Crystal structures, magnetic properties, and DFT calculation of B-site defected 12L-perovskites Ba₂La₂MW₂O₁₂ (M  =  Mn, Co, Ni, Zn)

Figure 6 shows the temperature dependence of the inverse magnetic susceptibilities ($\chi _{\text{M}}^{-1}$) for Ba₂La₂MW₂O₁₂ (M  =  Mn, Co, Ni). The ZFC data above 150 K were fitted by the Curie–Weiss law, and obtained effective magnetic moments (µ_eff) and Weiss constants (θ) are listed in table 3. The µ_eff values for M  =  Mn and Ni compounds are close to the spin only values of M²⁺ ion (${{\mu}_{{{\text{M}}^{2+}}}}$). On the other hand, for M  =  Co the µ_eff is much larger than ${{\mu}_{{{\text{M}}^{2+}}}}$  =  3.87 µ_B (3d⁷; S  =  3/2) which is attributed to the orbital angular momentum derived from the degeneracy of t_2g orbital [40]. The Weiss constants (θ_LT) were also calculated by using lower temperature data below 30 K (table 3), which is for excluding the influence from the slight curvature of $\chi _{\text{M}}^{-1}$ versus T plot due to the magnetic excited state and crystal field effect, etc. The negative (M  =  Mn) and positive (Co and Ni) θ_LT values suggest that the dominant magnetic interaction between M²⁺ ions are antiferromagnetic and ferromagnetic, respectively.

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Table 3. Effective magnetic moment(µ_eff), Weiss constant(θ) and transition temperature (T_N, T_C) for Ba₂La₂MW₂O₁₂.

M	µeff/µB	${{\mu}_{{{\text{M}}^{\text{2+}}}}}$/µBa	θ/K	θLT/K	TN, TC/Kb	Ref.
Mn	5.75(1)	5.92	−17.2(8)	−17.6(2)	<1.8 (AF)	This study
	6.05	5.92	−16.6			[24]
	5.73	5.92	−10.7		1.7 (AF)	[27]
Co	5.08(1)	3.87	−17.1(9)	1.25(11)	1.3 (F)	This study
	5.19	3.87	−22.6	1.6	1.28 (F)	[27]
Ni	3.06(1)	2.83	13.1(3)	6.04(2)	6.2 (F)	This study
	3.19	2.83	25.5		6.2 (F)	[27]

^aMagnetic moments of M²⁺ (spin-only values). ^bAF: antiferromagnetic, F: ferromagnetic.

The temperature dependence of specific heat and the field dependence of magnetization at 1.8 K for Ba₂La₂MnW₂O₁₂ are plotted in figures 7 and 8, respectively. In this compound, the magnetic transition was not observed down to 1.8 K. The specific heat divided by temperature (C_p/T) shows an upturn with decreasing temperature in contrast to the data of diamagnetic Ba₂La₂ZnW₂O₁₂. This result suggests an onset of magnetic transition occurs at lower temperatures. The magnetization at 1.8 K varies linearly against the magnetic field and does not saturate even at 5 T, which indicates that the magnetic ground state is antiferromagnetic. These results are corresponding to an antiferromagnetic transition at 1.7 K determined by Rawl et al [27].

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Figure 9 represents the temperature dependence of specific heat for the Co compound in an applied field of 0 and 5 T. A sharp anomaly is observed at 1.3 K indicating the occurrence of long-range magnetic ordering, and this anomaly is broadened and shifted to 5 K by applying the magnetic field. This result suggests that the observed anomaly is attributed to not an antiferromagnetic transition but a ferromagnetic one. In fact, the field dependence of magnetization (figure 8) shows a rapid increasing in a small magnetic field region and a saturation behavior (2.2 µ_B) above ~2 T. In order to obtain further information of this transition, the temperature dependence of magnetic entropy (S_mag) is calculated and plotted in figure 9. Here, the S_mag is obtained by ${{S}_{\text{mag}}}=\int{\left({{C}_{\text{p}}}-{{C}_{\text{lat}}} \right)}/T\,\text{d}T$ in which the C_lat means the lattice contribution of specific heat and the specific heat data of Ba₂La₂ZnW₂O₁₂ are used for this contribution. Above ~5 K the S_mag is converged to 5.5 J mol⁻¹ K⁻¹, which is close to R ln 2  =  5.76 J mol⁻¹ K⁻¹ (R: gas constant). This result indicates that the ground doublet state of Co²⁺ ion brings about this ferromagnetic transition.

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The temperature dependence of specific heat for Ni compound is plotted in figure 10, and an anomaly is found at 6.2 K. This anomaly agrees with the magnetic transition observed in the inverse magnetic susceptibility (inset in figure 6). Thus, the ferromagnetic ordering of Ni²⁺ ions occurs below T_C  =  6.2 K. From the magnetization measurement (figure 8), it is found that this compound shows a magnetic hysteresis loop with a residual magnetization of 1.25 µ_B and gradual increasing toward 2 µ_B. The temperature dependence of S_mag is calculated by the same way as Co compound and is also plotted in figure 10. The change of S_mag due to this ferromagnetic transition is determined to be 8.90 J mol⁻¹ K⁻¹. This value is close to R ln 3  =  9.13 J mol⁻¹ K⁻¹ expected from the S  =  1 ion with a spin degeneracy 2S  +  1; therefore the magnetic moments of Ni²⁺ ions are fully ordered at 1.8 K. The characteristic shape of M–H curve and smaller residual magnetization than 2 µ_B may be due to the single-ion anisotropy of Ni²⁺ ion by using a polycrystalline sample.

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In order to verify the electronic structure of Ba₂La₂MW₂O₁₂ (M  =  Mn, Ni, Zn), we carried out the mBJ  +  LDA calculations. Figure 12 displays the energy dispersions and the total and partial densities of states (DOSs) for Ba₂La₂ZnW₂O₁₂. The occupied and unoccupied bands form a band gap of 3.0 eV around the Fermi level (E_F). This value is smaller than the optical band gap of the UV–vis spectra, and this underestimation is generally shown in the DFT calculation.

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The valence bands (VBs) of Ba₂La₂ZnW₂O₁₂ demonstrates the hybridization between Zn 3d and O2 2p states over the broad range from  −3.7 eV to E_F. Below them, there exist further VBs dominated by the O 2p states; but the bonding orbital-like W 5d states are also situated in the same VBs indicating the W 5d–O 2p hybridization. Such bonding orbital-like 5d states are often found in hexavalent W oxides [43–45]. On the other hand, the bottom of conduction bands (CBs) in the narrow range from 3.0 to 3.8 eV mainly consists of W 5d and O1, O2 2p states. The dispersions reveal that the bottoms of CBs and the tops of VBs are located at the same points (L and F). This matching suggests that the ligand to metal charge transfer (LMCT)-type direct allowed transition (L  →  L and/or F  →  F) is predominant for the optical band gap observed in the UV–vis spectra.

Figure 13 displays the total DOS and the partial DOSs of total electrons of Ba, La, Mn, W, and O for Ba₂La₂MnW₂O₁₂. The rigid and narrow VBs are formed from Mn spin-up 3d states from  −1.4 eV to E_F and the CBs mainly consist of the W 5d and O1, O2 2p states between 0.8 to 1.9 eV; thus, the band gap is estimated to be 0.8 eV. Below the VBs of Mn spin-up states, there exist VBs consisting of O2 2p states between  −5.8 and  −2.6 eV and those consisting of W 5d and O 2p states between  −6.1 and  −8.3 eV.

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The results of DOSs reveal that the Mn ion is in the divalent state with the high-spin configuration because all the Mn spin-up 3d states are located below E_F and the spin-down 3d states exist above 2.5 eV. The spin-polarized Mn 3d states and the O2 2p states hybridize with each other, and this hybridization yields very small spin polarizations of O2 2p states and W 5d states via O2, resulting in the reduction of Mn moments (4.2 µ_B). The spin density distribution around the central Mn ion and its ligands O2 is depicted in figure 13(c). The spin distribution for Mn 3d is isotropic and has spherical symmetry originated from the half-filled 3d states.

Figure 14 displays the total DOS and the partial DOSs of total electrons of Ba, La, Ni, W, and O for Ba₂La₂NiW₂O₁₂. The energy dispersions are shown in figure S3. The VBs consist of the Ni 3d sates from  −1.3 eV to E_F and the CBs are mainly formed from the W 5 d and O1, O2 2p states between 1.5 to 2.5 eV. These bands form a band gap of 1.5 eV around the Fermi level. This value is smaller than the optical band gap (2.25 eV) obtained from the UV–vis spectrum as with the case of Ba₂La₂ZnW₂O₁₂. The gap arises from the LMCT-type direct transition at the L and/or F points (figure S3).

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Below the narrow VBs (Ni 3d states) from  −1.3 eV to E_F, the bands consisting of O2 2p states are located from  −4.8 to  −1.6 eV. The forbidden bandwidth (0.3 eV) between them significantly decreases as compared to that for Ba₂La₂MnW₂O₁₂ (1.2 eV). This decreasing causes an enhancement of hybridization between the M 3d states and O 2p states and broadens 3d bands. The 3d bands for Ba₂La₂NiW₂O₁₂ below E_F are slightly broader as compared with those of 3d bands for Ba₂La₂MnW₂O₁₂, and the contribution of O 2p states to the DOSs increase.

The partial DOSs in figure 14(b) show that all the spin-up 3d states and the t₂-like spin-down 3d states exist below the E_F level, and that the remaining e-like spin-down 3d states locate at around 3.2 eV. In fact, two peaks around 3 eV are observed in the UV–vis spectrum (figure 11), and they are considered to correspond with the Ni d–d transition from the t₂ to e bands. These results also reveal that the Ni ion is in the divalent state. This compound has the magnetic moments of 1.8 µ_B per Ni atom and the magnetic moment is slightly smaller than the theoretical one because of the same reason for Ba₂La₂MnW₂O₁₂. The spin density distribution around the central Ni ion and its ligands O2 is depicted in figure 14(c) and the distribution for Ni 3d expands toward O2 sites, indicating that the spin density consists of the spin-up 3d_x2−y2 and 3d_3r2−z2 states.

The band structures of Ba₂La₂MW₂O₁₂ are summarized as follows. In general, the energy difference between M 3d and O 2p bands decreases with increasing the atomic number of M with the same valence. The energy schemes are depicted in figure 15. The M 3d bands are split by the effect of crystalline field and d–d coulombic repulsion. The hybridization between M 3d and O 2p states broaden the M 3d bands, and the hybridization increases in the order of Mn, Co, Ni, and Zn.

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