Magnetostriction in microwave synthesized La_0.5Ba_0.5CoO₃

The family of hole-doped cobaltites with the general formula $R1−x3+Ax2+CoO3$⁠, where R is a rare earth and A is an alkaline earth cation, has been a topic of interest for many years because of various interesting physical phenomena exhibited by them such as the rare occurrence of ferromagnetism and metallicity among 3d perovskite oxides other than manganites,^1–3 spin-state transition of Co ions,⁴ spin polarons for low dopings,^5–8 giant magnetoresistance^9–11 etc. The undoped LaCoO₃ containing only Co³⁺ ions is a non-magnetic insulator and it transforms into a ferromagnetic metal upon doping holes (Co⁴⁺:d⁵) into Co³⁺:d⁶ matrix for x ≈ 0.25 in La_1-xA_xCoO₃ (A = Sr, Ba, Ca) and the ferromagnetic transition temperature increases with x up to x = 1.0.^2,12,13 While Co³⁺ ion is in the low-spin state (⁠$t2g6eg0$⁠, S = 0) at liquid helium temperature in the undoped LaCoO₃, intermediate-spin state (⁠$t2g5eg1$⁠, S = 1) is stabilized in ferromagnetic metallic compositions of La_1-xSr_xCoO₃. A recent Monte-Carlo simulation work underscores the relevance of magnetic frustration in the emergence of long-range ferromagnetism from interacting spin polarons.¹⁴ While the structural, electrical and magnetic properties of various combinations of R and A cations have been studied extensively,¹⁵ only a few studies are available on the interplay between magnetism and elastic properties of these oxides. Ibarra et al.¹⁶ reported giant anisotropic magnetostriction (λ_t ∼ 10^-3), a large difference between the strain measured parallel and perpendicular to the direction of the applied field, in ferromagnetic metallic compositions (x = 0.3 and 0.5) of La_1-xSr_xCoO₃ series, which is rare among 3d perovskite oxides. They attributed the origin of giant anisotropic magnetostriction to field induced spin state transition of Co³⁺ ions from low spin (⁠$t2g6eg0$⁠, S = 0) to Jahn-Teller active intermediate spin (⁠$t2g5eg1$⁠, S = 1). Kundys et al.¹⁷ investigated the magnetoelastic effect in La_0.7Sr_0.3CoO₃ thin films and suggested two mechanisms for the magnetostriction: magnetic field induced increase in the volume of ferromagnetic clusters and magnetic field induced spin-state transition of Co³⁺ ions. Contrary to the giant anisotropic magnetostriction effect found in Sr-doped LaCoO₃, Rotter et al.¹⁸ found anomalous volume expansion in the parent compound of LaCoO₃ which was attributed to low-spin to high-spin (⁠$t2g4eg2$⁠) state transition of Co³⁺ ions under external magnetic fields. However, a magnetic field H ≥ 60 T was needed to induce such a positive magneto volume effect in LaCoO₃ in contrast to few Tesla magnetic fields needed to induce anisotropic magnetostriction in the ferromagnetic compositions. Interestingly, magnetic shape memory effect in twined rhombohedral La_0.8Sr_0.2CoO₃ single crystal was reported recently:¹⁹ A magnetic field of H = 60 T induces twin boundary motion at room temperature and causes magnetostriction even though its ferromagnetic Curie temperature is well below the room temperature. The critical field needed to induce twin-boundary motion decreases with lowering temperature.

Since Ba²⁺ cation has larger average ionic radius (r_a = 1.46 Å) than the Sr²⁺ cation (r_a = 1.31 Å) and La³⁺ (r_a = 1.22 Å), it reduces the overall distortion from the ideal cubic structure and the tolerance factor approaches unity. The crystal structure of La_0.5A_0.5CoO₃ changes from rhombohedral for A = Sr to cubic for A = Ba and the ferromagnetic Curie temperature decreases from ∼ 248 K for the Sr cation to ∼ 180-190 K for the Ba cation.^20–22 La_0.5Ba_0.5CoO₃ adopts different lattice forms depending on the synthesis methods.^23,24 The unit cell of A-site ordered LaBaCo₂O₆ has tetragonal symmetry (space group I4/mcm), in which La and Ba cations alternatively order in LaO-BaO layers along the c-axis of the tetragonal unit cell. The disordered La_0.5Ba_0.5CoO₃ has a cubic structure wherein the A-site is randomly occupied by La and Ba cations and there is also a nanoscale ordered LaBaCo₂O₆ phase.²⁵ Interestingly, all these variants have close Curie temperatures (T_C ∼ 175-190 K). According to Fauth et al.¹⁷ ferromagnetism in the A-site disordered La_0.5Ba_0.5CoO₃ is accompanied by long-range tetragonal distortion arising from the cooperative Jahn-Teller distortion associated with the intermediate spin states of Co³⁺ and Co⁴⁺ ions. A very interesting thermal expansion behavior was reported in Ba-doped samples by Tan et al.²⁶ who studied thermal dependence of the lattice parameters in La_0.5Ba_0.5CoO_3-x system with controlled oxygen deficiency (x ∼ 0.04-0.23) using high resolution neutron and synchrotron X-ray diffraction methods. All the oxygen deficient samples were found to be cubic at room temperature but oxygen deficiency was found to promote G-type antiferromagnetic ordering at low temperatures. The Néel temperature (T_N) increased with the oxygen deficiency (T_N = 164 K for x = 0.1 and 390 K for x = 0.20). While the lattice parameter for x = 0.04 and 0.06 samples decreased smoothly with decreasing temperature below room temperature, negative thermal expansion was found below T_N in x = 0.10 – 0.18 and the samples with still higher oxygen deficiency showed zero thermal expansion over a certain temperature range, mimicking the behavior of INVAR alloys. Neutron diffraction under external magnetic fields recorded for x = 0.12 at 100 K indicates a transition from antiferromagnetic (high volume phase) to ferromagnetic phase (low volume) with increasing strength of magnetic field although cubic symmetry was maintained from 300 K to 2 K. These results motivated us to study the magnetic field dependence of macroscopic strain in bulk La_0.5Ba_0.5CoO_3-d.

In this paper, we report the synthesis of La_0.5Ba_0.5CoO_3-d by microwave irradiation and its magnetic, electrical and magnetostrictive properties. In microwave assisted synthesis, electric dipoles in a sample oscillate in response to the microwaves’ electric field, and the sample absorbs a maximum microwave power when the electric dipoles are driven to resonance.^27–29 The absorbed power is dissipated internally as volumetric heating and large dielectric loss promotes heating. Thus, heat is internally generated in a sample in microwave heating in contrast to the transfer of heat by thermal convection from the heating element to the sample in an electrical furnace. Due to rapid heating, the final product can be obtained within a few tens of seconds to tens of minutes compared to several days needed to obtain the final product using a conventional electrical furnace.²⁵ Gutierrez Sijas et al.³⁰ reported microwave synthesis of RCoO₃ (R = La-Dy) and studied their magnetic susceptibilities. However, neither microwave synthesis of La_0.5Ba_0.5CoO₃ and nor its magnetostrictive property has been reported so far.

A stoichiometric mixture of dehydrated La₂O₃, BaCO₃ and Co₃O₄ was ground well with an agate mortar and pestle. The powder was initially decarbonated at 1200 °C for 10 minutes in a muffle microwave furnace (Milestone PYRO mode MA 194-003) operating at 2.45 GHz with 1400 W power. After regrinding, the decarbonated powder was pressed into a circular pellet and irradiated with a microwave power of 1600 W. The temperature was set to reach 1200 °C in 20 min under microwave irradiation and maintained at 1200 °C for 20 min. Then, the microwave power was switched off and the pellet was allowed to cool to room temperature in 4 hours (300 °C/hr). A portion of the irradiated pellet was crushed into powder and analyzed for phase structural characteristics using X-ray diffraction (XRD) with Cu-Kα₁ (1.5406 Å) radiation. A pinch of crushed powder was spread over a carbon tape stuck on the aluminum stage and used to analyze the microstructure in a field emission scanning electron microscope (FE-SEM, JEOL JSM-6700F). Oxygen content in the MW synthesized sample was estimated from iodometric titration following the procedure described by E. L. Rautama et al.²⁴ and found to be 2.9±0.02. Magnetization was measured using a vibrating sample magnetometer probe inserted in the physical property measurements system (PPMS). Magnetostriction along the direction of the applied dc magnetic field was measured using a capacitance dilatometer probe that is inserted in the PPMS. A polished cube shaped sample of size 2 × 2 × 2 mm filled the space between two circular capacitive electrodes. The capacitance change of the dilatometer was measured using a high resolution capacitance bridge (Andeen Hagerling, model AH2500A) in the temperature range 300 K to 10 K. For the isothermal field sweep measurements, the field sweep rate was fixed to 60 Oe/sec for both the magnetization and magnetostriction. Magnetostriction is obtained as λ_par = [L(H)-L(0)/L(0)] x 10^-6 where L(H) and L(0) are the lengths of the sample at a fixed temperature in a magnetic field H and zero field respectively, measured in the direction of the applied dc magnetic field.

Fig. 1 shows the room temperature X-ray diffraction patterns of the MW synthesized La_0.5Ba_0.5CoO_3-d. The well-defined diffracted peaks disclose excellent crystallization of the sample. Bragg’s reflections are fitted through peak by peak fitting method using XRDA software and they are indexed with cubic symmetry (space group of Pm$3̄$m: JCPDS No.: 32-0480). The refined cell parameters of a = 3.886(2) Å and volume (V ≈ 59 ų) are close to the cell parameters reported for a disordered phase of stoichiometric La_0.5Ba_0.5CoO₃.^5,6 In Pm$3̄$m crystallographic structure, both La and Ba ions are statistically distributed at the body center site, whereas the Co ions are at the center of each octahedra formed by its six neighboring oxygen ions. FE-SEM micrograph illustrated in the inset of the figure suggests an average grain size of 3 micron.

Figure 2(a) shows the temperature dependence of magnetization (M) of La_0.5Ba_0.5CoO_3-d measured upon warming from 10 K after zero-field cooling (ZFC) and field-cooling (FC) to 10 K for three values of the magnetic field (H = 0.5, 1 and 3 kOe). The sample undergoes a paramagnetic to ferromagnetic transition at T_C = 177 K. The T_C is obtained from the inflection point of dM/dT for H = 0.5 kOe in the FC mode (shown in the inset). The ZFC curve for each field increases as the temperature is increased from 10 K and goes through a maximum value at the temperature T_m, which is much below T_C. With increasing strength of the magnetic field, T_m shifts toward low temperatures (T_m = 128, 108, 71 K for H = 0.5, 1, and 3 kOe, respectively) and the difference between ZFC and FC curves also decrease. The irreversibility of the magnetization together with low value of magnetization at 10 K for H = 50 kOe (shown later in Figure 3) suggest that the ferromagnetism is short-range in this compound.

The temperature dependence of the resistivity (ρ) is shown in Fig. 2(b) for both H = 0 and 70 kOe from 350 K to 10 K. ρ(T) shows an insulating behavior: ρ increases from 0.34 $Ω$ cm at 300 K to ∼ 37.33 × 10⁵ $Ω$ cm at 10 K. The applied magnetic field of 70 kOe does not destabilize the insulating state. Since the magnetoresistance appears to be small in the temperature sweep mode, we have measured magnetoresistance in the field sweep mode at three selected temperatures for clarity. The inset shows the magnetic field dependence of the magnetoresistance around T_C at T = 160, 170 and 180 K. The magnetoresistance increases with the magnetic field without saturation and the maximum value is small (∼ -2% for 70 kOe at 180 K). This magnitude is also smaller (∼6%) than found in the Sr analoague La_0.5Sr_0.5CoO₃.¹⁶ 

We would like to remind the readers that ρ(T) of La_0.5Ba_0.5CoO_3-d in zero magnetic field was found to exhibit different trends depending on the synthesis conditions according to existing literature. Nakajima et al.²¹ reported that ρ(T) of A-site disordered La_0.5Ba_0.5CoO₃ (T_C = 190 K) sample synthesized by solid state reaction at 1300 °C and annealed in oxygen changed from metallic like to semiconducting like while cooling below 140 K. Fauth et al.¹⁸ found semiconducting like behavior below 120 K and metallic behavior above. They attributed the semiconducting like behavior to the gradual ordering of the $d3z2−r2$ orbitals which blocked a channel for electron hopping. ρ(T) showed metallic like behavior from 300 K to 10 K in the sample of Rautuma et al.²² However, Tryonchuk et al.³¹ found only a weak bump around T_C in zero field resistivity in a La_0.5Ba_0.5CoO₃ sample which was cooled at a rate of 100 °C/hour after sintering at 1400 °C for 24 h in air. The magnitude and the temperature dependence of the resistivity could be influenced by the presence of both grain boundary resistance and oxygen non-stoichiometry. We have also synthesized La_0.5Ba_0.5CoO₃ sample by solid state reaction method with the final sintering of a pellet done at 1200 °C for 24 hr and cooled to room temperature at a rate of 60 °C/hr. Resistivity and magnetization were measured (not shown in this work due to lack of space). We found M = 1.54 µ_B/Co for H = 50 kOe at 10 K which is larger than in the MW synthesized sample and the resistivity ratio (ρ_10K/ρ_300K = 23.3) is four orders of magnitude smaller than the MW synthesized sample (ρ_10K/ρ_300K = 10.9 x 10⁴). Such a large increase in the resistivity for the MW synthesized La_0.5Ba_0.5CoO_3-d sample is most likely caused by charge localization due to lower oxygen content than the increase in grain boundary resistance. A detailed study will be published later.

Figure 3 illustrates the magnetic field dependence of magnetization M(H) of La_0.5Ba_0.5CoO_3-d on the left y-axis and magnetostriction (λ_par) on the right y-axis at 10 K. M(H) was measured after zero field cooling the sample. M(H) exhibits a wide hysteresis loop which is opened up to ± 10 kOe and a large coercive field (H_C = 1.86 kOe). M(H) does not show saturation up to H = 50 kOe, where it reaches 0.83 μ_B/Co ion, which is much lower than 1.75-1.9 μ_B/Co reported at the same field by other authors.^17,19,20,29 On the other hand, Tryounchuk et al.²⁹ noted that the value of magnetization at 10 K for H = 50 kOe decreased from 1.75 μ_B/Co for the sample cooled at a rate of 100 °C/hr (in the air from 1200 °C to 300 °C) to 1 μ_B/Co in the sample which was cooled at a rate of 300 °C//hr. In our experiment also, the cooling rate was ∼ 300 °C//hr, and thus there could be significant oxygen deficiency, which will decrease the Co⁴⁺ content.

The parallel magnetostriction λ_par is positive, i.e., the length of the sample elongates along the direction of the applied magnetic field. Though λ_par curve bend above 30 kOe, it does not show saturation up to the maximum field of 50 kOe. λ_par reaches a maximum value of 265 x 10^-6 at 50 kOe. λ_par also exhibits pronounced hysteresis up to H ∼ ± 30 kOe, above which curves traced while increasing and decreasing the magnetic field merge. The inset of Fig. 4 shows the field dependence of λ_par vs H at selected temperatures. Hysteresis is visible in the isotherms up to 160 K but the field range narrows and hysteresis is negligible for 180 K and 200 K. We collect the values of λ_par at the highest field from the λ_par vs H isotherms and plot them as a function of temperature in the main panel of Fig. 4. λ_par has a maximum value at 10 K, decreases with increasing temperature and becomes negligible above T_C. The maximum value of λ_par in La_0.5Ba_0.5CoO_3-d is much smaller than the value (λ_par = 900 x 10^-6) reported for the ferromagnetic La_0.5Sr_0.5CoO_3-d at 25 K, which is expected to increase slightly at 10 K.¹³ To explain the unusual high value of magnetostriction found in La_0.5Sr_0.5CoO_3-d, Ibarra et al.¹³ suggested orbital instability of Co³⁺ ions following the field induced spin-state transition from non-degenerate low-spin state (⁠$t2g6eg0$⁠, S = 0) to intermediate spin state (⁠$t2g5eg1$⁠, S = 1). With increasing magnetic field, the triply degenerate t_2g energy levels split into an orbital singlet (d_xy) with zero orbital moment as a ground state and an orbital doublet (d_yz, d_xz) with the unquenched orbital moment as a first excited state. The non-zero angular momentum of the orbital doublet couples with the spin angular momentum to create intra-atomic spin-orbit coupling. As the spins rotate, orbital also distorts which causes large magnetostriction along the field direction in La_0.5Sr_0.5CoO_3-d. Based on the non-saturation of M(H) at 10 K with a small value magnetization at 50 kOe, magnetic irreversibility between ZFC and FC-M(T) curves, and insulating behavior of the resistivity, we can exclude long range ferromagnetism in the MW synthesized La_0.5Ba_0.5CoO_3-d. Rapid cooling in MW synthesize promoted oxygen deficiency in this compound and an inhomogeneous ferromagnetic state is created. Ferromagnetism sets in small regions (clusters) where Co³⁺ and Co⁴⁺ are in the intermediate spin state. These ferromagnetic clusters are dispersed in non-ferromagnetic phase and are non-percolating. The non-ferromagnetic phase is most likely to be antiferromagnetic rather than paramagnetic. In the antiferromagnetic phase, Co³⁺ and Co⁴⁺ ions are in high spin states which favor antiferromagnetic interaction among the same valence Co ions and between 4+ and 3+ valance Co ions, unlike the intermediate spin state they adopt in the metallic phase. Antiferromagnetic spin ordering detected by neutron diffraction and increase in Néel temperature with increasing oxygen deficiency²⁴ in La_0.5Ba_0.5CoO_3-x support the view that the non-ferromagnetic phase is likely to be antiferromagnetic. The Néel temperature for x = 0.1 was found to be 164 K.²⁴ It is possible that antiferromagnetic ordering happens just below the ferromagnetic transition in our sample. In the background of strong signal from ferromagnetic clusters, antiferromagnetic transition is masked in the M(T) curve. Based on the absence of non-divergence in the field dependence of the third order non-linear magnetic susceptibility, Kumar et al.³² proposed that their La_0.5Ba_0.5CoO_3-d sample consisted of ferromagnetic and antiferromagnetic clusters. Their sample showed higher magnetization (1.9 μ_B/Co for H = 50 kOe at 10 K) than our sample. On the other hand, M(T) of the Ba-rich composition La_0.45Ba_0.55CoO_2.85 exhibited a pronounced peak at 100 K both in the ZFC and FC modes and neutron diffraction revealed G-type antiferromagnetic ordering.³³ Hence, the presence of antiferromagnetic phase in our compound cannot be neglected. The lower value of magnetostriction in La_0.5Ba_0.5CoO_3-d compared to La_0.5Sr_0.5CoO₃ is possibly due to the smaller volume fraction of the ferromagnetic phase in the former sample. The antiferromagnetic phase does not change into a ferromagnetic phase under 50 kOe but hinders the expansion of ferromagnetic clusters under magnetic field.

In summary, we have synthesized La_0.5Ba_0.5CoO_3-d by microwave irradiation method in a short time. Although the sample exhibits ferromagnetic transition at 177 K similar to the available data on solid state synthesized and oxygen annealed La_0.5B_0.5CoO₃ sample, the MW synthesized sample shows much reduced magnetization (∼ 0.83 μ_B/Co) compared to ∼ 1.9 μ_B/Co reported in oxygen stoichiometric compound. It is suggested that non-percolating ferromagnetic clusters coexist with the antiferromagnetic phase below the Curie temperature of ferromagnetic clusters. Magnetostriction is positive and a maximum value (265 x 10^-6) is obtained at 10 K. Future work needs to be focused on measuring both parallel and perpendicular magnetostrictions to calculate anisotropic magnetostriction and volume magnetostriction. Also, the dependence of the magnitude of magnetostriction on the oxygen content needs to be systematically investigated.

R.M. acknowledges the Ministry of Education, Singapore, for supporting this work (Grants numbers: R1444-000-422-114 and R144-000-428-114).

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.