Structural and electronic transformations in quadruple iron perovskite Ca_1−xSr_xCu₃Fe₄O₁₂

Abstract

Crystal structures and electronic transformations of quadruple iron perovskite solid solution Ca_1−xSr_xCu₃Fe₄O₁₂ (x = 0.2, 0.4, 0.6, and 0.8) have been investigated by synchrotrons X-ray powder diffraction, Mössbauer spectroscopy, and magnetization measurements. For x = 0.2, a charge disproportionation transition (2Fe⁴⁺ → Fe³⁺ + Fe⁵⁺) occur simultaneously with electron charge transfers from Fe to Cu below ∼200 K, as well as CaCu₃Fe₄O₁₂. In contrast, negative thermal expansions derived from continuous electron charge transfers from Cu and Fe are observed for x = 0.6 and 0.8 at low temperatures below room temperature, as in SrCu₃Fe₄O₁₂, followed by charge disproportionation transitions. A two-phase coexistence is observed at low temperature below ∼200 K for x = 0.4, indicating that the phase boundary locates in the vicinity of this composition. We have discovered that the Fe–O bond lengths are closely related to their covalency which were estimated from Mössbauer isomer shift parameters. The Fe–O bond covalency plays a crucial role in the types of electronic phase transitions for the Ca_1−xSr_xCu₃Fe₄O₁₂ and R³⁺Cu₃Fe₄O₁₂ (R: trivalent rare earth metal ions, Y, La–Lu) systems, where the two different low-temperature electronic phases are separated by a common isomer shift value of ∼0.17 mm s⁻¹.

Keywords:

• High-pressure synthesis
• Quadruple perovskite
• Charge disproportionation
• Charge transfer unusual high valence ion
• Electronic phase diagram
• Covalency

1 Introduction

Perovskite transition metal oxides are known for their rich variety of properties, including superconductivity, ferromagnetism, magnetoresistance, and ferroelectricity. Consequently, their structural and electronic properties have been extensively investigated over the past few decades [1 2013;3]. The application of high-pressure synthesis under several GPa has resulted in expanding variety of novel perovskites and related compounds owing to substantial changes in ionic radius ratio under high pressures. Recently, the quadruple perovskite series AA’₃B₄O₁₂ has been attracting much interest, exhibiting a wide range of intriguing phenomena such as a large magnetoresistance [4,5], giant dielectric constant [6,7], ordering of charge/spin/orbital [8], multiferroicity [9,10], and catalysis [11 2013;13]. Notably, the ACu₃Fe₄O₁₂ (A = Ca²⁺, Sr²⁺, trivalent rare-earth ions R³⁺, Bi³⁺, or Ce⁴⁺) [14 2013;19] series displays various electronic phase transitions. Thus, CaCu₃Fe₄O₁₂ undergoes a charge disproportionation transition (simplified representation: 2Fe⁴⁺ → Fe³⁺ + Fe⁵⁺) at temperatures below 210 K [14], whereas a nominally isoelectronic Sr-analog SrCu₃Fe₄O₁₂ exhibits a negative thermal expansion (NTE) induced by a gradual intersite charge transfer between Cu and Fe ions, at temperatures ranging between 200 and 270 K (crystal structure in Fig. 1) [20]. Similarly, isoelectronic R³⁺Cu₃Fe₄O₁₂ compounds display two contrasting electronic phase transitions. Thus, for smaller R ions (R = Y, Dy, Ho, Er, Tm, Yb, and Lu), charge disproportionation transitions (8Fe^3.75+ → 5Fe³⁺ + 3Fe⁵⁺) are predominant [17,18]. Conversely, abrupt intersite charge transfer transitions (3Cu²⁺ + 4Fe^3.75+ → 3Cu³⁺ + 4Fe³⁺) are favored by the larger R ions (R = La, Pr, Nd, Sm, Eu, Gd, and Tb) [15,18]. The origin of the difference between these two electronic phase transitions was initially investigated in terms of an instability of the charge-ordered states at an unequal abundance ratio of Fe³⁺ and Fe⁵⁺ species [21]. However, a systematic study unveiled that strains on R–O and Fe–O bonds dominate the types of electronic phase transitions in RCu₃Fe₄O₁₂ [18]. On the other hand, structural and electronic properties of CaCu₃Fe₄O₁₂–SrCu₃Fe₄O₁₂ solid solutions have not been elucidated to date. Herein, we demonstrate the crystal structures and electronic properties of the solid solution Ca_1−xSr_xCu₃Fe₄O₁₂ (x = 0.2, 0.4, 0.6, and 0.8). The electronic phase transitions depend on the Fe–O covalency associated with Fe–O bond lengths and Mössbauer isomer shifts (ISs). This relationship comprises the ACu₃Fe₄O₁₂ series.

Fig. 1 Crystal structure of Ca_1−xSr_xCu₃Fe₄O₁₂.

Fig. 2 Observed and calculated SXRD patterns for Ca_1−xSr_xCu₃Fe₄O₁₂ (x = 0.2, 0.4, 0.6, and 0.8) at 20 and 300 K. Circles (black) and solid lines (red) represent observed and calculated patterns, respectively. The differences between the observed and calculated patterns are shown at the bottom (blue). The vertical marks (green) indicate the Bragg reflection positions of Ca_1−xSr_xCu₃Fe₄O₁₂. The data of x = 0.4 at 20 K were refined using two-phase model.

Fig. 3 Room-temperature lattice constant (a) as a function of x for Ca_1−xSr_xCu₃Fe₄O₁₂ (x = 0, 0.2, 0.4, 0.6, 0.8, and 1). The data for x = 0 and 1 were taken from Refs. [25,26].

Fig. 4 (a) Temperature dependence of the lattice constant a for Ca_1−xSr_xCu₃Fe₄O₁₂ (x = 0, 0.2, 0.4, 0.6, 0.8, and 1). The data for x = 0, 0.6, and 0.8 were obtained from XRD data, x = 0.2 and 0.4 from SXRD data, and x = 1 from Ref. [26]. The error bars are included in the markers. (b) SXRD patterns of Ca_1−xSr_xCu₃Fe₄O₁₂ (x = 0.4) in a selected 2θ range (39.5 and 42°) collected at temperatures ranging between 20 and 450 K. The red and blue lines represent deconvoluted Bragg peaks of two phases. The fraction of the two phases at 20 K was estimated to be ∼1:1 by Rietveld refinement.

Fig. 5 Cu–O and Fe–O bond lengths at temperatures ranging between 20 and 300 K for Ca_1−xSr_xCu₃Fe₄O₁₂ (x = 0, 0.2, 0.4, 0.6, 0.8, and 1). The Fe–O bond lengths were calculated by averaging two Fe–O bonds for the charge-ordered phases (x = 0, 0.2 at 20 K). The data for x = 0 and 1 were taken from Refs. [25,26].

Fig. 6 Temperature dependence of the bond lengths and bond angle for Ca_1−xSr_xCu₃Fe₄O₁₂ (x = 0, 0.2, 0.4, 0.6, 0.8, and 1). The data for x = 0 and 1 were taken from Refs. [25,26].

Fig. 7 (a) Temperature dependence of the magnetic susceptibility in Ca_1−xSr_xCu₃Fe₄O₁₂ (x = 0, 0.2, 0.4, 0.6, 0.8, and 1) measured in field-cooling mode at temperatures ranging between 5 and 300 K. (b) Isothermal magnetization curves of Ca_1−xSr_xCu₃Fe₄O₁₂ (x = 0, 0.2, 0.4, 0.6, 0.8, and 1) at 5 K. The data for x = 0 and 1 were taken from Refs. [25,26].

Fig. 8 Mössbauer spectra for Ca_1−xSr_xCu₃Fe₄O₁₂ (x = 0.2, 0.4, 0.6, and 0.8). The sextet components attributed to α-Fe₂O₃ impurities were excluded in the fitting.

Fig. 9 (a) Atomic fractions of the Fe species at 4 K for Ca_1−xSr_xCu₃Fe₄O₁₂ (x = 0, 0.2, 0.4, 0.6, 0.8, and 1). The data for x = 0 and 1 were taken from Refs. [25,26]. (b) Estimated average Fe valence at 4 K for Ca_1−xSr_xCu₃Fe₄O₁₂ (x = 0, 0.2, 0.4, 0.6, 0.8, and 1).

Fig. 10 IS versus Fe–O bond length for Ca_1−xSr_xCu₃Fe₄O₁₂ (circles) and RCu₃Fe₄O₁₂ (R = Eu, Tb, Dy, Y, Lu; squares) systems at RT. The data for Ca_1−xSr_xCu₃Fe₄O₁₂ (x = 0, 1) and RCu₃Fe₄O₁₂ were taken from Refs. [25,26]. The red and blue markers represent the compounds undergoing charge ordering transitions and Cu-to-Fe electron charge transfer transitions, respectively. The lines are guides to the eye.

2 Experimental

Precursors were prepared using the polymerized complex method [20,22]. Stoichiometric mixtures of CaCO₃ (99.9%), SrCO₃ (99.9%), Cu(NO₃)₂·3H₂O (99.9%), and Fe(NO₃)₃·9H₂O (99.9%) at molar ratios of (1−x):x:3:4 were dissolved in nitric acid, to which a five-fold excess of citric acid and a one-fold excess of 1,2-ethanediol were added while stirring. The resultant solutions were heated to 573 K, while stirring, and maintained at this temperature for 1 h to dry. Subsequently, the dried powders were fired in a furnace at 673 K for 1 h and 948 K for 12 h in air with occasional grindings. The afforded precursors with a nominal chemical composition of Ca_1−xSr_xCu₃Fe₄O_12−δ (δ ∼ 2) were mixed with the oxidizing agent KClO₄ (99.9%) in a molar ratio of 8:5. The mixtures were charged into Pt capsules. The capsules were placed into a (Mg, Co)O pressure medium and compressed to 20 GPa using a high-pressure apparatus. The sample was subsequently heated to 1473 K for 20 min, maintained at this temperature for 30 min, and quenched to room temperature (RT, ∼300 K). During the heat treatment, the pressure was maintained at 20 GPa; it was released slowly after the heat treatment. The afforded polycrystalline samples were washed several times with distilled water.

X-ray powder diffraction (XRD) measurements were performed at temperatures ranging between 100 and 450 K using a Rigaku Ultima IV diffractometer with a Cu Kα radiation. Synchrotron X-ray powder diffraction (SXRD) data were collected at temperatures ranging between 20 and 450 K using N₂- and He-spray refrigerators installed at the BL02B2 beamline of SPring-8, Japan. Samples were contained in Lindemann glass capillary tubes (inner diameter of 0.2 mm), and the wavelength used was 0.42063 Å (determined by calicbation with a CeO₂ standard). Structure parameters were refined by Rietveld analysis using the RIETAN-FP program [23] and the crystal structures were drawn using the VESTA3 software [24].

The ⁵⁷Fe Mössbauer spectroscopy measurements for samples with x = 0.2, 0.4, 0.6, and 0.8 were performed in transmission geometry using ⁵⁷Co/Rh as a radiation source and α-Fe as a control for the velocity calibration and IS. The collected Mössbauer spectra were fitted computationally using the Lorentzian function. Magnetization measurements were conducted using a superconducting quantum interference device (SQUID, Quantum Design MPMS-XL) at temperatures ranging between 5 and 300 K under external magnetic fields ranging between 0.1 and 50 kOe.

3 Results

3.1 Crystal structures

Fig. 2 illustrates the observed SXRD patterns and Rietveld refinement results of Ca_1−xSr_xCu₃Fe₄O₁₂ at 20 and 300 K (also see Table 1). All SXRD patterns at 300 K could be indexed in the cubic quadruple AA’₃B₄O₁₂-type perovskite structure (space group: Im, No. 204). The a-axis length at this temperature increased monotonically from 7.295 (x = 0) to 7.360 Å (x = 1) (Fig. 3). These observations confirm that the solid solutions of Ca_1−xSr_xCu₃Fe₄O₁₂ at any composition could be successfully synthesized in this study. No significant amounts of oxygen deficiencies were confirmed in the Rietveld refinement results. Thus, we assumed that the nominal compositions were almost retained for any samples. Fig. 4(a) displays the temperature dependence of the a-axis length obtained from Rietveld refinement of the XRD (x = 0, 0.6, 0.8, 1) and SXRD (x = 0.2, 0.4) data. An abrupt drop was observed below ∼200 K for x = 0.2. This is attributed to the shrinkage (elongation) of the Fe–O (Cu–O) bonds due to Fe-to-Cu electron charge transfer, as has been reported for CaCu₃Fe₄O₁₂ [25]. The crystal structures of x = 0.2 sample below the phase transition temperature were refined with the charge-ordered structure model (space group: Pn, No. 201), as well as x = 0 [14]. Continuous NTEs in temperatures ranging between 180 and 280 K were observed in samples with x = 0.6 and 0.8, as well as in SrCu₃Fe₄O₁₂. This behavior is induced by the Cu-to-Fe electron charge transfer [26]. The structure refinement for x = 0.6 and 0.8 below phase transition temperatures were performed based on the charge-disordered structure model (space group: Im, No. 204), as well as x = 1 [26]. The x = 0.4 sample displayed coexistence of two phases with clearly different a-axis lengths below ∼200 K, as shown in Fig. 4(b). The peak broadenings induced by the local strains inhibit the phase transition [27], remaining in the two-phase coexistence at 20 K.

Table 1 Refined structure parameters, selected bond lengths and angles for Ca_1−xSr_xCu₃Fe₄O₁₂ at 300 and 20 K.

	300 K				20 K
	x = 0.2	x = 0.4	x = 0.6	x = 0.8	x = 0.2	x = 0.4		x = 0.6	x = 0.8
Space group^a
a (Å)	7.30355 (9)	7.31708 (17)	7.33013 (14)	7.34542 (15)	7.27630 (6)	7.2942 (7)	7.3164 (4)	7.33640 (15)	7.35387 (14)
x (O)	0.1749 (3)	0.1707 (5)	0.1719 (5)	0.1732 (5)	0.248 (2)	0.1707^c	0.1707^c	0.1725 (5)	0.1731 (5)
y (O)	0.3078 (3)	0.3053 (5)	0.3066 (5)	0.3076 (4)	0.4271 (4)	0.3053^c	0.3053^c	0.3088 (5)	0.3111 (5)
z (O)	–	–	–	–	0.5577 (3)	–	–	–	–
Uiso(Ca,Sr) × 10^3 (Å^2)	6.7 (7)	8.4 (1.1)	5.4 (8)	5.4 (7)	3.9 (7)	2^c	2^c	4.0 (8)	2.4 (5)
Uiso(Cu) × 10^3 (Å^2)	4.6 (3)	5.6 (5)	7.4 (4)	8.0 (4)	2.5 (3)	2^c	2^c	4.3 (4)	6.0 (3)
Uiso(Fe1) × 10^3 (Å^2)	2.0 (2)	1.8 (4)	2.1 (3)	1.6 (3)	0.5 (2)	2^c	2^c	1.1 (3)	0.6 (3)
Uiso(Fe2) × 10^3 (Å^2)	–	–	–	–	0.5^b			–	–
Uiso(O) × 10^3 (Å^2)	3.7 (4)	2.6 (7)	2.8 (6)	1.7 (7)	2.7 (5)	2^c	2^c	1.4 (6)	1.4 (6)
(Ca,Sr)–O (× 12) (Å)	2.586 (2)	2.559 (4)	2.577 (4)	2.593 (4)	2.583 (2)	–^c	–^c	2.595 (4)	2.618 (4)
Cu–O (× 4) (Å)	1.898 (2)	1.894 (3)	1.897 (3)	1.901 (3)	1.902 (3)	–^c	–^c	1.890 (3)	1.885 (3)
Cu–O (× 4) (Å)	2.758 (2)	2.799 (4)	2.792 (4)	2.786 (4)	2.735 (2)	–^c	–^c	2.782 (4)	2.777 (4)
Fe1–O (× 6) (Å)	1.9526 (8)	1.9614 (12)	1.9642 (11)	1.9672 (11)	1.957 (13)	–^c	–^c	1.9680 (10)	1.9752 (9)
Fe2–O (× 6) (Å)	–	–	–	–	1.925(13)	–^c	–^c	–	–
Fe–O–Fe (°)	138.49 (11)	137.69 (19)	137.81 (16)	137.97 (16)	139.18 (14)	–^c	–^c	137.49 (15)	137.12 (14)
Rwp (%)	5.628	8.105	7.128	6.638	6.491	7.496	–	7.179	6.294
RB (%)	1.438	2.377	2.645	2.764	2.285	2.132	2.620	2.414	1.877
S	1.2040	1.8882	1.7964	1.7388	1.1762	1.5378	–	1.5659	1.4496

^aAtomic sites: (Ca, Sr) 2a (0, 0, 0), Cu 6b (0, ¹/₂, ¹/₂), Fe 8c (¹/₄, ¹/₄, ¹/₄), O 24 g (x, y, 0) for Im-3 (No. 204); (Ca, Sr) 2a (¹/₄, ¹/₄, ¹/₄), Cu 6d (¹/₄, ³/₄, ³/₄), Fe1 4b (0, 0, 0), Fe2 4c (¹/₂, ¹/₂, ¹/₂), O 24 h (x, y, z) for Pn-3 (No. 201); The occupancy factor g for (Ca, Sr) site was fixed at the nominal x value; The occupancy factor g for Cu, Fe, and O sites was fixed at unity.

b The following constraint was adopted: U_iso(Fe1) = U_iso(Fe2).

c The atomic coordinates and isotropic displacements were fixed at the values at 300 K because reliable refinement could not be obtained. Thus, only a-axis lengths were refined.

The metal–oxygen bond lengths/angles were calculated from Rietveld refinement results using the SXRD data at temperatures ranging between 20 and 450 K (see Table 1). Fig. 5 demonstrates the x dependence of the Cu–O and Fe–O bond lengths in Ca_1−xSr_xCu₃Fe₄O₁₂. Reliable structure parameters (atomic positions) could not be obtained from the refinement for x = 0.4 at 20 K because of significant peak broadenings, thus only a-axis lengths were refined. The Cu–O bond lengths at 300 K were distributed across a small range (1.89–1.91 Å) for all compositions, implying that the Cu valence is almost identical at this temperature. We previously confirmed that the Cu valences of the CaCu₃Fe₄O₁₂ and SrCu₃Fe₄O₁₂ end-members at 300 K are almost identical (∼2.4) [25,26]. Thus, the Cu valence is held at the same level for all solid solutions. The Fe–O bond lengths at 300 K increased monotonically from 1.947 (x = 0) to 1.970 Å (x = 1). This does not signify that intrinsic changes in Fe valences are dependent upon x. The Fe–O bonds for Ca_1−xSr_xCu₃Fe₄O₁₂ are flexibly expanded by structural distortions with larger A-site ions, as observed in RCu₃Fe₄O₁₂ [18]. Thus, we conclude that the adequate ionic model of all Ca_1−xSr_xCu₃Fe₄O₁₂ phases at 300 K is retained as Ca²⁺_1−xSr²⁺_xCu^∼2.4+₃Fe^∼3.7+₄O₁₂ [25,26].

Fig. 6 displays the temperature dependence of the Cu–O/Fe–O bond lengths, and Fe–O–Fe bond angles for Ca_1−xSr_xCu₃Fe₄O₁₂. For x = 0.2, the Cu–O bond length increased on cooling to temperatures below ∼200 K, and the Fe–O bonds were split into longer and shorter bonds. The former indicates that the Fe-to-Cu electron charge transfer occurs simultaneously with the charge disproportionation transition, resulting in Cu reduction. The latter is due to the charge ordering of the charge-disproportionated Fe³⁺ and Fe⁵⁺ ions, as has been reported for CaCu₃Fe₄O₁₂ [25]. For x = 0.6 and 0.8, the Cu–O bonds gradually shrank, but the Fe–O bonds gradually extended on cooling below 300 K. This behavior is identical to that of SrCu₃Fe₄O₁₂, and is attributed to the electron charge transfer from Cu to Fe [20,26]. Similar to SrCu₃Fe₄O₁₂, for x = 0.6 and 0.8, the Fe–O–Fe bond angles decreased on cooling. The volume expansions were partly compensated according to the following relationship: a = 4d_Fe–O × sin(ψ/2), where d_Fe–O and ψ represent the Fe–O bond length and Fe–O–Fe bond angle, respectively. However, the Fe–O bond elongations exceeded these values, resulting in substantial NTE when x = 0.6 and 0.8. The Cu–O and Fe–O bond lengths at 20 and 300 K are compared in Fig. 5. The Cu–O elongations/shrinkages, and Fe–O shrinkages/elongations are closely coupled when x is in the ranges of 0–0.2 and 0.6–1, respectively. This reasonably distinguishes two contrasting phase transitions; type-I: Fe-to-Cu electron charge transfer accompanied by charge ordering of charge-disproportionated Fe³⁺/Fe⁵⁺ ions like CaCu₃Fe₄O₁₂ (x = 0–0.2), type-II: Cu-to-Fe electron charge transfer without charge ordering of charge-disproportionated Fe³⁺/Fe⁵⁺ ions like SrCu₃Fe₄O₁₂ (x = 0.6–1).

3.2 Magnetic properties

Magnetic properties are closely related to the above-demonstrated structural transformations. Fig. 7(a) illustrates the temperature dependence of the magnetic susceptibility for Ca_1−xSr_xCu₃Fe₄O₁₂. The type-I phases (x = 0, 0.2) exhibited ferromagnetic (ferrimagnetic) transitions simultaneously with charge-transfer/disproportionation/ordering transitions [14]. The Curie temperature (T_C) decreased from 210 K (x = 0) to 200 K (x = 0.2). This is derived from a decline in superexchange interactions on Fe–O–Fe due to the increase in the Fe⁵⁺ atomic fraction from 39% (x = 0) to 43% (x = 0.2), as indicated by Mössbauer spectroscopy in the next section. On the other hand, the type-II phases (x = 0.6, 0.8, 1) exhibited antiferromagnetic phase transitions at temperatures ranging between 180 and 190 K, simultaneously with charge disproportionation transition [20,26]. Fig. 7(b) illustrates the isothermal magnetization curves at 5 K for Ca_1−xSr_xCu₃Fe₄O₁₂. Almost the same saturation magnetizations [∼10 μ_B per formula unit (f.u.)] were observed when x = 0 and 0.2. In contrast, linear dependences, attributed to antiferromagnetic properties, were observed when x = 0.6, 0.8, and 1. The x = 0.4 sample displayed intermediate behavior, with saturation magnetization of ∼3.5 μ_B per f.u., which was much smaller than those observed for x = 0–0.2. This was interpreted as the decrease in the ferromagnetic fraction (estimated at ∼30%) of charge-ordered phase in a two-phase coexistence state. A intense hump was observed below transition temperature for x = 0.6, like TbCu₃Fe₄O₁₂ [18]. The origin is probably related to the electronic transformation accompanying charge transfer, but the detail is not clear at this stage.

3.3 Mössbauer spectroscopy

The electronic state transitions for Ca_1−xSr_xCu₃Fe₄O₁₂ were investigated by ⁵⁷Fe Mössbauer spectroscopy. Fig. 8 displays Mössbauer spectra for samples with x = 0.2, 0.4, 0.6, and 0.8 at low temperature (LT, 4–8 K), and RT (∼300 K). Singlet (B-site Fe, >90%) and doublet (A’-site Fe, <10%) paramagnetic components were predominantly observed at RT for all samples, as well as for CaCu₃Fe₄O₁₂ and SrCu₃Fe₄O₁₂ [25,26]. Small amounts of α-Fe₂O₃ impurity (∼5%) were excluded from the analysis. The Mössbauer hyperfine parameters are listed in Table 1. The IS of the paramagnetic singlet components increased monotonically from 0.16 (x = 0.2) to 0.19 mm s⁻¹ (x = 0.8), all of which are included in the range between 0.16 mm s⁻¹ (x = 0) and 0.20 mm s⁻¹ (x = 1) [25,26]. This increase does not imply any intrinsic valence reductions in the Fe ions, but indicates changes in the Fe–O bonding character. In other words, the Fe–O covalency decreases monotonically with an increase in x. This is associated with the crystal structures. Thus, the elongation of the Fe–O bond from 1.947 (x = 0) to 1.970 Å (x = 1) accordingly decreases the overlap of Fe 3d–O 2p orbitals, resulting in less covalent (or more ionic) character of the Fe–O bonds. The LT Mössbuaer spectra of the two groups (x = 0.2 and x = 0.4–0.8) differed. In the former group, three magnetic sextet components attributed to the Fe⁵⁺, Fe³⁺(1), and Fe³⁺(2) were found. This is similar to the behavior observed in CaCu₃Fe₄O₁₂ [25]. The Fe⁵⁺ and Fe³⁺(1) components are derived from the charge ordering of the Fe⁵⁺ and Fe³⁺ ions in a rock-salt-type manner. On the other hand, the Fe³⁺(2) component is attributed to the randomly distributed Fe³⁺ ions at the B- and A’-sites [25]. The slight increase in the Fe⁵⁺ abundance ratio from 39% (x = 0) to 43% (x = 0.2) indicates that the Fe-to-Cu electron charge transfer (Fe oxidation) is enhanced when x increases. Thus, the spectra of the x = 0.4–0.8 sample group were more complicated than that of x = 0.2 because of the apparent phase coexistence (x = 0.4) and/or charge disordering like SrCu₃Fe₄O₁₂ [26]. A clear difference in IS values between Fe³⁺ (0.4–0.45 mm s⁻¹) and Fe⁵⁺ (0–0.1 mm s⁻¹) species was adopted for the assignment of each component. The Fe³⁺(1) components for the samples with x = 0.4 and 0.6 were assigned to the Fe³⁺ ions in almost charge-ordered phases owing to hyperfine field values (∼430 kOe) that were similar to those of Fe³⁺(1) ions for the x = 0–0.2 sample group. In contrast, other Fe³⁺ components, Fe³⁺(2) and Fe³⁺(3) for the x = 0.4–0.8 sample group, were assigned to the Fe³⁺ ions in randomly distributed or charge-disordered phases, according to previous reports on La_1−x(Ca/Sr)_xFe^(3+x)+O₃ perovskites [28,29]. In these reports, two types of Fe³⁺ components with different hyperfine parameters in charge-disordered phases were distinguished. Fig. 9(a) displays the x dependence of the atomic fractions of the Fe³⁺ and Fe⁵⁺ species at LT. The increase in the Fe⁵⁺ fraction from x = 0 to 0.2 weakens the Fe–O–Fe superexchange interaction J (J is proportional of the product of spin quantum numbers) because of the smaller spin quantum number of Fe⁵⁺ (S = 3/2) when compared to that of Fe³⁺ (S = 5/3). This decreases the Curie temperatures gradually from ∼210 K (x = 0) to ∼200 K (x = 0.2), as shown in the magnetic susceptibility data. The Fe⁵⁺ fraction slightly decreases from x = 0.6 to 1, implying that the Cu-to-Fe charge transfer is enhanced by x in these compositions. This is consistent with the fact that the magnitude of NTE systematically increased from x = 0.6 to 1. Fig. 9(b) illustrates the calculated average Fe valences in the LT phases. The average Fe valence, initially increased from x = 0 to 0.2, suddenly decreased at the phase boundary (x = 0.4), and further decreased slightly from x = 0.4 to 1. This behavior indicates that the structural distortions induced by the A-site Ca/Sr ions dominate the Cu–Fe charge transfers (Table 2).

Table 2 Hyperfine parameters for Ca_1−xSr_xCu₃Fe₄O₁₂ (x = 0.2, 0.4, 0.6, and 0.8) at RT and LT.

RT (∼300 K)	IS (mm s^−1)	HF (kOe)	ΔEq (mm s^−1)	Ratio (%)	LT (4–8 K)	IS (mm s^−1)	HF (kOe)	ΔEq (mm s^−1)	Ratio (%)
x = 0.2					x = 0.2
Fe (B-site)	0.163	0	0	95	Fe^5+	0.042	237	0	43
Fe (A’-site)	0.405	0	1.82	5	Fe^3+(1)	0.422	435	0	45
					Fe^3+(2)	0.561	516	0	12
x = 0.4					x = 0.4
Fe (B-site)	0.171	0	0	96	Fe^5+	0.059	230	−0.08	31
Fe (A’-site)	0.379	0	1.77	4	Fe^3+(1)	0.419	421	0	26
					Fe^3+(2)	0.404	462	0	25
					Fe^3+(3)	0.455	495	0	17
x = 0.6					x = 0.6
Fe (B-site)	0.179	0	0	96	Fe^5+	0.053	230	–0.08	26
Fe (A’-site)	0.367	0	1.77	4	Fe^3+(1)	0.475	430	0	3
					Fe^3+(2)	0.420	468	0.02	53
					Fe^3+(3)	0.447	501	–0.02	18
x = 0.8					x = 0.8
Fe (B-site)	0.189	0	0	92	Fe^5+	0.077	230	–0.023	24
Fe (A’-site)	0.376	0	1.81	8	Fe^3+(1)	0.423	470	0	49
					Fe^3+(2)	0.443	501	0	27

4 Discussion

We consider structural and electronic properties of Ca_1−xSr_xCu₃Fe₄O₁₂ on the basis of SXRD, magnetic susceptibility, and Mössbauer spectroscopy data. Fig. 10 displays the IS of B-site Fe as a function of Fe–O bond lengths at RT for Ca_1−xSr_xCu₃Fe₄O₁₂ (x = 0, 0.2, 0.4, 0.6, 0.8, and 1), and RCu₃Fe₄O₁₂ (R = Y, Eu, Tb, Dy, and Lu) [17,18,25,26]. This diagram demonstrates two common features for Ca_1−xSr_xCu₃Fe₄O₁₂ and RCu₃Fe₄O₁₂. The first is that the IS values increase monotonically when the Fe–O bonds are elongated. This indicates that the Fe–O bond covalency is weakened to increase IS values when the Fe–O bonds become longer because the overlapping of Fe 3d–O 2p orbitals decreases. The second is that the common phase boundary of the LT electronic phases for ACu₃Fe₄O₁₂ is located at IS ∼0.17 mm s⁻¹. In other words, all compounds with IS values >0.17 mm s⁻¹ (x > 0.4 for Ca_1−xSr_xCu₃Fe₄O₁₂ and R = Tb and Eu for RCu₃Fe₄O₁₂, respectively) undergo Cu-to-Fe electron charge transfer transitions associated with volume expansions. In contrast, all compounds with IS values <0.17 mm s⁻¹ (x < 0.4 for Ca_1−xSr_xCu₃Fe₄O₁₂ and R = Y, Dy, and Lu for RCu₃Fe₄O₁₂, respectively) go through charge disproportionation involving Fe³⁺/Fe⁵⁺ charge ordering. These results reveal that the Fe–O bond covalency is closely related to the types of electronic phase transitions. This tendency supports the previously proposed bond–strain-based phase diagram of the RCu₃Fe₄O₁₂ system, where the forcedly elongated Fe–O bonds favor reduction to Fe³⁺ ions through intersite charge transfer (3Cu²⁺ + 4Fe^3.75+ → 3Cu³⁺ + 4Fe³⁺) although unstrained or compressed Fe–O bonds prefer charge disproportionation transitions (8Fe^3.75+ → 5Fe³⁺ + 3Fe⁵⁺) [18]. The disagreement between Ca_1−xSr_xCu₃Fe₄O₁₂ and RCu₃Fe₄O₁₂ lines is probably attributed to the difference in A-site ion sizes. Larger alkaline-earth ions (Ca²⁺:1.12 Å and Sr²⁺:1.26 Å) at A-sites expand Fe–O bonds compared to smaller rare-earth metal ions (0.977–1.066 Å for Lu³⁺–Eu³⁺), resulting in the shift to right side (larger Fe–O) in Fig. 10.

5 Conclusions

We investigated the crystal structures and electronic transformations of the quadruple perovskite solid solutions Ca_1−xSr_xCu₃Fe₄O₁₂. It has been found that the Fe–O bond lengths are closely related to their covalency which are estimated from Mössbauer isomer shift parameters for Ca_1−xSr_xCu₃Fe₄O₁₂ and R³⁺Cu₃Fe₄O₁₂. The electronic phase boundary dividing between charge-disproportionated phases involving Fe³⁺/Fe⁵⁺ charge ordering (x < 0.4 and R = Dy, Y, Lu) and others dominated by Cu-to-Fe electron charge transfer accompanying unit cell volume expansion (x > 0.4 and R = Eu, Tb) is commonly located at ∼0.17 mm s⁻¹. These findings demonstrate that the covalency of metal–oxygen bonds is an essential factor in determining the electronic states of ACu₃Fe₄O₁₂ perovskites

Acknowledgements

The synchrotron radiation experiments were performed at SPring-8 with the approval of JASRI (Proposal Nos. 2012A1619 and 2016A1229). This work was performed under the Visiting Researcher’s Program of Geodynamics Research Center, Ehime University. This work was supported by Grants-in-Aid for Scientific Research (B16H04220) from the Japan Society for the Promotion of Science, the Ministry of Education, Culture, Sports, and Science and Technology of Japan, and Toray Science Foundation.