Sinusoidal magnetic structure in a three-dimensional antiferromagnetic Co2(OH)AsO4: Incommensurate-commensurate magnetic phase transition

I. de Pedro,1,2 J. M. Rojo,2 J. Rodríguez Fernández,1 M. T. Fernández-Díaz,3 and T. Rojo2,* 1CITIMAC, Facultad de Ciencias, Universidad de Cantabria, 39005 Santander, Spain 2Departamento de Química Inorgánica, Facultad de Ciencia y Tecnología, Universidad del País Vasco, 48080 Bilbao, Spain 3Institut Laue-Langevin, BP 156X, F-38042 Grenoble Cedex, France Received 26 December 2009; revised manuscript received 10 March 2010; published 23 April 2010


I. INTRODUCTION
In the last years, the compounds showing a "metalinsulator" transition have attracted much attention in solidstate physics and chemistry since the discovery of additional fascinating magnetic phenomena.Many cobalt-based compounds present this type of phenomenology, such as the magnetic frustration system, Ca 3 Co 2 O 6 , 1 which shows in the magnetically ordered state a ferromagnetic coupling between the magnetic ions along the chains whereas the interchain nearest-neighbor interaction is antiferromagnetic ͑AF͒.Other Co-based systems with spin state S =3/ 2 show a threedimensional ͑3D͒ Neel ordering at low temperature, with unusually large magnetic anisotropy such as BaCo 2 Si 2 O 7 , 2 CoNb 2 O 6 , 3 CoV 2 O 6 , 4 and BaCo 2 V 2 O 8 . 5Moreover, in some cases, they present also interesting field-induced magnetic transitions.For example, a spin-flop transition in CoNb 2 O 6 ͑Ref.3͒ and an order-disorder transition in BaCo 2 V 2 O 8 ͑Ref.6͒ have been described.
In the case of the phosphate and arsenate cobalt compounds, additional useful chemical and physical properties ͑magnetic, heterogeneous catalysis, ion exchange, etc.͒ [7][8][9][10] have been found out.The stoichiometries and a wide variety of structural types built of interconnected MO 6 ͑M =Ti,V,Cr,Fe,Mo,...͒ octahedra and XO 4 ͑X =P,As͒ tetrahedra make them an appropriate domain to study the relationships between the physical properties and the crystal packing features. 7,8he crystal structure of the Co 2 ͑OH͒XO 4 ͑X =P,As͒ ͑Refs.11-13͒ compounds consists of condensed network of a vertex and edge-sharing CoO 6 , CoO 5 y XO 4 subunits ͑see Fig. 1͒.The Co͑II͒ ions can be sited in two different octahedral and trigonal bipyramidal topologies.The edge-sharing ͓Co͑2͒O 4 ͑OH͒ 2 ͔ octahedra give rise to linear chains propagated along the c axis whereas the edge-sharing ͓Co͑1͒O 4 ͑OH͔͒ trigonal bipyramids constitute dimeric entities.The chain of octahedra, the dimeric unites, and the tetrahedral groups share corners thereby forming a threedimensional network.
We have recently discovered in the hydroxy phosphate Co 2 ͑OH͒PO 4 ͑Ref.11͒ the coexistence of antiferromagnetic ordering and a spin-glass behavior in an insulator compound.In this phase, a magnetic frustration in the Co͑1͒ magnetic moments is observed as due to the presence of antiferromagnetic interactions between Co͑2͒ neighbor chains.Furthermore, it is worth mentioning the existence of a superexchange angle Co͑1͒-O͑3͒-Co͑2͒ with a value of 107°that involves ferromagnetic couplings between chain and dimer neighbors ferromagnetically coupled.This exchange angle was the higher angle found in the literature for a ferromagnetic exchange pathway and plays an interesting role in the magnetic behavior of this system. 11The partial substitution of transition-metal ions in the structure severely affects the magnetic properties 14,15 giving rise to the evolution of the 3D antiferromagnetic system in the Co 2−x Cu x ͑OH͒PO 4 solid solution 15 up to a spin-gap system in the Cu 2 ͑OH͒PO 4 phase, 16 the spin-glasslike state in the ͑Co, Ni͒ 2 ͑OH͒PO 4 detected below 10 K, 14 or the higher ferromagnetic interactions at lower temperatures in Co 1.7 Mn 0.3 ͑OH͒PO 4 coexisting with a similar spin-glass state observed in the nonsubstituted cobalt hydroxy phosphate. 17he similar ability of AsO 4 3− and PO 4 3− tetrahedra to stabilize anionic frameworks and the greater size of the AsO 4 3− anions predict some differences in the crystal packing features that could modify the complex magnetic properties exhibited in these phases.In this work, we present a deeper magnetic study of Co 2 ͑OH͒AsO 4 in order to determine ͑i͒ the nature of the main magnetic interactions and their anomalies, ͑ii͒ the magnetic structure of the low-temperature ordered phase, and ͑iii͒ the magnetic variations with respect to the isostructural Co 2 ͑OH͒PO 4 compound.Magnetostructural correlations of these cobalt ͑II͒ phases are also described.

A. Synthesis
Hydrothermal techniques have been used to prepare the Co 2 ͑OH͒AsO 4 synthetic phase in the laboratory.This arsenate has been found in the nature as a solid solution with adamite Zn 2 ͑OH͒AsO 4 mineral. 18,19Our synthetic pathway to obtain a pure cobalt phase begins with the preparation of the Co 3 ͑AsO 4 ͒ 2 •8H 2 O precursor, which was previously described. 20Due to the low solubility of the Co͑II͒ hydrated arsenates, long reaction times and pH values in the 6-8 range were needed.Approximately 0.2 g of the hydrated precursor were disgregated in 35 ml of water and placed in a Teflon-lined stainless-steel autoclave under autogeneous pressure generated by a temperature of approximately 170 °C.
The contents of Co and As were determined by inductively coupled plasma atomic emission spectroscopy performed with an ARL Fisions 3410 spectrometer, confirming the Co 2 ͑OH͒AsO 4 chemical formula.The thermogravimetric study was performed up to 800 °C under air in a Perkin-Elmer TGA-DSC System 7 thermobalance.The decomposition curve reveals an initial ͑ϳ1%͒ weight loss associated with water absorbed on the surface from the atmosphere and at 660 °C a second step ͑ϳ3.5%͒ attributed to the loss of water obtained from the decomposition of 2 f.u.At temperatures above 700 °C, additional weight losses were not observed on the thermogravimetric curve.These results are in good agreement with those obtained in other hydroxy phosphate and arsenate-related compounds. 11,12,14

B. X-ray and neutron powder-diffraction experiments
Room temperature x-ray powder-diffraction data of microcrystalline purple samples were used to evaluate the purity of the Co 2 ͑OH͒AsO 4 product.The data were collected in the 10°Յ 2 Յ 90°range in steps of 0.02°with an integration time of 16 s per step using a Philips X'Pert-MPD x-ray diffractometer with secondary beam graphite monochromated Cu K␣ radiation.The Co 2 ͑OH͒AsO 4 data were fitted using the pattern matching routine of the program FULLPROF, 21 in an orthorhombic cell with the Pnnm space group as previously determined by Keller et al. 13 The x-ray refined unit-cell parameters a = 8.281͑1͒, b = 8.566͑1͒, c = 6.038͑1͒Å, ␣ = ␤ = ␥ = 90°, V = 429.4͑1͒Å 3 , and Z = 4 are close to those reported ͓a = 8.286͑2͒ , b = 8.594͑2͒ , c = 6.051͑1͒Å,V = 430.9Å 3 , Z =4͔ from single-crystal data. 13o extra diffraction peaks were observed, concluding that the synthetic products correspond to a pure phase which will be used in the study of the magnetic properties.
Neutron powder-diffraction measurements were performed on the D1B and D2B powder diffractometers at the Institute Laue-Langevin ͑ILL͒ of Grenoble.About 5 g of Co 2 ͑OH͒AsO 4 were employed in the experiments, placed in a cylindrical vanadium container and held in a liquid-helium cryostat.The high resolution of D2B ͑1.5938 Å͒ was used to obtain extensive and accurate structural data at room temperature and 2 K respectively, over a large angular angle 0°Յ 2 Յ 150°.The structure determined by using x-ray single-crystal data of cobalt hydroxy arsenate 13 was used as a starting model for the refinements.High flux and medium resolution of D1B at 2.525 Å were used to study the thermal evolution of the sample in the temperature range 1.8-50 K to solve the magnetic contributions of the neutron patterns.The diffraction patterns were collected every 2 K and 25 min in the angular range 10°Յ 2 Յ 90°.The Rietveld method 22 was used to refine simultaneously the nuclear and magnetic structures.All the patterns were analyzed using the FULL- PROF program suite. 21The background was fitted using the polynomial refinable function and a pseudo-Voigt function was chosen to generate the line shape of the diffraction peaks.The D1B patterns were refined sequentially, taking as starting parameters of each pattern those resulting from the refinement of the proceeding one.

C. Magnetic measurements
dc magnetic-susceptibility measurements of powdered samples were performed using Quantum Design ͑QD͒ physical property measurement system-superconducting quantum interference device magnetometers whilst heating from 2 to 300 K in different applied magnetic from 1 to 90 kOe, after cooling in either the presence ͑field cooling, FC͒ or the absence ͑zero-field cooling, ZFC͒ of the applied field.Magne-tization as a function of field ͑H͒ was measured using a standard QD PPMS magnetometer in the −90Յ H / kOe Յ 90 range in the temperature range of 2-20 K after cooling the sample in zero field.ac magnetic-susceptibility measurements were performed using the same QD PPMS system with an alternate excitation field ͑H ac ͒ of 10 Oe and a frequency of 1000 Hz.Field-dependent data were collected from 2 to 60 K at a fixed frequency of 1000 Hz with applied fields from 0 to 90 kOe.
Heat capacity has been measured between 1.8 and 300 K with a standard relaxation method using a two-tao model.In order to guarantee a good thermal contact, apiezon N grease was used to glue the sample to the sample holder.The addenda ͑sample holder plus grease͒ was measured at different magnetic fields before the sample measurements and then subtracted from the total heat capacity in order to get the sample heat capacity.The sample was an 11.2 mg plate obtained compressing the original thin powder.

A. Nuclear structure
The structural refinements of Co 2 ͑OH͒AsO 4 were carried out from high-resolution neutron powder-diffraction patterns ͑D2B͒ recorded at room temperature with = 1.5938Å.The Rietveld refinement was fitted in the Pnnm space group and cell parameters reported for a single-crystal specimen by Keller et al. 13 as starting point.It should be noted that the quality of our results permits the localization of the hydrogen ions in the structure.The experimental, calculated, and difference neutron powder-diffraction profiles are shown in Fig. 2.There is no significant mismatch between the observed intensity and the calculated profile.The room-temperature structural parameters and the reliability factors from D2B data refinements are summarized in Table I.The final refined positional and thermal parameters are given in Table II.The main interatomic distances, angles for Co 2 ͑OH͒AsO 4 are listed in Table III.
The crystal structure of the Co 2 ͑OH͒AsO 4 phase can be described as formed by two crystallographically distinct sites for the metal ions ͑see Fig. 3͒.Co͑1͒ is fivefold coordinated by oxygen atoms in approximately trigonal-pyramidal geometry where one of the apical positions is occupied by an OH group.Co͑2͒ exhibits a distorted octahedral geometry with two long apical Co͑2͒-O͑3͒ bonds and four shorter equatorial links, two of which are hydroxide groups in cis configuration ͑see Table III͒.The axial and equatorial O-Co͑2͒-O mean angles in the Co͑2͒O 6 octahedra are 171°and 87°, respectively.The octahedra sharing the O͑2͒-O͑2͒ and the O͑4͒H-O͑4͒H edges give rise to linear chains propagated along the z axis.For the Co͑1͒O 5 polyhedra, each trigonal bipyramid exhibits three set of O-Co͑1͒-O angles around 95°, 123°, and an axial to 165°.In addition, the trigonal bipyramids constitute dimeric entities, sharing the O͑1͒-O͑1͒ edge ͑see Fig. 3͒.Both sublattices, Co͑2͒ chains and Co͑1͒ dimers are cross linked via oxygen ͓O͑3͒, O͑4͒H͔ bridges.
In the Co 2 ͑OH͒AsO 4 phase, the arsenate groups exhibit three different bond lengths and four different bond angles where mean distances and angles are 1.69͑1͒ Å and 109͑5͒°, respectively.The As-O values and O-As-O angular regions show that the AsO 4 tetrahedra are fairly regular as in the majority of the adamite-type M 2 ͑O / OH͒XO 4 compounds.This fact could affect the magnetic properties of the transition-metal arsenate compounds due to the degree of distortion of the M͑2͒O 4 ͑OH͒ 2 octahedra and M͑1͒O 4 ͑OH͒ trigonal bipyramidal geometries.Finally, the chain of octahedral, the dimeric unites, and the arsenate anions share corners, thereby forming a three-dimensional framework, resulting in a condensed structure without any identifiable channels or pores.The bond distances and angles obtained FIG. 2. ͑Color online͒ Observed ͑circles͒, calculated ͑solid line͒, and difference ͑at the bottom͒ neutron-diffraction ͑D2B, ILL͒ profiles for Co 2 ͑OH͒AsO 4 at room temperature.Vertical marks correspond to the position of the allowed reflections for the crystallographic structure.

B. Magnetic properties
Variable-temperature magnetic-susceptibility measurements between 1.8 and 300 K are represented in Fig. 4. The molar magnetic susceptibility shows a complex behavior with the presence of three different characteristic temperatures.First, m increases as the temperature decreases from room temperature and reaches a rounded maximum at approximately 30 K. Below 19 K, a strong increase in magnetic signal with a new inflexion point close to 6 K appears.
The experimental data obey a classical Curie-Weiss law above 80 K with a extrapolated Curie temperature close to −62 K and an effective paramagnetic moment per formula unit ͑f.u.͒ of eff = 3.26 B .The negative Weiss temperature together with the decrease in the m T vs T indicates that the major magnetic interactions in this compound are antiferromagnetic.The abrupt upturn of the susceptibility at T N Ϸ 19 K corresponds to the onset of AF order, as will be described later from neutron powder-diffraction data.It should be noted that this behavior is clearly different from that described for the homologous Co 2 ͑OH͒PO 4 compound where the AF ordered appears at approximately 70 K.
The temperature dependence of ZFC-FC curves at 1 kOe does not show any difference above 15 K ͓see inset in Fig. 4͔.Below this temperature, the curves show a small splitting attributed to the existence of a small ferromagnetic component in the Co 2 ͑OH͒AsO 4 compound.This magnetic irreversibility grows on increasing the applied field up to 20 kOe ͑Fig.5͒.When the applied field is higher, the irreversibility decreases in intensity and almost disappears for a magnetic field of 90 kOe.Besides, the irreversibility temperature is strongly dependent on the magnetic field ͑from 12 K down to 5 K at fields of 0.5 kOe and 90 kOe, respectively͒.
As can be seen in Fig. 5, above 20 K, the ZFC is not affected by the external magnetic field.However, the inflection point at around 18.2 K for a field 1 kOe, attributed to the antiferromagnetic ordering, is moved when the magnetic field is increased to a temperature of 20.1 K for an applied field of 90 kOe ͓see inset in Fig. 5͔.In addition, the inflexion point at around 6 K is transformed into a new and well-   defined maximum when the magnetic field is 20 kOe, as their intensity subsequently decreases as the field increases.Dependence on the magnetization with applied magnetic field at different temperatures has been represented in Fig. 6.As can be seen, at 2 K, the magnetization versus the applied field follows a process in stages characteristic of a metamagnetic transition.Up to 3.5 kOe, no magnetic irreversibility is observed while between 3.5 and 40 kOe, a small irreversibility appears with ⌬H max of 4.5 kOe ͑see inset figure of dM / dH͒.With increasing temperature, the magnetic irreversibility decreases, reaching a value of ⌬H max = 1.5 kOe at 10 K. Indeed, at 15 K, the magnetization still shows a weak metamagnetic transition at H = 12.5 kOe but no irreversibility is observed.Finally, at 20 K, the magnetization curve shows a lineal behavior in the whole applied field range suggesting the absence of magnetic order.It is worth mentioning that the magnetic moment at 2 K and 90 kOe is quite different from the theoretical saturation magnetic moment for this compound ͑3.4 B / mol͒, indicating the existence of a strong anisotropy.This general behavior is clearly different from that observed in the Co 2 ͑OH͒PO 4 compound in which the hysteresis loop has a small coercitivity characteristic of spin glasses. 11he thermal evolution of the ac susceptibility at different magnetic fields is shown in Fig. 7. Three different temperature regions as described for the magnetic-susceptibility data can be observed: ͑i͒ the presence of a rounded maximum at around 30 K in the real ͑Ј͒ component of the susceptibility which remains practically unchanged when applying magnetic field, ͑ii͒ the inflection point located on the real ͑Ј͒ component of the susceptibility below 20 K, associated with long-range antiferromagnetic ordering.It becomes more defined ͑more three dimensional͒, moving toward higher temperatures as the applied magnetic field is increased ͑see inset in Fig. 7͒, reaching a value of 20.3 K at 90 kOe.The absence of signal in the imaginary ͑Љ͒ component of the susceptibility above 15 K confirms the origin of the antiferromagnetic ordering, 11 and ͑iii͒ the inflection point at around 6 K, in the real ͑Ј͒ and imaginary ͑Љ͒ component of the susceptibility confirms that it turns into a maximum defined for an applied field of 5 kOe.This signal decreases in intensity, with shifts in temperature as the magnetic field increases becoming extinct in fields above 30 kOe.
The temperature dependence of the molar heat capacity ͑C p ͒ for Co 2 ͑OH͒AsO 4 is shown in Fig. 8. Calorimetric measurements in the absence of external magnetic field reveal a small maximum ͑⌬C p =2 J/ Kmol͒ centred at 18.6 K ͑see upper inset in Fig. 8͒.This anomaly does not have the typical appearance of a second-order transition of but it can be associated with the establishment of a three-dimensional antiferromagnetic order in good arrangement with the magnetic-susceptibility data.Besides, no anomaly is observed below 10 K, which prompted us to propose that the magnetic contribution around 6 K observed in the magneticsusceptibility measurements is not of a long-range type ͑implying a disordered magnetism͒.Above the peak, C p increases continuously due to the phonon contribution and does not show any tendency to saturation even up to room temperature, where the value of C p is 160 J/Kmol, still far from the expected value according to the Dulong and Petit law 23 ͑224.5 J/Kmol͒.This is due to the presence of light atoms with very high excitation energy.In order to extract the magnetic contribution ͑C mag ͒, that phonon ͑C pho ͒ should be determined.The exact calculation of C pho is difficult due to the absence of a suitable nonmagnetic isomorphous compound.As it was satisfactorily used for Co 2 ͑OH͒PO 4 , 11 an estimation of C pho was obtained using the Debye model 24 and considering the existence of two De-bye temperatures, the smaller one ͑ 1 ͒ associated to the heavy ions such us Co and As ͑n 1 ͒ and the higher one ͑ 2 ͒ associated to the O and H light ions ͑9−n 1 ͒.The best fit to the experimental data for T Ն 60 K is obtained for 1 = 270 K, 2 = 1048 K, and n 1 = 3.6 ions.The magnetic contribution ͑C mag ͒ with temperature dependence is shown in the lower inset of Fig. 8. Apart from the maximum associated with the three-dimensional magnetic order around 19 K, another anomaly like a shoulder circa 30 K is observed.This kind of broad maximum could come from different origins: ͑i͒ bidimensional magnetic ordering, ͑ii͒ short-range magnetic interactions, or ͑iii͒ a crystalline electrical field, as will be analyzed later in the discussion.
Heat-capacity measurements have been taken in the presence of several magnetic fields.Because the phonon contribution is not affected by the magnetic field, we have subtracted those values from the experimental data and obtained the magnetic contributions ͑see Fig. 9͒.Usually, the effects of the magnetic field on antiferromagnetic or ferromagnetic transition become more rounder ͑and decrease in height͒ the anomaly, shifting it to either low ͑antiferromagnetic͒ or high ͑ferromagnetic͒ temperatures.In our case, unexpectedly, the maximum associated to the three-dimensional or- dering grows with field and becomes better defined ͑see upper inset of Fig. 9͒.These anomalous results will be explained later from neutron powder-diffraction data.In order to understand this surprising phenomenon, we have plotted the evolution of both, the temperature of the maximum and the temperature of the inflexion point above the maximum as a function of the applied magnetic field.Both magnitudes evolve in the same way: nearly constant up to 10 kOe, a sudden increase between 2 and 60 kOe and, finally a tendency to saturation above 80 kOe ͑see lower inset in Fig. 9͒.

C. Low-temperature neutron diffraction
The thermal evolution of the D1B patterns is shown in Fig. 10.For the high-temperature NPD patterns, all the Bragg reflections can be indexed in the orthorhombic Pnnm space group.The refined lattice parameters at 50 K a = 8.241͑8͒ Å, b = 8.564͑8͒ Å, and c = 6.028͑6͒Å show a small shift with respect to the 300 K data ͓a = 8.258͑1͒ Å, b = 8.580͑1͒ Å, and c = 6.039͑6͒Å͔ due to effect of temperature.New peaks appear in the patterns with decreasing temperature below 25 K confirming the onset of a magnetic ordering with a T N value of 21 K.These new peaks can be indexed with the propagation vector k = ͑0,␦ ,0͒, indicating the existence of an incommensurate ͑IC͒ antiferromagnetic structure along the b direction.The modulation wave vector characterizing the oscillatory magnetic order is temperature dependent with a value of ͑0,␦ ,0͒, where ␦ = 0.430 at the lowest temperature ͑1.8 K͒ of these measurements.As can be seen in Fig. 10, the intensity of the magnetic reflections increases in a monotonous way below T N and reaches saturation at low temperature.Presence of anomalies indicating a modification of the long-range spin arrangement was not observed.
The magnetic structure was solved by means of symmetry-representation analysis 25 using the program BASIREPS.26 The possible representations were systematically checked with FULLPROF program. 21After refining, the Fourier components of the atomic magnetic moments for each irreducible representation, a ⌫1͑00Gz͒ for site 4b and the mixing of ireps ⌫2͑00fz͒ and ⌫3͑00az͒ for site 4g were observed as the best solution ͑see symmetric analysis in Appen-dix͒.Rietveld refinements of this solution with a magnetic moment perpendicular to the propagation vector in the z direction gave a fully satisfactory fit ͑Fig.11͒.Hence, Co 2+ moments are ordered with the magnetic moment modulated in a longitudinal sinusoidal wave perpendicular to the propagation vector.This ordering is visualized in Fig. 12.The components of the refined magnetic moments of Co͑1͒ and Co͑2͒ are 2.81͑1͒ B and 3.64͑3͒ B , respectively, with a resultant magnetic moment of 3.22͑2͒ B per Co 2+ ion.The nuclear and magnetic discrepancy factors are R p = 16.1,R wp = 14.4, 2 = 2.61, R Bragg = 6.9, and R mag = 14.4.The magnetic moment was refined from the D1B data at all available temperatures.The nuclear structure and anisotropic temperature factors were kept from the refined D2B data at 2 K.The thermal dependence of the ordered magnetic moments is represented in Fig. 13.It can be observed that the three-dimensional magnetic order starts at 21 K, the ordering temperature being similar in both sublattices.The curves of the Co͑1͒ and Co͑2͒ moments rapidly increase from 21 K to approximately 15 K with a change in the slope at around 12 K ͑Fig.13͒.The magnetic moment for the Co͑1͒ and Co͑2͒ ions in the dimer groups and chains slowly increases with practically linear variation from 2.64͑4͒ B and 3.46͑5͒ B at 12 K to 2.81͑1͒ B and 3.64͑3͒ B at 1.8 K. Furthermore, the refined magnetic moments of the Co͑2͒ octahedral ions are always higher than those of the Co͑1͒ trigonal bipyramidal geometry in the whole temperature range studied.In addition, the ␦ component of the magnetic propagation vector k continuously decreases with increasing temperature from 0.43 to 0.36 ͑see inset in Fig. 13͒.
Neutron powder diffraction at different temperatures and fields were performed using a 50 kOe cryomagnet coupled to D2B diffractometer ͑ = 1.5938Å͒.During the field experiments, the high-intensity nuclear reflection ͑3, 2, 0͒ was measured repeatedly to control the correct orientation of the sample.In Fig. 14, we present the results from magnetic neutron diffraction with magnetic field at 1.5 K.In addition, we show the neutron diffraction of zero field and 25 K ͑paramagnetic state͒ for comparison.
We find that the propagation vector k͑0,␦ ,0͒ is highly dependent on the magnetic field between 0 and 35 kOe.At zero field, magnetic Bragg intensities can be detected at ͑0, 0.43, 0͒ originations from an incommensurate antiferromagnetic structure along the b direction ͑Fig.11͒.When the magnetic field increases, the magnetic bragg reflections of IC phase continuously decrease in intensity and there appear new magnetic satellites that can be indexed with a propagation vector ͑0, 0.33, 0͒.At 35 kOe, a sudden drop in all incommensurate peak intensities, denoting the transition of the magnetic structure into collinear AF magnetic phase ͑Fig.15͒.The new increase in the magnetic field ͑50 kOe͒ produces significant changes in the magnetic intensities but not in the peak positions of the magnetic phase ͑Fig.14͒.This is a result of the increase in the magnetic ordering of commensurable structure in good agreement with the surprising phenomenon observed in specific-heat data.
As can be observed in Fig. 16, the applied magnetic field up to 50 kOe does not change the value of the ordering temperature.However, for values higher than 30 kOe, the external magnetic field seems to overcome the competing interactions that give rise to the incommensurate ordering.A magnetic phase transition takes place as a function of the magnetic field to a commensurate structure with propagation vector ͑0, 0.33, 0͒.The resolution of this commensurate structure is under way.The ordering of the magnetic moments of Co 2+ is in z direction for three crystallographic unit cells for the two crystallographic positions ͑dimers and chains͒.The sinusoidal modulation of the magnetic moments is also shown.Note that at a given temperature ͑2 K͒, there is only one propagator vector but there may be differences of phases between the magnetic sites.

IV. DISCUSSION AND CONCLUSIONS
The magnetic behavior of Co 2 ͑OH͒AsO 4 shows the presence of two types of magnetic interactions: ͑i͒ threedimensional antiferromagnetic interactions dominating at high temperatures, which are those responsible for the high extrapolated negative Curie-Weiss temperature and ͑ii͒ ferromagnetic interactions at temperatures lower than 15 K, where the field-cooled magnetization increases.This fact can be explained as due to the existence of ferromagnetic interactions in an overall antiferromagnetic behavior which predominates at high temperatures.
The dependence of the magnetization with applied magnetic field follows a process in stages characteristic of a metamagnetic transition below 19 K.The value of the magnetic moment at 2 K and 90 kOe is far below the theoretical saturation magnetic moment for this compound ͑3.4 B / mol͒, indicating the existence of a strong anisotropy.The magnetic irreversibility in ZFC-FC curves grows on increasing the applied field up to 20 kOe and almost disappears for a magnetic field of 90 kOe.In addition, the inflexion point at around 6 K, observed at 1 kOe, is transformed into a new and well-defined maximum when the magnetic field is  20 kOe.The fit of the magnetic data to a Brillouin law 27 at different fields in this region of temperature indicates the nonexistence of magnetic impurities ͑see supplementary ma-terial͒.
Three-dimensional antiferromagnetic ordering between Co 2+ ions appears at around 20 K, showing an unusual magnetic behavior with the magnetic field.The inflection point on magnetic-susceptibility data, associated with longrange antiferromagnetic ordering, becomes more defined ͑more three dimensional͒, moving toward higher temperatures ͑Ϸ2 K͒ as the applied field increases.Besides, regards heat-capacity data, another unusual effect with the magnetic field is observed.The maximum associated to the three-dimensional ordering grows with the field, becoming better defined.This behavior can be explained as an incommensurate-commensurate magnetic phase transition with the magnetic field.
Another anomaly appears at approximately 30 K as a rounded maximum or shoulder in magnetic-susceptibility and C mag data, respectively.The nonappearance of anomalies in this region of temperature in powder-diffraction data indicates the absence of long-range spin arrangement.This signal is not affected by the external magnetic field and it could be originated by the existence of bidimensional magnetic order, the presence of short-range magnetic interactions or crystalline electrical field.
The possible existence of a bidimensional magnetic order precursor to the three-dimensional ordering circa 30 K could be analyzed from the magnetic heat-capacity data with quasitwo-dimensional antiferromagnetic Heisenberg models with varying interplanar couplings, 28 The purely interplane contribution C inter and cross term C cross are given by where n are the numbers of bond operators in the expansion acting within a single layer ͑n p ͒ and between two layers ͑n z ͒ and N is the system of size.
The comparison of the experimental magnetic heat capacity of Co 2 ͑OH͒AsO 4 with the theoretical model shows a good agreement ͑Fig.17͒, where correlations between twodimensional coupling constants ͑shoulder width to 30 K͒ are lower than the dimensional coupling constants ͑peak at 19 K͒.
Another possibility is the presence of short-range magnetic interactions.However, the fit of the magneticsusceptibility data at 1 kOe above 25 K to a classical bidimensional model gave negative results.Besides, until now, an adequate theoretical model to study these types of interactions in heat-capacity data has been not described despite the presence of compounds that show similar magnetic behavior. 29inally, we have also considered the possible effect of the crystalline electrical field ͑C CEF ͒ on the magnetic contribution in this temperature region.Theoretical calculations 30 in-dicated that the hexacoordinated Co͑II͒ ion presents a low quadruplet separated by an energy ⌬ 1 from the first excited doublet whereas in the pentacoordinated Co͑II͒ ion, the lower levels are two doublets separated by an energy ⌬ 2 .The addition of these two contributions ͑C pho + C CEF ͒ to the heat capacity, fits the experimental data above the ordering temperature quite well ͑Fig.18͒.The best fit is obtained for values of 1 = 299 K, 2 = 1057 K, n 1 = 3.7, ⌬ 1 = 80 K, and ⌬ 2 = 85 K, respectively.Therefore, from these results, we can conclude that all contributions proposed to explain the magnetic anomaly at approximately 30 K should be taken into consideration.
The incommensurate magnetic structures are characterized by modulations of their spin arrangements over periods which are long compared to the size of the chemical cell and not commensurate with the underlying lattice. 31In our case, the Co 2 ͑OH͒AsO 4 phase shows an incommensurate antifer- The magnetic structure of Co 2 ͑OH͒AsO 4 consists of ferromagnetic arrangements between the Co͑2͒ octahedral chains and Co͑1͒ trigonal bipyramidal dimers along the c-axis-modulated antiferromagnetic between subnets in direction b ͑Fig.12͒.The magnetic interactions in each sublattice, ͓Co͑2͒O8͔ ϱ octahedral chains, and ͓Co͑1͒ 2 O8͔ dimeric units, together with the interactions through the ͉OH − ͉ and arsenate groups give rise to a three-dimensional antiferromagnetic coupling in good agreement with the results obtained from the magnetic measurements.Electronic paramagnetic resonance and reflectance diffuse spectroscopies indicate that only Co 2+ ions are present in this phase. 30,32In this way, the markedly different saturated magnetic moments in Co 2 ͑OH͒AsO 4 with two chemically similar Co 2+ cations must be based on the differences between the geometries around the two cation sites.Spontaneous static ordering of the magnetic moments at low temperatures is caused by exchange interactions between the moments, making it energetically favorable for them to align, either parallel or antiparallel.
If we consider the commensurate AF structure of the isomorphous Co 2 ͑OH͒PO 4 phase, 11   It is worth mentioning the comparison of the magnetic exchange interaction, Co͑1͒-O͑3͒-Co͑2͒, between dimers and their neighbor chains in the Co 2 ͑OH͒XO 4 ͑X = P and As͒ phases ͑Table IV and Fig. 19͒.In this way, in the phosphate phase, this magnetic exchange has a striking angle of 107°͑ for ferromagnetic interactions through the xz plane͒ which was considered essential in the competition between dimers and chains in order to ensure cooperativeness of the freezing process associated to a spin-glass state of this phase. 11However, the substitution of the PO 4 3− by AsO 4 3− anions modifies substantially the magnetic exchange Co͑1͒-O͑3͒-Co͑2͒ angle from 107°to 116.9°for the phosphate and arsenate, respectively, relaxing the magnetic frustration system of Co 2 ͑OH͒PO 4 leading to an incommensurate phase with antiferromagnetic interactions ͑sinusoidal amplitude modulated͒ in Co 2 ͑OH͒AsO 4 ͑Fig.13͒.Finally, the magnetic interactions propagated via ͉XO 4 ͉ tetrahedra ͑X =P,As͒ characterized by both the O-X-O and X-O-Co angles give rise to a threedimensional antiferromagnetic coupling.
In summary, the obtained results indicate the existence of an anomalous three-dimensional antiferromagnetic ordering influenced by the magnetic field in the Co 2 ͑OH͒AsO 4 phase.The presence of both the strong anisotropy of the Co͑II͒ ions and the magnetic frustration in the Co͑1͒ and the neighboring Co͑2͒ sublattices could be responsible for the complex magnetic behavior observed in this compound.Besides, an incommensurate-commensurate magnetic phase transition from IC to collinear commensurate antiferromagnetic state can explain the unusual magnetic properties observed in this compound.
The decomposition of the full reducible magnetic representation ⌫ ͑of dimension three times the number of atoms in the primitive cell͒ for 4b is ⌫ 4b = ⌺Ϯn ⌫ =3⌫ 1 Ϯ 3⌫ 2 Ϯ 3⌫ 3 Ϯ 3⌫ 4 , the corresponding decomposition for the two 4g sites is ⌫ 4g1,4g2 = ⌫ 1 Ϯ 2⌫ 2 Ϯ⌫ 3 Ϯ 2⌫ 4 .The number of free parameters for a magnetic structure corresponding to an irep is equal to the product ͑n free = n d ͒ of the number of times ͑n ͒ the irep ⌫ n is contained in ⌫ and the dimension ͑d ͒ of the irep.This is also the total number of independent basis function vectors.
The magnetic moment of the atom "j," in the cell with origin at the lattice point R n , in a magnetic structure characterized by the set of propagation vectors ͕k͖, is given by the Fourier series, m nj = ⌺ ͕k͖ S kj e 2kiRn , where the sum is extended to the whole set of propagation vectors.For k at the interior of the Brillouin zone, the vector −k should also be present and S kj = S kj ‫ء‬ .The physical meaning of the basis functions of the irep ⌫ in describing a magnetic structure is that the Fourier coefficients S kj are linear combinations of the constant vectors S ␣͑k , v , ͉ j͒ so that For a given propagation vector k and a given irep ⌫ n, the index ␣ runs between 1 and n and between 1 and d ͑for details, see Ref. 25͒.The coefficients C ␣ can be real or purely imaginary.By varying these coefficients, we obtain the whole class of magnetic structures satisfying the symmetry of the propagation vector.Let us consider two examples for the cobalt sublattices constructed with the representation ⌫ 3 .The irep is of dimension 1 ͑so = 1 and the summation index over is therefore removed͒ and it is contained three times in ⌫ 4b so the number of coefficients is 3 ͑␣ =1,2,3͒.The possible magnetic structures described by this irepare given by If, e.g., C 1 = C 3 = 0, the structure corresponds to a collinear longitudinal sinusoidal structure.If C 2 = 0, and C 1 = iC 3 with C 3 purely imaginary, the structure corresponds to a helix with a cylindrical envelope.If C 1 = 0 and C 2 = iC 3 the structure is a cycloid, etc.
To solve the magnetic structure, one has to look for the set of coefficients that give rise to the best agreement between observed and calculated magnetic intensities.This part of the analysis may be undertaken simply by trial and error, by hand or using Monte Carlo techniques.*teo.rojo@ehu.es

FIG. 3 .
FIG. 3. ͑Color online͒ Partial polyhedral view of the packing of Co 2 ͑OH͒AsO 4 in the z direction.Tetrahedra have not been shown for clarity.

FIG. 5 .
FIG. 5. ͑Color online͒ Low-field ZFC-FC magnetic susceptibility at difference fields.The inset shows the field dependence of the long-range ordering temperature.

FIG. 11 .
FIG.11.͑Color online͒ Neutron diffraction profiles of Co 2 ͑OH͒AsO 4 at 2 K obtained in D2B.Crosses are experimental, solid line calculated, and blue line differential data.First line of vertical marks corresponds to the position of the allowed reflexion for the crystallographic structure and the second line marks the magnetic reflexions.

FIG. 12 .
FIG.12.͑Color online͒ Incommensurate antiferromagnetic structure of Co 2 ͑OH͒AsO 4 along the b direction.The ordering of the magnetic moments of Co 2+ is in z direction for three crystallographic unit cells for the two crystallographic positions ͑dimers and chains͒.The sinusoidal modulation of the magnetic moments is also shown.Note that at a given temperature ͑2 K͒, there is only one propagator vector but there may be differences of phases between the magnetic sites.

FIG. 13 .
FIG.13.͑Color online͒ Magnetic moment for Co 2 ͑OH͒AsO 4 refined from neutron data obtained with D1B as a function of temperature for chains and dimers of the Co 2+ ions.The inset shows the magnitude of the propagation vector ͑0,␦ ,0͒ as a function of temperature.Solid lines are only visual guidelines.

FIG. 14 .
FIG. 14. ͑Color online͒ ͑Left͒ Evolution of the neutron-diffraction peaks of Co 2 ͑OH͒AsO 4 at different fields at 1.5 K obtained in D2B compared with the zero field and 25 K. ͑Left͒ Magnetic peaks are marked with ‫ء‬ sign.Step narrows are visual guidelines for the eyes showing the shift of the ͑010͒-k peak.͑Right͒ Enlargement of the low angle diffraction.

FIG. 16 .
FIG. 16. ͑Color online͒ Magnetic phase diagram of Co 2 ͑OH͒AsO 4 .Blue circles are neutron diffraction obtained in D2B.The thin broken curve marks a boundary where different magnetic phases could not be resolved in the diffraction pattern.

TABLE II .
Final refined positional and thermal parameters from the neutron-diffraction pattern ͑D2B͒ at room temperature for Co 2 ͑OH͒AsO 4 .

TABLE IV .
Selected geometrical parameters, bond lengths ͑Å͒, and angles ͑deg͒ related to the possible magnetic superexchange pathways for Co 2 ͑OH͒XO 4 ͑X = P and As͒.The data were obtained from D2B. ͑OH͒XO 4 ͑X = P and As͒.Interactions via vertex oxygen bridges of the phosphate and arsenate groups.ferromagneticinteractions in both compounds.On the other hand, superexchange interactions Co͑1͒-O͑4͒H-Co͑2͒ ͑Fig.19͒ with a mean exchange angle of 123.2°and 126.2°for phosphate and arsenate, respectively, give rise to antiferromagnetic couplings.
FIG. 19.͑Color online͒ Schematic view of the exchange pathways for Co 2