Structural transformation and magnetoelectric behaviour in Bi_1−xGd_xFeO₃ multiferroics

It has been known that single phase BiFeO₃ is quite difficult to prepare by the standard solid-state chemistry route. According to the Bi₂O₃–Fe₂O₃ phase diagram [26], the kinetics of phase formation can easily lead to the appearance of two impurity phases along with perovskite-structured BiFeO₃. Indeed, the high volatility of Bi₂O₃ leads to the formation of Bi-poor phase Bi₂Fe₄O₉, but a small excess of Bi₂O₃ in the reactants results in the formation of Bi-rich phase Bi₂₅FeO₃₉.

Figure 2 compares the room temperature XRD patterns of Bi_1−xGd_xFeO₃ samples with x = 0, 0.05, 0.1, 0.15 and 0.2. The major peaks can be readily indexed using the BiFeO₃ rhombohedral cell. The presence of non-perovskite Bi₂Fe₄O₉ secondary phase peaks (marked by * in figure 2) was routinely observed in undoped BiFeO₃ (figure 1) [27, 28]. These impurity peaks are still present in Bi_0.95Gd_0.05FeO₃. Increase in the Gd content prevents the formation of the second phase and pure phase Bi_0.9Gd_0.1FeO₃ was obtained with all the peaks corresponding to rhombohedral structure with the R3c space group. This supports the idea that doping with a certain amount of Gd stabilizes the perovskite BiFeO₃ phase [29].

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Analysis of the XRD patterns (figure 2) reveals that the lattice symmetry gradually changes from rhombohedral (R3c) to orthorhombic (Pnma). It is clear from the two insets of figure 2 that two separate peaks in BFO in the vicinity of 2θ = 40° and 58° are overlapped when Bi atoms are substituted by Gd. Moreover, extra reflections appeared for x > 0.1 which are inconsistent with the R3c symmetry. The Bi_1−xGd_xFeO₃ compounds with x = 0.15 and 0.20 were indexed in an orthorhombic system isostructural to parent orthoferrite (Pnma) GdFeO₃ [30]. Rietveld refined crystal structure parameters are listed in table 1. The data confirm the unit cell contraction due to the substitution of smaller Gd³⁺ ions for the larger Bi³⁺ ions. The similar phase transformation behaviour and close values of lattice parameters were also observed in the Gd-doped BFO ceramics by Khomchenko et al [31].

Figure 3(a) shows the room temperature FTIR spectra of the BGFO compounds. Reflectivity spectrum consists of an IR-active phonon structure and an electronic background at low frequency. The former is composed of a transverse optical (TO) and a longitudinal optical (LO) mode of the Fe-O oscillations which correspond to the peaks and dips, respectively. Hence, the strong TO phonon peaks near 550 cm⁻¹ and the small one near 435 cm⁻¹ are assigned to the Fe–O stretching and bending vibrations, respectively, being characteristics of the octahedral FeO₆ group in the perovskite compounds. The introduction of Gd³⁺ ions into the BFO parent structure causes an increase in the absolute value of the reflectivity for x < 0.15. It is also seen that larger x leads to broader and stronger peaks with their positions being shifted to lower frequency region. A clear deviation of the FTIR spectra for x > 0.1 from the rest of the samples was also observed in terms of a very broad absorption peak near 547 cm⁻¹, which indicates again the presence of a structural transformation.

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The real ε₁ and imaginary ε₂ parts of the complex dielectric function ε = ε₁ + iε₂ of BGFO, derived from the R reflectivity spectra trough Kramers–Kronig transformations, are shown in figures 3(b) and (c). Their features in the infrared region indicate the predominance of the ionic bonding in BGFO compounds and the presence of dielectric polarization mechanisms, related to the elastic displacement of electrons and ions.

In case the external frequency is in the range between the frequencies of the LO and TO phonons, where the real part of dielectric function ε₁ is negative, the incident wave experiences a significant reflection (area of the 'metallic reflection') (figure 3).

The dc magnetization curves versus temperature M(T) in a field of 0.2 T are shown in figure 4(a). It should be noticed that the difference in the magnetic moment measured in ZFC and FC sequences is insignificant. All of the curves for Gd-doped BFO show a constant magnetization at high temperatures and a Curie-like upturn below 50 K for the sample with x = 0.05, and below 150 K for the sample with x = 0.2. Figure 4(b) shows the temperature variation of the inverse magnetization below 50 K for Gd-doped compounds. These dependences were found to follow nearly perfectly a Curie–Weiss law. The value of magnetization increases with the increase in the Gd content and no inflexion point can be seen for BGFO. These values and behaviour of magnetization curves for BGFO ceramic samples are consistent with the data reported by Khomchenko et al [31]. However, a clear anomaly in temperature dependence of magnetization for BiFeO₃ in the range from about 240 to 270 K can be seen from the inset of figure 3. As has been already mentioned, the secondary phase Bi₂Fe₄O₉ was observed (see figure 1) in BGFO ceramic samples for x below 0.1. This impurity phase is paramagnetic at room temperature and undergoes a transition to an antiferromagnetic state at near T_N = 264 K [32]. Therefore, the anomaly in magnetization curve of BFO may be due to the presence of the secondary Bi₂Fe₄O₉ phase. As temperature decreases from 200 to 40 K, the magnetization decreases in accordance with the well-known temperature-dependent magnetization of antiferromagnetics and it shows an increase below 40 K. Similar features in ZFC and FC magnetization curves at low temperatures were reported for single crystals [14, 33] and 245 nm particles of BFO [34]. However, the splitting of ZFC and FC magnetization curves was reported in [33, 34] revealing a spin-glass behaviour at low temperatures. In contrast to that, our ZFC and FC curves for ceramic BFO almost coincide (see the inset of figure 4(a)) thus, possibly, excluding spin-glass transition down to the lowest investigated temperature of 2 K.

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Figures 5(a)–(c) show the magnetization hysteresis M–H loops for BGFO (x = 0–0.2) samples with an applied field up to 8 T. Figure 5(b) presents a zoom of figure 5(a) to highlight the opening-up of the hysteresis loops. For pure BFO, M–H curves exhibit linear field dependence at room temperature with the absence of remanent magnetization (figure 5(c)), as expected for an antiferromagnetic alignment of the Fe³⁺ magnetic moments. As can be seen from figure 5(b), at 5 K the BFO sample shows a weak ferromagnetism (M_r ≈ 0.002 emu g⁻¹), consistent with the other report [27]. The deviation from linear behaviour appears even at room temperature upon 5% substitution of Bi³⁺ by Gd³⁺ ions (see figure 5(c)). The enhancement of magnetic response with increasing Gd content in BGFO compound is more prominent at low temperatures in contrast to room temperature M–H curves which are not saturated at 8 T, thus confirming the basic antiferromagnetic nature of the compound. Indeed, the magnitude of the saturation magnetization at 5 K for the BGFO compounds with x ⩾ 0.1 is an order of magnitude higher than that of BFO (figure 5(a)). It is worth noting that BGFO with x = 0.2 exhibits unusual shape of M–H curves, which is peculiar to orthoferrite Pnma structure [35].The remanent magnetization of BGFO with x = 0.05 and 0.1 achieved at the level around 0.04 emu g⁻¹ and 0.07 emu g⁻¹ at room temperature, respectively, shows an abrupt rise with subsequent increase of Gd (figure 5(d)). It is known that the substitution of Bi³⁺ ions changes the Fe–O–Fe bond angle, providing the suppression of the spiral SMSS and hence the appearance of weak ferromagnetism [36]. Obviously, at x > 0.1 the gadolinium substitution induces a structural phase transition $(R3c\to {\it Pnma})$ which leads to the collapse of the SMSS and therefore to the noticeable enhancement of magnetization. Moreover, Gd³⁺ ions with their own large magnetic moments make an important paramagnetic contribution to the net magnetization. Khomchenko et al [37] showed that in Bi_0.8(Gd_1−xBa_x)_0.2FeO₃ system Gd³⁺ magnetic moments tend to align in the same direction as the weak ferromagnetic component of iron sublattice, thus providing a significant rise to the magnetization.

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Another possibility for interpreting the observed results is to consider the percolation process. The low-level x doping obviously leads to the formation of small isolated magnetic clusters where all spins are parallel. In the composition range 0 < x ⩽ 0.1, the ferromagnetic Fe–Gd clusters are isolated from each other by the Fe–Bi domain. These ferromagnetic mini-clusters grow in size by the substitution of Bi with Gd and in the region of 0.1 < x ⩽ 0.2 (beyond the critical percolation concentration P_c) the ferromagnetic clusters become large enough to be connected with each other, producing macroscopic magnetic moment.

The ME effect is a polarization response to an applied magnetic field, or conversely, the magnetization response to an applied electric field [38]. The ME effect was first theoretically predicted by Landau and Lifshitz for some spin-ordered materials [38] and soon confirmed experimentally by Astrov in antiferromagnetic Cr₂O₃ [39]. In the presence of magnetic and electric fields the induced polarization in multiferroic materials is obtained from the expansion of the free energy [1]:

$$\begin{eqnarray*}\fl P_i &=(E,H;T)=-\frac{\partial F}{\partial E_i }=P_i^{\rm S} +\varepsilon _0 \varepsilon _{ij} E_j +\alpha _{ij} H_j\\ \fl&\quad+\frac{1}{2}\beta _{ijk} H_j H_k +\gamma _{ijk} H_i E_j -\cdots, \end{eqnarray*}$$

where P^S denotes the spontaneous polarization, ε_ij is the relative permittivity. The tensor α_ij corresponds to induction of polarization by a magnetic field which is described as the linear ME effect. The third rank tensors β_ijk and γ_ijk are associated with the higher order ME interactions.

Bary'achtar et al [41] predicted that magnetically ordered medium should become electrically polarized near a magnetic inhomogeneity. If the magnetic ordering is inhomogeneous (that is magnetization M varies over the crystal), an electric polarization P arises in the vicinity of this inhomogeneity. The symmetry of the spatial distribution of this polarization is determined by the symmetry of the magnetic inhomogeneity. In the simplest case of cubic symmetry the form of the magnetically induced electric polarization is [42]

$$\begin{equation*} {\bit P}=\gamma \chi _{\rm e} [({\bit M}\cdot \nabla ){\bit M}-{\bit M}(\nabla \cdot {\bit M})]), \end{equation*}$$

where χ_e is the dielectric susceptibility in the absence of magnetism.

It was shown by Brown et al [43] that the ME response is limited by the relation $\alpha _{ij}^2 <\chi _{ij}^{\rm e} \chi _{ij}^{\rm m}$, where $\chi _{ij}^{\rm e}$ and $\chi_{ij}^{\rm m}$ are the electric and magnetic susceptibilities. Consequently, ferromagnetic ferroelectrics are prime candidates for displaying giant ME effects.

The most critical indicator of the ME coupling in multiferroics is the ME coefficient α_ME. Figure 6(a) presents the temperature dependence of ME coefficient at a fixed frequency f = 0.7 kHz of the ac magnetic field H_ac = 10 Oe. With the temperature increasing, the α_ME gradually increases for all samples and shows a sharp dip around 265 K for BGFO with x < 0.1. The position of the dip is consistent with the temperature of the antiferromagnetic–paramagnetic phase transition in Bi₂Fe₄O₉ impurity phase [32] and coincides with the position of the anomaly in magnetization versus temperature curve for pure BFO (see the inset of figure 4(a)). Our results are in a good agreement with the model proposed by Rado [44]. Using two-sublattice model, it was predicted that as the temperature increases towards the Néel temperature, the longitudinal ME coefficient should increase first to some maximum value and then decrease to zero. This qualitative assumption has been verified experimentally in Cr₂O₃ by Folen et al [45]. In [44] Rado explained the physical origin of the ME effect as a result of spin–orbit coupling.

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The variation of ME coefficient with dc bias magnetic field at room temperature is shown in figure 6(b). For rhombohedral BGFO compounds with x < 0.15, ME coefficient increases with increasing magnetic field and exhibits maximum around H = 0.3 kOe. These observations are in agreement with those already reported by Caicedo et al for undoped BiFeO₃ [2]. In the case of orthorhombic Gd-doped BFO, ME coefficient increases with increasing magnetic field up to 1.2 kOe and attains a maximum value of 9.15 mV cm⁻¹ Oe⁻¹ for x = 0.2. Further increase in magnetic field up to 10 kOe does not bring about any significant variation in the output.

These data present clear evidence for the ME coupling in BGFO ceramic compounds. The observed ME coupling could also be explained through the piezoeffect. In a piezomagnetic BFO [46] an applied magnetic field induces mechanical strain, which, in turn, can induce an electric polarization via piezoelectric effect. It has already been shown that coupling of magnetic and ferroelectric orders in BiFeO₃ single crystals [9] and thin films [12] results from the coupling of both antiferromagnetic and ferroelectric domains to underlying ferroelastic domain structure. Application of an electric field reversibly switches ferroelastic domains and is inducing changes in the magnetic structure. So far, the origin of the bulk ME coupling is unclear and further investigations are needed.