Unravelling the elusive antiferromagnetic order in wurtzite and zinc blende CoO polymorph nanoparticles

CoO nanoparticles with zinc blende and wurtzite structures are found to be antiferromagnetic below T N ~ 225 K and 109 K, respectively. Although the zinc blende phase has a conventional antiferromagnetic structure, the antiferromagentic order of the wurtzite phase is more complex with two orthogonal components (one of them incommensurate). The nanoparticles also present a large number of uncompenstaed spins.

overwhelmed by the uncompensated spins, which confer the system a ferromagnetic-like behavior even at room temperature.
To elucidate the magnetic properties of wurtzite-CoO and zinc blende-CoO we developed a large scale nanoparticle synthesis that allowed carrying out a rational investigation of their structural and magnetic properties comprising a comprehensive magnetic and powder neutron diffraction study. The results indicate that zinc blende-CoO is antiferromagnetic with a 3 rd type structure and a Néel temperature of about TN (zinc blende)  225 K. On the other hand although wurtzite-CoO exhibits also an antiferromagnetic order (with a rather complex structure) with T N  110 K, the uncompensated spins overwhelm the magnetization behavior leading to a ferromagnetic-like response.

Results and Discussion
The fits of the x-ray diffraction (XRD) patterns determine that the nanoparticles synthesized in a small batch present a pure wurtzite-CoO structure (space group P63mc) with hexagonal lattice parameters a = 3.2509(3) Å and c = 5.1954(5) Å (where the values in brackets correspond to the estimated standard deviation with a 76% of confidence interval, taking into account both statistical and systematic errors) and a crystallite size, <D>, of <D>W = 17(1) nm (Figure 1a). The values for a and c are in line with previously reported lattice parameters of wurtzite-CoO (JCPDS no. . [4,51,52,54,56,61,63] On the other hand, the sample obtained in a large batch shows a mixture of wurtzite-CoO (a = 3.2526(1) Å, c = 5.1976(1) Å; <D>W = 32.0(5) nm) and cubic zinc blende-CoO structures (space group m F 3 4 ; a = 4.5533(1) Å, <D>ZB = 13.0(5) nm - Figure 1b). The volume ratio of the two phases, wurtzite/zinc blende, is 63/37. Moreover, the fit of the mixed sample (synchrotron data) reveals that both phases present oxygen vacancies and that wurtzite shows also microstrains. Using different concentrations of both oleic acid and cobalt (II) acetylacetonate has been shown to be a good strategy to obtain different CoO polymorphs. The zinc blende polymorph has been reported as the primary phase of the particles once they had nucleated under this synthetic conditions, even this is not the most stable phase, which suggest the reaction is kinetically controlled [12] .
Then, wurtzite CoO is formed by nucleation on growth faults or pre-existing boundaries on zinc blende crystals. The final product is strongly related to the zinc blende crystallite size. In the large batch, under high-concentrated precursors conditions, the transformation from zinc blende to wurtzite is only partial because part of the zinc blende nuclei overcomes a critical radius and it cannot be transformed to wurtzite and, consequently, it can be also found in the final product as a metastable phase. [64] On the other hand, for low-concentrated precursor conditions (small batch) the nucleus size of the generated zinc blende CoO was not large enough so a complete transformation to wurtzite CoO can take place.
Importantly, none of the samples show any traces of the most stable CoO phase (i.e., rock salt-CoO) or metallic Co. Note that from this type of synthesis, which is carried out under inert/mild reducing conditions, it is reported that the rock salt-CoO phase is not formed below 320 ºC [12] unless some surfactants, which acts as catalyzers, are added into the reaction such as oleylamine. [65,66] Interestingly, it has been observed that the use of inert gases such argon or nitrogen as well as the use of carboxylic acids as surfactants is critical for the formation of the target CoO polymorphs. [4] The transmission electron microscopy (TEM) characterization of the pure wurtzite-CoO sample shows that nanocrystals have a pyramid shape morphology (similar to the one already reported for wurtzite-CoO) [52][53][54] with length of the edges between 20 and 30 nm (Figure 2a).  Figure S1b). Moreover, the HRTEM images of each type of particle evidence different lattice spacings depending on their shape (Figure 2f), where the triangular particles correspond to wurtzite, while the spheroidal particles are zinc blende.
Finally, the SAED analysis corroborates the presence of the two different types of phases in the sample (Figure 2g).
The temperature dependence of the magnetization of the pure wurtzite-CoO particles shows a rather featureless behavior down to 20 K, with a monotonic increase of the magnetization (M) as the temperature decreases (Figure 3a). Namely, at first glance there is no obvious sign of any magnetic transition. However, it is important to highlight that the FC and ZFC do not overlap (see Figure S2), indicating that the material has a ferromagnetic-like behavior.
Analogous results have been previously observed by other authors in wurtzite-CoO. [51][52][53][54]56,62] Interestingly, a similar behavior has been also noted in most antiferromagnetic transitionmetal oxide nanoparticles (rock salt-CoO, NiO, CuO, MnO). The non-overlapping ZFC-FC curves and lack of any obvious transition is typically ascribed to the presence of uncompensated spins either at the surface (due to surface spin disorder, because of the change in atomic coordination) or in the bulk (due to defects). [67][68][69] These uncompensated spins have a large magnetization, which overwhelms any signal arising from the antiferromagnet itself, . This non-monotonic behavior could tentatively be ascribed to a magnetic transition. Importantly, the cusp is virtually field independent (see  (Figure 3a). Note that small anomalies in M(T) have been observed in a few cases in wurtzite-CoO, although they were not discussed in detail. [53,56] At very low temperatures a clear transition is observed (Figure 3a, [51][52][53] and in several antiferromagnetic transition metal oxides (e.g., NiO). [70] In concordance with other nanoparticle systems, this transition is ascribed to the slowdown of the thermal fluctuations as the temperature decreases, followed by the increase of the magnetic correlation of the surface spins that freeze in a spin-glass like state at 7 K.
The presence of uncompensated spins is confirmed by the hysteresis loop measured at 5 K, which shows a rather large saturation magnetization (MS) of 25 emu g -1 , (i.e., extrapolation of the high field magnetization to H = 0) at low temperatures ( Figure 4a) and a clear hysteresis.
MS decreases rather fast at low temperatures as the temperature increases, although it levels off at a small, but finite, value above about 100 K; MS(T > 100 K) = 0.25 emu g -1 (Figure 4b).
Namely, wurtzite-CoO presents a ferromagnetic-like behavior at room temperature. These results are in concordance with earlier studies in wurtzite-CoO, which show a ferromagnetic response, [51][52][53]62] even at room temperature. [53,62] Note that the strong ferromagnetic-like behavior can be tentatively explained by the presence of uncompensated spins arising from the existence of a rather large amount of oxygen vacancies (note CoO0.7 stoichiometry of the particles), with the FM signal being roughly proportional to the number of such vacancies. [71,72] Concerning the dependence of the coercivity, HC, with temperature it can be observed that at low temperatures, there is an increase in HC, determined by the increase of the magnetic anisotropy related with the freezing of the surface disorder. However, at higher temperatures, the HC(T) shows a somewhat unusual behavior, exhibiting a broad maximum at around 100 K (Figure 4c). Similar effects have been observed in NiO [67,68] and rock salt CuO [73] and they have been tentatively ascribed to the ordering of the antiferromagnetic core or to a blocked state of the magnetization of the core. [74] In fact, this maximum could be linked to the enhanced coercivity typically observed in ferromagnetic/antiferromagnetic systems at the Néel (or blocking temperature) temperature of the antiferromagnetic counterpart. [75,76] In this framework, and taking into account the bump at about 125 K in M(T), the maximum in HC could indicate a coupling between the uncompensated spins and an antiferromagnetic phase, hence preliminarily implying an antiferromagnetic character of wurtzite-CoO.
The mixed wurtzite-zinc blende sample exhibits a similar magnetic behavior. The temperature dependence of the magnetization is rather featureless with a peak at very low temperatures   5a). This HR corresponds to a g-value of 2.23 which is in agreement with the experimentally observed for Co 2+ , S = 3/2, which lies in the 2.1-2.8 range. [77][78][79] When the temperature decreases the asymmetry of the resonance becomes more evident (Figure 5a), i.e., a secondary peak splits from the main resonance line and shifts to lower field as the system cools. Note that usually the FMR signal of a powder sample is asymmetric because the material has an angular distribution of the magnetization easy axes respect to the external field. In fact, the observed spectra present a typical FMR line shape with uniaxial anisotropy.
Moreover, the anisotropy field HA= 2K/M, which is proportional to the peak-to-peak linewidth, increases when the temperature decreases and at T ~ 110 K the resonance signal vanishes. In order to obtain the physical parameters that characterize the spectra, the lines were fitted using the Smith-Beljers formalism for the case of material with a ferromagnetic component and uniaxial anistotropy. [80,81] Then, from the magnetic free energy of the system F=-MS.H+K sin 2 , where K corresponds to the uniaxial effective magnetic anisotropy constant, MS is the saturation magnetization of the system and  is the angle between the M and the uniaxial axis, the resonance condition is: [82]   where HA = 2K/M is the anisotropy field,  is the gyromagnetic ratio, H is the angle between  [83][84][85] and the demagnetizing field, which increases as the temperature decreases. Moreover, due to the thermal fluctuations of the magnetic moment, in nanoparticles the effective anisotropy tends to decrease as the temperature increases. [82,86,87] Interestingly, at low temperatures, HR shifts with respect to the expected one from the Co 2+ gvalue. This behavior has been observed in several FMR studies of nanoparticles and it is ascribed to the presence of additional internal fields, usually produced by dipolar or exchange interparticle interactions, which shift the resonance toward lower fields. [82,87,88] Figure 5b shows also a remarkable decrease of HR and IFMR below ~130 K, followed by the disappearance of the signal at T ~ 110 K. This behavior is typically found when the system develops an antiferromagnetic transition, where the antiferromagnetic resonance mode can no longer be excited due to the presence of large anisotropies and exchange fields. [89] Note that the antiferromagnetic transition is usually smoother in nanoparticles [85] than in bulk materials. [90] Remarkably, the loss of IFMR below TN indicates that the uncompensated spins must be strongly coupled, leading to an increased magnetic anisotropy. As a consequence, when the nanoparticle orders antiferromagnetically, the signal of the uncompensated spins is also lost, because the resonance frequency is larger than the excitation microwave frequency. [85] This fact makes it impossible to study the features related to the coupling between the uncompensated and antiferromagnetic spins using FMR (as it is often done in weakly coupled ferro(i)magnetic/antiferromagnetic thin film and core/shell systems [76,[91][92][93] ).
Similarly, the vanishing IFRM also prevents observing any features related to the spin glasslike transition observed in the M(T) data. [94,95] Similar to the pure wurtzite-CoO nanoparticles, the mixed sample shows at room temperature a single resonance line centered at HR ~ 7.60 kOe, which corresponds to a g-value of ~2.27.
The inhomogeneously broadened line observed in the whole temperature range probably stems from the convolution of several resonances. In fact, the resonance in the mixed sample is considerably broader than in pure sample, which does not allow an easy deconvolution and, consequently, it precludes obtaining information on the internal structure. For example, while the peak-to-peak linewidth at room temperature is Hpp ~ 1.8 kOe for pure wurtzite-CoO, it becomes Hpp ~ 4.0 kOe for the mixed sample. The HR, H and IFMR resonance parameters where obtained by fitting the experimental spectra to a Lorentzian lineshape curve (Figure   5c). In contrast to the pure wurtzite sample, the FMR parameters exhibit a rather smooth evolution with temperature down to low temperatures (Figure 5d). However, a change in slope is observed for HR, H and IFMR around 240 K and 110 K. Since these temperatures are close to the transition temperatures of zinc blende (~225 K) and wurtzite (~110 K) CoO structure hinted in the magnetic measurements, these features can be associated with the successive magnetic ordering of the different CoO phases. Therefore, below T ~ 240 K the H and IFMR increase as a consequence of the FMR of the uncompensated moment of the zinc blende magnetic phase, which probably shows a resonance line down to low temperatures.

Besides, at T ~ 110 K the wurtzite-CoO phase orders antiferromagnetically and it no longer
contributes to the resonance, as a consequence the H and IFMR slope decrease.
To confirm the presence of uncompensated spins we carried out XMCD measurements. As can be seen in Figure 6,  Figure S3). [96][97][98] Moreover, the XMCD signal at 300 K is considerable weaker than at low temperatures, where the magnetic moment (roughly proportional to the area of the XMCD spectra) decreases a factor 100 from 15 K to 300 K (Figure 6, inset), in full agreement with the temperature dependence of MS, hence, corroborating the uncompensated spins as the origin of the ferromagnetic-like behavior in the samples. The uncompensated spins probably arise from surface effects and due to internal defects such as oxygen vacancies or stacking faults.
To be able to unambiguously determine the nature of the magnetic phases we carried out neutron diffraction experiments. However, the amount of sample synthesized in a small batch, the organic material present in the sample (surfactants) and the nanocrystalline character of the sample, led to exceedingly noisy neutron diffraction patterns to perform any quantitative analysis. Thus, the experiment was carried out only in the mixed wurtzite zinc blende-CoO sample (obtained from the large batch). The low temperature patterns clearly show the presence of magnetic peaks in both the zinc blende and the wurtzite structures (Figure 7a).
This is in contrast to the only existing neutron diffraction study on wurtzite CoO, in which only a small broad magnetic peak at low temperatures was observed and ascribed to a frustrated short range magnetic order. [56] It is worth emphasizing the magnetic peaks in the neutron diffraction pattern correspond only to either zinc blende or wurtzite CoO, consequently, discarding any other ordered magnetic phases in the sample.
The fitting of the neutron diffraction pattern shows that the zinc blende-CoO structure presents a simple antiferromagnetic order with a magnetic structure of the 3 rd type in a face centred cubic lattice (following Corliss-Elliot-Hasting notation) [99] with an average magnetic moment of 2.3(3) µB/ion. This structure is similar to the zinc blende structure of -MnS, with the magnetic moments ordered along the x-axis and consist in a spin configuration where 2/3 of the neighbors spins are antiparallel and 1/3 parallel per each Co 2+ ion. For the next-nearest neighbors 1/3 of the spins are aligned antiparallel and 2/3 parallel. [99] The experimentally obtained magnetic moment is in concordance with theoretical predictions of zinc blende-CoO, 2.74 µB/ion. [13] The temperature dependence of the magnetic peaks of the zinc blende-CoO shows that this phase remains clearly magnetic up to 110 K (Figure 7b). However, room temperature measurements evidence that 300 K is already above its TN. A fit of the temperature dependence of the intensity of the main magnetic peak to a mean field On the other hand, the magnetic structure of the wurtzite-CoO phase is much more complex.
Namely, the magnetic moments are tilted due to the coexistence of two different magnetic orders within the structure. Along the c-axis the Co atoms are ordered antiferromagnetically, with a 2 nd type structure (following Corliss-Elliot-Hasting notation, [99] similar to the -MnS wurtzite structure [99] ) and a magnetic moment of 1.4(1) µB/ion. In the 2 nd type antiferromagnetic structure half of the nearest neighbors are aligned antiparallel and the other half parallel. In addition, all the next-nearest neighbors are aligned antiparallel. [99] Additionally, in the plane, the atoms present a rather unusual incommensurate magnetic order along the y-axis with 2.8(2) µB/ion. That is, the magnetic periodicity does not correspond with the structural order. [100,101] Instead of the expected Néel type order with a wave vector of k = 0, ½, 0, it shows k = 0, 0.4559(3), 0. The combination between the commensurate order along the c-axis and the incommensurate structure in the y-axis implies that each atom has a different tilt angle, ranging from 0 º (spins along the c-axis) to 63 º . Moreover, this incommensurate structure presents only a short-range order, since it has a small correlation length along the c-axis. Remarkably, the temperature dependence of both magnetic structures shows a TN ~ 109 K (Figure 7b). This TN is consistent with the transition temperatures inferred from the other techniques.
The origin of this complex magnetic structure in wurtzite-CoO may arise from the arrangement of the Co-O-Co atoms in the hexagonal structure which should weaken and geometrically frustrate the super-exchange between the Co atoms (since there is no way to arrange the spins to satisfy all the interactions simultaneously), [44,59] in contrast to the Co-O-Co alignment in the cubic rock salt-CoO that favors conventional antiferromagnetic arrangements. [102] In fact, the frustration of the wurtzite structure may be the origin of the diversity in the reported magnetic results in wurtzite-CoO, where defects not only induce uncompensated spins, [103] but they may also stabilize the antiferromagnetic order by lifting the degeneracy inherent in frustrated spin arrangements (as for example observed in pyrochlore, kagomé or some spinel structures), [104,105] leading to a long range magnetic order. Hence, depending on the morphology or size of the wurtzite-CoO specimen or the amount and type of defects in its structure (e.g., oxygen vacancies, stacking faults and so on; which are given by the synthetic conditions), dissimilar magnetic behaviors may manifest.

Conclusions
Summarizing, a systematic study of the magnetic properties of the wurtzite and zinc blende nanoscale polymorphs of CoO has been performed. Notably, the results evidence that although the intrinsic magnetic order of both wurtzite and zinc blende-CoO is antiferromagnetic, the systems present a large number of uncompensated spins which result in a ferromagnetic-like behavior even at room temperature. Moreover, while zinc blende-CoO shows a rather simple spin structure, the one for wurtzite-CoO is somewhat complex, comprising two different magnetic components (one of them incommensurate) orthogonal to each other.

Experimental Section
The synthesis of CoO nanoparticles has been carried out by thermal decomposition of cobalt (II) acetylacetonate (Co(acac)2) in the presence of oleic acid and 1-octadecene.
Two different reactions were carried out: (i) small batch: 1 g Co(acac)2 (~ 4 mmol, Aldrich 97%) and 0. . The spectra were recorded at the Co L2,3 edges using total electron yield mode at 10 K in a 50 kOe magnetic field. The simulation of the XMCD spectra were carried out using the CTM4XAS Program. [106] Powder neutron diffraction was carried out at the D1B beamline in the Institute Laue     M(emu/g)    Figure 6. Co L2,3-edge XMCD spectra at T = 15 K a for the the pure wurtzite (blue) and mixed wurtzitezinc blende (red) CoO samples. Shown in the inset are the spectra at T = 300 K of the same samples.