Transition metal oxides characterized by a triangular geometry of their metallic sublattice have received considerable attention because of their complex magnetic behavior. However, the ability of these lattices to generate properties in view of applications has not been fully developed as compared with square-like lattices such as those of perovskites, which are used as ferroelectrics, high T_C superconductors, magnets, or colossal magnetoresistive materials. We report herein on recent studies of two classes of oxides with attractive properties either as multiferroics or as low-dimensional magnets.

1 Swedenborgite CaBaCo₄O₇ family: promising ferrimagnetic ferroelectrics

In the first class of oxides, the metallic cations form MO₆ octahedra or MO₄ tetrahedra and are displayed generally on a three-dimensional (3D) M_n sublattice built up of M₄ tetrahedra and M₃ triangles. This configuration induces geometric magnetic frustration, as shown in the numerous studies of the pyrochlore oxide family [1], and in a more general way produces frustrated magnets such as in kagome lattices of the spinel structure and in garnets [2–4].

Recently, complex magnetic transitions correlated to structural and/or electric transitions were observed and studied in pure tetrahedral kagome frameworks of the swedenborgite-type “114” LnBaCo₄0₇ cobaltates [5–21]. The room temperature hexagonal P31c structure of these oxides (Fig. 1a) consists of a 3D framework of corner-shared CoO₄ tetrahedra, built up of two sorts of layers, kagome layers (K) and triangular layers (T) as shown in Fig. 2. As a consequence, the metallic [Co₄] sublattice of these oxides is built up of “Co₅” bitetrahedra interconnected through “Co₃” triangles (Fig. 3). It results in a 2D geometric frustration in the (001)_H plane, which strongly competes with the 1D magnetic ordering along c in the original hexagonal cell. Thus, these oxides have been considered as a new class of frustrated magnets, which out-of-plane magnetic coupling acts as an external magnetic field with respect to the in-plane 2D magnetic frustration [15].

To modify the competition between this geometric 2D frustration and 1D magnetic ordering the possibility to replace the trivalent lanthanide by a divalent cation, calcium, was considered. The synthesis of the cobaltate CaBaCo₄O₇ [22,23] allows the mixed valence Co²⁺/Co³⁺ to be strongly modified, with an increase in the Co³⁺ content up to 50% with respect to LnBaCo₄O₇. This leads to a dramatic change in both structural and magnetic properties. Although closely related to LnBaCo₄O₇ oxides, the structure of CaBaCo₄O₇ (Fig. 1b) differs by a strong buckling of the kagome layers, the triangular layers remaining flat [23]. The first important structural character of this oxide deals with the very large orthorhombic distortion of its cell, which lifts the geometric frustration. It results in the appearance of charge and magnetic ordering. A complex ferrimagnetic structure is indeed observed at less than 64 K [23] (Fig. 4): it consists of ferromagnetic Co²⁺ zigzag chains, which are antiferromagnetically coupled with isolated mixed valent cobalt species Co³⁺/Co²⁺3d⁶/3d⁷L. The second remarkable feature concerns the fact that the structure of CaBaCo₄O₇ is noncentrosymmetric, with the Pbn2₁ space group, a necessary condition for the coexistence of ferroelectricity and ferrimagnetism, for the realization of multiferroic properties.

On the basis of the aforementioned considerations, the dielectric properties of this cobaltate were first investigated on polycrystalline samples [24,25]. The dielectric permittivity and loss curves versus temperature measured at 100 kHz on these samples clearly show a peak at the same temperature as the ferrimagnetic transition T_C = 64 K (Fig. 5a), which was interpreted as spin–charge coupling. Measurements of the electric polarization versus temperature with an electric field of 111 kV/m (Fig. 5b) performed on the same polycrystalline samples evidence also a transition around T_C and importantly a sign change in the polarization by reversing the electric field. This behavior was then attributed to spin-driven ferroelectricity [24,25]. The study of large crystals of CaBaCo₄O₇ allowed us to confirm the multiferroic character of this oxide and showed that it is a remarkable magnetoelectric material [26] (Fig. 6). One indeed observes a sharp transition of the magnetization along b at 64 K, which coincides perfectly with the sharp peak of ε′ measured along c. Importantly, this oxide exhibits a gigantic variation in its induced electric polarization along c, ΔP = 17,000 μC/m², a value never reached for magnetically induced ferroelectric polarization in multiferroic oxides, six times larger than that obtained for the perovskite CaMn₇O₁₂ [27,28]. However, Caignaert et al. could not observe switching of the electric polarization by reversing the electrical field for the crystal [26] in contrast to the polycrystalline samples [24,25].

From the latter results, Johnson et al. [29] reinvestigated the magnetoelectric coupling in CaBaCo₄O₇, using ab initio calculations and Landau theory; these authors showed that the observed giant variation in polarization is also compatible with exchange striction and that the strong magnetoelectric coupling close to T_C originates from magnetoelastic coupling. From the fitting of their model with the crystal data extracted from Ref. [26], Johnson et al. concluded that CaBaCo₄O₇ is not a ferroelectric but a ferrimagnetic pyroelectric [29]. Unfortunately this latter study does not explain the switching behavior of the polarization observed on polycrystalline samples [24,25]. The recent investigation of this multiferroic by Fishman et al. [30] sheds light on this issue. Upon rotating a CaBaCo₄O₇ crystal about c in a fixed magnetic field applied along a, these authors showed, from the threefold splitting of the spin wave frequencies, that the latter is not a single crystal but a hexagonally twinned crystal. Magnetization measurements on crystals, combined with powder neutron and terahertz absorption spectroscopy allowed magnetic domains with a complex spin order in each domain to be evidenced [30]. Describing the cobalt framework as bitetrahedral chains parallel to c and ferrimagnetically coupled with each other in the ab plane Fishman et al. [30] concluded that the lifting of the geometric frustration in CaBaCo₄O₇ allows ferrimagnetism and ferroelectricity to coexist [30]. On the basis of the previously observed large changes in spin-induced polarization [26], these authors suggest that this oxide may have important technological applications, when a modest magnetic field less than 1 T is applied along b [30] close to T_C. The high sensitivity of the magnetic properties of this swedenborgite to the doping of the cobalt sites with different cations such as Zn, Ga, Li, Al, Fe, and to the doping of Ba sites with Sr or Ln [31–39] offers many possibilities for tuning the characteristics of this multiferroic. The recent study of the ferroelectric Ni-doped CaBaCo₄O₇, which exhibits an enhanced ordering temperature at 82 K [40], supports this statement.

2 Spin chain oxides Sr_4–xCa_xMn₂CoO₉: toward low-dimensional magnets

The second class of oxides belongs to the triangular spin chain oxide family. Their hexagonal structure consists of single chains of face-sharing MO₆ octahedra and trigonal prisms displayed at the corners of a triangular lattice. The Ca₃Co₂O₆ cobaltate, whose [Co₂O₆] chains exhibit a 1:1 ordering of the CoO₆ prisms and CoO₆ octahedra (Fig. 7a), is the archetype of these spin-chain compounds. The latter was found to exhibit several original features [41–48] such as a strong Ising-like character due to antiferromagnetic interchain and ferromagnetic intrachain coupling, with magnetization plateaus, originating from the close energy values of the cobalt moments in the triangular planes perpendicular to the cobalt chains. The isotypic Ca₃MnCoO₆ compound [49] also characterized by a 1:1 intrachain ordering of the MnO₆ octahedra and CoO₆ prisms was revealed to be a multiferroic with complex magnetic behavior [50–53]. For these Ca₃MM′O₆ oxides, partially disordered antiferromagnetism was often reported to describe the magnetic interactions between the Ising chains on the triangular lattice [54–58].

The oxides Sr₄Mn₂CoO₉ [59] and Sr₃CaMn₂CoO₉ [60] can be described as the second members of this spin chain oxide family: in this hexagonal structure (Fig. 7b), the [Mn₂CoO₉] chains are also formed of face-sharing MnO₆ octahedra and CoO₆ prisms, but a 2:1 ordering “Mn₂Co” between the octahedra and the prisms within each chain is observed. The magnetism of the latter compounds has not been intensely studied in contrast to the first members, most probably because of the ill-defined glassy character of their magnetic properties. Indeed, Sr₄Mn₂CoO₉ [59] was found to exhibit a behavior close to a spin glass, whereas the enhancement of magnetic correlations was observed for Sr₃CaMn₂CoO₉ [60], but no long-range ordering could be reached. Bearing in mind that the interchain distances should significantly influence the magnetic interactions between the chains, the size effect of the Ca²⁺/Sr²⁺ cations was recently investigated in the oxides Sr_4–xCa_xMn₂CoO₉, by comparing the magnetic behavior of Sr₄Mn₂CoO₉ (x = 0) and Sr₂Ca₂Mn₂CoO₉ (x = 1) [61]. The χ′(T) curves of these phases (Fig. 8) showed that they both exhibit a frequency-dependent bump around 6 K (labeled as regime 2 in Fig. 8), but differ in their behavior at higher temperature. Sr₂Ca₂Mn₂CoO₉ is characterized by a frequency-independent maximum of χ′ around 29 K (labeled as regime 3 in Fig. 8), whereas Sr₄Mn₂CoO₉ displays a strongly dependent frequency peak around 10–15 K (labeled as regime 1). The regime 3 observed for Sr₂Ca₂Mn₂CoO₉ could easily be attributed to the existence of long-range antiferromagnetic ordering (LRO) with T_N = 29 K in agreement with neutron diffraction data. The regime 1 observed for Sr₄Mn₂CoO₉ and the regime 2 observed for both compounds were clearly identified from χ″(T) curves and from Argand plots that were shown to be consistent with the Cole–Cole model.

The relaxation time curves τ_c (1/T) extracted from these investigations (Fig. 9) summarize these results. The temperature-independent character of τ_c observed for Sr₂Ca₂Mn₂CoO₉ (regime 3 in Fig. 9) originates from LRO. The Arrhenius-like evolution of τ_c versus 1/T observed for Sr₄Mn₂CoO₉ (regime 1 in Fig. 9) rules out the possibility of a spin glass behavior for this compound and is similar to that of a single chain magnet (SCM). Moreover, the values of τ₀ ∼ 10⁻¹¹ s and of Δ ∼ 167 K obtained from the maxima in χ″(T), close to those reported for SCM molecular compounds containing Co²⁺ [62–64] confirm this statement. The genuine SCM behavior of this phase was then demonstrated further by χ_dc measurements and from M(H) hysteresis loops. In this way, it was shown that blocking effects associated with slow spin dynamics yield remanence and coercivity in the absence of LRO for Sr₄Mn₂CoO₉ [61]. The τ_c (1/T) evolution of regime 3 (Fig. 9), similar for both oxides, which coexists with SCM in Sr₄Mn₂CoO₉ and with LRO in Sr₂Ca₂Mn₂CoO₉ was attributed to the fact that Co²⁺ can act as a single ion magnet (SIM), in agreement with the behavior observed for SIM in Co²⁺ complexes [65–68].

These observations of SCM and SIM behaviors in purely anhydrous inorganic materials are quite unique. They show the possibility to realize low-dimensional magnets (0D or 1D) similar to those obtained for the large family of molecular compounds, which have been extensively studied for the generation of single molecule magnets [69,70] and SCMs [62,71]. In these oxides and especially in Sr₄Mn₂CoO₉, the Sr²⁺ cations because of their larger size allow the distances between the magnetic chains to be sufficiently increased to considerably weaken the 3D magnetism. In this way, they play the role of organic ligands or molecules that are generally used for shielding the magnetic interactions between the transition metal clusters or chains in molecular magnets. Bearing in mind that low-dimensional magnets have been the object of considerable interest for their potential applications in information storage [72,73] and in quantum computation [74], these oxides, which are highly stable as compared to molecular compounds, open the route for future investigations.

3 Conclusions

These recent studies show that transition metal oxides, which involve triangular metallic sublattices, exhibit besides magnetic frustration a great potential for the generation of materials with attractive properties in view of applications either as ferroelectric multiferroics or as low-dimensional magnets. Bearing in mind that the appearance of such properties stems from either the lifting of the geometric frustration or the weakening of chain interactions in triangular systems, this opens the route to the investigation of numerous alkaline earth-based transition metal oxides. In these systems the inter-related structural and chemical parameters such as distortion of the structure, valence of the transition element, oxygen stoichiometry, size of alkaline earth cation, and order–disorder phenomena have to be controlled carefully.