A. Crystal structure

Typical θ–2θ XRD patterns of TbMnO₃, Tb₂MnCoO₆, and TbCoO₃ are shown in Fig. 1. Rietveld refinements using the MAUD software were successful using a simple distorted perovskite model (formula ABO₃; A = Tb, B = Mn, Co; and A₂BB′O₆; A = Gd, B = Mn, B′ = Co) with orthorhombic space group Pbnm. Table I shows the structural parameters derived from these refinements for TbMnO₃, Tb₂MnCoO₆, and TbCoO₃. All samples were identified as orthorhombic perovskite structures with space group Pbnm (62). The lattice parameters of TbMnO₃ were found to be a = 5.302 (5) Å, b = 5.854 (0) Å, and c = 7.406 (0) Å, and the cell volume was V = 229.8 (8) ų, Z = 4. The lattice parameters of Tb₂MnCoO₆ were a = 5.278 (3) Å, b = 5.579 (4) Å, c = 7.513 (4) Å with a cell volume V = 221.2 (6) ų, Z = 2. The lattice parameters of TbCoO₃ were a = 5.200 (1) Å, b = 5.401 (6) Å, c = 7.423 (4), V = 208.5 (1) ų, Z = 4. The changes in lattice parameters confirmed that the Mn atoms have been partially replaced by Co atoms.

FIG. 1.

XRD patterns of the polycrystalline TbMnO₃, Tb₂MnCoO₆ and TbCoO₃.

TABLE I.

Structural parameters (space group, lattice parameters, fractional coordinates and isotropic temperature factors), and reliability factors obtained from the Rietveld refinement data for TbMnO₃, Tb₂MnCoO₆, and TbCoO₃.

Occu. = Occupy

Figure 2 shows the representative Rietveld refinement pattern of Tb₂MnCoO₆. The reliability factors R _P and R _WP were 2.12%, 1.98%, 1.51%, and 2.58%, 2.46%, 2.14% for TbMnO₃, Tb₂MnCoO₆, and TbCoO₃, respectively (see Table I). Figures 3(a) and 3(b) depict the crystal structure of Tb₂MnCoO₆. The double perovskite structure with formula A₂BB′O₆, in which A is an alkali, alkaline earth, or rare earth element, consists of a cubic, corner connected network of BO₆ and B′O₆ octahedra, where each BO₆ octahedron is connected only to B′O₆ octahedra. The A-site cation is surrounded by 12 equidistant O²⁻ ions, while the B-site (B′-site) cation constitutes an octahedron structure with O²⁻ ions. ^{Reference Masud, Ghosh, Sannigrahi and Chaudhuri2,Reference Sharma, Saha, Kaushik, Siruguri and Patnaik3} Figure 3 shows the evolution of the bond lengths and bond angles in the BO₆ (B′O₆) octahedra. Fig. 3(c), 3(e), and 3(g) show the top views of the crystal structures for TbMnO₃, Tb₂MnCoO₆, and TbCoO₃, respectively. The most significant change is in the bond lengths. TbMnO₃ (TbCoO₃) shows a distorted BO₆ octahedron with long and short B–O distances in the ab-plane. The substitution of Co for Mn decreases this distortion: the longest B–O bond length decreases, while the shortest one increases, and ultimately, the overall BO₆ octahedra tend to be more regular [see Fig. 3(e)]. The side views of these crystal structures show that the bond lengths increase and bond angles decrease slightly along the c-axis with increasing substitution [Figs. 3(d), 3(f), and 3(h)]. These results are in agreement with the variety among a-, b-, and c-lattice parameters (Table I).

FIG. 2.

Final Rietveld refinement plots of the compound Tb₂MnCoO₆. The small cross (+) and continuous line correspond to the experimental data and calculated pattern, respectively. The vertical bar (|) indicate the positions of Bragg peaks. The bottom trace depicts the difference curve between the experimental and the calculated patterns.

FIG. 3.

(a and b) Crystal structure of Tb₂MnCoO₆. (c, e, and g) and (d, f, and h) Top view and side view of crystal structure for TbMnO₃, Tb₂MnCoO₆, and TbCoO₃, respectively.

B. FT-IR and XPS measurements

Figure 4 gives the FT-IR spectra of polycrystalline samples of TbMnO₃, Tb₂MnCoO₆, and TbCoO₃. The IR spectrum shows an absorption band around ∼580 cm⁻¹ in these samples. The band around 580 cm⁻¹ (in pure TbMnO₃) and 592 cm⁻¹ (in pure TbCoO₃) can be attributed to the stretching vibration of the Tb–O bond. The band around 530 cm⁻¹ suggests the Mn–O bending vibration, and the 489 cm⁻¹ band corresponds to the MnO₆ octahedron stretching vibration in polycrystalline samples of TbMnO₃. ^{Reference Sivakumar, Gedanken, Bhattacharya, Brukental, Yeshurun, Zhong, Du, Felner and Nowik13} In comparison with TbMnO₃, the absorption peak positions of Tb₂MnCoO₆ are shifted to longer wavelengths, appearing at 503 and 457 cm⁻¹, respectively. This shift is attributed to the replacement of Mn by Co in the TbMnO₃, leading to distortion of the MnO₆ octahedra and a change in the lattice constant. The shift to lower frequency can be explained on two grounds: (i) the strength of the coulombic interaction of Co²⁺ with oxygen is weaker than for Mn³⁺, and (ii) of the two cations, Co²⁺ has a larger ionic radius, making the Co–O bond longer than the Mn–O bond. In addition, as the substitution progresses, a negative charge is produced, and oxygen vacancies appear to maintain electrical neutrality. Simultaneously, the distortion of MnO₆ decreases with Co substitution, leading to a further reduction in lattice vibration energy. ^{Reference El-Sheikh and Rashad14}

FIG. 4.

FT-IR spectrum of polycrystalline TbMnO₃, Tb₂MnCoO₆, and TbCoO₃.

To gain insight into the valence states of Mn and Co in Tb₂MnCoO₆, XPS measurement was performed. The XPS spectra of Mn 2p and Co 2p for Tb₂MnCoO₆ are shown in Fig. 5. The Mn 2p region consists of a spin–orbit doublet with Mn 2p_1/2 containing of a binding energy of approximately 654.3 eV and Mn 2p_3/2 with a binding energy of approximately 642.6 eV [Fig. 5(a)], indicating a mixed-valence manganese system (Mn⁴⁺and Mn³⁺). ^{Reference Cuartero, Blasco, García, Lafuerza, Subías, Rodríguez-Velamazán and Ritter10,Reference Han, Huang, Huang and Goodenough15} The two core peaks at 795.9 and 780.6 eV [Fig. 5(b)] correspond to Co 2p_1/2 and Co 2p_3/2, respectively, providing evidence for a mixed Co^3+/2+ state in Tb₂MnCoO₆. ^{Reference Li, Xie, Wu, Li and Zhang16,Reference Chen, Zhang and Fu17} Therefore, there is a charge redistribution in double perovskite Tb₂MnCoO₆, but the ‘formal equilibrium’ Mn³⁺ + Co³⁺ ↔ Mn⁴⁺ + Co²⁺ is not completely shifted to the right, giving rise to a mixed valence state of Mn³⁺/Mn⁴⁺ and Co³⁺/Co²⁺, as occurs in the LaMn_1−x Co _x O₃ series. ^{Reference Sikora, Kapusta, Knízek, Jirák, Autret, Borowiec, Oates, Procházka, Rybicki and Zajac18}

FIG. 5.

XPS spectra of Mn 2p (a) and Co 2p (b) for Tb₂MnCoO₆ samples.

C. Magnetic properties

Figure 6 presents the ZFC and FC temperature dependence of direct current (dc) magnetization (magnetization–temperature [M–T]) of the synthesized TbMnO₃, Tb₂MnCoO₆, and TbCoO₃. An AFM transition can be observed at ∼8 K (in TbMnO₃) and ∼3 K (in TbCoO₃) corresponding to the ordering of Tb³⁺, which is consistent with previous reports. ^{Reference Ikeda and Matsubara19,Reference Pekala, Drozd, Fagnard, Vanderbemden and Ausloos20} Meta-magnetic behavior is observed at ∼92 K in Tb₂MnCoO₆, which is much higher than for TbMnO₃ and TbCoO₃. Metamagnetism is related to the strong magnetoelectric effect of the parent compound, TbMnO₃. Tb³⁺ moments are ordered at low temperature coupled to the Mn sublattice. The application of a magnetic field induces a metamagnetic transition in the ordering of Tb moments modifying both the cycloid and the polarization directions. ^{Reference Aliouane, Schmalzl, Senff, Maljuk, Prokes, Braden and Argyriou21} This interesting meta-magnetic behavior in Tb₂MnCoO₆ is considered to be related to the coexistence of Co and Mn. It is known that the valence of Co ion in TbCoO₃ is 3⁺, and the valence of Mn ion in TbMnO₃ is also 3⁺, but in Tb₂MnCoO₆, Co³⁺ and Mn³⁺ are partially transformed to Co²⁺ and Mn⁴⁺ because the Mn⁴⁺–Co²⁺ coupling is more stable than the Mn³⁺–Co³⁺ coupling, which is consistent with the XPS results mentioned above. As a result, both the FM interaction caused by the superexchange Mn⁴⁺–O–Co²⁺ and the double exchange Mn⁴⁺–O–Mn³⁺ and the AFM interaction caused by the superexchanges Co²⁺–O–Co²⁺, Mn³⁺–O–Mn³⁺, and Mn⁴⁺–O–Mn⁴⁺ were formed in the Tb₂MnCoO₆ structure. Similar magnetic transition behavior has been investigated before, e.g., such phenomena have been reported in LaMn _x Co_1−x O_3+δ, and their meta-magnetic behavior was also ascribed to the presence of both Co²⁺ and Mn⁴⁺magnetic ions. ^{Reference Cuartero, Blasco, García, Rodríguez-Velamazán and Ritter11,Reference Cuartero, Blasco, Rodríguez-Velamazán, García, Subías and Ritter22} In addition, the deviation of the ZFC and FC curves was observed in both TbMnO₃ and Tb₂MnCoO₆. Such behavior is normally related to the existence of grain boundaries in the bulk perovskite manganites. ^{Reference Rivadulla, Lopez-Quintela, Hueso, Sande, Rivas and Sanchez23–Reference Zhang, Song, Ma, Yang, Zhao, Dai and Sun25}

FIG. 6.

The FC and ZFC temperature dependence of dc magnetization (M) of (a) TbMnO₃, (b) Tb₂MnCoO₆, and (c) TbCoO₃.

D. Electrical transport properties

The temperature-dependent electrical transport properties of TbMnO₃, Tb₂MnCoO₆, and TbCoO₃ were measured in the temperature range from 80 K to 150 K, and the results are shown in Fig. 7. It was observed that the resistance increased with decreasing temperature, showing a semiconductor-like behavior [see Fig. 7(a)]. Figure 7(b) presents the Arrhenius plots and their linear best fits. The resistance in such materials can be described by the following Eq. (1):

(1) $$\ln \,R = \ln \,{R_0} + {{{E_{\rm{g}}}} \over {2{k_{\rm{B}}}}}{1 \over T}\quad .$$

where R is resistance (Ω), T is temperature (K), (E _g/2) is the activation energy, and k _B is the Boltzmann constant. From the slope of the lines in Fig. 6(b) and Eq. (1), we obtained the relationships (2), (3), and (4):

FIG. 7.

(a) The temperature dependent electrical resistance curves of TbMnO₃, Tb₂MnCoO₆, and TbCoO₃, (b) ln R − 1/T and fit curves of TbMnO₃, Tb₂MnCoO₆, and TbCoO₃.

For TbMnO₃:

(2) $$\ln \,R = 0.65107 + 3195.64782{1 \over T}\quad .$$

For Tb₂MnCoO₆:

(3) $$\ln \,R = 3.89778 + 2261.77562{1 \over T}\quad .$$

For TbCoO₃:

(4) $$\ln \,R = - 1.17304 + 3553.05{1 \over T}\quad .$$

The activation energies for TbMnO₃, Tb₂MnCoO₆, and TbCoO₃ are 0.2754, 0.1949, and 0.3062 eV, respectively. The activation energy of TbMnO₃ agrees with the value reported in the literature. ^{Reference Chan, Liu, Yang, Li, Lien, Huang and Lee26} The activation energy of Tb₂MnCoO₆ is lower than TbMnO₃ and TbCoO₃, indicating that the double perovskite structure is more conductive than its two counterpart single perovskite structures. Similar phenomena can be observed in other double perovskite structures (Table II). ^{Reference Prasatkhetragarn, Kaowphong and Yimnirun27–Reference Orlandi, Righi, Cabassi, Delmonte, Pernechele, Bolzoni, Mezzadri, Solzi, Merlini and Calestani30} As we mentioned above, the coexistence of Co and Mn leads to the generation of Co²⁺ and Mn⁴⁺ (see Fig. 5), which will promote the double exchange behavior between Co ion and Mn ion. ^{Reference Chan, Liu, Yang, Li, Lien, Huang and Lee26} In addition, the Tb₂MnCoO₆ crystal unit cell owns the smallest Mn–O–Mn (Co) bond angle [see Fig. 3(e)]. This decrease in Mn–O–Mn bond angle is known to strengthen the double exchange interaction, ^{Reference Salamon31} which in turn results in an increase in electron transport ability.

TABLE II.

Activation energies of several double perovskite materials from references.