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Study of Structural, Magnetic and Electrical properties on Ho - substituted BiFeO3

The polycrystalline Bi1-xHoxFeO3 (x=0, 0.05, 0.1) compounds were synthesized by conventional solid-state route. Rietveld refinement reveals that all the compounds were stabilized in rhombohedral structure with R3c (IUCr No. 161) space group. A competing ferro and anti-ferro magnetic interaction was observed in Ho-substituted compounds. A change in the Fe-O-Fe bond-angle and Fe-O bond distance increase the Neel Transition temperature with increasing Ho concentration. The appearance of peak in imaginary part of impedance (Z") for each concentration and shifting of this peak with temperature towards higher frequency side indicated that the presence of electric relaxations. Correlated Barrier Hopping model (CBH) was employed to explain the frequency and temperature dependence of ac conductivity and the mechanism of transport in the material BFO and Ho substituted BFO. Density of states near Fermi level was calculated by using the ac conductivity data.


Introduction
Materials which exhibit simultaneous presence of magnetic and electric ordering are called multiferroics [1][2][3]. These materials have been studied due to both, their potential applications for electronic devices and interesting physics in it. BiFeO 3 (BFO) is a well-known multiferroic at room temperature having para-to ferro-electric transition temperature T C ~ 1103K and a G-type antiferromagnetic transition at T N ~ 643K [4]. BFO , in its bulk form, crystallizes in rhombohedral structure with R3c space group. In BFO, ferroelectricity arises due to the stereochemical activity of 6s 2 lone pair electrons of Bi 3+ , while the indirect magnetic exchange interaction between Fe 3+ ions through O 2causes G-type antiferromagnetic ordering. But, BFO has a serious drawback of high leakage current due to either the presence of impurities or oxygen vacancies which promotes the low resistive path for conduction. To reduce the leakage current and to understand the underlying mechanism, various methods have been employed [5,6]. To improve the physical properties, substitution is one of the best techniques [7][8][9]. Generally, rare earth ions or divalent alkaline earth ions will be substituted at A-(here Bi) site and transition metal elements at B-site (here Fe). But substitution of divalent ions at A-site may increase the oxygen vacancies [10] in order to make charge neutrality in the compound. This will enhance the leakage current which will deteriorate the electric properties of the compounds. So the multiferroic nature of the compounds can be improved by substitution of rare earth elements at A-site which creates internal chemical pressure within the lattice. This internal chemical pressure plays an important role to suppress the leakage current and improve the electric and magnetic properties [11]. It has been reported that substitution of lanthanides like La 3+ [12], Nd 3+ [13], Eu 3+ [14] and Gd 3+ [15] for Bi 3+ in BFO would affect the crystal structure which in turn show an improved magnetic and electric properties. There are some reports on dielectric properties and impedance spectroscopy studies on BFO [16][17][18]. But to the best of our knowledge, there is no detailed study on ac conductivity and charge carrier mechanism in BFO.
In this report, we have studied the electrical properties of BFO and substituted BFO. We employed correlated barrier hopping model to describe the charge carrier mechanism and calculating the number of density of states near Fermi surface for the first time to our knowledge for BFO.
In this present work, Ho 3+ ion has been chosen to substitute for Bi 3+ ion due to its smaller ionic radius (1.015 Å) as compared to Bi 3+ (1.17 Å). The Ho 3+ ions will create internal chemical pressure which will effect significantly the distortion in the structure. This distortion presumably may improve the physical properties of the system.

Experimental Details
BFO and Bi 1-x Ho x FeO 3 (BHFO) [x = 0.05 (BHFO5), 0.1 (BHFO10)] polycrystalline compounds were synthesized by conventional solid-state reaction technique using the high purity Bi 2 O 3 , Fe 2 O 3 and Ho 2 O 3 (purity > 99.9%) as starting materials. These powders were mixed with their stoichiometric ratios and ground thoroughly for 2h. The powders were calcined in two step process at 780 o C for 2h and then at 815 o C for 3h. The calcined powder were pelletized in the form of circular disc of size 8 mm diameter and 1.5 mm thickness and sintered at 815 o C for 3h with a heating rate of 5 o C / min. The crystal structures of the compounds were examined by an X-ray diffractometer (Panalytical X'pert PRO) with Cu K α radiation. Raman studies were performed using Raman Spectrometer (Senterra). The magnetic properties of these compounds were measured using vibration sample magnetometer (ADE systems, Model no-EV9, USA).
Deferential scanning calorimetry (DSC) was performed on a TA-Q200 calorimeter at a heating rate of 10 o C / min. Dielectric properties were measured using Wayne Kerr 6500B impedance analyzer.  [19,20]. These impurity phases always exist along with the main phase (BFO). But with the substitution of Ho, the intensity of this secondary phase decreased. Lattice parameters are refined by using R3c space group in a hexagonal unit cell using Full Prof software. The Goldschmidt tolerance factor t, defined as where <r A > is the average radius of Bi 3+

Structural Properties
and Ho 3+ ions at A site and and are the radii of Fe 3+ and O 2respectively. As the Ho content increases, the average radius at Bi-site decreases. Consequently tolerance factor will decrease.
This means that crystal structure will change from high symmetric state to low symmetric state.
Due to this crystal distortion, lattice parameters, bond angles and bond distances will change. A systematic variation in the lattice parameters and Fe-O-Fe bonds angle have been observed with the increase of Ho content which in turn consistent with an average A -site ionic radii (<r A >).
The volume of the unit cell decreases continuously with the Ho content, which is due to the smaller ionic radius of Ho 3+ as compared to that of Bi 3+ . Variation of lattice parameters, bond angles and bond distances of BFO and BHFO compounds are given in the table I. bonds. As the Ho content increases in BFO, the frequency of these modes shift gradually to higher frequency side. If k is the force constant and M is the reduced mass, then the frequency of the mode is proportional to (k / M) ½ provided it is governed by the local factors [24]. If we assume the radius of Ho 3+ ion is same as the radius of Bi 3+ , since the valence of Ho 3+ is same as that of Bi 3+ , k is assumed to be independent of substitution as a zero approximation. As the mass of Ho 3+ ion is 21% less than the mass of Bi 3+ ion, the relatively light Ho 3+ ion may increase the frequency of vibration of the modes.

Magnetic properties
Isothermal magnetization (M -H) curves of BFO and BHFO compounds have been recorded up to a maximum magnetic field of 20 kÖe at room temperature as shown in Fig. 3. In BFO, the Fe 3+ magnetic moments are coupled ferromagnetically in the pseudo cubic (111) planes, but antiferromagnetically between the adjacent planes. The existence of superimposition of spiral modulated spin structure with the G-type antiferromagnetic spin ordering prevents both the observation of any net magnetization and the linear magnetoelectric effect. The existence of a weak ferromagnetic moment is permitted by the crystal symmetry of BFO [25]. As the Ho content increases, the average radius at Bi-site decreases. This will create the change in the angle T N is also increasing which is consistence with our observations. Fig. 4 shows the frequency dependence of real and imaginary parts of impedance (Z′ and Z″) for BFO and BHFO at room temperature where as Fig. 5(a-c)  region in all the compounds indicate that the conductivity of these compounds increases with the increase of frequency due to the increase of hopping of charge carriers between the localized ions. At low frequency, the value of Z′ for these compounds decreases with the increase of temperature and these values merge at high frequency region due to the increase of ac conductivity i.e. existence of negative temperature coefficient of resistance (NTCR) in the compounds. Decrement of Z′ with the increase of temperature and frequency suggests a possible release of space charge and consequently lowering of barrier properties in these materials [30].

Impedance studies
For a given temperature, with the increase of Ho concentration in BFO, Z′ increases (see Fig. 5) which indicates an enhancement of the bulk resistance of the compounds with the substitution.  Asymmetric broadening of peaks indicates distribution of spread of relaxation times [31]. The magnitude of Z″ at f max decreases with the temperature indicating the presence of space charge polarization at low frequency which disappears at high frequency [32]. The magnitude of Z″ at f max increases with the increase of Ho content. The peak in the Z″ data shifted in the low frequency side with the increase of Ho. This may be attributed to a phenomenon with maximum capacitive effects on Ho substitution. Fig. 6 shows the frequency variation of ac conductivity at different temperatures. The response of the material to the applied electric field is described by the ac conductivity. The nature of transport process will be known by ac conductivity studies. The ac electrical conductivity was calculated by using the relation,

AC Conductivity studies
Where the thickness and S is the surface area of the pellet.
At room temperature, the frequency dependence of ac conductivity obeys the universal power law [33]  ac = Aω s …3 Above room temperature this dependence follows the equation [34]  ac = A 1 ω s 1 +A 2 ω s 2

…4
Where A, A 1 and A 2 are temperature dependent parameters and s, s 1 and s 2 are both temperature and frequency dependent parameters. The values of s 1 and s 2 are determined by the slopes in the low and high frequency regions respectively. But from the observed data, s values are lower than 1 and decrease with the increase of temperature. With the increase of temperature, the value of s 1 is decreasing and approaching to zero at high temperature. This indicates that at high temperatures and at lower frequencies, the dc conductivity dominates and obeys Joncher's power law [35]: Where, σ (0) is the frequency independent part of conductivity.
At lower frequencies, as the temperature increases,  ac is very nearly equal to σ (0) due to interwell hopping which is responsible for dc conduction. As the frequency increases, ac conductivity σ (ω) increases which is presumably due to dominance of intra-well hopping over the inter-well hopping.
Generally, in the case of Quantum Mechanical Tunneling (QMT) through the barrier separating the two localized sites, s should be independent of temperature and slightly decreases with frequency while in the case of Correlated Barrier Hopping (CBH), s should decrease with the increase of temperature. Fig. 6 shows the temperature dependence of ac conductivity. Inserts in Fig. 6 show the temperature dependence of s. It is observed from the figure that s values are less than 1 and decreasing with temperature. Further the values of s in the low frequency region decreases and approaches to zero as the temperature is increased. So the observed data is consistent with the CBH model. This indicates that the conduction process is thermally activated. These materials have band gap similar to that of semiconductor and hopping conduction mechanism in these materials is generally consistent with the existence of a high density of states. Polarons are formed due to localization of charge carriers and the hopping conduction may occur between the nearest neighboring sites [36].
Based on the CBH model, the number of density of states N(E f ) near the Fermi level was calculated by the ac conductivity data using the following relation [37] ... 6 Where f o is the photon frequency and α is the localized wave function, assuming f o = 10 13 Hz and the polarizability α = 10 10 m -1 at various operating temperatures and frequencies. Fig. 7(a-c) shows frequency dependence of number of states N(E f ) for BFO and BHFO compounds at