The electron spin resonance (ESR) and magnetization (M) studies of Bi-manganites were undertaken to understand the coexistence of various magnetic phases and their effect on charge ordering as a function of composition and temperature. The studies on several compositions of Bi-manganites reveal that the electronic phase separation (PS) is an intrinsic phenomenon in this system.
- electronic phase separation
The perovskite structure is represented by general composition ABO3. Manganites belong to this family with A as trivalent (La3+, Pr3+, Bi3+, etc.) and/or divalent (Ba2+, Ca2+, Sr2+, etc.) ion and B as Mn ion. Manganites have a complex phase diagram and display interesting properties like colossal magnetoresistance (CMR) and giant magnetoresistance (GMR) [1‒7]. These properties are the result of strong coupling between the charge, spin, and orbital degrees of freedom. The strength of this coupling depends on hydrostatic pressure [8, 9], magnetic and electric fields [10, 11], grain size [12, 13], and disorder created due to substitution at A-/B-site. The trivalent rare-earth ions doping of different sizes into the perovskite structure causes disorder in the sample due to change in chemical pressure, leading to the evolution of coexistence of various magnetic phases viz: paramagnetic (PM), ferromagnetic (FM), canted-antiferromagnetic (C-AFM), and antiferromagnetic (AFM). The phenomenon of phase separation (PS) has been proposed to explain the properties of manganites in view of inhomogeneities arising due to doping of the material. The PS can be electronic or structural. The electronic PS occurs when cluster formation takes place at nanometric level. The structural PS, which is due to disorder, can induce formation of up to micrometer-size clusters, which assist in percolation leading to first-order transitions [14–16]. The Griffiths Phase (GP) concept  has been used to explain the coexistence of FM and AFM domains in different types of manganites.
Bi1-xCaxMnO3 (BCMO) and Bi1-xSrxMnO3 (BSMO) manganites are insulating over the entire range of compositions with various phases [18–20]. The charge ordering temperature (TCO) is 300–500 K for these materials, which is high compared to rare-earth materials. The charge ordering (CO) in these materials does not depend on the one electron bandwidth mechanism like in other manganites as it is due to highly polarizable 6s2 lone pair of Bi3+ions.
In this chapter, we will review the recent work reported on these systems. The effect of substitution of various elements including transition elements at Bi- and Mn-site of these systems is reviewed. The study on various systems is considered to elucidate the intrinsic nature of PS phenomenon in these systems. In order to understand the evolution of various magnetic phases as a function of dopants at different sites and grain size; the following series of samples synthesized by solid-state (SS) or sol–gel (SG) methods are considered.
Bi1-xCaxMnO3 (x = 0.30–0.90) (BCMO)
Bi0.5-xPrxCa0.5MnO3 (x = 0.0–0.50) (BPCMO)
La-doped Bi-manganites [Bi0.7-xLaxCa0.3MnO3 (x = 0.07–0.70) and Bi0.30La0.37Ca0.33MnO3]
Bi0.5Ca0.5Mn0.95TE0.05O3 (TE = V, Cu, and Zn)
Bi0.5Ca0.5Mn0.95TM0.05O3 (TM = Ni, Fe, Co, and Cr)
Bi0.55Ca0.45MnO3 and Bi0.5Ca0. 5MnO3 nanoparticles
The properties of the samples were studied using the following characterization techniques.
X-ray diffraction (XRD)
Scanning electron microscopy (SEM)
Energy dispersive x-ray spectroscopy (EDX)
Electron spin resonance (ESR)
Magnetization by vibrating sample magnetometer.
2. Electron spin resonance
There are two experimental techniques, namely magnetic resonance and inelastic neutron scattering, which can be used to describe the spin dynamics. Since double-exchange (DE) interaction mechanism is an intrinsic dynamical process, the investigation of spin dynamics and their static properties is crucial to study the magnetic properties of manganites. Although neutron scattering can provide information about magnetically ordered phases, but it has limitations in probing the spin dynamics of PM phases. The electron spin/paramagnetic resonance (ESR/EPR) is a sensitive technique which can help to understand the spin structure and its dynamics in complex magnetic-ordered phases. This technique has been used by several scientists to study the spin dynamics of manganites. In the present work, the ESR technique is used to investigate various dynamical processes over a wide range of temperatures.
2.1. Origin of ESR in manganites
The Mn2+ ion (S = 5/2) is the most common ion detected by ESR. The Mn3+ (3d4 with S = 2) exhibits a large zero-field splitting and strong spin-lattice relaxation and so unlikely to be ESR active . The Mn4+ ions (3d3 with S = 3/2) give an ESR signal usually at low temperatures. The manganese ions, Mn3+ and Mn4+, are commonly seen in doped manganites. Theories suggesting that the two Mn3+ ions transforming into Mn2+ and Mn4+ ion pairs via thermally excited disproportionation were common [22–24]. It is generally accepted that manganites do not have, or have a very small ratio of, Mn2+ ions and hence do not contribute to the ESR signals exhibited by manganites. ESR signals obtained in La-based manganites have been attributed primarily to Mn4+ ions in an octahedral anion crystal electric field in ground state with a weak spin-lattice relaxation , which makes this ion ESR active even at higher temperatures . Shengelaya et al.  attributes the ESR signal to Mn4+ in a system of three components such as Mn4+ ions, Mn3+ ions, and the lattice, and predicted an FM Curie–Weiss like behavior for the double-integrated line intensity, which is proportional to the static susceptibility arising from the FM couplings of the Mn4+ and Mn3+ magnetic subsystems . But the ESR signals cannot be attributed to isolated Mn4+ ions. The origin of ESR signal observed in manganites has been assigned to some combinations or clusters of Mn3+–Mn4+ ions coupled by a strong short-range FM–DE interaction [4, 27]. All the Mn ions are assumed to contribute to the ESR signal and the normalized double-integrated intensity (DI) is therefore proportional to the number of ESR centers and also a measure of ESR susceptibility (χESR) [4, 28].
2.2. Theoretical background
The experimental ESR spectra (Fig. 1) was analyzed by Lorentzian expression given as
where H0 is the resonance field, ΔH is the linewidth, and A is a quantity proportional to the area under the curve which is related to the intensity of the signal [21, 29, 30]. The two terms in Eq. 1 describe the contribution from the clockwise and anticlockwise circularly polarized components of microwave radiation.
It was suggested  that when the ESR signals are intense near the critical point (Curie temperature, TC), even for relatively small amount of samples, the ΔH depends strongly on the number of spins in the sample. Whenever large amount of samples are used, the sample size effects arise from overloading the cavity through magnetic losses [28, 31]. The ESR signals remain Lorentzian as long as the magnetic losses are not large enough to drive the diode detector out of linearity . When the sample is loaded in the cavity, at a fixed microwave frequency, ∆H can be given by the following expression
where χESR is the static susceptibility corresponding to resonant species, η is the fitting factor, and QL is the loaded Q of the microwave cavity. Similarly, the changes in line intensity (I) also occur by size effects due to magnetic losses, and the expression for this can be given  as
These two equations (2) and (4) have certain limitations such as the value of b should be « 1. In addition to the sample dependent effects, frequency or applied field dependences of ∆H have also been reported [28, 32, 33]. Apart from the above-mentioned parameters, skin depth (δ) also affects the parameters I and ΔH of the ESR signal, and it is given by the expression
where ρ is the resistivity of the sample measured at room temperature (RT), µo (= 4π × 10–7 Vs/Am) is the permeability of free space, and ω (= 2π × 9 GHz) is the microwave frequency. The estimated values of δ are found to be in the range 0.2–1.5 mm, and it is larger than that of the size of samples . In the present work, we have also taken care of cavity over loading problems. This ensures that the observed ESR signal intensity, ΔH, and resonance field (H0) as a function of temperature are intrinsic in nature.
The study of magnetic properties of the samples with ESR technique is limited in the low temperatures due to its instrumental limitations. In order to support the ESR findings and to study the magnetic properties down to the temperature up to 5 K (from 350 K), the Quantum design Physical Property Measurement System (PPMS) was used. Magnetization as a function of temperature was measured in both zero field cooled (ZFC) and field cooled (FC) by applying a field of 500 Oe.
2.3. Studies on Bi1-xCaxMnO3 (x = 0.30–0.90)
Figure 2 depicts the Rietveld refinement of XRD pattern for the sample with x = 0.65. With the refinement, XRD data are well reproduced with Pnma space group orthorhombic structure of all the samples except the sample with x = 0.30. Using the refined parameters crystal structure is generated for all the samples, as shown in Fig. 3 for Bi0.35Ca0.65MnO3 which is representative of all the samples. With increase in Ca content, decrease in unit cell volume is observed. This is ascribed to lower ionic radii of Ca2+ (1.12 Å) than that of Bi3+ (1.24 Å) ion.
Figure 4 shows DI of ESR signal as a function of temperature. For samples with 0.40 ≤ x ≤ 0.80, as the temperature decreases from high temperature (453K), DI increases and reaches its maximum, which is assigned as charge ordering temperature (TCO) . Below TCO, DI decreases, evidencing the existence of AFM correlations and reaches a minimum and then it increases with further decrease in temperature for samples with 0.65 ≤ x ≤ 0.80. For x = 0.30 sample, a weak TCO is observed. For x = 0.85 and 0.90 samples, no TCO is observed. For x = 0.85 and 0.90 samples, on cooling from high temperature, DI increases gradually. For 0.30 ≤ x ≤ 0.80 samples, sharp decrease in DI below the temperature ~126–150 K is assigned as the temperature at which onset of long-range AFM ordering takes place, that is, Neel temperature (TN).
The 1/DI vs T plots for various samples are shown in Fig. 5. The linear fit in the high-temperature range is as per Curie–Weiss law . The positive intercept on the x-axis in the temperature range T > TCO for samples with 0.30 ≤ x ≤ 0.80, indicates the existence of FM–DE correlations. The charge ordering transition of 0.65 ≤ x ≤ 0.80 samples is smeared compared to what is observed for samples with x ≤ 0.60. The CO transition at 303 K is weak for sample with x = 0.75. The existence of Bi-rich CO phase, a chemical phase separation in the samples, with x = 0.75, 0.70, and 0.65 may be the reason for this. The upward and downward trend in 1/DI vs T plots below TCO is an indication whether AFM or FM interactions dominate in the respective temperature range . The minima in these plots indicate the onset of CO or AFM ordering. For samples with x = 0.65, 0.75, and 0.80, 1/DI vs T plots show a broad peak at ~160 K, which is attributed to C-type AFM correlations. The down turn behavior of 1/DI in the temperature range below 148 K for the samples with x = 0.85 and 0.90 can also be explained in view of short-range ordering of FM clusters in PM matrix as per Griffiths theory. The negative intercept on the x-axis for samples with x = 0.85 and 0.90 indicates dominant AFM-superexchange (SE) interactions above 150 K. Below 150 K, localized FM correlations dominate [4–6].
Figure 6 shows ΔH as a function of temperature. For samples with x ≥ 0.65, ∆H shows prominent minima at ~150 K. The ESR signal persists only for a few degrees below 150 K for all the samples and then it disappears indicating the onset of long-range AFM state (TN). ∆H increases linearly with increase in temperature in the temperature range T≥TCO. ∆H saturates with increase in temperature as TCO decreases with increase in x. This effect is clearly seen for sample with x = 0.8. ∆H increases with decrease in temperature for the sample with x = 0.90, indicating the strengthening of AFM interactions with lowering of temperature.
Figure 7 shows magnetization vs temperature (M vs T) plots for various samples. As the temperature decreases from 350 K, both ZFC and FC curves show a peak at TCO for samples with 0.30 ≤ x ≤ 0.80. M decreases slightly on further decrease in temperature. The broad maximum at ~150 K observed for samples with x ≤ 0.50 represents long-range AFM order . The sharp rise in M for samples with x ≤ 0.60 at ~50 K is related to the spin-glass (SG) or cluster-glass (CG) transitions which arises due to competition between FM interaction in BiMnO3-type clusters and AFM coupling in clusters in which Mn3+ orbits are frozen in random orientations . For these samples, M vs T plots in ZFC mode show a peak in M at spin freezing temperature (Tf). A small peak in M at ~120 K observed for sample with x = 0.50 is ascribed to field-induced spin canting in the AFM phase aided by the spontaneous canting moment . The trend and the conclusions drawn from 1/χ vs T (not shown) and 1/DI vs T plots are similar.
Figure 8 shows the estimated values of TCO and TN from the ESR and magnetization data for Bi1-xCaxMnO3. The magnetic phase in the temperature range T > TCO is dominated by FM–DE interactions for samples with 0.30 ≤ x ≤ 0.80. The PM–AFM transition at ~150 K coexists with PM to C-AFM transition at ~120 K for samples with 0.50 ≤ x ≤ 0.80, whereas for samples with x = 0.85 and 0.90, only PM to C-AFM transition is observed.
2.4. Studies on Bi0.5-xPrxCa0.5MnO3 (0.0 ≤ x ≤ 0.50) manganites
The XRD study of the Bi0.5-xPrxCa0.5MnO3 (0.0 ≤ x ≤ 0.50) samples  confirms the single-phase orthorhombic nature with Pnma space group. A sharp decrease in the unit cell volume is observed as Pr content increases from x = 0.0 to 0.05. However, the unit cell volume increases steadily with further increase in Pr content from 0.05 to 0.50. The Bi3+ has effective ionic size of 1.170 or 1.24 Å depending on whether the 6s2 lone pair character is constrained or dominant, respectively . The higher cell volume of undoped sample may be due to the strengthened dominant lone pair character of Bi3+ ion, whereas the sharp drop in the cell volume for sample with x = 0.05 indicates that the constrained effect of the 6s2 lone pair becomes strong due to Pr doping. The increase in cell volume for samples with x > 0.05 indicates that the constrained effect of the lone pair maintains the Bi3+ ionic size at 1.170 Å, that is, smaller than Pr3+ ionic size (1.179 Å).
The temperature dependence of ΔH of ESR signal is shown in Fig. 9. As temperature decreases from high temperature (453 K), ∆H decreases and reaches a minimum value at TCO. At ~200 K, ΔH decreases sharply and reaches a minimum at 130, 150, and 160 K for samples with 0.05 ≤ x ≤ 0.15, 0.20 ≤ x ≤ 0.40, and x = 0.50, respectively. These minima indicate the existence of FM magnetic clusters embedded in the AFM matrix. Further, decrease in temperature leads to increase in ΔH due to the evolution of canted-AFM (C-AFM) phase.
The value of TCO, as a function of Pr content (Fig. 10), estimated from ESR data matches quite well with those estimated from magnetization data analysis. TCO decreases as x increases from 0.0 to 0.20 and becomes independent of doping content with further increase in x. For samples with 0.0 ≤ x ≤ 0.15, TCO decreases and Curie–Weiss temperature (θC) increases with increase in Pr doping.
The sharp rise in M (Fig. 11) value below 45 K for undoped sample and below 115 K for doped samples is observed, which is characteristic of FM-cluster glass (CG) behavior. The temperature Tf is called spin-freezing temperature. Below this temperature, M in ZFC mode decreases due to the competition between the evolving FM and AFM interactions, whereas M in FC mode continuously increases with decreasing temperature.
2.5. Studies on La-doped Bi-manganites
The base compound, Bi0.7Ca0.3MnO3, has monoclinic structure, and the details are given in section 2.3, whereas the La-doped Bi-manganites, Bi0.7- xLaxCa0.3MnO3 (x = 0.07, 0.14, 0.28, 0.35 and 0.7), have cubic structure. The unit cell volume increases with increasing La content.
Figure 12 shows the ESR spectra for x = 0.07 and 0.70 samples at some selected temperatures. For all samples, the ESR spectra above a particular temperature (~260–270 K) show a single resonance line at resonance field of 325 mT, which is characteristic of the existence of PM phase. Below this temperature, FM correlations evolve in the PM matrix as indicated by the appearance of a shoulder (shown with ‘↓1’) in the low-field region of the ESR signal. This shoulder can be assigned to a low-moment state. With further decrease in temperature, FM correlations grow at the expense of PM interactions, as a result of which a complete PM–FM transition occurs below ~180 K. This is indicated by the shift of the shoulder toward further lower-field region (shown with ‘↓2’). The data indicate development of a high-moment state as temperature decreases.
Figure 13 shows M vs T plots of all the samples. M increases with increasing La content. The spin or cluster glass behavior of Bi- and La-containing samples is similar to that of Bi1-xCaxMnO3 (x ≤ 0.6) system . The samples show the coexistence of PM–FM phases over a wide temperature range. The estimated TC, θC, and the temperature at which ∆H becomes minimum (Tmin) increase with increase in La content.
The critical behavior of Bi0.30La0.37Ca0.33MnO3 (orthorhombic structure with Pnma space group) manganite at the critical point, where the system undergoes phase transition from PM to FM state, is investigated by using modified-Arrott plots (Fig. 14), Kouvel-Fisher method (Fig. 15), and critical isotherm analysis .
The sample shows second-order phase transition near the critical point . The estimated critical exponents are close to as per the prediction by mean-field theory (MFT).
Using scaling equation,
where f+ for T > TC and f- for T < TC are regular functions , we have plotted as shown in Fig. 16. There are two curves, one above the TC and the other one below TC, in agreement with the scaling theory. This indicates that the calculated critical exponents are reliable.
Bi1-xCaxMnO3 (BCMO) exhibits charge ordering property in the composition range 0.30 ≤ x ≤ 0.80, which is related to first-order transition [3–6]. At critical point, La1-xCaxMnO3 (LCMO) manganite shows first-order transition in the composition range 0.30 ≤ x ≤ 0.40 and second-order transition in the composition range 0.18 ≤ x ≤ 0.25 and 0.40 ≤ x ≤ 0.48 [37–39], whereas the present Bi0.30La0.37Ca0.33MnO3 sample also exhibits second-order transition which is similar to La0.7Sr0.3MnO3 (LSMO) . In the present system, due to La3+ doping, the average A-site ionic radius increases, as in the case of Sr2+-doped La-manganite. The increased average A-site radius might be responsible for the observed second-order phase transition.
The ESR and magnetization studies on La-doped Bi-manganites reveal that the La-doping increases M as well as various transition temperatures describing the evolution of various magnetic phases. These changes are ascribed to the difference in ionic radii of Bi3+ and La3+ ions and the variations in 6s2 lone pair character of Bi3+ ions with La-doping.
2.6. Comparative studies on fixed doping level of transition element (TE = V, Cu and Zn) at Mn-site in Bi0.5Ca0.5MnO3 system
XRD data analysis indicates that all the samples possess orthorhombic structure . The difference between a and b lattice parameters decreases, and the c lattice parameter increases with doping. The change in the lattice parameters with doping confirms that the dopants are substituted at the Mn-site .
ESR (Fig. 17) studies on Bi0.5Ca0.5Mn0.95TE0.05O3 with TE = V, Cu, and Zn as a function of temperature and composition show a strong interplay between FM and AFM interactions. FM and AFM phases coexistence in the temperature range TCO > T > TO for all the samples. In the temperature range T > TCO, all samples show FM-dominated interactions in PM state.
The magnetization data in Fig. 18 supports the ESR observations. The estimated values of θC in the temperature range TCO > T > TO (Fig. 18) are 5, ‒7, ‒93, and ‒172 K for undoped, V-, Cu-, and Zn-doped samples, respectively. The changes in magnetic properties of BCMO system with TE doping at Mn-site are due to the electronic nature of the dopants .
2.7. Comparative studies on fixed doping level of transition metals (TM = Ni, Fe, Co, and Cr) at Mn-site in Bi0.5Ca0.5MnO3 system
All the samples have orthorhombic structure . The Mn replacement by TM was confirmed by change in the lattice parameters with respect to lattice parameters of undoped one. This effect is weak for Co-doped sample compared to Fe-, Cr-, and Ni-doped samples. The peak widths of Cr-doped XRD pattern are essentially broader than for other TM-doped samples. It can be due to the non-homogeneous Cr-doped phase. It can also be due to smaller crystallite size in Cr-doped sample than other samples .
The ESR (Fig. 19) and magnetization (Fig. 20) data on the present BCMO and BCMTMO samples show that the FM correlations dominate in the temperature region T > TCO. In the temperature range, TCO > T > TO, FM and AFM coexist for the undoped, Ni- and Fe-doped samples. The 3d TM doping melts the charge ordering and AFM ordering. The effect of Fe, Co, and Cr doping is same and stronger compared to Ni. This suggests that the dopants modify the interaction between Mn ions and possibly alter the band structure of the material instead of participating directly in the magnetic interaction mechanisms .
2.8. Studies on nanoparticles
The comparative ESR studies (Fig. 21) on bulk and nanometer-size (grain size 21 and 15 nm) samples of Bi0.55Ca0.45MnO3 show that TCO decreases from 313 to 306 K as sample grain size changes from bulk to 15 nm. The TN value remains around 153 K for all the samples. In Fig. 21, the solid lines are as per Curie–Weiss law. Above TCO, the positive intercepts on the x-axis indicate the dominant FM correlations. In the temperature range, TCO > T > TN, the domains of FM and AFM spin correlations coexist . The FM phase volume decreases, and the transitions become sharp with decrease in grain size .
The ESR data have been explained  in view of the Griffith’s phase theory . Griffith’s theory suggests that above TG large FM clusters form. Below TG, smaller-sized clusters form, reducing the average size of the FM clusters. In Fig. 21, nonlinear decrease of 1/DI with decrease in temperature indicates existence of FM cluster in a PM matrix. In the temperature range, TCO > T > TN, orbital ordering sets in, bringing about long-range AFM ordering. In this temperature range, the Mn spins do not completely undergo OO and hence there is a coexistence of FM and AFM phases.
The effect of grain size on the properties of Bi0.5Ca0.5MnO3 manganite samples synthesized by SG method is also studied. The samples with grain size (27, 450, and 1080 nm) were obtained by appropriate heat treatment schedule. The magnetic behavior of samples with grain size 450 and 1,080 nm is similar to that of bulk sample described in (section 2.3), whereas for sample with GS 27 nm, the long-range charge ordering and AFM ordering transitions are suppressed (Fig. 22). Magnetization results (Fig. 23) also support the ESR findings.
For these samples, M in FC mode increases with decreasing temperature. However, the ESR and magnetization results reveal that even for sample with GS 27 nm the AFM correlations still exist in the form of short-range order. The shift in FM–CG transition and Tf toward higher temperature and the sharp rise in M below 50 K for sample with GS 27 nm are observed. The evolving different magnetic correlations with decrease in GS are ascribed to increase in surface-to-volume ratio of grains.
The ESR and M studies of Bi-manganites of various compositions synthesized by SS or SG methods are reviewed. The effect of substitution of divalent (Ca2+) and trivalent (Pr3+ and La3+) cations at Bi-site and partial replacement of Mn by transition elements on the structure and magnetic properties of these materials is reviewed. The effect of grain size on the evolution of various magnetic interactions is also described. The study on various systems is useful in understanding the evolution of various magnetic phases as a function of composition and temperature. The studies on several compositions of Bi-manganites reveal that electronic phase separation is an intrinsic phenomenon in this system.
Ramesh Ade would like to thank the award of UGC-(JRF+SRF) from CSIR India.