Magnetic clusters and ferromagnetic spin glass in the novel hexagonal perovskite 12R-Ba₄SbMn₃O₁₂

Abstract

A 12-layer hexagonal perovskite Ba₄SbMn₃O₁₂ (space group: R3̄m; a = 5.72733(3) Å, and c = 28.1770(3) Å) has been synthesized by high-temperature solid-state reactions and studied using powder X-ray and neutron diffraction and magnetization measurements. This 12R polytype structure contains one corner-sharing (Sb, Mn)O₆ octahedron and a trimer of face-sharing MnO₆ octahedra per formula unit. Ba₄SbMn₃O₁₂ displays a paramagnetic state of the Mn₃ magnetic cluster at 100–200 K, which partially disassociates into individual Mn ions at 250–300 K. The ferromagnetic interaction between these Mn₃ clusters is mainly mediated by Mn³⁺ at the M1 site, leading to dynamic ferromagnetic clusters below T_D = ∼70 K and ferromagnetic spin freezing transition at T_g = ∼11.5 K. The stability of Mn₃ magnetic clusters in the 12R polytypes is related to the intracluster Mn–Mn distance.

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1 Introduction

Manganese oxides have been the focus of materials research for many decades owing to their technological applications as heterogeneous catalysts,¹ Li-ion batteries,^2,3 SOFC electrode materials,⁴ CMR materials,⁵ and quantum materials.^6,7 This has motivated the investigation of the hexagonal perovskite BaMnO_3−δ system, which shows a diversity of crystal structures and magnetic properties.^8–12 A series of BaMnO_3−δ polytypes (2H → 15R → 8H → 6H → 10H → 4H) have been found as the oxygen vacancy concentration δ increases.^8,11 Further perovskite polytypes may be produced when Mn and Ba are replaced by other cations.

Many Mn-substituted BaM_xMn_1−xO₃ systems have been investigated, for instance, with M = Ca,¹³ In,^14,15 Sn,^16,17 Sb,¹⁸ Ti,¹⁹ Fe,²⁰ Ru,²¹ Ir,²² Nb,²³ and rare earth Ln.^24–26 This led to the discovery of a series of M-cation ordered 12R perovskites Ba₄M_1+xMn_3−xO₁₂ (M = Ti⁴⁺ and Sn⁴⁺),^17,19 Ba₄MMn₃O_11.5 (M = In³⁺ and Y³⁺)^14,27 and Ba₄MMn₃O₁₂ (M = Nb⁵⁺, Ce⁴⁺, and Pr⁴⁺).^23,26 The 12R perovskite Ba₄MMn₃O₁₂ contains close-packed BaO₃ layers in a (cchh)₃ sequence and accommodates the M and Mn ions in the corner-sharing octahedral centre M1 and face-sharing octahedral centres M2 and M3 respectively (Fig. 1a). Partial disorder of M and Mn elements occurs on the M2 site in case of M = Ti⁴⁺ and Sn⁴⁺,^17,19 and oxygen vacancies are present for the M = In³⁺ and Y³⁺ case.^14,27

Fig. 1 The crystal structures of (a) 12R Ba₄MMn₃O₁₂ and (b) 10H Ba₅MMn₄O₁₅ viewed along [110], showing the stacking sequence of BaO₃ and corner-sharing octahedron center M1 and face-sharing octahedron center M2 and M3. Color code: barium (green sphere), M (orange sphere), manganese (purple sphere), oxygen (red sphere), MnO₆ (purple octahedron), and MO₆ (orange octahedron).

Polymorphs of BaMnO_3−δ have long-range antiferromagnetic (AFM) order of all the Mn spins, with T_N = 220–270 K.^10,11 However, the long-range magnetic order is suppressed in the 12R perovskites upon low-level nonmagnetic doping, and the substituted M ions plays a key role in the magnetic behaviour of these materials. Ba₄YMn₃O_11.5,²⁷ Ba₄Sn_1.1Mn_2.9O₁₂ (ref. 17) and Ba₄CeMn₃O₁₂ (ref. 24) undergo an AFM transition at T_N = 4–6 K, while Ba₄InMn₃O_11.5 (ref. 14) and Ba₄Ti₂Mn₂O₁₂ (ref. 19) display no magnetic order, and Ba₄NbMn₃O₁₂ shows a ferrimagnetic transition at T_C = 42 K (ref. 23) (Table S1†). Furthermore, the Nb, Ti and Sn-doped 12R polytype show meta-magnetism, with linear Mn₃ magnetic clusters arranged in a triangular lattice, leading to magnetic frustrations.^17,23,28 Therefore, the 12R perovskite materials are potential quantum materials, such as quantum spin liquid and spin ice. The exploration of new 12R perovskite BaM_xMn_1−xO₃ is of great concern.

In the BaSb_1−xMn_xO₃ system, two perovskite polymorphs 6H Ba₃MnSb₂O₉ (ref. 29) and 10H Ba₅Sb_1−xMn_4+xO_15−δ have been identified. The Ba₅Sb_1−xMn_4+xO_15−δ has close-packed BaO₃ layers in (cchhh)₂ sequences and features tetramers of face-sharing MnO₆ octahedra (Fig. 1b).¹⁸ Regarding the close relationship between the 10H and 12R polymorphs, one wonders whether the 12R perovskites BaSb_1−xMn_xO₃ can exit. If the 12R BaSb_1−xMn_xO₃ is stabilized, it would be a good material with magnetic clusters and frustration. Motived by such ideas, we started a series of investigations on the BaSb_1−xMn_xO₃ materials. Herein we report the synthesis, crystal structure, and magnetic properties of 12R Ba₄SbMn₃O₁₂ perovskite.

2 Experimental

2.1 Synthesis

The polycrystalline Ba₄SbMn₃O₁₂ was synthesized from BaCO₃ (99.5%, Aladdin), MnCO₃ (99.95%, Aladdin), and Sb₂O₃ (99.9%, Aladdin) reagents with solid-state reaction methods. These starting materials were thoroughly mixed with alcohol in an agate mortar and pestle and heated in a platinum crucible at 1173 K for 10 hours to decompose the carbonates. The materials were then reground, pressed into pellets (20 ton cm⁻²), placed on platinum crucibles, and sintered at 1573 K for 36 hours with heating and cooling rates of 5 K min⁻¹. At several intermediate steps, the materials were re-ground and re-pressed, and powder X-ray diffraction (XRD) was performed at each step to follow the reaction to completion.

2.2 Characterization

The phase purity of the samples was characterized by XRD using a PANalytical X'Pert Pro powder diffractometer with Cu Kα radiation at 40 kV and 40 mA. High-quality XRD data were collected on the 2θ range 5–120° at room temperature (RT) for Rietveld analysis carried out using the Topas Academic software.³⁰ Bond valence sum (BVS) was calculated using standard parameters with Brown and Altermatt's method.³¹ Low-temperature XRD data were collected in the 5–298 K range with an interval of 10 K, using a Rigaku SmartLab X-ray diffractometer with Cu Kα radiation at 45 kV and 200 mA.

Time of flight (TOF) neutron powder diffraction (NPD) data were collected from a 5 g powder sample of Ba₄SbMn₃O₁₂ using the General-Purpose Powder Diffractometer (GPPD) at the China Scattering Neutron Source (CSNS, Dongguan, China). Scanning electron microscopy (SEM) imaging and X-ray energy dispersive spectroscopy (EDS) elemental analysis were carried out using a GeminiSEM 300 (ZEISS, Germany) scanning electron microscope with an Ultim Max (Oxford, U.K.) EDS spectrometer.

Magnetic measurements were performed on Quantum Design's MPMS-3 Superconducting Quantum Interference Device (SQUID) magnetometer. Direct-current (dc) magnetic susceptibility was recorded in a magnetic field of 1000 Oe while heating the sample from 2 K to 300 K after zero-field cooling (ZFC) and field cooling (FC). Alternating-current (ac) magnetization was measured with an ac amplitude of μ₀h_ac = 10 Oe at frequencies of 3 ≤ f ≤ 250 Hz in the temperature range 5–15 K. Isothermal field-dependent magnetization was performed at the applied field from −6 to 6 T and temperature of 2 K, 5 K, 15 K, 20 K, 30 K, 40 K, 50 K, 60 K and 100 K.

3 Results and discussions

3.1 Phase formation

The initial Ba₄SbMn₃O₁₂ samples consisted of mixed 12R perovskite phase and Mn-rich phases such as 8H BaMnO_3−δ (marked with asterisks), due to the loss of antimony oxides during the sintering process (melting point of Sb₂O₅ and Sb₂O₃ are ∼655 K and ∼928 K).³² The Mn-rich phase was reduced through extra Sb doping. The 12R perovskite phase was isolated as a single phase at the nominal composition of Ba₄Sb_1.03Mn₃O₁₂, while beyond this Sb doping level other impurity reflections were observed, as marked as arrows in Fig. 2.

Fig. 2 XRD patterns of nominal Ba₄Sb_1+xMn₃O₁₂ samples, showing a pure phase 12R perovskite at the x = 0.03 composition. The reflection from BaMnO_3−δ polymorphs and other impurities are marked with asterisks and arrows, respectively.

The chemical composition of the nominal Ba₄Sb_1.03Mn₃O₁₂ sample is most likely to be consistent with the stoichiometric perovskite of Ba₄SbMn₃O₁₂, which is reasonably supported by the Ba : Sb : Mn ratio of 4.00(20) : 1.01(4) : 2.73(12) from the EDS elemental analysis (Fig. 3) and the following Rietveld refinements.

Fig. 3 SEM image and EDS elemental mapping image on the Ba₄SbMn₃O₁₂ sample, indicating the homogeneous distribution of elements.

3.2 Crystal structure

The light oxygen atoms are not well located with X-ray diffraction in the presence of heavy elements such as barium. Neutron diffraction (ND) is more sensitive to oxygen because the neutron scattering length of oxygen (5.083 fm) is comparable to that of Ba (5.07 fm).³³ Therefore, to find the accurate oxygen position, neutron diffraction data were collected on the Ba₄SbMn₃O₁₂ sample. The Rietveld refinements against the XRD and NPD data simultaneously were performed, based on the structural model of 12R Ba₄NbMn₃O₁₂ (Fig. 1a). During the refinements, the lattice parameters, the atomic coordinates, and the thermal displacement parameters (Beq) were varied freely. Anisotropic peak broadening was described with the Stephen model. In the first step, the occupancies of Sb and Mn at M1, M2, and M3 sites were refined with the total occupancies on each site subject to unity. A negative value of Sb on the M3 site was found, excluding the presence of Sb at the M3 site. In the following refinement, the occupancies of Sb and Mn were refined only at M1 and M2 sites, with the total ratio of Sb : Mn constrained as 1 : 3. In the second step, the oxygen occupancies were refined, and no vacancies were found at the oxygen sites within the refinement error. Therefore, the occupancies at both O1 and O2 sites were set as unity. The final refinement rapidly converged at the R_wp parameters of 5.50% and 4.32% for XRD and NPD data respectively (Fig. 4a and b). The refined structural parameters and selected bond distances and angles are summarized in Tables 1 and 2.

Fig. 4 Rietveld refinement plots of (a) XRD data and (b) ND data for the Ba₄SbMn₃O₁₂ sample, showing observed (red crosses), calculated (green line), and difference curve (grey line). The reflection positions for Ba₄SbMn₃O₁₂ are marked with blue bars in both plots.

Table 1 Refined structural parameters of Ba₄SbMn₃O₁₂^a

Atom	Site	x, y, z	Occupancy	Beq	BVS
a a = 5.7273(1) Å, and c = 28.1770(3) Å, space group: R3̄m.
Ba1	6c	0, 0, 0.1288(1)	1	0.1(1)	2.22
Ba2	6c	0, 0, 0.2860(1)	1	0.7(2)	2.42
(Sb/Mn)M1	3a	0, 0, 0	0.84/0.16(1)	1.9(1)	4.94/2.96
(Mn/Sb)M2	6c	0, 0, 0.4110(1)	0.92/0.08(1)	0.5(1)	3.47/5.24
MnM3	3b	0, 0, 0.5	1	0.5(2)	3.89
O1	18h	0.4834(1), 0.5165(1), 0.1236(1)	1	0.7(1)
O2	18h	0.4994(2), 0.5006(2), 0.2928(1)	1	1.1(2)

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Table 2 Selected bond lengths and angles of Ba₄SbMn₃O₁₂

Bond length (Å)	Bond length (Å)	Bond angle (degree)
(Sb/Mn)M1–O2 (×6) 2.014 (2)	MnM3–O1 (×6) 1.921 (1)	(Sb/Mn)M1–O2–MnM2 177.97 (7)
(Mn/Sb)M2–O1 (×3) 1.972 (2)	MnM2–MnM3 2.506 (2)	MnM2–O1–MnM3 80.14 (5)
(Mn/Sb)M2–O2 (×3) 1.953 (2)

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In the crystal structure of 12R Ba₄SbMn₃O₁₂, Sb and Mn atoms are mixed on two crystallographic independent sites M1 and M2, with occupancy of 84% Sb/16% Mn and 8% Sb/92% Mn respectively. The BVS results listed in Table 1 show that the formal Mn charges are segregated, with Sb⁵⁺ and Mn³⁺ (which have similar ionic radii of 0.60 and 0.645 Å (ref. 34) respectively) at the corner-sharing M1 site, mixed Mn³⁺, Mn⁴⁺ and Sb⁵⁺ at the M2 site, and Mn⁴⁺ at the M3 site. Based on the charge neutrality, this corresponds to the chemical formula Ba₄(Sb1_0.84⁵⁺Mn1_0.16³⁺)(Sb2_0.08⁵⁺Mn2_0.42³⁺Mn2_0.5⁴⁺)₂(Mn3⁴⁺)O₁₂, where Mn1 corresponds to Mn at site M1, etc. This chemical formula has an average charge of Mn2 of +3.54, essentially identical to the BVS of 3.47.

The cationic distributions in Ba₄SbMn₃O₁₂ are different from those of the Sn, Y, and Nb-analogue.^17,23,27,35 In Ba₄Sn_1.1Mn_2.9O₁₂, Sn⁴⁺ and Mn⁴⁺ are mixed on the corner-sharing M1 (Sn : Mn ratio of 0.88 : 0.12) and face-sharing M2 (Sn : Mn ratio of 0.11 : 0.89) sites.¹⁷ In Ba₄YMn₃O_11.5 and Ba₄NbMn₃O₁₂, the substituted Y³⁺/Nb⁵⁺ and Mn⁴⁺(and Mn³⁺) ions are well separated over the M1 and M2 sites respectively. The structure of Ba₄SbMn₃O₁₂ contains a higher proportion of magnetic Mn³⁺ cations (∼16%) at the M1 sites that interconnect the Mn₃O₁₂ trimers of face-sharing octahedra, which has a strong impact on the magnetic properties as discussed in the following sections.

It should be noted about the distortion of the outer MnO₆ octahedra in the trimers. The Mn_M2 atom shifts toward the c-BaO₃ layers, forming three short Mn–O bonds (∼1.95 Å) and three long ones (∼1.97 Å), while the inner Mn_M3O₆ octahedron has no distortion constrained by its local site symmetry (D_3d). This leads to a short Mn–Mn distance d_Mn–Mn of ∼2.5 Å inside the Mn₃O₁₂ trimer, which is comparable with that in the elemental α-Mn.³⁶ This phenomenon could indicate a degree of d-orbital overlap between neighboring Mn ions forming Mn₃ magnetic clusters.

Phase stability of Ba₄SbMn₃O₁₂ was investigated by low-temperature XRD (Fig. 5a). No phase transition was observed in the range of 5–298 K. The lattice parameters and cell volume keep constant below ∼70 K and increase linearly as temperature increases above 70 K, showing thermal expansion coefficient of α_a = 7.9 × 10⁻⁶ K⁻¹, α_c = 7.0 × 10⁻⁶ K⁻¹ and α_V = 2.2 × 10⁻⁵ K⁻¹.

Fig. 5 Temperature-dependent (a) XRD data for Ba₄SbMn₃O₁₂ and (b) cell parameters relative to the 5 K values (a₀ = 5.72318(9) Å, c₀ = 28.1536(6) Å, V₀ = 798.62(3) ų), with the fits shown as the solid lines.

3.3 Magnetic properties

The dc magnetization data for Ba₄SbMn₃O₁₂ (Fig. 6a) were corrected against two background terms: the susceptibility of the capsule determined as −5.6 × 10⁻⁶ emu with a blank measurement, and the diamagnetic susceptibility of Ba₄SbMn₃O₁₂, which can be estimated as −2.91 × 10⁻⁴ emu f.u.⁻¹ (or equally −1.00 × 10⁻⁴ emu per mol Mn⁴⁺) using Pascal's constant.³⁷ The susceptibilities are nearly constant above 150 K and increase as the temperature goes down, which is typical for localized spin systems. A broad peak in magnetic susceptibilities (χ_dc) appears at around T_m = 10.5 K, indicating a magnetic phase transition. Ferromagnetic components are present below T_C as suggested by the divergent ZFC and FC susceptibilities.

Fig. 6 (a) ZFC (filled circles) and FC (empty circles) magnetic susceptibility for Ba₄SbMn₃O₁₂ per mol Mn, with low-temperature data shown in the inset. (b) Inverse magnetic susceptibilities. The red and blue lines show the linear fits on 100–200 K and 250–300 K, corresponding to μ_eff = 3.05 and 3.46μ_B per mol Mn. The inset to (b) shows the schematics of the most possible arrangements of Mn³⁺ and Mn⁴⁺ in the Mn₃ magnetic clusters of Ba₄SbMn₃O₁₂.

The susceptibilities between 100 and 200 K can be well fitted based on the equation χ = C/(T − θ), yielding the Weiss temperature θ_cw of ∼43.4 K and C ∼ 1.16 emu K mol⁻¹ (Fig. 6b). This corresponds to a paramagnetic moment μ_eff of ∼3.05μ_B per mol Mn or ∼5.28μ_B per mol Mn₃ cluster. The former is significantly smaller than the expected value of 4.24μ_B calculated from spin only Mn³⁺ : Mn⁴⁺ moment in the proportion 1 : 2, and this contradicts the paramagnetic states of individual Mn spins. The latter value is essentially identical to the expected values of ∼4.89μ_B, as estimated with the most possible Mn₃ cluster of Ba₄SbMn₃O₁₂ containing one terminal Mn³⁺ and two Mn⁴⁺ ions (Fig. 6b inset). This observation indicates the stabilization of Mn₃ magnetic clusters in a paramagnetic state at 100–200 K. Ferro- or ferri-magnetic interactions occur between the Mn₃ clusters as indicated by the positive θ_cw ∼ 43.4 K.

The Curie–Weiss fits of magnetic susceptibility at 250–300 K range leads to an μ_eff = 3.45(1)μ_B per mol Mn or μ_eff = 5.98μ_B per mol Mn₃ cluster equally. This result is larger than the expected value of Mn₃ clusters and smaller than that of Mn ions. This phenomenon indicates the Mn₃ magnetic cluster is partially destroyed, leading to the coexistence of individual Mn ions and Mn₃ clusters in this temperature range, although an exclusively paramagnetic state of Mn ions requires a higher temperature.

Similar Mn₃ magnetic clusters have been evidenced with different stability in 12R Sn- and Nb-doped analogs.^17,23 Compared with that in Ba₄SbMn₃O₁₂ (d_Mn–Mn = ∼2.506 Å), the Mn₃ cluster in Ba₄NbMn₃O₁₂ (d_Mn–Mn = ∼2.469 Å) is more stable without dissociation at RT,²³ while the Mn₃ cluster in Ba₄Sn_1.1Mn_2.9O₁₂ (d_Mn–Mn = ∼2.523 Å) is unstable at RT and split into Mn ions.¹⁷ The stability of Mn₃ clusters can be associated with the intra-cluster d_Mn–Mn. A smaller Mn–Mn distance would mediate stronger direct exchange interactions via a greater overlap between the t_2g orbitals of Mn ions, leading to greater stability of Mn₃ clusters in these 12R perovskites.

Isothermal M–H data were performed at 2–100 K to study the magnetic ground states of Ba₄SbMn₃O₁₂ (Fig. 7a). Linear M–H dependence at 100 K is consistent with the paramagnetic states of Mn₃ clusters. Magnetic hysteresis and saturation are observed at 2–60 K. In contrast with the isotropic magnetization at 15–60 K, small magnetic anisotropy is observed with a coercive field of 100 mT and 12 mT at 2 K and 5 K respectively. This indicates Ba₄SbMn₃O₁₂ displays a ferro- or ferri-magnetic state below 60 K. The saturated moment M_s can be estimated with the intercept from the linear M–H fit at the high field range. Being a constant of ∼1.61μ_B at 2–5 K, the M_s decreases linearly at increasing temperatures above T_C and disappears at T_D ∼ 70 K from extrapolation (Fig. 7b). Here, T_D represents the temperature dynamical ferromagnetic clusters initially form, while T_C represents the spin-freezing temperature. This critical linear behavior is different from the saturation behavior in typical long-range ferromagnet SrFe_0.5Co_0.5O₃,³⁸ and indicates the nature of ferromagnetic spin glass.³⁹ The T_D/T_C of about 6 keeps with those observed in other spin glass systems.^40,41

Fig. 7 (a) Magnetization of Ba₄SbMn₃O₁₂ from −6 T to 6 T at various temperatures. The inset expands the M–H curves at the low-field region. (b) The saturated moment M_s, with the variation trends shown in dashed lines.

The spin-glass behavior is further studied by the ac susceptibility, and the real (and imaginary) component of the ac susceptibility χ′ (and χ′′) versus temperature at different frequencies is plotted in Fig. 8 (and Fig. S1†). The peak in dc susceptibility at T_m ≈ 10.5 K appears to be a frequency-dependent peak in the ac susceptibilities. The temperature T_m at the broad peak maximum shifts to higher values as the frequency increases (Fig. 8 bottom inset). The frequency dependence of T_m can be well fitted to a critical power law (Fig. 8 top inset),^41,42 with the best power-law fit,

where τ = (2πf)⁻¹, τ₀ is the average relation time and T_g is the static glassy transition temperature, and zv is the dynamic critical exponent. The fitted T_g = 11.6(3) K is close to the T_m in dc susceptibilities. The τ₀ = 10^−8.3(6) s keeps with the fitted characteristic relation time of 10⁻⁸ to 10⁻¹² s for canonical spin glass,^41–43 while the zv = 3.5(7) is also comparable to that in typical spin glass materials.

Fig. 8 Temperature dependence of the real ac susceptibility component χ′ at frequencies of 3 ≤ f ≤ 250 Hz. The bottom inset shows the data around T_m for clarity. The top inset shows the frequency dependence of the freezing temperature T_m with the best power-law fit.

Another important factor for characterizing a magnetic glassy transition is the frequency shift K, which gives a relative variation in the peak temperature T_m with the angular frequency and is defined as follows:

The frequency shift K on Ba₄SbMn₃O₁₂ is estimated to be about 0.016, much smaller than the values for super-paramagnets and close to those observed in spin glasses. This indicates the magnetic state of Ba₄SbMn₃O₁₂ is a spin glass rather than a super-paramagnet.

The magnetic saturation and frustration blew T_C may arise from the partial occupancy of Mn³⁺ at the M1 sites, as observed in Ba₅Sb_1−xMn_4+xO_15−δ systems.¹⁸ The dominant magnetic super-exchange interactions between Mn₃ magnetic clusters are associated with the near-linear M1–O–M2 connections in the 12R structure type (see Table 2). The hexagonal average lattice symmetry is incompatible with long-range orbital order, but when Mn³⁺ ions are present at the M1 sites, local orbital order concerning the Mn³⁺ and Mn⁴⁺ ions at the six neighboring M2 sites is likely in such a highly connected manganite network. This gives rise to a mixture of strong ferromagnetic Mn_M1³⁺–O–Mn_M2⁴⁺ and antiferromagnetic Mn_M1³⁺–O–Mn_M2³⁺ interactions (both types are found in long-range orbitally ordered and spin-ordered manganites such as La_0.5Ca_0.5MnO₃ and LaMnO₃ (ref. 44)).

According to the Sb_M1⁵⁺ : Mn_M1³⁺ ratio of ∼5.25, we can assume each Mn₃ trimer connects with six Sb⁵⁺ or five Sb⁵⁺ and one Mn³⁺ on the adjacent M1 site, while each Mn_M1³⁺ has six Mn₃ trimers as neighbors. As a result, about 96% of Mn₃ clusters assemble into isolated superclusters of (Mn₃)₆Mn³⁺ via Mn³⁺ on the M1 site, while minor (∼4%) Mn₃ clusters are isolated with six adjacent Sb⁵⁺ ions. The local (Mn₃)₆Mn³⁺ supercluster possesses three kinds of Mn_M2–O–Mn_M1³⁺–O–Mn_M2 linear bridge related to the charge state of terminal Mn ions. The charge symmetric bridges Mn_M2⁴⁺–O–Mn_M1³⁺–O–Mn_M2⁴⁺ and Mn_M2³⁺–O–Mn_M1³⁺–O–Mn_M2³⁺ would mediate a parallel alignment between Mn₃ clusters spins, while the charge asymmetric bridge Mn_M2³⁺–O–Mn_M1³⁺–O–Mn_M2⁴⁺ would lead to an antiparallel alignment. As Sb⁵⁺, Mn³⁺, and Mn⁴⁺ mixes on the M2 site at the ratio of 0.08 : 0.42 : 0.5 (see Table 1), the Mn_M2–O–Mn_M1³⁺–O–Mn_M2 bridges in the (Mn₃)₆Mn³⁺ supercluster consist of 42.64% charge-symmetric, 42% charge-asymmetric, and 15.36% diamagnetic Sb⁵⁺ ions containing ones. Therefore, these charge-symmetric Mn_M2–O–Mn_M1³⁺–O–Mn_M2 bridges would mediate 40.9% of all Mn₃ cluster spins frozen in a parallel arrangement in the magnetic ground state of 12R Ba₄SbMn₃O₁₂, and leads to expected saturated moments of 1.63μ_B, which is essentially identical with the observed M_s of 1.61μ_B at 2–5 K.

The presence of a significant proportion of Mn³⁺ at the M1 sites in Ba₄SbMn₃O₁₂ appears to be essential for the pronounced ferromagnetism. This can be indicated by Ba₄Sn_1.1Mn_2.9O₁₂, which hosts Mn⁴⁺ and Sn⁴⁺ on the M1 site and displays weak ferromagnetism with M_s of ∼0.09μ_B at 2 K. Compared with the magnetic Mn₄ cluster with all spin canceled, the Mn₃ cluster has net spins and also contributes to ferromagnetism. This explains the reduced ferromagnetism of 10H Ba₅Sb_1−xMn_4+xO₁₅ with higher content of Mn³⁺ (∼24–36%) on the M1 site compared with that of 12R Ba₄SbMn₃O₁₂. Further studies of magnetic order using theoretical calculation will be needed to account more fully for the spin ordering phenomena.

4 Conclusions

The new 12R perovskite Ba₄SbMn₃O₁₂ has been synthesized by high-temperature solid-state reactions. The material has an ordered arrangement of Sb and Mn cations, and trimers of face-sharing MnO₆ octahedra. The paramagnetic state of Ba₄SbMn₃O₁₂ at 100–200 K can be described with the Mn₃ magnetic clusters, which partially disassociate into individual Mn ions at 250–300 K. The stability of Mn₃ magnetic clusters in the 12R polytypes is related to the intracluster Mn–Mn distance. The ferromagnetic interaction between these Mn₃ clusters is mainly mediated by Mn³⁺ at the M1 site, leading to dynamic ferromagnetic clusters below T_D = ∼70 K and ferromagnetic spin freezing transition at T_g = ∼11.5 K. Ba₄SbMn₃O₁₂ is another rare example of a periodical lattice that shows cluster magnetism due to the cationic order beyond orbital molecules.⁴⁵

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The National Natural Science Foundation of China (No. 51662013, 22161014, 21850410458), Guangxi Natural Science Foundation (No. 2020GXNSFAA297220, 2019GXNSFGA245006, AD19245097), and the Foundation of Guilin University of Technology (No. GUTQDJJ2018115) are acknowledged for their financial support.

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Footnote

† Electronic supplementary information (ESI) available. CCDC 2212931. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d3ra00607g

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