High Pressure Induced Insulator-to-Semimetal Transition through Intersite Charge Transfer in NaMn₇O₁₂

Abstract

The pressure-dependent behaviour of NaMn₇O₁₂ (up to 40 GPa) is studied and discussed by means of single-crystal X-ray diffraction and resistance measurements carried out on powdered samples. A transition from thermally activated transport mechanism to semimetal takes place above 18 GPa, accompanied by a change in the compressibility of the system. On the other hand, the crystallographic determinations rule out a symmetry change to be at the origin of the transition, despite all the structural parameters pointing to a symmetrizing effect of pressure. Bond valence sum calculations indicate a charge transfer from the octahedrally coordinated manganese ions to the square planar ones, likely favouring the delocalization of the carriers.

1. Introduction

Strongly correlated oxides can display a wide spectrum of intriguing properties, including magnetoresistance, half-metallicity, superconductivity, heavy fermion behaviour, and metal-insulator transition (MIT), with potential applications such as spintronics, superconductive devices or magnetoresistive memories. Often, different perturbations, like magnetic or electrical fields, temperature, doping or strain and pressure, can modify the material’s electronic band structure [1]. Aside from the obvious structural variations (shortening of the bond distances, increased density, Jahn-Teller (JT) distortion), the application of external pressure to strongly correlated systems may lead to a wide range of phenomena, such as quenching of the orbital moment, spin crossover (high- to low-spin transition), metal-metal inter-valence charge transfer, MIT, etc. Mott insulators are likely to show metallization at high pressure due to competition between Coulomb repulsion and bandwidth. The latter is more susceptible to applied pressure [2], and therefore, experiments in which the bandwidth can be controlled with pressure represent an experimental proof for the existing theories on the behaviour of the strongly correlated electron systems, as reported in MnO [3], BaCoS₂ [4], Ba₂IrO₄ [5], Ca₂RuO₄ [6] and in the organic compound bis(ethylenedithio)tetrathiafulvalene [7]. Quite often, pressure-induced MIT is associated with symmetry changes, as for instance in SrTiO₃ [8] or BiNiO₃ [9,10], where the suppression of charge disproportionation involving the Bi³⁺/Bi⁵⁺ ions is reported to bring from a triclinic insulating phase to higher-symmetry metallic phase. A similar case is PbCrO₃ [11], where at ambient pressure, Cr³⁺/Cr⁶⁺ charge disproportionation occurs with the 6s-6p hybridization of the Pb²⁺ orbitals with the oxygen 2p ones accounting for the insulating properties, while high pressure induces a single Cr⁴⁺ state which gives rise to the metallic phase. In some cases, however, isostructural MIT can take place when the crystallographic modifications induced by applied pressure modulate the structural features without symmetry breaking, as in the case of PrNiO₃ [12], metal osmium [13], FeAs [14] and VO₂ [15]. In WSe₂, the MIT is caused by the anisotropic character of the compressibility, which induces a structural transition characterized by a sliding of the 2D layers [16]. In MoS₂. similar phenomena are observed, but accompanied by a discontinuous change in the lattice parameters variation with pressure [17]. Other mechanisms may be at the origin of high temperature metallization, as in the case of LaMnO₃, where the phenomenon is claimed to be caused in the paramagnetic phase by orbital splitting of the majority-spin e_g bands [18,19]. The effect of pressure on ordering phenomena is crucial, as in Pr_1−xCa_xMnO₃ [20], where the suppression of charge order is identified as the origin of the MIT, while in Pr_0.6Ca_0.4Mn_0.96Al_0.04O₃ the quenching of JT distortion [21] is the driving force of metallization.

“Quadruple-perovskite” manganites, having general formula A Mn₃Mn₄O₁₂, exhibit strong electronic correlations [22]. These materials are characterized by A site cation ordering, where ¾ of the original perovskite A sites are occupied by Mn³⁺ ions in an uncommon square planar coordination (Figure 1), only stabilized by high-pressure/high-temperature (HP/HT) synthesis. The valence of the A ion tunes the Mn³⁺/Mn⁴⁺ ratio on the B site, determining the crystal symmetry based on the specific charge and orbital ordering, as reported for compounds with A = Na [23], Ca [24], (Sr, Cd) [25], Pb [26], La [27,28], Bi [29,30], Y [31], and Pr [32]. The high electronic correlations, the significant lattice distortions, the full oxygen occupation (contrary to what usually happens in the conventional “simple” perovskites) and the chemical order (hetero-valent manganese atoms occupy different crystallographic sites), make this class of materials an intriguing playground for the study of possible instabilities induced by external stimuli on both the structural and physical properties.

The sodium-substituted quadruple-perovskite manganite, NaMn₇O₁₂ (NaMn₃Mn₄O₁₂), shows features that make it particularly interesting for pressure-dependent crystallographic and physical studies. The presence of Na⁺ at the A site induces a 1:1 ratio of Mn³⁺ and Mn⁴⁺ on the B site. At room temperature, the symmetry is cubic (Im-3) as a consequence of the delocalization of the Mn³⁺ e_g electrons [33], while below 175 K, the JT effect leads to a complete charge and orbital ordering, giving rise to superlattice reflections with propagation vector (1/2, 0, −1/2) observed by electron diffraction and powder synchrotron diffraction data [34]. The charge and orbital order scheme is then described by a monoclinic super-structure with C2/m symmetry, which, in agreement with band structure calculations [22], is characterized by a periodic scheme of JT apically elongated MnO₆ octahedra. The structural phase transition is accompanied by a change in both the resistivity and magnetic susceptibility and is clearly observed by diffraction techniques. The compound undergoes two different magnetic transitions at 125 K and 90 K related to the ordering of the Mn ions at the B and A’ sites respectively. The weakly ferromagnetic transition observed below 125 K is related to spin canting of an E-type AFM structure with (½ 0 ½) propagation vector due to the large buckling of the MnO₆ octahedra. The 90 K transition is purely antiferromagnetic, and is ascribed to the ordering of the square planar Mn ions.

In the present work, the pressure dependent behaviour of NaMn₇O₁₂ is studied by means of single-crystal X-ray diffraction and resistance measurements up to about 40 GPa, showing the presence of an isostructural insulator-to-semimetal transition around 18 GPa, associated to an abrupt drop in the electrical resistance.

2. Experimental

NaMn₇O₁₂ samples were obtained by solid-state HP/HT reaction using a multi-anvil apparatus, as reported in Ref. [35]. The synthesis conditions were P = 6.0 GPa, T = 830 °C and reaction time 1 h. The NaMn₇O₁₂ crystals, having a typical size of 100 μm, were mechanically extracted by the bulk matrix. High-pressure electrical resistance measurements up to 40 GPa were performed on finely ground pure NaMn₇O₁₂ powder, with the van der Pauw method integrated in a Diamond Anvil Cell (DAC), using 300 μm culet anvils. A rhenium gasket was first filled with an insulator Al₂O₃-NaCl mixture (3:1 atomic ratio), which also acts as a pressure medium. The crystalline samples were placed inside a 100 μm cavity drilled within the pressed insulating layer. Six platinum thin strips were used as electrical probes for resistance measurements, as shown in Figure 2; the measurements were carried out in all cases using 4 of the 6 contacts in the Van der Pauw mode, the two “additional” Pt strips were placed to have backup contacts in case of breaking, which quite often happens as the pressure is increased. The Pt contacts were connected to copper leads, at the base of the diamond anvil, using a silver epoxy. At each pressure, under both compression and decompression cycles, the sample resistance was measured by the standard four-probe method as a function of temperature in a cryostat.

Diffraction experiments were performed at the ID09 beam line of the ESRF (Grenoble, France) [36]. NaMn₇O₁₂ crystals were extracted from the HP/HT ceramic sample and introduced into a DAC with helium as a pressure medium to provide nearly hydrostatic conditions up to 40.8 GPa. For both resistivity and diffraction measurements, small rubies were inserted in the DAC, whose fluorescence was used as a pressure reference. The monochromatic X-ray radiation wavelength was set to λ = 0.41456 Å and diffraction data suitable for structure refinement were collected using a Mar555 flat panel detector in the range 2.5° < θ < 19° by 0.5° ω step in the angular interval ±30°. The structure refinement was carried out by the SHELXL software (SheldrickGoettingen, Germany) [37], making use of anisotropic atomic displacements parameters (a.d.p.) for all atoms.

3. Results and Discussion

3.1. Transport Analysis

In the “low-pressure” regime (P < 15 GPa), the DAC in situ electrical measurements performed on NaMn₇O₁₂ are in agreement with previous observations [33]. Electrical resistance vs. T show a semiconductor-like thermal activated transport mechanism related to the manganese e_g electrons delocalized by kT energy (Figure 3a). By increasing pressure, a sharp resistance drop is observed above 18 GPa, yielding a semimetallic behaviour (Figure 3b), with almost temperature invariance of the resistance vs. temperature. By lowering T, no decreasing trend of resistance is detected up to the maximum value of the applied pressure, so that the high-pressure state of NaMn₇O₁₂ behaves like a semimetal rather than a conventional metal.

The Arrhenius plot derived from the R vs. T curves in the semiconducting regime shows the two critical temperatures of NaMn₇O₁₂, namely the charge ordering temperature T_CO = 176 K and the T_N = 90 K, distinguishable as deviations from the linear trend expected for a pure semiconductor, more evident at lower applied pressure (Figure 4). The E_A measured at the lowest reachable pressure (110 meV) is different from the value previously reported at ambient pressure (47 meV, [33]); measurements conducted on bulk pellets or ground powders are likely to give slightly different results, since the extrinsic phenomena and the occurrence of different percolative paths significantly affect the electrical transport mechanism. Moreover, the employed technique allows effective sample-wire contact only after the application of a (small) pressure; as a consequence, it was not possible to measure the electrical resistance below 0.4 GPa.

As the pressure increases, the charge-order transition anomaly becomes weaker and broader, in agreement with the symmetrizing effect of hydrostatic pressure, and is expected to finally lead to the melting of the charge and orbital orders. On the other hand, the anomaly observed at the T_N seems to move towards lower temperatures while getting more pronounced. By increasing pressure, the slope of the curves decreases, in accordance with the expected reduction of the thermally activated transport mechanism activation energy E_A, driven by the enhancement of the mechanical energy reducing the separation between the conduction and valence bands. Consequently, the E_A terms (obtained by the linear fit of the Arrhenius curves in the intermediate regime T_N < T< T_CO) plotted vs. the applied pressure, shows a linear decrease from 110 to 87 meV (Figure 5).

3.2. Structural Analysis

Single-crystal XRD experiments were carried out at room temperature in the 0.1–40.1 GPa range. Although the use of the DAC did not permit the collection of a significant portion of the Ewald sphere, the high symmetry of the analysed phase provides a sufficient number of equivalencies. The structure refined against the 0.3 GPa data is in excellent agreement with the previously reported crystallographic information: Im-3 symmetry (S.G. number 204), compatible with the absence of charge and orbital ordering [33]. The Na ion lies at the 2a site, while Mn1 and Mn2 are located at the 6b and 8c positions, respectively. Mn2 displays an octahedral coordination, while Mn1 a strongly distorted dodecahedral environment, often reported as square planar due to the large elongation of eight Mn-O bonds, four of which exceed 2.5 Å and four of which are above 3 Å (Figure 1).

It should be noted that all the atoms are located at high-symmetry positions with fixed x, y, z coordinates, except the sole oxygen atom, which is found at a low-symmetry site: 24 g with (0, y, z) coordinates.

While the Im-3 symmetry and the crystal structure are retained through the entire investigated pressure range, a very small change in the compressibility coefficient is detectable around the electrical transition, as shown in Figure 6. The refined lattice parameters, relevant bond distances and Mn-O-Mn tilt angle are reported in

Table 1. Lattice parameter, cell volume and selected bond lengths of NaMn₇O₁₂ at different applied pressures.

P (GPa)	a (Å)	V (Å2)	Na1-O1 (Å)	Mn1-O1 (Å)	Mn1-O1 (Å)	Avg. Mn1-O1	Mn2-O1 (Å)	Mn2-O1-Mn2 (°)
0.3	7.301(2)	389.2(9)	2.644(7)	1.943(2)	2.6867(6)	2.3149(10)	1.916(7)	139.9(4)
2.8	7.264(2)	383.2(9)	2.629(4)	1.9320(15)	2.6734(6)	2.3027(8)	1.909(4)	140.1(2)
5.5	7.237(2)	379.0(9)	2.618(7)	1.924(3)	2.6648(6)	2.2944(15)	1.904(7)	140.2(4)
8.4	7.205(2)	374.0(9)	2.605(8)	1.918(3)	2.6610(12)	2.2895(16)	1.901(8)	140.3(4)
11.2	7.174(2)	369.3(9)	2.593(4)	1.9063(14)	2.6411(6)	2.2737(8)	1.891(4)	140.4(2)
14.5	7.142(2)	364.3(9)	2.582(3)	1.8974(11)	2.629(6)	2.263(3)	1.884(3)	140.45(16)
17.2	7.102(2)	358.3(9)	2.566(3)	1.8853(10)	2.6128(6)	2.2491(6)	1.878(3)	140.70(15)
20.4	7.062(2)	352.2(9)	2.546(4)	1.8745(13)	2.6042(6)	2.2394(7)	1.868(4)	140.7(2)
23.3	7.041(2)	349.1(9)	2.538(7)	1.867(2)	2.5932(6)	2.2301(10)	1.8682(7)	141.1(4)
25.4	7.026(2)	346.9(9)	2.534(4)	1.8637(14)	2.5881(6)	2.2259(8)	1.863(4)	142.0(2)
28.5	6.995(2)	342.3(9)	2.537(11)	1.857(10)	2.5606(6)	2.2088(6)	1.854(3)	141.2(6)
35.9	6.959(2)	333.2(9)	2.516(4)	1.8510(13)	2.5763(6)	2.2135(7)	1.859(4)	141.8(2)
40.1	6.933(2)	330.7(9)	2.490(6)	1.834(2)	2.5566(6)	2.1953(10)	1.853(6)	141.8(4)

. All the parameters show monotone variations in the investigated pressure range, with the cation-oxygen bond lengths decreasing with increasing pressure.

On the other hand, at about 18 GPa (matching the insulator to semimetal transition), the compressibility of the manganese-oxygen bond system abruptly decreases, with the Mn1 atom in square planar coordination displaying the most relevant variation (Figure 7).

Interestingly, the Mn-O-Mn bond angles (Figure 8) retain a linear trend over the whole pressure range, showing an opposite slope for the octahedral tilt angle (Mn2-O1-Mn2), which increases with pressure, contrary to (Mn1-O1-Mn2). This behaviour is a consequence of the symmetrizing effect of pressure, which forces the framework towards the undistorted simple perovskite geometry, where the Mn2-O1-Mn2 and Mn1-O1-Mn2 are 180° and 90°, respectively. In order to qualitatively evaluate the valence variations on the two symmetry-independent manganese ions induced by pressure, bond valence sum (BVS) calculations were performed by using the refined crystal data [38]. To this end, the Mn-O bond distances were normalized following the formula: d_norm = d_P·a_P0/a_P, where d_P is the bond distance at a chosen pressure, a_P is the lattice parameter at the same pressure and a_P0 is the NaMn₇O₁₂ lattice parameter at room pressure. This operation is required to eliminate from the calculation the simple effects of the compressibility, since the reference bond length used in BVS is valid at room pressure.

The obtained d_norm values and the corresponding valence of the manganese ions are reported in Figure 9. It should be noted that d_norm only depends on the oxygen atom displacement within the unit cell, given that the lattice parameter contribution to compressibility has been stripped out through normalization. Consequently, the linear trend displayed by the normalized values of Mn1-O1 and Mn2-O1 distances over the whole investigated pressure range, indicates that the anomaly previously observed in the refined bond length trends is directly related to the change in the lattice compressibility observed at the insulator-to-semimetal transition.

Moreover, the normalization procedure reveals a completely different behaviour for the Mn1 and Mn2 ions with respect to the unprocessed data. Indeed, the Mn-O bond distance in the square planar coordination increases by increasing the pressure, contrary to the octahedral site. The BVS values at the lowest reachable pressure (0.3 GPa), being 3.03 and 3.67 for the square planar and octahedral coordination, respectively, are quite close to the values expected by the nominal formula NaMn^III₃(Mn^III₂Mn^IV₂)O₁₂ (3 and 3.5). It is interesting to note that, when the average manganese valence is taken into account, the calculated value is not only in good agreement with the nominal one (3.29, given by 5 Mn³⁺ and 2 Mn⁴⁺ in the structure), but also remains practically constant, ranging from 3.39 to 3.36, over the whole pressure range. This indicates the substantial accuracy of the normalization applied to the bond distances and of the used model. On the other hand, it turns out that the system experiences, with increasing pressure, a relevant charge transfer from the Mn2 to the Mn1 sites. The BVS of Mn2 undergoes a 3% increase from 3.67 to 3.78, whereas those of Mn1 decreases from 3.03 to 2.79 (8%), causing the observed decrease of the normalized volume of the MnO₆ octahedra accompanied by the elongation of the normalized square planar bonds (Figure 9). On the basis of these results, the increase in pressure progressively extends the delocalization, even to the A’ site electrons, playing an important role in determining the electric transition. Similar phenomena are reported for LaCu₃Fe₄O₁₂ [39], where intersite charge transfer at room temperature occurs by applying pressure between the A-site Cu and B-site Fe, leading to a first-order transition from LaCu³⁺₃Fe³⁺₄O₁₂ (at low pressure) to LaCu²⁺₃Fe^3.75+₄O₁₂ (high pressure). The transition is accompanied by a structural phase transition related to the different charge ordering scheme yielding significant reduction of unit-cell volume and a change from antiferromagnetic-insulating to paramagnetic-metallic state. No symmetry change is observed in the present case, being NaMn₇O₁₂ not charge and orbital ordered at ambient conditions. As a consequence, the role of pressure in modifying the electronic band structure cannot be ruled out, but the charge transfer between octahedral to square planar sites probably plays the central role in inducing the semimetallic behaviour at high pressures instead of the pure metallic character observed in LaCu₃Fe₄O₁₂.

4. Conclusions

The in situ, high-pressure powder electrical resistance measurements demonstrate that NaMn₇O₁₂, a metastable, charge-ordered manganite with quadruple-perovskite structure, undergoes an insulator-to-semimetal transition at about 18 GPa.

Across such transition, as refined by high-pressure single-crystal X-ray diffraction, NaMn₇O₁₂ retains the cubic (Im-3) structure with no symmetry breaking and non-relevant anomalies, or jump in the unit cell volume vs. P. On the contrary, charge transfer from the Mn2 (on the B site) to the Mn1 ions (on the A’ site) is detected as the pressure increases, explaining the transformation of the system from an insulating to a semimetallic state. In this framework, the drop of the electric resistance can be interpreted as a significant electronic charge delocalization at the A’ site favoured by the narrowing of the band gap.