Selective interlayer ferromagnetic coupling between the Cu spins in YBa2Cu3O7−x grown on top of La0.7Ca0.3MnO3

Studies to date on ferromagnet/d-wave superconductor heterostructures focus mainly on the effects at or near the interfaces while the response of bulk properties to heterostructuring is overlooked. Here we use resonant soft x-ray scattering spectroscopy to reveal a novel c-axis ferromagnetic coupling between the in-plane Cu spins in YBa2Cu3O7−x (YBCO) superconductor when it is grown on top of ferromagnetic La0.7Ca0.3MnO3 (LCMO) manganite layer. This coupling, present in both normal and superconducting states of YBCO, is sensitive to the interfacial termination such that it is only observed in bilayers with MnO2 but not with La0.7Ca0.3O interfacial termination. Such contrasting behaviors, we propose, are due to distinct energetic of CuO chain and CuO2 plane at the La0.7Ca0.3O and MnO2 terminated interfaces respectively, therefore influencing the transfer of spin-polarized electrons from manganite to cuprate differently. Our findings suggest that the superconducting/ferromagnetic bilayers with proper interfacial engineering can be good candidates for searching the theorized Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state in cuprates and studying the competing quantum orders in highly correlated electron systems.


II. Transport properties of YBCO/LCMO bilayers
The resistivity of bilayer samples was measured using the standard four-probe method. The results are shown in Fig. S2(a) as well as in Fig. 3(d) in the manuscript. The superconducting transition temperatures are determined to be ∼ 70 and 55 K for MnO 2 and La 0.7 Ca 0.3 O terminated bilayers respectively. The Curie temperature, which is the onset temperature of ferromagnetism in the LCMO layer, is estimated by intersecting the linear extrapolation of the high temperature leading edge of dM(T )/dT curve to zero. The extrapolation is shown as the dashed line in Fig. S2(b) and the Curie temperature is estimated to be 190 K, with an uncertainly on the order of 10 K.
In Fig. 3(b) in the manuscript, the onset of RSXS intensity (red markers) is slightly higher than the Curie temperature (open arrow) and this can be understood as the following. For magnetization, the recorded signal is the sum of magnetic moments from different ferromagnetic domains. When these magnetic domains are not properly aligned, say pointing along the easy axes (Mn-O bond direction) but antiparallel to each other, cancellation can lead to a smaller reading in M(T ). On the other hand, the RSXS intensity measures primarily the sum of the square of these moments. Thus even in this scenario, as long as the c-axis ferromagnetic coupling is established, the RSXS intensity from these anti-aligned domains will add up. Thus it is plausible that in the temperature regime between 200 K and 150 K, the discrepancy between M(T ) and RSXS data is caused by the intricate re-alignment of microscopic ferromagnetic domains. Moreover, a short range ordering preceding the establishment of bulk ferromagnetism would also lead to a higher onset temperature for the RSXS intensity than the Curie temperature by a similar mechanism as mentioned above.

III. Two-peak structures in the resonance profile of YBCO (001) Bragg peak
In Fig. 2 of the manuscript, we show the resonance profiles (thick solid lines) of YBCO (001) Bragg peak from MnO 2 and La 0.7 Ca 0.3 O terminated bilayers. Unlike pure YBCO film which shows just one feature at Cu L 3 and L 2 edges, bilayer samples exhibit two peaks at these edges (the additional peak at L 3 edge is labelled B).
The two-peak structure is intrinsic to the bilayers. Although one might speculate that it could come from two types of Cu 2+ with different binding energies, this scenario can be ruled out as the similarity between the XAS spectra from these three samples does not support two distinct Cu 2+ states with such large energy difference (∼ 2.5 eV apart). Furthermore, we also try to simulate the RSXS spectra of bilayers by using the ones from pure YBCO film with a 2.5 eV relative energy shift. Although the simulated spectrum (black curve, Fig. S3) seems to capture the gross spectral lineshape, the differences can still be clearly seen at selected photon energies (see arrows in Fig. S3).
The self-absorption effect, where x-rays emitted from deep inside the sample are re-absorbed when they come out of the sample, tends to suppress the high intensity features in XAS spectra recorded in the fluorescence yield mode. This effect becomes appreciable around the elemental absorption edges at which the x-ray penetration depth is significant reduced. Self-absorption correction is often performed when the x-ray penetration depth is comparable to or shorter than the thickness of sample. In our case where the thickness of YBCO film is around 15 nm (at 35 o grazing incidence angle, the effective thickness is around 26 nm) and the minimum x-ray penetration depth at Cu L 3 edge is around 140 nm (attenuation length determined from the CXRO website; http://henke.lbl.gov/optical constants/), the self-absorption effect is not expected to significantly alter the intensity ratio between features A and B. Thus it cannot be used to account for the observed two-peak structure in RSXS data.
The intensity of XAS is proportional to the imaginary part of atomic scattering form factor f " (E), whereas the RSXS intensity is related to its square ( f (E)) 2 + ( f " (E)) 2 modulated by a phase factor from the spatial arrangement of these scatterers (see description in the manuscript). f (E) and f " (E) are related to each other through Kramers-Kronig relations. We notice that the intensity of YBCO (001) Bragg peak is much weaker than other (00L) Bragg peaks and this is due to an effective destructive interference between Cu charge scatterings from the CuO chain and two CuO 2 planes within the unit cell. Such interference can be disrupted by a slight shift in the resonance energies or variations in the spatial arrangement of the scatterers. The former one will affect the energy denominator in f (E) and f " (E), whereas the later one will affect the phase factor. Simulating the RSXS lineshape will require the full knowledge of the spatial arrangement of Cu charges within the unit cell and their energetic upon heterogeneity, but to lowest order, these two factors can explain the relative intensity change between feature A and B in Fig. 2 in the manuscript. Irrespective to which origin, the distinct RSXS resonance profiles seen in the bilayer samples implies that the local energetic of electronic states is altered upon heterostructuring.

IV. Azimuthal angle dependence of the RSXS intensity
Unlike the magnetization, RSXS has the unique elemental, chemical and bonding specificity to differentiate the origins of the magnetic moments. Complementary to the x-ray magnetic circular dichroism (XMCD), RSXS intensity dependence on the tensorial nature of scattering channels can be helpful in identifying the magnetic couplings between the CuO 2 planes when the ordering vector overlaps with the structural Bragg peak whose intensity is dominated by the charge scattering.
In the current study, the scattering plane is horizontal and the incident photon polarization is in this scattering plane (π-polarization). We have used the single channel detector (photodiode) without polarization analyzer to record the scattering signal. The recorded signal will contain both σ -and π-polarization components. Although this may complicate the analysis of spin states, we will show that it still can offer some useful insight.
We follow the formalism outlined in Hill & McMorrow 2 and Lovesey & Collins. 3 Since the incident photon energy is tuned close to Cu 2+ L 3 absorption edge, we only consider the dipole (E1) transition and neglect the much weaker quadrupole (E2) transition. Equation (15) in ref 2 is reproduced here: −z 2 (z 1 sin(θ ) − z 3 cos(θ )) z 2 (z 1 sin(θ ) + z 3 cos(θ )) −cos 2 (θ )(z 2 1 tan 2 (θ ) + z 2 3 ) with F (0) ,F (1) ,and F (2) defined in ref. 2 We need to include these three terms because the Kronecker δ that conserves the wave 3/6 vectors becomes 1 in this case. We only need to consider the second column in the matrix because these elements are relevant to the signal in the π i → σ o and π i → π o channels (here, π i and σ o refer to the incident π and scattered σ polarizations). θ is the YBCO (001) Bragg angle and is ∼ 34.79 o in the current study. z i are the components of spin unit vector projected onto three crystalline axes. They are: Here α is the angle between the unit vector and c-axis, and φ is the sample azimuthal angle. Firstly, it is clear that if the moment is completely along the c-axis (α = 0 o ), there will be no azimuthal angle dependence in the RSXS intensity. To simplify the discussion, we consider the extreme case where α = 90 o . Putting these terms together, we have: The RSXS intensity is proportional to sum (over the superlattice) of the square of f 0) | 2 (cos 2 (θ )cos 2 (φ ) + sin 2 (2θ )sin 2 (φ )) + |F (2) | 2 |F (0) | 2 (sin 4 (θ )cos 4 (φ ) + sin 2 (θ )sin 2 (φ )cos 2 (φ ))} Usually, F (0) is much larger than F (2) and F (1) so that the ferromagnetic signal would be very weak compared to the charge signal in the Bragg peak. However, the destructive interference between charge scatterings leads to a much weaker YBCO (001) Bragg peak (see previous discussion). This makes the ratio Σ superlattice [F (1,2) /F (0) ] not so negligible. But even so, we do not expect the ratio can be on the order of 1. Thus we argue that the high order terms (last three terms in the equation) can be dropped out in the following discussion. By doing so, the scattering intensity will have the azimuthal angle dependence of a + b * sin(φ ) + c * cos 2 (φ ) where the coefficients b and c are related to F (1) F (0) and Fig. 3(f) of the manuscript, the Bragg peak intensity changes from ∼ 1.5 at 0 o to ∼ 1.1 at 90 o above the charge background of ∼ 1.0. Having the spin moment along the c-axis would increase the constant base line and reduce the [F (1,2) /F (0) ] ratio. The strong sinusoidal oscillation implies that the in-plane spin component is larger than the out-of-plane component. It also suggests that F (1) is much smaller than F (2) , as expected from the extremely weak Cu XMCD versus XLD signal.
Although YBCO has CuO chains that naturally break the four-fold symmetry, the bilayer samples under study are twinned. It is possible that the twinned domains with two distinct CuO chain orientations have unequal volume fractions that give the observed two-fold symmetry, we also notice that the 80 K measurement temperature is below the structural distortion of underlying STO substrate around 105 K. 4,5 This distortion naturally breaks the four-fold symmetry and further aligns the ferromagnetism in LCMO layer as shown in the magnetization. (color online) q-scans at 80 K (blue) and 300 K (red) from the MnO 2 terminated bilayer at 925.25 eV. The photodiode intensity was normalized by the incident photon flux only (photocurrent from upstream Au mesh), and no background subtraction was applied.

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V. Determining the layer thickness using synchrotron reflectivity Synchrotron reflectivity is used to determine the YBCO and LCMO layer thickness in the heterostructures. The measurement temperature was set to 80 K and the incident photon energy was tuned to 1240 eV, well above the Mn and Cu resonances. The blue markers in Fig. S4 are the data while the red curve is the fitting with YBCO / LCMO layer thickness of 15 nm / 7.5 nm respectively with roughness around 0.6 nm. The agreement between data and fit justifies the fitting parameters of layer thickness and roughness. Note that the discrepancy around 2θ ∼ 50 o is caused by the YBCO (001) Bragg peak.
The Kiessig fringes that overwhelm the YBCO (001) Bragg peak become negligible when the incident photon energy is tuned to Cu L 3 resonance. As can be seen in Fig. S5, the spectra recorded in q-scan can be nicely fitted by a Lorentzian function on top of a monotonic background.