Magnetism and charge order in the ladder compound Co3O2BO3

D. C. Freitas,1 C. P. C. Medrano,2 D. R. Sanchez,2 M. Nuñez Regueiro,3 J. A. Rodrı́guez-Velamazán,4,5 and M. A. Continentino1,* 1Centro Brasileiro de Pesquisas Fı́sicas, Rua Dr. Xavier Sigaud 150, Urca, 22290-180 Rio de Janeiro, RJ, Brazil 2Instituto de Fı́sica, Universidade Federal Fluminense, Campus da Praia Vermelha, 24210-346 Niterói, RJ, Brazil 3Institut NEEL/CNRS-UJF, Department MCBT, F-38042 Grenoble, France 4Instituto de Ciencia de Materiales de Aragon, CSIC Universidad de Zaragoza, E-50009 Zaragoza, Spain 5Institut Laue Langevin, CNRS, F-38042 Grenoble, France (Received 25 May 2016; published 4 November 2016)


I. INTRODUCTION
The only two known homometallic oxyborates with a ludwigite structure, Fe 3 O 2 BO 3 and Co 3 O 2 BO 3 , have transition metal ions with a local moment and exchange interactions expected to be similar. However, the magnetic, structural, and transport properties of these materials are very different. Understanding the reason for these differences in systems with the same low-dimensional characteristics can lead to deep insight into the nature of magnetism and charge ordering in transition metal compounds. In this paper, we present the solution for why Co behaves so differently from Fe in the ludwigite structure. We obtain neutron scattering results that yield the magnetic structure of Co 3 O 2 BO 3 and show this is different from that of Fe 3 O 2 BO 3 . This is due to a subtle competition between magnetism and charge ordering at the microscopic level of the rungs of the three-legged ladders (3LL) common to both systems. The unique balance attained in each system determines their distinct macroscopic physical properties. In Co 3 O 2 BO 3 nature exploits the low spin of a Co 3+ ion to avoid the structural distortion associated with the charge density wave (CDW) formation in Fe 3 O 2 BO 3 .
The ludwigites belong to the family of oxyborates. Their structure is formed by subunits consisting of three-legged ladders that confer to them a low-dimensional character (Fig. 2). The oxyborates are known by their complex magnetic behavior [1]. Among these, we mention the partial magnetic ordering in the ludwigites Fe 3 O 2 BO 3 [2,3] and CoFe 2 O 2 BO 3 [4], the random singlet phase in the warwickite MgTiOBO 3 [5], and the two-dimensional antiferromagnetism in the hulsite Co 5.52 Sb 0.48 (O 2 BO 3 ) 2 [6].
The ludwigites crystallize in the space group Pbam and their structure can be described by two different types of 3LL. The metallic ions on the ladders occupy the centers of * mucio@cbpf.br oxygen octahedra. The general formula of these systems is where M and M are divalent and trivalent metallic ions, respectively. There are two known homometallic (M = M ) ludwigites: Co 3 O 2 BO 3 [7] and Fe 3 O 2 BO 3 [2,3]. The former orders magnetically near 42 K and the latter has two ordering temperatures where the magnetic ions in different ladders order at two distinct temperatures, namely, 110 and 70 K. The physical properties of these mixed-valence homometallic ludwigites are quite different. Besides the partial magnetic ordering, Fe 3 O 2 BO 3 [8,9] has a transverse charge density transition near room temperature that has not been found in Co 3 O 2 BO 3 . The magnetization curve of Co 3 O 2 BO 3 at the lowest temperature (T = 2 K) is at least one order of magnitude larger than that of the Fe system [7]. This has been taken as an indication that ferromagnetic interactions are more important in the former system. Using neutron powder diffraction (NPD), Bordet et al. [9] have determined the magnetic structure of Fe 3 O 2 BO 3 . They have shown that there is a very weak magnetic coupling between the 3-1-3 and 4-2-4 ladders (see Fig. 2) that order independently in this system.
In this paper, we present a neutron powder diffraction study of Co 3 O 2 BO 3 , above and below its single magnetic ordering temperature. Our analysis of the neutron data allows us to determine the magnetic structure of this material and reveals some unexpected and interesting behavior. We find a coexistence of low and high spin states Co ions occupying well-defined octahedral sites in the structure. We show that the low-temperature magnetic order implies a charge ordering phenomenon in the system. Our results represent another example of the rich variety of physical behavior exhibited by low-dimensional transition metal oxides.

II. EXPERIMENT
The crystals were synthesized according to Freitas et al. [7]. A NPD experiment was carried out in the D1B instrument of the Institut Laue-Langevin (ILL) in Grenoble. For the measurements, 3 g of well-ground needle-shaped black crystals were confined into a cylindrical vanadium can and put inside a cryostat. A wavelength of 1.28Å was used, which corresponds, in the D1B instrument, to the best compromise between flux, resolution, and absorption of boron. The sample was cooled down to 2 K and diffraction patterns covering the angular range 0.8 • -128.8 • were collected for 3 h at 2, 30, 50, and 300 K. The data were analyzed using the FULLPROF Suite programs [10]. The treatments included a full structural refinement of the crystal structure, with a single isotropic atomic displacement parameter (ADP) for each atom type.

III. RESULTS
The neutron diffraction patterns show the occurrence of long-range magnetic order with the appearance of a set of magnetic peaks below T N = 42 K, accompanied by a small decrease of background intensity at low angles, as shown in Fig. 1. The magnetic ordering temperature is consistent with previous magnetic measurements [7]. We did not observe structural transitions in the entire range of measured temperatures with the changes of the magnetic structure between 2 and 30 K accounting for all variations in the spectra. The results of the magnetic structure refinements at 2 K are given in Table I and the plot of the Rietveld refinement in Fig. 1. The NPD data at 2 K give lattice parameters of a = 9.317(3) A, b = 11.950(4)Å, and c = 2.9646(7)Å (R Bragg = 8.0%, R F = 6.2%). All magnetic contributions can be indexed with the nuclear unit cell, i.e., with a magnetic propagation vector k = 0. The magnetic structure determination was done by a symmetry analysis, following the representation analysis technique described by Bertaut [11] using BASIREPS software [10]. For the P bam space group, we found eight real irreducible representations for the little group Gk associated with k = 0, 1 -8 . Since a single magnetic ordering temperature is observed [7], it is expected that the magnetic structure is described within the same magnetic representation for all magnetic sublattices. Only the odd irreducible representations ( 1 , 3 , 5 , 7 ) appear in the magnetic representation M for all the Wyckoff positions, with 5 the one that best reproduces the experimental data (R mag values: 1 = 27.2, 3 = 25.9, 5 = 8.6, 7 = 13.4).
The magnetic structure is shown in Fig. 2. The Co 3 O 2 BO 3 system has a ferromagnetic spin configuration in the rungs of the 4-2-4 ladders with an effective moment of 8.2μ B per cell and a ferrimagnetic configuration in the rungs of the 3-1-3 ladders with about 8μ B per cell, which gives 1.4μ B per Co cation. This is in agreement with previous magnetic measurements [7] that found a residual moment of 1.1μ B /Co and a predominance of ferromagnetic interactions when compared to Fe 3 O 2 BO 3 . All the moments are nearly parallel to the b axis, making this the easy magnetization axis in accord with bulk magnetic anisotropy measurements [12]. ion, but the magnetic moment in site 4 is surprisingly small. This suggests that these sites are occupied by Co 3+ ions in low spin (LS) states. The sites in the ladder 3-1-3 are all occupied by divalent Co 2+ ions in high spin states. They are associated with the large magnetic moments shown in Table I. The value of the magnetic moment expected for HS Co 2+ is 3μ B and 1μ B for the LS state, considering only the spin contribution, as is usual for these systems. The values obtained in Table I indicate that there is a reasonable orbital contribution to the moments. Bulk 3d long-range magnetic order in the system due to the interaction between the 3LL is guaranteed by the presence of a magnetic Co ion on site 2, which is the one more strongly coupled to the 3-1-3 ladder [9].

IV. DISCUSSION
The spin state of Co 3+ ions in an octahedral environment is determined by a competition between intra-atomic exchange energy (Hund's rule) and crystal field energy [13,14]. The exchange energy favors the high spin (HS) state (t 4 2g e 2 g , S = 2) while the crystal field favors the low spin state (LS) (t 6 2g e 0 g , S = 0). For Co 3+ and Fe 2+ very often these states are close in energy and include also the possibility of an intermediate spin state (IS) with the configuration (t 5 2g e 1 g , S = 1). Among the Co oxides, LaCoO 3 and GdCoO 3 exhibit a thermal transition from low spin to high spin, probably with an intervening IS [13][14][15], and Co 2 O 3 exhibits a low spin to high spin transition with decreasing pressure [16].
The electron count in a rung of the 4-2-4 ladder corresponds to a background of three Co 3+ ions with an extra itinerant electron per rung [1,8]. The magnetic configuration obtained by neutrons implies a localization, or charge ordering, of this extra electron on site 2 of the rung, leaving two low spin Co 3+ ions in the two outer sites 4 of the rung and a Co 2+ on the center. Since site 2 is a symmetric site, this charge ordering is not necessarily accompanied by a structural transition as in the case of the Fe homometallic ludwigite.
The susceptibility of the Co ludwigite above the ordering temperature obeys a Curie-Weiss law [7] that allows one to obtain the effective magnetic moment. This turns out to be p eff = 7.2μ B , to be compared with the value of 7.4μ B expected if all the Co ions including the trivalent ones are in high spin states and there is no orbital contribution. Since these values are very close, the crossover or transition from HS to LS spin could be present in Co 3 O 2 BO 3 . Useful information on the spin states can also be obtained from the temperature-dependent entropy at the magnetic transition. Figure 3 shows the entropy curves obtained from the measured specific heats for three ludwigites, the two homometallic [3,7] and for Co 2.5 Sn 0.5 O 2 BO 3 [17] that has only Co 2+ ions. The Co 3 O 2 BO 3 has the smallest entropy at T N , considerably less than the expected value of 36.41 J/mol K if all Co ions were in the HS states [S = R ln(2S + 1)]. The theoretical value for the entropy released at the magnetic transition for Co 2.5 Sn 0.5 O 2 BO 3 , where all Co ions are in Co 2+ high spin states, is 28.8 J/mol K. For Co 3 O 2 BO 3 assuming Co 2+ in HS and Co 3+ in LS states, the expected entropy is 23.0 J/mol K, still larger than the experimental value, as can be checked in Fig. 3. We now compare the magnetic structures and properties of the two homometallic ludwigites as obtained in the neutron scattering experiments. First, the magnetic ordering in the Co system is a single step phenomenon in which the magnetic moments in the two different ladders order simultaneously. This is in contrast to Fe 3 O 2 BO 3 where 4-2-4 ladders order at 110 K and the 3-1-3 ladders order at 70 K. As concerns the magnetic structures, the moments in the ladders are coupled in different ways in these systems. In the Fe system the magnetic moments in a rung of the 4-2-4 ladders couple ferromagnetically, pointing along the b axis [9]. The coupling between the magnetic moments in consecutive rungs of these ladders along the c axis is antiferromagnetic. Notice that due to the staggered CDW ordering at ≈283 K one should distinguish between sites 4a and 4b in the 4-2-4 ladders of Fe 3 O 2 BO 3 . However, the moments in these sites were found to be nearly the same [9]. Co 3 O 2 BO 3 has a ferromagnetic spin configuration in the rungs of the 4-2-4, but along the c axis the moments are ferromagnetically aligned. In Fe 3 O 2 BO 3 , the magnetic moments in the 3-1-3 ladders have a ferrimagnetic coupling along a rung with the moments pointing into the a direction. These in turn are ferromagnetically coupled along the c axis [9]. The Co 3 O 2 BO 3 has a ferrimagnetic configuration but the moments are all pointing almost into the b direction.
In both homometallic ludwigites, ferromagnetic ordering between the moments in a rung of the 4-2-4 ladders favors delocalization of this extra electron that gains kinetic energy. Since there is no structural transition in Co 3 O 2 BO 3 , this delocalized electron could partially Kondo screen the moments in the rung of this ladder. This mechanism, however, is not sufficient to explain the small value of the magnetic moments found in the neutron experiments and especially why this occurs for the moments on sites 4 and not for that on site 2. Also in the oxyborates there are many competing magnetic interactions. The moments at site 4 are connected through different superexchange paths to several other magnetic ions in the structure. This results in conflicting information with  [19], where the HS and LS states exchange stability. a cost in energy for the system. A nonmagnetic, LS Co 3+ occupying this site avoids the system to have to account for this energy cost.
In an effort to clarify the mechanism responsible for the coexistence of high and low spin states in the Co ludwigite, we calculated the V zz component of the electric field gradient (EFG) on the different Co sites surrounded by oxygen octahedra. This parameter is a measure of the deviation of the environment from symmetric octahedra. Following Ivanova et al. [12] and taking the z axis along the major axis of the oxygen octahedra, we calculated V zz for all the Co sites. We find that site 4 has the smallest V zz , showing that this is the most symmetric site in the compound. When lowering the temperature, this parameter decreases, going from V zz (4) = 0.0322 e/Å 3

V. CONCLUSIONS
In summary, neutron powder diffraction as a function of temperature in the compound Co 3 O 2 BO 3 allowed us to obtain its magnetic structure in the ordered phase, which is shown in Fig. 2. The magnetic transition occurs near 42 K, with a ferromagnetic coupling between the ab planes and a ferrimagnetic coupling in this plane. The moments order close to the b direction, in agreement with previous bulk magnetic anisotropy measurements [7,12]. We found that Co ions on sites 4 of the 4-2-4 ladders have a surprisingly small magnetic moment, consistent with low spin Co 3+ ions occupying these sites below the ordering temperature. The magnetic moments on the remaining sites of the ladders, including those on sites 2 of the 4-2-4 ladders, are in agreement with these sites being occupied by Co 2+ ions in high spin states. This coexistence of low and high spin Co ions has been found previously in oxides [13][14][15][16], but this is time it is found in a ludwigite, a system where the metallic ions occupy only octahedral sites. A subtle microscopic mechanism occurs at the level of the rungs of the 4-2-4 3LL in which the itinerant electron shared by the three Co 3+ ions on a rung of this ladder localizes on site 2 of the rung. The charge ordering of this itinerant electron leaves two low spin Co 3+ ions in the outer sites 4 of this ladder and a magnetic Co 2+ with the localized electron on site 2. The low spin state of the ions occupying site 4 is favored by the highly symmetrical octahedral environment of these sites and their short Co-O distances. Furthermore, a nonmagnetic Co 3+ on these sites adds positively to the energy balance by avoiding frustration in the system. This unique charge and magnetic balance allows for the Co ludwigite to avoid the structural distortion associated with the staggered CDW observed in the Fe system.