262685} & \ref{194306}. From Rietveld results, the bond angle of BiFeO3 (Fig. not shown), Bi0.9Sm0.1FeO3 and Bi0.85Ho0.05Sm0.1FeO3 along [111] direction are found to be 154.139°(0), 154.760°(0) and 155.062°(1) respectively. The tilt angle of FeO6 octohedra tilt angle can be calculated using the relation
\(\cos\ \theta_1=\frac{2\ -5\ \cos^2\phi_1}{2+\cos^2\phi_1}\) (2)
\(\cos\ \theta_2=\frac{1-4\ \cos^2\phi_1}{3}\) (3)
where θ1 and θ2 are the two Fe - O - Fe angles related to tilt angle φ of the FeO6 octohedra around pseudocubic [111] directions [\cite{Chatterji_2002}]
The tilt angles (φ) of FeO6 octohedra were calculated for BiFeO3, Bi0.9Sm0.1FeO3 and Bi0.85Ho0.05Sm0.1FeO3 samples and found to be 15.54°, 15.52° and 15.33° respectively. According to Nayek et al, the canting of Fe3+ ions in BiFeO3 is understood from antisymmetric Dzyaloshinskii Moriya (DM) exchange energy[\cite{Nayek_2014}]. i.e., for any rare earth substituted BiFeO3, Fe - O - Fe bond angle is deviated from the ideal pervoskite angle (180°) because of the DM exchange energy between Fe ions and favours spin canting [\cite{Nayek_2014}]. Hence it is expected that the magnetic behaviour will be altered in Bi0.85Ho0.05Sm0.1FeO3 with respect to Bi0.9Sm0.1FeO3 and BiFeO3
The Surface morphology of BiFeO3, Bi0.9Sm0.1FeO3 and Bi0.85Ho0.05Sm0.1FeO3 ceramics are shown in Fig. \ref{416705} & \ref{323149} . From the SEM images, it is observed that all the samples are crystallizes in micrograins range. The average particulate size were estimated to be pristine BiFeO3 is found to be 1.17 μm. Whereas the particulate sizes of Bi0.9Sm0.1FeO3 and Bi0.85Ho0.05Sm0.1FeO3 possess a non-uniform grains with decrease in grain size and increase in grain boundaries than BiFeO3. The decrease in grain size may be due to the reduction of oxygen vacancies in FeO6 octahedral site. However, Bi0.85Ho0.05Sm0.1FeO3 image exhibits voids of irregular dimension due to presence of porosity which might reduce the density in the ceramics [\cite{Pattanayak_2013}]
3.3. Magnetic studies
Fig.\ref{671833} shows magnetization as a function of magnetic field (M - H) for BiFeO3, Bi0.9Sm0.1FeO3 and Bi0.85Sm0.1Ho0.05FeO3 at ambient temperature. The magnetization curves of all the samples are varying up to 15 kOe specifying an antiferromagnetic ordering with corkscrew modulated spin structure. The magnetization values at magnetic field of 15 kOe for BiFeO3, Bi0.9Sm0.1FeO3 and Bi0.85Sm0.1Ho0.05FeO3 are found to be 0.088 emu /g, 0.1616 emu /g, and 0.2370 emu /g respectively.
BiFeO3 is known to be a weak antiferromagnetic substance with canted spin structure. Significant increase of magnetization in Bi0.9Sm0.1FeO3 and Bi0.85Sm0.1Ho0.05FeO3 ceramic are due to partial suppression of spiral spin ordering and results in the variation of Fe - O - Fe canting angle [\cite{Karthik_2012}]. Because ruette et al shows that the modulated spiral spin ordering gets completely destroyed at a magnetic field of 18 T (i.e., 180 kOe). Here, the magnetization values are observed at a maximum field of 1.5 T (15 kOe). This conforms the partial suppression of spiral spin ordering [\cite{Ruette_2004}].
On the other hand, the magnetization behaviour of Bi0.85Sm0.1Ho0.05FeO3 ceramic gets considerably enhanced than other two ceramics. This is because, Ho3+ is known to be magnetically active ion and comparatively the ionic radii of Ho3+ is smaller than Bi3+ and Sm3+ ions. Hence 5% of Holmium added to Sm doped BiFeO3 ceramics might experience a interaction between Fe3+ and Ho3+ ions in octahedral site and decouples the antiferromagnetic interactions with Fe3+ ions to some extent. As a result, the magnetization values gets improved. These results are comparable with some of the alkali rare earth doped polycrystalline ceramics [\cite{Zhang_2011}].
Further the remanent magnetization (2Mr) of BiFeO3, Bi0.9Sm0.1FeO3 and Bi0.85Sm0.1Ho0.05FeO3 are found to be 0.0021 emu /g, 0.0387 emu /g, and 0.0439 emu /g respectively, According to Kumar et al and karthick et al, the increase in Mr value may be due to the suppression of spiral spin ordering and coexistence of antiferromagnetic and weak ferromagnetic orderings [\cite{Karthik_2012}\cite{Uniyal_2009}] In order to justify the favouring of magnetic ordering (ferro magnetic or antiferromagnetic) in BiFeO3, Bi0.9Sm0.1FeO3 and Bi0.85Ho0.05Sm0.1FeO3 ceramics, Arrott - Belov - Kouvel (ABK) plots are drawn which is based on Weiss molecular field theory [\cite{Singh_2013}]. ABK plots are analysed using a linear function and then extrapolated to get Y intercept which is considered as saturation magnetization (Ms). If the Y intercept at H = 0 is negative, then contribution of antiferromagnetic ordering is favoured in the ceramics. Instead, if the Y intercept at H= 0 axis is positive, then the contribution of ferromagnetic ordering is favoured. Fig. \ref{578650} shows ABK plots of all the three samples at ambient temperature. The ABK plot reveals a negative Y intercept without any spontaneous magnetization at H = 0, representing an antiferromagnetic ordering is favoured in all the three ceramics [\cite{Kumar_2015}].
3.4. Dielectric studies
Fig. \ref{267928} and the inset of \ref{267928} shows frequency dependent dielectric constant and dielectric loss of BiFeO3, Bi0.9Sm0.1FeO3 and Bi0.85Sm0.1Ho0.05FeO3 at ambient temperature. Initially, dielectric constant are higher at lower frequencies and start decreasing on increasing the frequencies in all the three samples. Finally all of them are approaching towards constant value at higher frequencies. The high value of dielectric permittivity at lower frequencies are due to charge accumulation at grain boundaries. The extremely large permittivities/losses accompanied by a strong dispersion are due to charged defects such as vacancies which contribute to the interfacial polarization due to the Maxwell-Wagner effect. [\cite{Suresh_2016}]. The dielectric constants at 1 MHz for BiFeO3, Bi0.9Sm0.1FeO3 and Bi0.85Sm0.1Ho0.05FeO3 are found to 26, 79 and 50 which is comparable with some of the alkali rare earth doped polycrystalline ceramics [ \cite{Hussain_2015} \cite{Muneeswaran_2015}]. Comparing the dielectric constant value of pristine BiFeO3 with Bi0.85Sm0.1Ho0.05FeO3, high values of ɛr is observed which may be ascribed due to the suppression of secondary phases and/ or due to the presence of oxygen vacancies in FeO6 octahedral site. The dielectric loss at 1 MHz for BiFeO3, Bi0.9Sm0.1FeO3 and Bi0.85Sm0.1Ho0.05FeO3 are found to 0.268, 0.429 and 0.206 respectively. The value of dielectric loss for Bi0.85Sm0.1Ho0.05FeO3 ceramic is comparatively lower than other ceramics because of the reduction of Fe2+ ions in Fe3+ / Fe2+ redox couple which might reduce the conductivity and losses values [\cite{SINGH_2004}].
Fig \ref{786969} and the inset of Fig. \ref{786969} shows temperature dependent dielectric permittivity and the tangent loss of Bi0.85Ho0.05Sm0.1FeO3 ceramic in the frequency range to 5 kHz to 5 MHz respectively. Temperature dependent dielectric permittivity (ɛr’) at different frequencies shows strong dispersion over the measured temperature ranges. For the measured wide region, two anomalies are observed in Bi0.85Ho0.05Sm0.1FeO3 ceramics. Anomaly at 290° C corresponding to Neel temperature (TN) and other at 481° C corresponding to Curie temperature (Tc). The observed dielectric anomaly around TN may arise because of different reasons such as (i) resistive component of dielectric behaviour along with Maxwell - Wagner effect [\cite{Catalan_2006}] (ii) intrinsic magneto electric coupling due to the vanishing magnetic order over the electric order as predicted by Landau - Devonshire theory of phase transition [\cite{Benguigui_1972}]. In order to verify the origin of anomaly in ɛr’(T), temperature dependent resistivity across TN is also measured between 1 kHz to 1 MHz as shown in Fig. \ref{541683}. The observed results clearly pointing out that, there is no anomaly in the DC resistivity curve especially at the Neel temperature (TN) range and conforms the anomaly in temperature dependent dielectric constant is due to the intrinsic magnetoelectric coupling in Bi0.85Ho0.05Sm0.1FeO3 ceramics.
In case of temperature dependent dielectric loss (tan δ), the value of tan δ is low at lower temperatures and start increasing as the temperature increases. Around 200° C, the dielectric loss decreases rapidly as the frequency increases from 5 kHz to 5 MHz which is attributed to the influence of conductivity behaviour triggered by the presence of Fe2+ ions in the sintered Bi0.85Ho0.05Sm0.1FeO3 ceramics [\cite{Abdelkafi_2017}]. Also, high value of dielectric loss at higher frequencies is ascribed to the presence of coexistence of Fe2+ and Fe3+ ions in octahedral sites due to electron hopping conduction mechanism and presence of oxygen vacancies originating from the volatile nature of Bi3+ and / or transition from Fe3+ to Fe2+ ions [\cite{SINGH_2004}].
3.5. Ferroelectric and leakage current studies
Fig. \ref{978818} shows the ambient temperature electric field dependence of polarization (P - E) of polycrystalline BiFeO3, Bi0.9Sm0.1FeO3 and Bi0.85Sm0.1Ho0.05FeO3 ceramics at 100 Hz. The P - E loops of all the ceramics shows a loosy trend which might be due to presence of leakage current. However, the shape of P - E loop is significantly improved in Bi0.85Sm0.1Ho0.05FeO3 compare to the Bi0.9Sm0.1FeO3 and BiFeO3 samples and showing a nearly saturated ferroelectric behaviour to some extent. The remanent polarization (Pr) of BiFeO3, Bi0.9Sm0.1FeO3 and Bi0.85Sm0.1Ho0.05FeO3 are 0.0126 μC / cm2, 0.045 μC / cm2 and 0.0753 μC / cm2 respectively. This means that the ferroelectric behaviour is considerably enhanced by Holmium doping on Sm doped BiFeO3 ceramics. These results are comparable and better than some of the rare earth doped BiFeO3 either in nano or polycrystalline bulk form [\cite{Muneeswaran_2015}]. From these observations, it is found that the ferroelectric behaviour is considerably increased in Bi0.85Sm0.1Ho0.05FeO3 ceramic.
Fig.\ref{789888} shows the leakage current density of BiFeO3, Bi0.9Sm0.1FeO3 and Bi0.85Sm0.1Ho0.05FeO3 ceramics at ambient temperature. From J - E curves, it is found that at an applied field of 20 kV/cm, the leakage current density of Bi0.85Sm0.1Ho0.05FeO3 is 5.753 x 10-10 A / cm2, which is approximately one order and three orders less in magnitude than Bi0.9Sm0.1FeO3 (3.83 x 10-9 μC / cm2) and BiFeO3 (1.87 x 10-7 μC / cm2) hence the leakage current density of Bi0.85Sm0.1Ho0.05FeO3 is decreased on substituting Holmium content in Sm doped BiFeO3 ceramic [\cite{Zhang_2011}]. The reason behind reduced leakage current and higher remanent polarization are may be due to the reduction of oxygen vacancies which might induce the pinning effect on polarization switching domains thereby improving the ferroelectric properties [\cite{Mao_2011}].
3.6. Magnetoelectric coupling
The change in magnetization for an applied electric field or of polarization by magnetic field leads to magnetoelectric effect. This coupling effect is demonstrated by measuring the P-E loop of Bi0.85Sm0.1Ho0.05FeO3 ceramic at a particular frequency, with static magnetic field.
Here the polarization and hence the dielectric constant are found to be varying with applied magnetic fields.
The dielectric behaviour of the sample in the presence of magnetic field leads to the magnetodielectric (MD) effect and can be expressed as [\cite{Zhang_2011}\cite{Dai_2016}].
\(MD\ =\frac{\epsilon\left(H\right)-\epsilon\left(0\right)}{\epsilon\ \left(0\right)}\ .\ 100\%\) (4)
where & are the dielectric constant with presence and absence of the magnetic field. The value of magnetodielectric effect at a frequency of 100 Hz is increased for increasing magnetic field (Fig. \ref{767408}) and the coupling coefficient is found to be 0.91 % at 4 kOe. This is because, whenever there is a rotation of oxygen octahedron, the tilt angle gets varied and favours Dzyaloshinskii-Moriya (DM) magnetic moments which results in increasing the intrinsic spin lattice coupling [\cite{Tirupathi_2013}]. Further, in order to conform the presence of magnetoelectric coupling in Bi0.85Sm0.1Ho0.05FeO3 ceramic, Magnetic poling was performed on this ceramics at ambient temperature as shown in Fig. \ref{791753}. After 25 minutes of poling under 9 kOe of DC magnetic field, the remanent polarization (2Pr) changes from 0.18 μC / cm2 to 0.11 μC / cm2. Also, the area of P - E loop before and after pooling (9 kOe) of magnetic field are found to be 1.06% and 0.64%. This clear change in the area of P - E loop conforms the signature of magnetoelectric coupling present in the ceramic. Similar trend was already identified by Tirupathi et al for Bi1-xCaxFeO3 ceramics. Here, the magnetoelectric coupling appears on Bi0.85Sm0.1Ho0.05FeO3 ceramic is based on the qualitative explanation put forward by Palkar et al [\cite{Palkar_2004}]. According to Palkar et al, when magnetic field is applied to multiferroic material, due to the coupling between magnetic and ferroelectric domains, the material will be strained. As a result, this strain induces a stress in the ferroelectric domain and tempts an electric field in the material. Therefore the polarization and dielectric constant varies accordingly.
4. Discussion
BiFeO3 is known to an interesting material for the reasons that it is found to be a multiferroic as well as magnetoelectric. All magnetoelectric materials need not be multiferroic and vice versa. Literature shows that a partial substitution of trivalent metal ions like Sm3+[\cite{Khomchenko_2010}], La3+\cite{Jangid_2012}, Dy3+\cite{Muneeswaran_2015} ,Ho3+\cite{Durga_Rao_2012} and Gd3+\cite{Pattanayak_2013} would distort the crystal structure of the host BiFeO3 to enhance the multiferroic ordering. Also, as the doping concentration of trivalent metal ions exceeds 15% in BiFeO3 most of the system involves a structural phase transformation
Eventhough there are number of articles in single phase Sm doped BiFeO3 ceramics with enhanced multiferroic behaviours due to structural changes, particularly due to the change in bond length and reduced secondary phases. Here, we went for co-doping because as Sm doped BiFeO3 shows strong signature of secondary phases in XRD analysis and may violate the aim. Now when both Sm and Ho trivalent ions are substituted at Bi site (in very small concentration), it is found that it retains the structure of host BiFeO3 reducing all the secondary phases. Here the role of Ho3+ is not only to enhance the multiferroic behaviour but also to supress the secondary phases and to reduce the high leakage current density. \cite{Uniyal_2009,Zhang_2011,Kumar_2013} .
5. Conclusion
Single phase polycrystalline Bi0.85Sm0.1Ho0.05FeO3 is successfully prepared through solid state route and the variation of bond angle and bond length influencing the electrical and magnetic properties are investigated from Rietveld refinement analysis. The magnetization and ferroelectric polarization are found to be significantly improved in Bi0.85Sm0.1Ho0.05FeO3 than Bi0.9Sm0.1FeO3 and BiFeO3 ceramics. Temperature dependent dielectric constant shows an anomaly at 290° C nearer to TN, which is due to the intrinsic magnetoelectric coupling of Bi0.85Sm0.1Ho0.05FeO3 ceramic. A clear change in area of P - E loop after magnetic pooling also conforms the signature of magnetoelectric coupling. Hence it is concluded that, Bi0.85Sm0.1Ho0.05FeO3 is one of the probable candidate in the family of BiFeO3 to enhance magnetoelectric effect at ambient temperature and helpful for device applications.
Acknowledgements
One of the author R. Rajesh would like to thank the following centres:
SAIF, IIT Madras, Department of Nanoscience and Technology, Karunya University, Coimbatore, Department of Physics, Alagappa University , Karaikudi , ACIC, St. Joseph College, Trichy. The author KR acknowledges UGC for emeritus scheme.