Magnetic ordering in La1.5Ca0.5CoO4 revealed by resonant magnetic x-ray scattering and neutron diffraction

PHYSICAL REVIEW B 103, 184422 (2021) Magnetic ordering in La1.5Ca0.5CoO4revealed by resonant magnetic x-ray scattering and neutron diffraction G. Subías ,1,2,*J. Blasco ,1,2,†J. Herrero-Martín ,3J. A. Rodríguez-Velamazán,4 M. Valvidares,3R. Fan,5P. Steadman,5and J. García1,2 1Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza, Zaragoza 50009, Spain 2Departamento de Física de la Materia Condensada, Universidad de Zaragoza, C/ Pedro Cerbuna 12, Zaragoza 50009, Spain 3ALBA Synchrotron Light Source, Carrer de la Llum 2-26, 08290 Cerdanyola del Vallès, Barcelona, Spain 4Institut Laue-Langevin, 71 avenue des Martyrs, CS 20156, 38042 Grenoble Cedex 9, France 5Diamond Light Source, Didcot, Oxfordshire OX11 0DE, United Kingdom (Received 22 January 2021; revised 24 March 2021; accepted 5 May 2021; published 20 May 2021) We report a comprehensive study on the magnetic ground state of La1.5Ca0.5CoO4combining single crystal neutron diffraction and resonant magnetic x-ray scattering at the Co L2,3edges. Three single-crystal samples obtained from the same boule were investigated exhibiting magnetic phase transitions from a high-temperature paramagnetic phase to an antiferromagnetic phase at TN≈52 K. Single crystal neutron diffraction reveals that the crystal structure at room temperature shows an orthorhombic A-centered lattice but with aand baxes almost equal in length. The structural phase transition (charge-ordering-like) from the parent tetragonal cell takes place above 523 K into the space group A2mm where two nonequivalent compressed and expanded CoO6octahedra are ordered showing a checkerboard pattern in the ab plane. The charge segregation between the nonequivalent Co sites is about 0.4(1) electrons. Resonant magnetic x-ray reflections indexed as (1/4,1/4,0)t,(1/4,1/4,1)t, and (1/4,1/4,1/2)tin the parent tetragonal cell were observed at low temperature at the Co L2,3-edge energy range. The resonant spectral shape, with a noticeable absence of any resonant enhancement at the CoL2edge, indicates that only Co2+-like ions participate in the magnetic ordering. The polarization analysis discloses that the orientation of Co magnetic moments is the same for the three magnetic orders and they are long-range ordered along the diagonal in the ab plane of the parent tetragonal cell with a slight tilt in the caxis. Despite the onset temperatures for the three resonant magnetic reflections being the same, ≈55 K, different thermal behavior is observed between (1/4,1/4,1/2)tand (1/4,1/4,L)t(L=integer) reflections whose intensities maximize at different temperatures, suggesting the coexistence of two magnetic arrangements. Moreover, the intensity of the (1/4,1/4,1/2)tmagnetic reflection is at least ten times larger than that of the (1/4,1/4,L)t (L=integer) ones. On the other hand, neutron diffraction measurements only detect a single type of antiferromagnetic ordering following the propagation vector k=(1/4,1/4,1/2)tthat involves half of the Co atoms in the unit cell. We conclude that the bulk magnetic order in La1.5Ca0.5CoO4corresponds then to this propagation vector k=(1/4,1/4,1/2)twhile (1/4,1/4,0)tand (1/4,1/4,1)tmagnetic reflections correspond to a minority magnetic phase that must be due to changes in the oxygen stoichiometry near the surface. DOI: 10.1103/PhysRevB.103.184422 I. INTRODUCTION Hole-doped single-layered transition-metal perovskites have attracted the attention of many researchers due to their intriguing and diverse properties [1–3] These compounds adopt the K2NiF4tetragonal cell (I4/mmm) at high temperature. Initially it was thought that universal properties had been detected in half doped single-layered perovskites [4]. In this way, La0.5Sr1.5MnO4and La1.5Sr0.5CoO4are characterized by a checkerboard charge order (CO) at relatively high temperature that is followed by magnetic orderings at much lower temperature [5–7]. However, significant differences began to be revealed between different families of these *Corresponding author: [email protected] †Corresponding author: [email protected] compounds. Starting from CO, in La1−xSr1+xMnO4samples, the checkerboard CO is stable on cooling but the actual charge disproportionation is very small [8] and it is only commensurate for x=0.5. Overdoped samples exhibit incommensurate reflections that can be explained on the basis of a charge density wave whose periodicity is related to the number of Mn 3dholes [9]. On the other hand, in La2−xCaxCoO4the checkerboard CO remains commensurate for doping values well away from the optimal value of x=0.5. [10,11]The reason for the difference between the La1−xSr1+xMnO4and the La2−xCaxCoO4series is their different chemical behavior. While layered manganites keep their nominal oxygen stoichiometry and Sr doping induces holes in the Mn 3dorbitals, Co+2.5mixed valence is very stable in layered cobaltates and Ca(Sr) doping rather produces changes in the oxygen stoichiometry of the samples (interstitial oxygen excess for underdoped samples and vacancies for overdoped ones) [12]. The CO state is thus very robust and the checkerboard pattern 2469-9950/2021/103(18)/184422(11) 184422-1 ©2021 American Physical Society G. SUBÍAS et al. PHYSICAL REVIEW B 103, 184422 (2021) gets composed of expanded and compressed CoO6octahedra with a charge disproportionation between the two Co sites of about 0.4(1) electrons, [11] that is, approximately half the expected value between nominal Co2+and Co3+. Focusing on the magnetic properties, the differences can be even greater given the ability of Co atoms to appear under different spin states in the case of cobaltates. Co2+is one of the few electronic configurations in 3dmetals where the orbital angular moment acquires a significant non-negligible value. Moreover, Co3+can adopt up to three different electronic configurations: low spin Co3+(LS, t2g6eg0), intermediate spin Co3+(IS, t2g5eg1), and high spin Co3+(HS, t2g4eg2). Preliminary magnetic studies on single crystals of La1.5Sr0.5CoO4 revealed a strong anisotropic behavior with significantly higher magnetic susceptibility values when the magnetic field is parallel to the tetragonal ab plane (χab) than when it is parallel to the caxis [13]. A broad maximum in the χab(T) curve at about 60 K is indicative of the onset of magnetic correlations. The authors concluded the occurrence of HSCo3+ions but they did not contemplate the unquenched orbital moment of Co2+. A later study using soft x-ray absorption spectroscopy at the Co L2,3edges disclosed that Co3+are LS for La1.5Sr0.5CoO4in agreement with a full multiplet analysis [14,15]. Moreover, our recent study on the Co Kβemission spectra of La1.5Sr0.5CoO4and La1.5Ca0.5CoO4confirms that HS-Co2+is the only magnetic atom in these compounds [12]. Neutron scattering measurements found that although magnetic correlations start at 60 K, the long-range magnetic order is only achieved below 31 K. Above that temperature, the existence of a spin canting or the loss of coherence between magnetic domains [16] is suggested. The magnetic structure is characterized by a slightly incommensurate vector, k=(1/4−δ, 1/4−δ, 0)twith δ=0.005, in the frame of the tetragonal I4/mmm cell (indicated by the subscript t). The magnetic order only affects half of the Co ions in the cell (HS-Co2+), and the magnetic peaks are broad indicating a small coherence length and competitive magnetic interactions. Moreover, the magnetic properties seem to be very sensitive to small variations of the samples. In this way, a recent work on a polycrystalline La1.5Sr0.5CoO4sample reported a Griffiths-like phase at high temperature indicating that short CO correlation lengths seem to favor glassiness. The authors proposed a metamagnetic transition at low temperature and a stabilization of the antiferromagnetic (AFM) state at a magnetic field of 2.2 kOe [17]. Although La1.5Ca0.5CoO4is isostructural to La1.5Sr0.5CoO4, the CO correlation length of the Ca-based system is longer than that of the Sr-based one [11,18]. Accordingly, the AFM phase is more stable and long range magnetic ordering appears at about 55 K [10]. Neutron scattering measurements revealed two types of magnetic reflections. Sharp magnetic reflections follow the propagation vector k1=(1/4,1/4,1/2)twhile broad reflections follow the propagation vector k2=(1/4,1/4,0)t[18]. The presence of these two magnetic reflections in La1.5Ca0.5CoO4recalls previous studies on the La0.5Sr1.5MnO4manganite. In this sample, CO is made up of two magnetic atoms (nominally Mn3+and Mn4+) and the two magnetic propagation vectors agree with a CE-type magnetic structure [19], consisting of ferromagnetic zigzag chains in the ab plane that are coupled antiferromagnetically with each other and along the caxis. This similarity led Horigane et al. [18] to suggest that Co3+ would not be in a LS state in La1.5Ca0.5CoO4. A later work by the same authors extended the study to the La2−xCaxCoO4 (0.3⩽x⩽0.8) series [10]. In the lower doping region (x<0.5), only magnetic peaks with the propagation vector k1=(1/4,1/4,1/2)tare observed while in the high doping region (x>0.5), the magnetic periodicity agrees with the propagation vector k2=(1/4,1/4,0)t. Half doping seems to be a critical point where both types of magnetic reflections coexist. This result weakens the hypothesis of a magnetic Co3+to stabilize a CE-type magnetic structure. Nevertheless, the authors reported in the same study [10] a different set of weak magnetic reflections following the propagation vector k3=(1/8,0,1/2)toriginating from HS-Co3+but a definitive magnetic structure has not been proposed. All this mixture of magnetic components makes La1.5Ca0.5CoO4 a unique compound very interesting to study where it is possible to learn about the correlation between the spin configuration and magnetic interactions. With this purpose, we have performed a thorough study on the magnetic order of La1.5Ca0.5CoO4using single crystal neutron diffraction and resonant magnetic x-ray scattering (RMXS) at the Co L2,3 edges on the same specimens. Full polarization analysis [20] of selected RMXS reflections is performed to determine the precise magnetic structure. Despite using the same single crystals for the two experiments the obtained results seem to be contradictory. Whereas (1/4,1/4,1/2)t,(1/4,1/4,0)t, and (1/4,1/4,1)tmagnetic reflections were observed by RMXS, only (1/4,1/4,1/2)t-type reflections were detected in single crystal neutron diffraction. This controversy is explained as due to the enhanced sensitivity of RMXS in the soft x-ray region to the sample surface and hence to small changes in the oxygen stoichiometry near the surface. II. EXPERIMENT Polycrystalline La1.5Ca0.5CoO4was prepared by the solid state chemistry method as reported elsewhere [11]. The powders were pressed into rods and sintered at 1300 °C to be used for crystal growth. This growth was carried out in a homemade floating zone furnace [21] with two semielliptical mirrors, in dry air atmosphere with a growth speed of 6 mm/h. The total length of the obtained crystalline rod was 55 mm with a diameter of 4 mm. Single crystals with a typical cylindrical shape (diameter of 4 mm and length of 3 mm) were cut from the boule with different orientations. The chemical composition of the boules was tested using wavelength dispersive x-ray fluorescence spectrometry (Advant’XP+model from Thermo-ARL) and the La:Ca:Co stoichiometry agreed with the expected values within the experimental error (1%). Selected parts of the boule were ground and previously characterized by synchrotron x-ray powder diffraction [12]. Rietveld analysis of the x-ray patterns using the FULLPROF package program [22] indicated that the crystal was a single phase without detectable impurities [23]. The oxygen content of La1.5Ca0.5CoO4.02 was determined by cerimetric titration and an automatic Crison titrator. The studied single crystal 184422-2 MAGNETIC ORDERING IN … PHYSICAL REVIEW B 103, 184422 (2021) displays an oxygen stoichiometry/nominal average Co oxidation state of La1.5Ca0.5CoO4.02/Co2.54+[12]. Magnetic measurements were carried out between 2 and 300 K by using a commercial superconducting quantum interference device (SQUID) magnetometer from Quantum Design. The measurements were performed warming the sample after zero-field cooling (ZFC) and field cooling (FC) conditions at two different external magnetic fields (0.1 and 50 kOe). Neutron diffraction experiments on two single crystals were performed at two four-circle instruments of the Institute Laue Langevin (Grenoble, France). D9 was used to determine the crystal structure at room temperature. A single crystal with cylindrical-like shape was glued with the [1,1,0]tdirection in the horizontal plane and a wavelength of λ=0.834 Å was used. D10 was employed to determine the magnetic contribution. Two crystals of the same boule, the one characterized at D9 and a second crystal with a polished [1,1,4]tdirection, were measured yielding similar results. A helium-flow cryostat was utilized to vary temperatures between 2 and 60 K and a λ=2.36Å was used to be more sensitive to the low Q region. Three single crystals of the same growth were cut and polished to achieve mirrorlike surfaces normal to the [1,1,0]t, [1,1,2]t, and [1,1,4]tdirections in order to respectively investigate the presence of (1/4,1/4,0)t,(1/4,1/4,1)t, and (1/4,1/4,1/2)tmagnetic reflections using soft x rays. RMXS was carried out at the CoL2,3absorption edges using two beamlines from two synchrotron facilities: BOREASBL29 beamline [24] of ALBA (Cerdanyola del Vallès, Spain) and I10 beamline of the Diamond Light Source (Didcot, UK). The energy dependence of all magnetic reflections was recorded at the MaRes end station of the BOREAS beamline. The crystal La1.5Ca0.5CoO4.02 (110)twas mounted on the diffractometer with the [0,0,1]tcrystal axis perpendicular to the beam propagation direction in grazing incidence (θ=0◦). In this experimental configuration, the electric-field vector of the incident beam was adjusted parallel (linear σpolarization) or normal (linear πpolarization) to the caxis which is orthogonal to the scattering plane [Fig. 1(a)]. A helium-flow cryostat allows sample cooling down to 20 K in ultrahigh vacuum conditions. The BOREAS undulator allows changing the polarization of the incident beam in a continuous way from σto πbut no polarization analyzer for the scattered beam is provided. This is not the case for Diamond’s I10 beamline, where two W/B4C multilayer polarization analyzers optimized for working at the CoL2,3absorption edge energies [Fig. 1(b)] allowed a full polarization analysis of the scattered beam [25]. We note here that the same sample crystals were used in the experiments at the two synchrotron beam lines. The 2θangles found for (1/4,1/4,0)t,(1/4,1/4,1)t, and (1/4,1/4,1/2)tat the Co L2,3edges (770–800 eV) were within 91–96 °, 143–160 °, and 103–109 ° ranges, respectively. On the other hand, Co L2,3-edge polarization-dependent x-ray absorption spectroscopy (XAS) spectra of the crystal La1.5Ca0.5CoO4.02(1,1,0)twere measured in total-electronyield (TEY) mode with incident light polarization εc (ε⊥c) at the HECTOR XMCD end station of the BOREAS beamline at room temperature under no applied magnetic field. FIG. 1. (a) Experimental configuration of the BOREAS magnetic scattering end station at ALBA operating in a horizontal scattering geometry. The incident x-ray polarization ˆεσis perpendicular to the scattering plane and ˆεπis parallel to the scattering plane. (b) Experimental configuration of the I10 magnetic scattering end station at Diamond operating in a vertical scattering geometry. The incident (ˆεi) and scattered (ˆε s) x-ray polarization vectors are defined by χand η, respectively and the ˆuivectors define a basis for the magnetic structure. χ(η)=0◦and χ(η)=90◦correspond to an incident (scattered) beam with σand πpolarization, respectively. In both scattering reference frames, ˆ kand  kare the incident and scattered wave vectors and 2θis the scattering angle of the magnetic reflection. III. RESULTS The experiments were performed on a specimen previously characterized by synchrotron x-ray powder diffraction [12]. The pattern at room temperature agrees with a tetragonal lattice (space group I4/mmm) without significant splitting of diffraction peaks (Supplemental Material Fig. S1 [23]). However, the presence of a superstructure peak at temperatures up to 523 K that vanishes at 623 K [23] reveals that the cell is no longer tetragonal (see inset of Fig. S1). This is consistent with a previous report [26] that revealed a tiny orthorhombic distortion compatible with the space group A2mm using the convergent-beam electron diffraction technique. A2mm is a subgroup of I4/mmm with the following transformation matrix of their lattice parameters: ao=(1,1,0)t,bo= (−1,1,0)tand co=(0,0,1)t. This tetragonal to orthorhombic structural transition is related to the CO differentiating two Co ions with different charge [10–12,26]. This type of transition was also reported for La1.5Sr0.5CoO4despite no clear transition being determined but the CO state persisted at least up to 600 K [7,27]. Magnetic properties were also measured in our single crystal [23] (see Fig. S2). Magnetic anisotropy is observed between the measurements carried out with the external field parallel or perpendicular to the caxis. In both cases, the 184422-3 G. SUBÍAS et al. PHYSICAL REVIEW B 103, 184422 (2021) temperature dependence of the magnetic susceptibility shows a peak at 69 K indicating the onset of a magnetic phase transition typical of an AFM ordering. These properties agree with the ones reported for similar crystals [13,26]. A. Resonant magnetic x-ray scattering Figure 2compares Co L2,3XAS spectra and the energy dependence of the RMXS intensity at (1/4,1/4,0)t, (1/4,1/4,1/2)t, and (1/4,1/4,1)treflections across the Co L2,3edge at 20 K, below TN. The linearly polarized XAS spectra [Fig. 2(a)] show similar spectral features to those observed [14]intheCo2pXAS spectra of La1.5Sr0.5CoO4.The spectra are dominated by the Co 2pcore-hole spin-orbit coupling which splits the spectrum roughly in two parts, namely, the L3(E≈776–784 eV) and L2(E≈793–797 eV) white line regions. As for the RMXS spectra, we observe the occurrence of strong resonances at the Co L3edge but no resonant features can be roughly seen at the Co L2edge that resembles very much the resonant spectral line shape of Co2+-based oxides [28]. In addition, RMXS spectra of the three studied magnetic reflections show the same spectral features [Fig. 2(b)–2(d)]. We have compared the energy dependent RMXS spectra with a simulation obtained by |f m|2+|f m|2, taking into account that the imaginary part of the magnetic scattering amplitude (f m) is proportional to the x-ray magnetic circular dichroism (XMCD) data [29] and the real f mand imaginary f mparts are related to each other by a Kramers-Kronig transformation (inset of Fig. 3). Figure 3compares the measured RMXS spectrum at Q=(1/4,1/4,1/2)t, corrected from self-absorption effects by multiplying it by the average XAS line shape, with the spectrum simulated using the experimental XMCD data of a polycrystalline La1.5Sr0.5CoO4.02 sample measured at 300 K at an applied magnetic field of 6 T as f m.Thesimulated RMXS spectrum reproduces the experimental one quite well suggesting that both RMXS and XMCD signals should originate from the same Co electronic and magnetic state. Furthermore, the XMCD is also almost zero at the Co L2edge while it is largely negative at the L3edge (inset of Fig. 3). This is a direct indication that the orbital contribution to the Co magnetic moment must be important [30]. The unquenched orbital moment in Co oxides has been closely related to the high-spin Co2+3d7electronic configuration [28,30]. Therefore, the three resonant reflections are originated by the same Co electronic structure that is the high-spin Co2+. The temperature evolution of the integrated intensity of the three resonant reflections at the maximum of the Co L3 edge (778.5 eV) is displayed in Fig. 4. All three reflections disappear above ∼55 K, consistent with the onset of the antiferromagnetic ordering deduced from the magnetic susceptibility data (see the Supplemental Material [23]). This points to a magnetic origin of these resonant reflections. However, we observe a clearly different thermal behavior between the magnetic ordering with Q=(1/4,1/4,1/2)tand those with Q=(1/4,1/4,L)twith Linteger. The magnetic resonant contribution for (1/4,1/4,1/2)tstrongly increases below 55 K and maximizes at T≈40 K. On the other hand, the intensity for both (1/4,1/4,1)tand (1/4,1/4,0)treflections show a smoother increase, saturating at a lower temperature of 30 K. We note here that all reflections were FIG. 2. Total-electron-yield Co L2,3edges x-ray absorption spectra measured at room temperature (a) and energy dependence of the (1/4,1/4,0)tmagnetic reflection intensity at 20 K across Co L2,3 edges of La1.5Ca0.5CoO4.02 (1, 1, 0) single crystal for σ(broken lines) and π(solid lines) incident x-ray polarizations (b). Energy dependence of the (1/4,1/4,1/2)t(c) and (1/4,1/4,1)t(d) magnetic reflection intensities at 20 K across Co L2,3edges for σincident x-ray polarization. 184422-4 MAGNETIC ORDERING IN … PHYSICAL REVIEW B 103, 184422 (2021) FIG. 3. Co L2,3energy scan of the RMXS intensity in La1.5Ca0.5CoO4.02 at Q=(1/4,1/4,1/2)tafter correction for selfabsorption effects compared to a simulated RMXS spectrum obtained from the measured XMCD signal. The inset shows the real and imaginary parts of the magnetic scattering at the Co L2,3edges in La1.5Ca0.5CoO4.02. normalized to their value at base temperature in Fig. 4but the (1/4,1/4,1/2)treflection shows about ten times larger intensity than the other two analyzed reflections, namely (1/4,1/4,0)tand (1/4,1/4,1)t. Therefore, we can conclude that two different magnetic ordered phases are present in La1.5Ca0.5CoO4.02, even if both can be associated to the same high-spin Co2+electronic ground state. The amplitude of a RMXS signal depends anisotropically on the direction of the magnetic moments. Thus, we performed a polarization analysis of the three resonant reflections to first unambiguously prove their magnetic character and second determine the orientation of the Co2+magnetic moment. In the case of CoL2,3electronic dipole transition, the resonant scattering form factor for a single magnetic ion at site jis to first order given by fj(E)=f0·(ˆε∗ s·ˆεi)−if 1(ˆε∗ s׈εi)·ˆmj,(1) where ˆεiand ˆε sare the polarization unit vectors of the incident and scattered x rays, respectively; the f0and f1terms are the FIG. 4. Temperature dependence of integrated intensities of magnetic reflections with q=(1/4,1/4,0)t(blue circles), q= (1/4,1/4,1)t(red squares), and q=(1/4,1/4,1/2)t(black diamonds) at the maximum of CoL3edge. All reflections were normalized to their value at base temperature (∼20 K) for comparison. charge and linear magnetic part of the energy-dependent resonant amplitude, respectively, and ˆmjis the unit magnetization vector at the jth site. The f0term describes the anomalous charge scattering and the f1term accounts for the resonant magnetic scattering (f m+if m). Although f0and f1terms are energy dependent, we can take them as constant since the xray energy is fixed during the polarization analysis. Therefore, the structure factor for a resonant magnetic reflection becomes just a function of the momentum transfer, given by the scattering vector Q=k−k, where k(k) is the wave vector of the incident (scattered) x rays, F(Q)∝ j fjexp(iQ·rj),(2) where the summation is over the Co sites with position vector rj. For a collinear antiferromagnetic order, all the Co magnetic moments are parallel to a unique axis and the polarization dependence of the magnetic scattering is the same as for a single Co site in Eq. (1). Furthermore, as it will be mentioned later, the scattered intensity for the three measured reflections in the σ−σpolarization channel is zero so the anomalous charge scattering amplitude is strictly zero and the structure factor gets reduced to F(Q)∝−iF1(ˆε∗ s׈εi)·ˆ M(3) with F1=jexp(iQ·rj)·f1and ˆ Mthe unit magnetization vector. Thus, the dependence of the scattered intensities (proportional to F2) on the incident and scattered polarization vectors and the Co magnetic moment direction can be easily modelled. The general orthogonal coordinates frame (ˆu1,ˆu2,ˆu3) used in resonant magnetic x-ray scattering [31–33] has been considered for our polarization analysis [Fig. 1(b)]. The components of ˆ Mare defined in standard spherical coordinates by the polar (β) and the azimuth (γ) angles with respect to the direction of the scattering vector Qand a direction −ˆu1in the perpendicular plane [Fig. 1(b)]. The incident (ˆεi) and scattered (ˆεs) x-ray polarization vectors are defined by χand ηangles, respectively. We have then fitted the experimental polarization analysis curves for the three magnetic reflections at the CoL3 edge using Eq. (3) for the structure factor with βand γangles as the only fitting parameters. Figure 5shows the experimental scattered intensities at the maximum of the Co L3edge (778.5 eV) for the (1/4,1/4,0)t reflection as a function of the incident x-ray polarization vector defined in the scattering frame by the χangle [Fig. 1(b)]. The experimental dependence follows a sinusoidal behavior with χ=0◦and χ=90◦corresponding to an incident beam with σand πpolarization, respectively. The total scattered intensity is almost independent of the incident x-ray polarization χfor the (1/4,1/4,0)treflection [Fig. 5(a)], which is a clear indication that the Co magnetic moment should lie almost along the scattering vector. In this crystal, the scattering plane contains the −ˆu3=[1,1,0]tand −ˆu1=[1,−1,0]tcrystallographic directions whereas the ˆu2=[0,0,1]tcrystallographic direction is perpendicular to the scattering plane [Fig. 1(b)]. In this experimental configuration, the polar (β) and the azimuth (γ) angles are defined with respect to the [1,1,0]tand the 184422-5 G. SUBÍAS et al. PHYSICAL REVIEW B 103, 184422 (2021) 0 30 60 90 120 150 180 0.0 0.2 0.4 0.6 0.8 1.0 Scattered Intensity (arb. units) Fangle (degrees) (1/4, 1/4, 0) t (a) 0 30 60 90 120 150 180 0.0 0.2 0.4 0.6 0.8 1.0 K=0º K=90º Scattered Intensity (arb. units) F angle (degrees) (b) (1/4, 1/4, 0) t FIG. 5. Full polarization analysis of the (1/4,1/4,0)tmagnetic reflection at 20 K. In top panel (a), total scattering intensity is recorded at the maximum of the Co L3edge as a function of the incident x-ray polarization χ. Circles denote the experimental data whereas red lines are the best fitted curves. Alternatively, in bottom panel (b), the Co L3edge scattered intensity is plotted as a function of χfor two different ηpositions of the multilayer analyzer. [1,−1,0]tcrystallographic directions, respectively. The best fit for the orientation of the magnetic moment in this crystal yielded β=3(1)◦and γ=75(5)◦. Values in parentheses are estimated errors in the last digit. This indicates that the direction of the Co magnetic moment is along the [110]tcrystallographic direction, i.e., along the diagonal in the tetragonal ab plane, with a likely slight tilt towards the c-axis direction [Fig. 1(b)]. We note here that the La1.5Ca0.5CoO4.02 crystal is twinned in the ab plane so the two domains with Q=[1,1,0]t and Q=[1,−1,0]tare indistinguishable. To verify the accuracy of these results, we have also measured the scattered intensity as a function of the incident x-ray polarization χfor different orientations ηof the multilayer analyzer that serves as an x-ray polarizer [Fig. 1(b)]. Figure 5(b) shows the experimental polarization analysis curves of the (1/4,1/4,0)treflection for two different positions ηof the multilayer analyzer compared to the best fits obtained. χ=η=0◦corresponds to the so-called σ−σscattering channel that leads to systematic extinction according 0306090120150180 0.0 0.2 0.4 0.6 0.8 1.0 (a) K=0º K=50º K=10º K=60º K=20º K=70º K=30º K=80º K=40º K=90º Scattered Intensity (arb. units) F angle (degrees) (1/4, 1/4, 1/2) t 0 30 60 90 120 150 180 0.0 0.2 0.4 0.6 0.8 1.0 (1/4, 1/4, 1) t (b) K=0º K=15º K=30º K=45º K=60º Scattered Intensity (arb. units) F angle (degrees) FIG. 6. Full polarization analysis of (1/4,1/4,1/2)t(a) and (1/4,1/4,1)t(b) magnetic reflections at 20 K. The Co L3edge scattered intensity is plotted as a function of χfor different ηpositions of the multilayer analyzer. Circles denote the experimental data whereas solid lines are the best fitted curves. to the RMXS theory [31–33]. For the (1/4,1/4,0)tresonant reflection, the CoL3experimental scattered intensity in the σ−σchannel was zero, confirming that this reflection is of magnetic origin [Fig. 5(b)]. The orientation of the Co magnetic moments as obtained from the best fits corresponds to β=173(1)◦[or −7(1)◦] and γ=−135(5)◦for (1/4,1/4,0)t. Within the errors, these values agree with Co magnetic moments aligned along almost the same direction as that aforementioned using no polarization analyzer [Fig. 5(a)] but opposite in sign. The experimental full polarization analysis curves of the (1/4,1/4,1/2)tand (1/4,1/4,1)treflections are plotted in Fig. 6as a function of the incident and scattered x-ray beam polarization vectors, denoted by χand η, respectively. Best fit calculated curves are also shown in Fig. 6. Again, a sinusoidal behavior was found in both cases and the Co L3experimental scattered intensity in the σ−σchannel (χ=η=0◦) was zero, confirming that both (1/4,1/4,1/2)t and (1/4,1/4,1)twere also magnetic reflections. The best fit for the orientation of the Co magnetic moments yielded β=156.8(1)◦[or −23.2(1)◦] and γ=−250(5)◦ 184422-6 MAGNETIC ORDERING IN … PHYSICAL REVIEW B 103, 184422 (2021) TABLE I. Fractional atomic coordinates and anisotropic temperature factors (Å2)oftheLa 1.5Ca0.5CoO4.02 single crystal obtained from Rietveld analysis of neutron diffraction data at room temperature. The x coordinate of Co1 was fixed as origin. The lattice parameters are a=5.4247(1) Å, b=5.4128(1) Å, and c=12.3702(2) Å. The reliability factors of the fit were RF=0.029 and Rw=0.039. Co1 Co2 La/Ca1 La/Ca2 O1basal O2basal O3apical O4apical x0 0.503(6) 0.003(5) 0.503(4) 0.242(5) 0.751(5) 0.000(5) 0.499(4) y0 0.5 0 0.5 0.2494(5) 0.7542(5) 0 0.5 z0 0 0.36145(5) 0.36221(5) 0 0 0.16681(7) 0.17375(8) B11 0.004(2) 0.003(2) 0.0051(6) 0.0040(6) 0.002(2) 0.004(2) 0.0114(9) 0.0157(9) B22 0.0020(3) 0.0024(3) 0.0050(1) 0.00051(1) 0.0039(3) 0.0043(3) 0.0113(2) 0.0156(2) B33 0.0009(1) 0.0011(1) 0.0008(1) 0.0007(1) 0.0023(2) 0.0019(1) 0.0012(1) 0.0013(1) B12 00 0 0−0.0015(7) 0.0005(6) 0 0 B13 00−0.0006(2) −0.0006(2) 0 0 0.0012(4) −0.0002(4) B23 00 0 0 0 0 0 0 for the (1/4,1/4,1/2)treflection [Fig. 6(a)]. Meanwhile, β=136(1)◦[or −44(1)◦] and γ=−272(5)◦were found for the (1/4,1/4,1)treflection [Fig. 6(b)]. The dependence of the total scattered intensity of the (1/4,1/4,1/2)tand (1/4,1/4,1)treflections upon the incident x-ray polarization χwas also measured for completeness (Fig. S3 [23]), giving consistent results with the aforementioned full polarization analysis [23]. For these two single crystals with Q=(1/4,1/4,1/2)t and Q=(1/4,1/4,1)t, only the crystallographic direction of the scattering vector is known in the experimental configuration. Thus, only the refined polar (β) angles can give us information on the orientation of the magnetic moment within the crystallographic unit cell for the (1/4,1/4,1/2)tand (1/4,1/4,1)tmagnetic reflections. We recall here that the polarization analysis of the (1/4,1/4,0)treflection showed that the Co magnetic moments lie almost along the [1,1,0]t crystallographic direction. To check if the same orientation of the Co magnetic moments is found for the other two magnetic orders, we have calculated the angles formed between the [1,1,0]tand either the [1,1,2]tor the [1,1,4]t crystallographic planes. These angles are 23.7 ° and 41.3 °, respectively and agree within the error with the polar βangles deduced from the best fits of the polarization analysis curves of the (1/4,1/4,1/2)tand (1/4,1/4,1)tmagnetic reflections. Therefore, the orientation of the Co magnetic moments we derive is—within the errors—the same for the three magnetic orders, i.e., along a diagonal of the tetragonal ab plane slightly off-tilted along the caxis. B. Neutron diffraction The structure analysis at room temperature was performed using single crystal neutron diffraction since this technique is more sensitive to the position of oxygen atoms than xray diffraction. The crystal symmetry at 295 K is confirmed as orthorhombic with aand baxes almost equal in length. The observed reflections agreed with an A-centered lattice arising from the distortion of the high temperature cell with ao≈√2at. The crystal is heavily twinned in the ab plane. The A-centering cell implies some extinction rules (k+l= 2n+1 and the comparison of the reflections allowed by each domain indicates that the crystal seems to have a perfect twinning with an even ratio of the two domains. Following previous studies [26], the experimental data were refined using the space group symmetry A2mm (no. 35, standard setting Cmm2). The results yielded by the best fit are summarized in Table I. These results are similar to those published by Horigane et al. [26] but we observe a minor polar distortion in our sample. In fact, our experimental data can be fitted using the centrosymmetric space group Ammm with similar accuracy. If we look at the errors derived for xcoordinates (Table I), only one basal oxygen atom significantly shifts from the inversion center position. In the previous report [26], this happened with the apical oxygen atoms. We have applied a symmetry mode analysis using the AMPLIMODES program [34] to gain insights into the transition from the high temperature phase into the orthorhombic one. Table II shows the mode decomposition for this transition with a comparison of the normalized amplitudes between the two refinements. In both cases, the primary mode for the transition belongs to the irrep X1+while modes belonging to the irreps GM1+and X4− are secondary. The main difference between both refinements concerns the value of the polar modes belonging to the irrep GM5−, which are larger for the data reported by Horigane et al. [26] although the estimated error in these modes is much higher than in the rest (around 36%). The global distortion calculated for this transition is small, 0.12 and 0.17 Å for the data reported by this study and by Horigane et al. [26], respectively. That small distortion was consistent with the difficulty in detecting it using x-ray diffraction techniques [23]. Our refinement distinguishes two distinct Co environments that give rise to two types of CoO6octahedra. Co1O6is compressed with the following interatomic TABLE II. Summary of mode decompositions of the A2mm structure with respect to the parent I4/mmm structure of La1.5Ca0.5CoO4.02 reported in this work and in Ref. [26]. Amplitude (Å) This Horigane Kvector Irrep Direction Dim. work et al. [26] (0,0,0) GM1+(a) 2 0.028 0.022 (0,0,0) GM5−(a,a) 5 0.055 0.105 (1/2,1/2,0) X1+(a,−a) 4 0.103 0.119 (1/2,1/2,0) X4−(a,−a) 3 0.013 0.049 184422-7 G. SUBÍAS et al. PHYSICAL REVIEW B 103, 184422 (2021) distances: Co1-O1 =1.883(19) Å, Co1-O2 =1.896(19) Å, and Co1-O3 =2.0635(9) Å. Co2O6is expanded with longer bond lengths: Co2-O1 =1.961(30)Å, Co2-O2 = 1.924(29) Å, and Co2-O4 =2.149(1) Å. The bond valence sum (BVS) method was used to estimate the charge disproportionation between the two nonequivalent Co sites. Using the reference parameters [35]forCo 3+, BVS calculation yields oxidation state values of +2.65(5) and +2.25(7) for Co1 and Co2, respectively. However, using the reference parameters [36]forCo 2+, the results are +3.05(5) and +2.61(7), respectively. Both calculations agree with a checkerboard pattern of compressed and expanded CoO6octahedra with a charge segregation of 0.44(7) electrons between the two Co sites, in agreement with previous reports [11,12]. If we average out the two calculations, we obtain +2.43(7) for Co2 and +2.87(5) for Co1 as oxidation states, in excellent agreement with our previous spectroscopic results [12]. Figure 7shows different Qscans performed at 2 K in the single crystal with surface normal to the [1,1,0]tdirection. Charge-superstructure reflections are shown in Fig. 7(a) in the Qscan along the [1,0,L]Odirection referred to the orthorhombic cell (indicated by the subscript O)astheirintensity remains almost constant upon heating up to 55 K [Fig. 7(c)]. We note here that the tetragonal (h/2,h/2,l)tand (h/2,−h/2,l)treflections transform into the orthorhombic (h,0,l)Oand (0,k,l)Oones, respectively. Due to the symmetry conditions of the A2mm space group, the (0,k,l)O reflections are only allowed for k+l=even while the (h,0,l)Oones are allowed for l=even. We observe structural reflections for both L=even and L=odd, as expected for a crystal with perfect twin structure. On the other hand, the magnetic contribution appeared in the neutron patterns below 55 K [Fig. 7(c)]. The new magnetic peaks follow the propagation vector k1=(1/2,0,1/2)Oas shown in Fig. 7(b). There is no indication of any other type of magnetic contribution as no (1/2,0,l)Oreflections with linteger were detected [Fig. 7(b)]. This result is at odds with a previous report [26] and our own results using the RMXS technique (see previous section). Therefore, we decided to mount the single crystal with a polished (1,1,4)tface where (1/2,0,l)Owith linteger magnetic peaks had been detected by RMXS. The results were identical to the previous crystal and we only detected the same family of (h/2,0,l/2)Omagnetic peaks. In order to analyze the magnetic structure, the strong twinning should be taken into account since we detected both (h/2,0,l/2)Oand (0,k/2,l/2)Osets of magnetic peaks, each one coming from one of the two domains. Accordingly, it is hard to differentiate between the two possible k1= (1/2,0,1/2)Oor k 1=(0,1/2,1/2)Opropagation vectors in a crystal with a perfect twinning. In the case of k1, the basic IRREPS of the A2mm space group offer two possible solutions, either the moments of the magnetic atom (Co2+like) are coupled antiferromagnetically along the orthorhombic b axis or they are within the ac plane. The refinements clearly opt for the second option with the moments mainly aligned along the aoaxis with a small tilt in the cdirection. It is noteworthy that as A2mm is a noncentrosymmetric group, the propagation vector k1is not equivalent to −k1and the occurrence of two propagation vectors within the first Bril0 200 400 600 800 1000 1200 1400 02468 Intensity (counts) Q-scan (a) (1 0 L)O 0 200 400 600 800 1000 012345 Intensity (counts) Q-scan (b) (1/2 0 L) O 0 5 10 15 20 25 10 20 30 40 50 60 Intensity (counts/sec) T (K) (1, 0 ,2)O (1/2, 0, 3/2)O (1/2, 0, 1/2)O (c) FIG. 7. Reciprocal space (Q) scans along the [1,0,L]O(a) and [1/2,0,L]O(b) directions at 2 K in La1.5Ca0.5CoO4.02 single crystal. (c) Temperature variation of intensities of structural (1,0,2)O and magnetic (1/2,0,1/2)Oand (1/2,0,3/2)Oreflections. For the sake of clarity, it is noteworthy to remember that (1,0,L)Oand (1/2,0,L)Oorthorhombic reflections are equivalent to (1/2,1/2,L)t and (1/4,1/4,L)ttetragonal ones. louin zone makes it hard to differentiate phase shifts between both vectors by diffraction techniques. In our case, the magnetic cell is commensurate and we have considered the same magnetic moment for all the Co2+-like sites in the cell in agreement with the RMXS results. The magnetic cell can be seen in Fig. 8. Regarding the orthorhombic ab plane, the 184422-8 MAGNETIC ORDERING IN … PHYSICAL REVIEW B 103, 184422 (2021) FIG. 8. Schematic view of the refined magnetic structure for the La1.5Ca0.5CoO4.02 sample. For clarity, we only show Co atoms and basal oxygens. magnetic ordering is the result of the AFM superexchange Co2+-O-Co3+-O-Co2+interaction (see later in the Discussion section). The magnetic structure shows an AFM alignment in one of the orthorhombic axes but FM in the other. Along the caxis, there is an AFM coupling between next-neighbor planes of Co2O6octahedra, i.e., between Co2+-like cations with z=0 and z=1/2(orz=1/4 and z=3/4). Accordingly, any Co2+-like moment displays an even mixture of FM and AFM couplings along this direction adopting a ↑↑↓↓ structure (see Fig. 8). Finally, one must bear in mind that if the propagation vector were k 1=(0,1/2,1/2)O, the results would be orthogonal to those indicated in Fig. 8. The ordered magnetic moment on the Co atom at 2 K in the antiferromagnetic phase is μ=2.35(5)μBwith refined components μx=2.35(5) and μz=0.13(6)μB. This value is lower than the effective paramagnetic value obtained by the Curie-Weiss law in our recent x-ray absorption and emission spectroscopic study, which shows that its angular moment is not completely quenched [12]. This study showed that the charge disproportion in La1.5Ca0.5CoO4.02 is not complete and Co2+-like atoms in this compound are found to be in a mixed-valent state Co+2.4with holes mainly located in Co 3d-O2phybridized states. These covalent effects probably result in a reduced ordered magnetic moment. It is interesting to underline that similar values of ordered magnetic moments have been obtained from neutron diffraction for related highspin Co2+double-perovskites that are always lower than the corresponding effective paramagnetic moments [37]. IV. DISCUSION AND CONCLUSIONS We first discuss the disparity of results obtained by neutron diffraction experiments between the work of Horigane et al. [26] and the present study. In a second step, we comment on the inputs provided by our study using the combination of two different but complementary techniques in the same single crystals. Horigane et al. [26] reported on the occurrence of magnetic reflections in a La1.5Ca0.5CoO4crystal following two different propagation vectors: (1/2,0,1/2)Oand (1/2,0,0)O. These two types of magnetic peaks were only observed in a single specimen because underdoped samples (Ca content less than x=0.5) only show magnetic peaks ascribed to the k1=(1/2,0,1/2)Ovector whereas overdoped compounds (x>0.5) only display magnetism associated to the k2=(1/2,0,0)Ovector. In addition, similar changes are observed when the Co sublattice is slightly doped. Thus, doping with Cr stabilizes one type of magnetic reflections, (h/2,k,l/2)O, while doping with either Mn or Fe gives place to only (h/2,k,l)Omagnetic reflections [38]. The uniqueness of the La1.5Ca0.5CoO4specimen suggested that it was located at a critical point in the phase diagram where various types of magnetic arrangements are able to coexist. Furthermore, they reported on a third type of (h/4,k/4,l/2)Omagnetic reflections suggesting that Co3+should be also magnetic. Nevertheless, our present neutron diffraction measurements on two La1.5Ca0.5CoO4.02 single crystals only detected one type of magnetic contribution ascribed to either k1= (1/2,0,1/2)Oor k 1=(0,1/2,1/2)Opropagation vectors. On the other hand, RMXS experiments could successfully detect (1/2,0,1/2)O,(1/2,0,0)O, and (1/2,0,1)Omagnetic peaks suggesting the occurrence of two magnetic phases, one of them hidden to neutron diffraction. In addition, the spectral shape of the RMXS spectra clearly concurs with the contributions of only HS Co2+cation without any trace of the participation of Co3+cations in the magnetic order for any of the two magnetic phases. Our previous spectroscopic study on the Co electronic (valence and spin) state of the La2−xCaxCoO4series disclosed that the electronic state of Co is very similar for all 0.3⩽x⩽0.7 compounds [12]. Co is in a fluctuating mixed valence state in the high temperature phase and below the CO transition, a partial charge disproportionation [δ≈0.5(1)] leads to a checkerboard pattern of two distinct Co atoms. Therefore, we can conclude that the magnetic structure change between underand overdoped samples cannot be ascribed to changes of the Co electronic state. Instead, we have observed the key role of the oxygen sublattice to modulate the charge ordering along this series, in agreement with the results previously reported for the Sr half-doped compound, where a significant hole density in the O2pstates was concluded [14]. Oxygen excess as interstitial oxygen around the La/Ca atoms is observed in underdoped samples while oxygen vacancies at the apical position are noticed in overdoped samples. Our La1.5Ca0.5CoO4.02 crystal has a small oxygen excess so a ground magnetic state similar to that found in underdoped samples with k1=(1/2,0,1/2)O propagation vector is a consistent result. On the other side, vacancies are usually formed on the oxide’s surface. In such a case, sharp surface regions with oxygen vacancies can be magnetically ordered following the k2=(1/2,0,0)Opropagation vector as it happens in overdoped samples. The RMXS technique is very sensitive to surface properties (including magnetism) but it does also prove the magnetic order of the bulk crystal. Neutron diffraction, instead, is only sensitive 184422-9