Possible helimagnetic order in Co⁴⁺-containing perovskites Sr_1−xCa_xCoO₃

Searching for novel magnetic phases in a simple system is an attractive, yet challenging, task in condensed matter physics. One promising approach to discovering exotic magnetic phases is to focus on the system with competing exchange interactions. While this is typified by antiferromagnetic (AFM) insulators with geometrically frustrated spin lattice,¹ frustrated magnetic metals with competing exchange interactions have attracted attention for their novel spintronic phenomena, as highlighted by the emergence of magnetic skyrmion lattice in non-centrosymmetric magnets with the Dzyaloshinskii–Moriya interaction.^2,3

As centro-symmetric counterparts of frustrated magnetic metals, perovskite-type oxides with unusually high valence Fe⁴⁺, Co⁴⁺, and Ni³⁺ ions have been known to show rich magnetic phases.^4–6 This is exemplified by the observation of various topological spin orders involving multiple-Q helimagnetic (HM) states in SrFeO₃^7–10 and a room-temperature ferromagnetic (FM) order in SrCoO₃.^11–16 Although they exhibit apparently different magnetic behavior, there are important similarities between them; both of them share the cubic perovskite-type structure, the strong p-d hybridization with a negative charge-transfer energy, and the e_g¹ configuration, provided that Co⁴⁺ is in the unique intermediate spin IS state (t_2g⁴e_g¹), which has been under debate.^{11–15,17,18} Considering the fact that the negative charge transfer energy and the e_g¹ configuration have been discussed as important conditions for the emergence of the spin spiral in SrFeO₃,⁶ it is tempting to expect the emergence of the novel HM phase in the Co⁴⁺-containing perovskites as well.

So far, the Fe⁴⁺-containing perovskites AFeO₃ have been systematically synthesized to study the A-site dependent variation of the magnetic ground state.^5,19,22 Substitution of the A-site in SrFeO₃ results in a significant change in the helimagnetic propagation vector in BaFeO₃ and CaFeO₃, the latter of which shows a metal–insulator transition, accompanied by charge disproportionation of Fe⁴⁺.^5,19–21 On the other hand, the Co⁴⁺-containing perovskites—ACoO₃, Sr_1−xBa_xCoO₃, and CaCoO₃—have been successfully synthesized by a high pressure technique.^23–25 While Sr_1−xBa_xCoO₃ has been reported to retain the cubic structure and show the change in the ground state from FM to HM at around x = 0.4, there remains a missing link between cubic SrCoO₃ with the FM state and orthorhombically distorted CaCoO₃ showing AFM behavior.

In this paper, we have systematically synthesized perovskite-type cobaltates Sr_1−xCa_xCoO₃ by a high-pressure technique and investigated the change in the structure and the magnetic states, while revealing the structure–property relationship. As the Ca content x increases, the structure changes from cubic to orthorhombic at around x = 0.6, and the magnetic ground state changes from FM to AFM at around x = 0.8 in the orthorhombic phase. We discuss the origin of variation in the magnetic ground states and the possibility of the helical spin order in the AFM state in terms of the bandwidth narrowing and the competing exchange interactions inherent to the orthorhombic distortion.

Polycrystalline samples of Sr_1−xCa_xCoO₃ were prepared by following the procedure reported in Ref. 23. The starting materials, SrCO₃, CaCO₃, and Co₃O₄, were stoichiometrically mixed. The mixture was heated at 1173 K for 12 h in air. The obtained powder was pelletized and sintered again at 1373 K for 24 h in a flow of oxygen (1 atm), followed by quenching into water at room temperature. Through these processes, oxygen-deficient perovskites Sr_1−xCa_xCoO_3-δ were synthesized. To obtain fully oxidized compounds, the quenched pellet was pulverized and packed into a gold capsule, together with an oxidizer, NaClO₃. The capsule was annealed at 753 K for 1 h at a high pressure of 8 GPa using a cubic-anvil-type high-pressure apparatus. Note that the oxidation of the compound with x = 0.2 was completed by the dip in an aqueous solution of sodium hypochlorite for 12 h, which turned out to yield a more oxidized sample as compared to the samples prepared by the high-pressure process. The synchrotron powder x-ray diffraction (XRD) with a wavelength of 0.689 75 Å was carried out at BL-8A, Photon Factory, KEK, Japan. The diffraction patterns were analyzed by the Rietveld refinement using RIETAN-FP.²⁶ The magnetization M, electrical resistivity ρ, and specific heat C were measured using MPMS and PPMS manufactured by Quantum Design, respectively. The magnetization up to 55 T was measured using the non-destructive pulsed magnet with a pulse duration of 36 ms at the International MegaGauss Science Laboratory at the Institute for Solid State Physics.

To evaluate the structural stability of SrCoO₃ and CaCoO₃ under ambient and high pressures, we performed DFT calculations using the plane-wave-basis projector augmented wave (PAW) method²⁷ with GGA-PBEsol approximations, as implemented in Quantum Espresso package.²⁸ We performed structural optimization calculations on cubic and orthorhombic perovskite-type structures at 0 and 10 GPa. Non-magnetic (NM) and ferromagnetic (FM) configurations were assumed for Co ions, and the electron correlation U was set to 5 eV. The cutoff energies for wavefunctions and charge density were set to 60 and 445 Ry, respectively. The Monkhorst–Pack k-point meshes of 9 × 9 × 9 and 6 × 4 × 6 or more were adopted for the cubic and the orthorhombic structures, respectively.

Figure 1(a) shows magnified powder XRD patterns of Sr_1−xCa_xCoO₃, with selected compositions of x = 0.2, 0.4, 0.6, 0.7, 0.8, and 1.0. The diffraction patterns for x = 0.2 and 0.4 and x = 0.8 and 1.0 were indexed with a cubic unit cell (S.G.: Pm-3m) and a GdFeO₃-type orthorhombic unit cell (S.G.: Pbnm), respectively. The XRD patterns with Rietveld refinement for the cubic phase with x = 0.4 and the orthorhombic phase with x = 0.8 can be found in Fig. S1 in the supplementary material. The lattice parameters are summarized in Table I, and the refined structures for x = 0 and 1.0 are shown in Fig. 1(b). It is noted that the diffraction peaks of x = 0.6 and 0.7 tend to be diffused, implying that these samples are located around the first-order structural phase boundary and contain both cubic and orthorhombic phases coexisting on a microscopic scale. In Figs. 1(c) and 1(d), the unit cell volume divided by the number of atoms per unit cell Z and the Co–O–Co bond angle are presented as a function of x. The unit cell volume of both structures decreases with increasing x, reflecting the smaller ionic radius of Ca²⁺ compared to Sr²⁺. Using the Co–O bond lengths, we estimated the bond-valence sums for Co ions,²⁹ which are in the range +3.86–4.08 (see Table I). Thermo-gravimetric (TG) measurements support this high Co valence; the TG measurements suggest that this system is sufficiently oxidized with little oxygen deficiency, implying that the valence of Co is close to +4 (see the supplementary material).

To examine the stability of cubic and orthorhombic perovskite structures for SrCoO₃ and CaCoO₃, respectively, the enthalpies at 0 and 10 GPa were calculated based on ab-initio calculations. Figure 2 shows the enthalpy of the orthorhombic phase relative to that of the cubic phase for SrCoO₃ and CaCoO₃ with ferromagnetic (FM) and non-magnetic (NM) states. It is notable that the orthorhombic structure tends to be more stable than the cubic structure not only for CaCoO₃, but also for SrCoO₃. Assuming the FM state at a high pressure of 10 GPa, while the orthorhombic structure remains to be stable for CaCoO₃, the cubic structure becomes more stable than the orthorhombic one for SrCoO₃, implying the importance of the FM interaction for the phase formation. This result is qualitatively consistent with our experimental results that the cubic structure found for SrCoO₃ is replaced by the orthorhombic structure as the Ca content x increases.

Figure 3(a) shows the temperature dependence of magnetization M divided by a magnetic field H of 0.1 T, M/H, measured in field cooling (FC) runs. As x increases from 0 to 0.7, the FM transition temperature T_c decreases systematically, which is accompanied by the emergence of a stepwise transition at x = 0.6 and 0.67. The observation of the successive FM transitions reflects the coexistence of cubic and orthorhombic phases with different T_c, consistent with the XRD experiments. For x = 0.8, with orthorhombic structure, the FM transition was observed at 120 K, followed by the decrease of M/H below 90 K. Eventually at x = 1.0, the FM transition disappeared, and, instead, an antiferromagnetic (AFM) transition was found at 95 K (=T_N), as shown in Fig. 3 (b).

Further insight into the magnetic ground state of Sr_1−xCa_xCoO₃ is provided by the field dependence of M at 2 K, as shown in Fig. 3(c). For x = 0.2 and 0.4, the magnetization shows a characteristic field dependence similar to ferromagnetic SrCoO₃. The saturated moment of ∼2.0 μ_B/Co is slightly smaller than that of the single crystal of SrCoO₃ (∼2.5 μ_B/Co),¹¹ but comparable to that of the polycrystalline sample (∼2.1 μ_B/Co).^30–32 The FM behavior was also observed for x = 0.6–0.7, while the hysteresis loop was enlarged and the saturation moment was slightly diminished, probably due to the emergence of the orthorhombic phase. At x = 0.8, the M–H curve shows a nonlinear and hysteretic behavior, suggesting that an AFM state tends to predominate over the competing FM state as the magnetic ground state. The magnetization curve of x = 1 shows AFM-like linear behavior without saturation up to 7 T, unlike the other compounds showing hysteretic and FM-like behavior. To gain more insight into the magnetism of the compound with x = 1, we performed magnetization measurements under high fields up to 55 T at various temperatures, as shown in Fig. 3(d). The M–H curve at 4.2 K was almost saturated above 40 T, with the moment of 1.6 μ_B/Co. The abrupt increase above 9 T can be ascribed to a spin–flop transition possibly inherent to the non-collinear or helical spin structure. The magnetization of x = 1 at 40 T is slightly smaller than that of x = 0.4, which may be a sign of the partial emergence of the low-spin state (∼1.0 μ_B/Co). On the other hand, the effective Bohr magneton number P_eff = 3.35–3.98 μ_B for all compounds estimated from the Curie–Weiss law M/H(T) = C_w/(T-θ), where C_w is the Curie constant (see Figs. S3 and S4 in the supplementary material), is close to the theoretical value of 3.87 μ_B expected for the intermediate spin state of Co⁴⁺ (t_2g⁴e_g¹) with S = 3/2. Thus, it is likely that the spin state of Sr_1−xCa_xCoO₃ remains to be the intermediate spin state for all compositions, even though the Co–O bond length slightly decreases upon the Ca substitution with x up to 0.6. Considering the fact that the spin state of cubic perovskites Sr_1−xBa_xCoO₃ has also been found to be independent of the Ba content,²⁵ it is presumable that the intermediate spin state in the Co⁴⁺-containing perovskites is stable over a wide range with respect to the Co–O bond length. Here, we note that SrFeO₃ shows a similar field-induced transition from helimagnetic to conical spin state at 4 K and a positive Weiss temperature θ. Figure 4(c) shows the x dependence of the Weiss temperature θ for Sr_1−xCa_xCoO₃, which is evaluated by the Curie–Weiss law. Upon the increment of the Ca content x, θ decreases monotonically, while maintaining a positive value, indicating the predominance of the FM interaction in all x regions. In fact, a CaCoO₃ of a cubic variant is reported to show FM behavior and the stability of FM state at high pressures is also predicted in the first-principles calculations.³³ We, hence, presume that CaCoO₃ adopts HM spin structure rather than G-type spin structure in the AFM phase, as in the case of SrFeO₃, showing the pressure-induced-transition from a HM to FM state.³³ 

Figure 1(e) depicts the magnetic phase diagram of Sr_1−xCa_xCoO₃ as a function of x and T, where the transition temperatures T_c and T_N are determined by the M/H–T curves. The value of T_c gradually decreases with increasing x, and the two types of FM phases are found in the cubic (FM1) and orthorhombic (FM2) structure phases. The drop of T_c upon the change from FM1 to FM2 can be associated with the bandwidth narrowing caused by the first-order structural transition from the cubic to the orthorhombic phase. For x = 0.8, the AFM (HM) ground state emerges below the FM transition temperature. Finally, the FM transition was indiscernible for x = 1.0. This phase diagram suggests that the FM and AFM interactions are competing with each other in Sr_1−xCa_xCoO₃, and the FM interaction seems to be reduced by the Ca substitution. Here, the suppression of T_c with increasing x in the cubic phase is inconsistent with the naive expectation that the nearest neighbor FM interaction (double exchange interaction) should be enhanced via the bandwidth broadening, accompanied by the decrease of the Fe–O bond length. In fact, the application of pressure for SrCoO₃ was found to enhance T_C.¹⁴ For the origin of this T_c suppression, two possible mechanisms can be considered: (i) Sr/Ca disorder similar to Ln_1/2Ba_1/2MnO₃ (Ln = La–Tb), where the A-site disorder suppresses T_c in the vicinity of the multi-critical composition, where FM and AFM phases are competing with each other^34,35 and (ii) local disorder of the orthorhombic structural distortion observed in the solid solution of perovskite-type oxides,^36,37 which should play important roles in the variation of the magnetic ground state, as discussed below.

Below, we discuss the possible origin of the AFM (HM) phase in terms of the change in the crystal structure and electronic states. As shown in Fig. 1, the unit cell volume decreases with increasing x, and the CoO₆ octahedra are largely tilted: the average Co–O–Co bond angle is about ∼157°. First, the clear JT distortion is absent in the CoO₆ octahedra. In order to quantify the relative distortion of the deviation of the octahedra, we define the Δ_d parameter, denoting the deviation of Co–O distances d_n with respect to the average ⟨Co–O⟩ value as $Δd=(1/6)∑n=1,6[(dn−d)/d]2$⁠. For CaCoO₃, Δ_d is evaluated to be ∼3 × 10⁻⁵, which is substantially smaller than that of the JT system LaMnO₃ (∼5 × 10⁻³),³⁸ but comparable to that of the non-JT system RCoO₃ (∼5 × 10⁻⁵, R = Pr − Lu).³⁹ 

The orthorhombic structural distortion influences the electronic properties as characterized by the x dependence of ρ and C. Figure 4(a) shows the temperature dependence of ρ, which is seemingly nonmetallic, with a small magnitude of less than 3 mΩ cm at room temperature. The ratio of the electrical resistivity at 2 K to that at room temperature, ρ_2K/ρ_300K, is enhanced especially for x > 0.7, as shown in Fig. 4(d), implying that the orthorhombic distortion changes the system to the incoherent metallic state, which is called a “bad metal,” ubiquitously observed in the vicinity of the Mott insulator. The substantial orthorhombic distortion also affects the specific heat C. The T² dependence of C/T is shown in Fig. 4(b). The Debye temperature θ_D and the electronic specific heat coefficient γ were evaluated with equation C/T = γ + (12/5)π⁴NRθ_D⁻³T² (R = 8.31 J/mol K and N = 5). θ_D changes discontinuously at the critical composition (x = 0.6), reflecting the structure transition from the cubic to the orthorhombic phase, whereas γ shows a gradual change, with a kink at x = 0.6 [see Fig. 4(e)]. The observation of large γ of 40–50 mJ mol⁻¹ K⁻² in all compositions suggests that the effective mass of the conduction electron is enhanced by the electron correlation, as reported for the perovskite-type cobalt oxides (Ca,Y)Cu₃Co₄O₁₂.⁴⁰ As the Ca content increases in the orthorhombic phase, γ gradually decreases presumably, owing to the pseudo-gap formation, causing the suppression of the density of states at the Fermi level, which is accompanied by the orthorhombic distortion. A recent band calculation with GGA + U for the orthorhombically distorted CaCoO₃ shows that only the majority e_g bands are responsible for metallicity, while the minority t_2g band opens a bandgap.⁴¹ These theoretical conjectures are compatible with the variation of the electronic properties of Sr_1−xCa_xCoO₃, i.e., the incoherent metallic behavior with the low resistivity value (<10 mΩ cm) and suppression of γ can be explained by the gap formation of the t_2g bands while maintaining the itinerant e_g bands. This is in contrast to the insulating ground state of CaFeO₃ exhibiting the charge disproportionation of Fe⁴⁺ ions with e_g bands near the Fermi level.

Finally, let us discuss the lattice dependent variation of the magnetic ground states of Sr_1−xCa_xCoO₃. We can propose two possible mechanisms of the AFM (HM) ground state near x = 1. One is the double exchange mechanism for transition-metal oxides with the e_g¹ configuration and a negative p-d charge-transfer energy Δ.^6,42 Assuming that this model, in which the pd hybridization plays an important role in the phase stability, holds for Sr_1−xCa_xCoO₃ with the e_g¹ configuration and negative Δ; the orthorhombic distortion shown in Fig. 1(d) presumably stabilizes the HM state rather than the FM state through the reduction of the pd hybridization. The other is the frustration⁴³ between the FM double exchange interaction J₁ and the AFM superexchange interaction J₂, the latter being comparable to the former when the orthorhombic distortion is significant, as shown in Fig. 1(d).^42,44 The orthorhombic distortion not only reduces the FM double exchange interaction due to the band narrowing but also enhances a next-nearest-neighbor (NNN) superexchange interaction through the decreasing in Co–O(1)–O(1)–Co exchange path, where the t_2g electrons play an important role.⁴⁵ Given that the NNN superexchange interaction J₂ is an AFM one, a non-collinear magnetic ground state is expected to manifest itself, reflecting the competition with the nearest-neighbor FM interaction. To get further insight into the magnetic ground states, microscopic measurements using single crystals are indispensable.

The present work establishes the structure and magnetic phase diagram of Sr_1−xCa_xCoO₃ and demonstrates a great potential of the Co⁴⁺-containing perovskites as an interesting platform to explore a novel helimagnetic phase. Furthermore, this system can be an important reference to study topological helimagnetic phases in Fe⁴⁺-containing perovskites.⁹