Revealing orbital and magnetic phase transitions in Pr0.5Ca0.5MnO3 epitaxial thin films by resonant soft x-ray scattering

We report the study of magnetic and orbital order in Pr 0.5 ?> Ca 0.5 ?> MnO 3 ?> epitaxial thin films grown on ( LaAlO 3 ) 0.3 ?> – ( SrAl 0.5 ?> Ta 0.5 ?> O 3 ) 0.7 ?> . Resonant soft x-ray scattering revealed significant modifications of the magnetic order in the film as compared to the bulk. Namely (i) a different magnetic ordering wave vector, (ii) different spin directions and (iii) an additional magnetic reordering transition. We demonstrate that an analysis of the resonant scattering which is based solely on local symmetries and which does not involve a modeling of energy-dependent lineshapes allows to extract this detailed microscopic information. This approach significantly simplifies the analysis and interpretation of resonant scattering data.


Introduction
Hole-doped perovskite manganites − R A x x 1 MnO 3 , where R is a rare-earth ( = R La, Nd, Pr) and A is an alkaline-earth atom (A = Sr, Ba, Ca) have attracted much attention because they exhibit remarkable physical properties such as colossal magnetoresistance and complex electronic ordering phenomena [1][2][3][4][5][6][7][8]. For the latter, the half-doped manganites provide a particularly prominent and extensively studied example, namely the so-called CE-phase [9]. This phase is commonly discussed in terms of cooperative spin, charge and orbital order, where ferromagnetic zig-zag chains are formed, which are coupled antiferromagnetically to each other. Although the detailed microscopic structure of this electronic order remains to be fully understood [10,11], it is clear that it couples strongly to the lattice via the orbital degree of freedom. Epitaxially strained thin films thus enable one to tune the electronic ordering properties in the doped manganites and to engineer their electronic properties. It is therefore very important to investigate and understand the electronic modifications in doped manganite films, which can be dramatic. For example, it was recently shown that epitaxial strain effects can control charge ordering (CO) in thin films of Mn oxides [12,13]. A transition between CO and ferromagnetic metallic states was observed in Nd 0.5 Sr 0.5 MnO 3 films on SrTiO 3 (011) c substrates, whereas Nd 0.5 Sr 0.5 MnO 3 films on SrTiO (001) c 3 substrates exhibit only insulating behavior at all temperatures [12]. Here the substrate orientation is given in the standard cubic notation as indicated by the subscript c. Also in Pr Ca MnO 3 films on LSAT (001) c substrates have a much higher CO transition temperature around 300 K [13].
Here we present a resonant soft x-ray scattering (RSXS) study of the electronic order in Pr Ca MnO 0.5 0.5 3 thin films grown epitaxially on LSAT (011) c . RSXS at the Mn p 2 edge has been shown to provide a unique means to study ordered states in Mn oxides [14][15][16][17][18][19][20]. Non-resonant x-ray scattering is dominated by charge scattering and the relative intensity of magnetic scattering to charge scattering is ω , where ω is the x-ray energy and m c e 2 is the electron mass. In RSXS one can obtain a strong magnetic signal by using a large spin-orbit splitting (∼10 eV) in p 2 core levels of the d 3 transition metals. This technique is especially suitable for studying the magnetic structures in small samples due to the large resonant enhancement and the high photon flux at present synchrotron radiation sources. Consequently it has been successfully applied to reveal the magnetic orderings in thin films of non-collinear magnetic NdNiO 3 [21] and multiferroic YMnO 3 [20]. Our results show that the microscopic magnetic order in films can differ significantly from that of the corresponding bulk materials, and indicate that epitaxial strain couples to the spin order via the orbital degrees of freedom, which provides a potential route towards tuning the magnetic properties of doped manganite films.

Experiment
Pr Ca MnO 0.5 0.5 3 thin films with the thickness of 40 nm were grown on LSAT (011) c substrates by pulsed laser deposition. Details of the fabrication and characterization of the thin films were described elsewhere [13]. RSXS experiments at the Mn p 2 edge were performed at the BESSY undulator beamline UE46-PGM1 and 10ID-2 (REIXS) of the Canadian Light Source [22] in a horizontally scattering geometry. Scattering spectra were measured using horizontally (π) or vertically (σ) polarized light. We will refer to the resonant intensity measured in the π σ → ′, π′ and σ σ → ′, π′ channels as π I and σ I , respectively (primes denote the polarization of the scattered x-rays). The pressure during measurements was below × − 5 10 9 Torr, and the temperature was varied between room temperature and 25 K. We also performed x-ray absorption spectroscopy (XAS) measurements in the total-electron-yield mode.
In the following, the HKL ( ) indexes for the film reflections and directions refer to the orthorhombic unit cell of the Pr Ca MnO 0.5 0.5 3 thin film [13]. At this point it is important to realize that the Pr Ca MnO 0.5 0.5 3 thin films contain structural domains with interchanged aand b-axesso-called twin domains. We will refer to these twin domains as D1 and D2, respectively, and designate the reflections and directions of these domains with a corresponding index. Using this convention, the orthorhombic (100) D1 and (011) D1 directions were parallel to the scattering plane as shown in figure 1(a), which corresponds to (010) D2 and (101) D2 of the other twin domain. The coexistence of the domains D1 and D2 is also shown in figure A1 of appendix A. In a scattering experiment, the diffraction patterns of D1 and D2 are superimposed. This means that close to the position of H ( , 0, 0) D1 , the H (0, , 0) D2 reflection can be observed, if it occurs as well. However, because ≠ a b, these two reflections possess slightly different scattering angles. This orthorhombic peak splitting allows the identification of H ( , 0, 0) D1 and H (0, , 0) D2 reflections from the different domains.

Results and discussion
Figure 1(c) shows the temperature dependence of the resonant intensity measured around the (1/2, 0, 0) D1 position with incoming π-polarization. The photon energy was set to 643.6 eV, which corresponds to the Mn p 2 absorption peak (cf appendix). RSXS intensity appears around 210 K and strongly gains intensity with decreasing temperature. This result is in good agreement with the charge/orbital-ordering transition temperature = T 220 CO/OO K reported in [13].
The position of the superlattice peak as a function of temperature is shown in figure 1(d). A clear shift of the peak position is observed at the magnetic ordering temperature T N = 150 K, even though the lattice parameters do not change significantly at this temperature [13]. Above T N and below T CO/OO , the peak position corresponds exactly to the (1/2, 0, 0) D1 reflection, identifying it as the superlattice reflection due to the orbital order in D1. Note that the orbital order causes a doubling of the orthorhombic a-axis only, i.e. the (0, 1/2, 0) D2 does not occur in the orbital ordered phase. However, with the onset of magnetic order below T N , the peak position jumps to (0, 1/2, 0) D2 , implying that the observed intensity is now due to the magnetic order in twin domain D2. As we will discuss further below, the orbital scattering of D1 still exists below T N , but its intensity is much smaller than the magnetic scattering of D2. We can also exclude non-collinear or incommensurate spin arrangements because the observed shift in figure 1(d) is simply due to the different domains with different lattice constants.
The peak widths in figure 1(c) do not show much temperature dependence with almost constant full width at half maximum Δq of Å − 0.01 1 . This gives a common correlation length ξ π Δ = ∼ q 2 / 60 nm of the orbital order along a and the magnetic order along b, which are both comparable to the thickness of the thin film. Figure 2 shows the photon-energy dependence of the intensity observed at the (1/2, 0, 0) D1 position across the Mn p 2 edges at various temperatures using π and σ polarizations. To facilitate a comparison of the lineshapes, panels (c) and (d) show the same data as given in (a) and (b), but this time normalized to the area. As can be observed in figure 2, π I and σ I are of very similar magnitude and exhibit the same lineshapes for 150 < < T K 200 K, i.e. ≃ π σ I I for the orbital (1/2, 0, 0) D1 peak. These lineshapes are reminiscent to that of corresponding bulk materials [14,15,17], supporting interpretation in terms of orbital ordering. However, the present data for the film display differences from those for the bulk, indicative of a modified orbital state. The condition ≃ π σ I I clearly breaks down at 150 K upon cooling: while π I shows a strong increase by a factor of ∼10 accompanied by a clear lineshape change, σ I remains almost unaltered. Furthermore, whereas the peak in π I apparently shifts in position, as described above (cf figure 1), the peak in σ I does not move at T N . Since the additional scattering from D2 sets in at T N , we conclude that it is resonant magnetic scattering of the Mn-sublattice, which corresponds to (0, 1/2, 0) D2 of D2. Interestingly, the magnetic signal is almost entirely restricted to π I , whereas σ I is due to the orbital (1/2, 0, 0) D1 peak of D1. We observe another dramatic change of the RSXS linshapes at = T 75 2 K well below T N . This time, σ I displays clear changes of lineshape and intensity, as shown in figures 2(b) and (d). The variation of σ I across T 2 signals a third phase transition, which has not been reported earlier and is absent in the bulk material. We also note that the resonant magnetic scattering of the film exhibits a lineshape, which is very different from that of related bulk materials [17].
The phase transitions at T N and T 2 are also clearly revealed by the data presented in figure 3(a), which shows π I and σ I integrated over the Mn p 2 3/2 and p 2 1/2 regions. One can see a large increase of the total scattering intensity by a factor of more than 10 in π I around 150 K. This demonstrates the sensitivity of the RSXS-intensity in going from orbital to orbital plus spin order. σ I increases strongly around = T 75 2 K. Following the approach of earlier studies [15,17], we plot the so-called branching ratio as a function of temperature in figure 3(b), which makes the changes at T N and T 2 even more apparent. Branching ratios are defined by the intensity contributions from the Mn p 2 3/2 region divided by that from the Mn p 2 1/2 region [23]. The branching ratios change strongly around 150 K for a π polarization, and similarly around 75 K for a σ polarization. An anomaly of the branching ratio was also reported at T N in the orbital-ordered peak of layered manganites La Sr MnO 0.5 1.5 4 [17], but the anomaly is much smaller, and it is related to T N while the large anomaly we observe is well below T N and so has a very different origin. Note that the existence of these phase transitions was not observed by macroscopic measurements (see the appendix), showing the advantage of RSXS for studying the magnetic structures in thin films.
In order to gain a better understanding of the experimental results, we have investigated the resonant structure factor F at the Mn p 2 edges. Referring to the standard model of the CE-phase, we describe the so-called   gives σπ′-and πσ′-scattering only and yields = π σ I I , which is identical to previous results and in good agreement with the present experiment.
A more interesting situation arises when orbital and magnetic order coexist ( < T T N ). As discussed above, the shift in position accompanying the increase of π I implies that the additional intensity has to be attributed to the magnetic (0, 1/2, 0) superlattice peak. The structure factor of this magnetic reflection is given byˆ=ˆˆ+ˆˆ· These terms are related to the circular magnetic dichroism in XAS [24], i.e. the (0, 1/2, 0) reflection is given by terms odd in s as it should be.
Comparing temperatures. In contrast to this, the lineshape in π I does change dramatically with the onset of magnetic order, due to the strong additional magnetic intensity stemming from the (0, 1/2, 0) D2 peak. The changed lineshape is easily explained qualitatively by the different fundamental spectra, which enterF orb andF mag .
Furthermore, the experimental results show that for T N > > T T 2 the magnetic intensity is almost exclusively confined to π I , while there is almost no magnetic scattering in σ I . This very specific feature of the magnetic scattering provides information about the spin directions in this temperature range: we first note that, since ≪ , (cf [24]), we can take the approximationˆ=F F (1) , which yields (see the appendix) and corresponds to an easy axis close to ϕ φ = s (cos , sin , 0) 0 with ϕ =°110 . Note that the spin orientation determines how the different fundamental spectra contribute to the total intensity. In other words, the RSXS lineshape of σ I and π I depends strongly on the directions of the ordered spins. From this we conclude that the dramatic changes of σ I below T 2 are due to a spin reorientation, which results in ≠ σπ′ A 0.

Summary
In summary, we performed RSXS studies of the orbital and magnetic order in Pr Ca MnO 0.5 0. 5 3 thin films grown on LSAT (011) c substrates. The different scattering angles together with the polarization and energy-dependent lineshapes enable us to separate the orbital and magnetic scattering originating from different twin domains. We find clear differences between the half doped bulk materials and the studied film samples: (i) the magnetic (0, 1/2, 0) modulation of the thin film is different from the (0, 1/2, 1) modulation observed for the bulk CE-phase. In contrast to the bulk materials, the film exhibits ferromagnetic spin correlations along the c-axis. (ii) We observe an additional spin reorientation transition at T 2 . These modifications of the magnetic structure of the PCMO film might be a result of the epitaxial strain. However, we cannot exclude slight deviations in the stoichiometry away from half doping, which could have similar effects [9]. Nonetheless, our study demonstrates that RSXS combined with an analysis based on solely local symmetries allows to extract detailed microscopic information about electronic order even in thin film samples. Specifically, we not only determine the magnetic ordering wave vector, but also learn about the spin directions by using this symmetry-based approach. The direct relationship between the RSXS lineshape and the spin orientation is new and will surely be very useful in future analyses and theoretical studies.
Even more information, however, could be extracted from a detailed lineshape analysis, and this is also expected to answer the question of the exact nature of the ordered states as proposed in [10,11]. On the one hand, the present study clearly shows that such a spectral shape analysis obviously cannot be done in the simple and much used spherical approximation, in which the non-spherical local symmetry of the scatterers in a crystalline environment is neglected. On the other hand, a full calculation including the local spin, orbital, and charge as well as the local hybridization with the O orbitals and probably more than a single Mn site in a cluster [25] leads to a rather complicated problem. This is why the above analysis, which is based only on symmetries and selection rules, is so important.
The calculation of the structure factor for the ordered phase starts from the expressions derived in [24] for the resonant scattering length in D h 4 and O h symmetry. The former point symmetry is assigned to the + Mn 3 site and the latter to the + Mn 4 site, respectively. All 16 Mn sites within the CE unit cell are taken into account [26,27], whereas small shifts of the lattice sites away from the high-symmetry positions and tilts are neglected. Different from the standard CE-order we assumed ferromagnetic spin correlations along the orthorhombic c direction (Pbnm setting).
The polarizations e i f , and the spin directionsŝ l are expressed in the local coordinate system of the Mn sites given by x, y, z, where x, y, and z are along the Mn-O bond directions of the octahedron and z is parallel to the orthorhombic c-direction. Using the unit vectorŝ =ū (1 1 1) 3 1 (within the scattering plane),ˆ=ū (1 1 2) 6 2 (perpendicular to the scattering plane) andˆ= u (1 1 0) 2 3 (along the scattering vector), which are also expressed referring to x, y, and z, the polarization vectors of the incoming and outgoing beam are written as = =′ σ σ u e e 2 , ϑ ϑ =ˆ+π u u e sin cos 1 3 , and ϑ ϑ = −ˆ+′ π u u e sin cos 1 3 , where ϑ ≃°60 is the Bragg-angle of the (1/2, 0, 0)/(0, 1/2, 0) reflection at the Mn p 2 edge. In order to describe the orbital ordering, the resonant structure factors in D h 4 with the C 4 -axis along x and y are needed. In the specific case of − − x r y r 2 orbital order, this axis is perpendicular to the occupied orbital. It is important to note here that the current analysis holds for both cases and does not depend on the specific type of orbital order. It also does not make any assumptions about the size of the charge disproportionation δ, which describes occurrence of x , where R x (R y ) describes a π /2-rotation about x (y). With these conventions we obtain for the (1/2, 0, 0) orbital order reflection:  This means that there is a spin-dependent contribution to the orbital ordering peak, which is given byF (2) . However, since we do not observe strong changes in the lineshape of σ I below T N , the contribution due toF (2) seems to be small. For the magnetic (0, 1/2, 0) superlattice peak