Emergent surface magnetic ordering and surface electronic dipole layers in a two-dimensional spin=1/2 La₂CuO₄ film

Abstract

The surfaces of strongly correlated materials can exhibit exotic properties that differ substantially from the bulk. Investigation of these surface effects requires both high quality surfaces, and an experimental technique capable of disentangling surface and underneath layers or bulk. Herein, we overcome these two challenges, using newly developed grazing-incident-angle resonant soft x-ray and magnetic scattering techniques to study ultrathin films of Spin(S) = 1/2 La₂CuO₄, the parent compound of high-critical-temperature (high-T_c) superconductor. We observe emergent surface magnetic ordering and surface-like electronic dipole layers at room temperature. As a function of temperature, intrinsic holes from Cu²⁺ and O^2- ions are mitigated from the surface into subsurface layers and back into the surface. The intrinsic hole and oxygen ion mitigation have different rates, yielding strong temperature hysteresis. Supported with theoretical calculations, these surface orderings consist of a mixture of Cu²⁺ 3d⁹ (S = 1/2) and Cu¹⁺ 3d¹⁰-like (S = 0) with strong magneto-electronic coupling through the many-body upper Hubbard band. Our results highlight intrinsic holes and oxygen ion mitigations, yielding surface-like electronic dipole and magnetic orderings and the potential of grazing-incident-angle resonant soft X-ray and magnetic scattering to elucidate, layer-by-layer, magnetic and electronic structures.”

Disentangling the exotic phases that can emerge at the surfaces of strongly correlated materials from the bulk is experimentally difficult. Here, Jain, Diao, Ong, Rusydi, and coauthors succeed in doing so, using grazing incident-angle dependent resonant X-ray scattering to find an emergent surface magnetic ordering and surface electronic dipole layers in the two-dimensional film of La2CuO4

Introduction

Surfaces are believed to contain rich exotic properties, which are different from that of the bulk¹. Recent efforts are to understand surface magnetic and electronic properties in strongly correlated electron systems. Of particular interest is the well-known Heisenberg model for S = 1/2 system, a two-dimensional (2D) La₂CuO₄ layer. The La₂CuO₄ is the parent compound of high-critical-temperature (high-T_c) superconductor² and its bulk exhibits antiferromagnetic³ insulator⁴ with a Neel temperature around 325 K⁵. The La₂CuO₄ is a model of a CuO₂ layered system, i.e., […-CuO₂-LaO-CuO₂-…], where the Cu site is surrounded by the six O sites. The two oxygen atoms are located above and below the CuO₂-layer, known as apical oxygen, while the remaining four oxygen atoms are in-plane oxygen and lie within the CuO₂-layer, forming an octahedron arrangement³. Due to strong on-site Coulomb repulsion⁶, the Cu 3d⁹ (S = 1/2) band splits into a localized occupied lower Mott-Hubbard band (LHB) and a localized unoccupied upper Mott-Hubbard band (UHB), which are separated by broad oxygen p bands. The parent compound La₂CuO₄ is classified as a charge transfer insulator in the Zaanen-Sawatzky-Allen scheme⁷. In the CuO₂-layer, the many-body UHB has mostly Cu $d_{x^2-y^2}$ character hybridized with O 2p_xy⁸. While CuO₂ -layers are believed to be the main place for those exotic properties, of, however, till today, magnetic and electronic structures at the surface of the CuO₂-layer of La₂CuO₄ ultra-thin film remain far from being understood.

With today’s advancing growth techniques, it is now possible to fabricate high-quality surfaces and ultra-thin films via atom-by-atom methods. Optimizing and controlling the surface is critical for fundamental studies as well as for the development of new technologies and applications. However, directly measuring surface magnetic and electronic properties of unconventional insulators, such as Mott insulators or charge transfer insulators in strongly correlated electron systems, has been far more challenging than probing their bulk properties, especially with conventional techniques^9–17. It has been documented that when devices and films reach nanometer and even atomic-scale thicknesses, such as surface states or single-layer films, conventional bulk measurement techniques are not successful in directly detecting such weak signals from surfaces or single-layer films, which then led to fundamental discrepancies^11,14,16. A number of techniques have been developed for probing surface magnetism, including spin-resolved angle-resolved photoemission spectroscopy^18,19, low-energy muon spin rotation spectroscopy²⁰, and diamond quantum magnetometry²¹. Detecting surface states is, though, primarily challenging for the following reasons. First, surface magnetic and surface electronic signals are becoming extremely significantly weak, while bulk signals are dominating in most techniques. Second, the surface of cuprates and strongly correlated electron systems, in general, consists of unconventional insulators and/or unconventional metals¹⁷, yielding severe surface charging problems, which hinder conventional electron-based spectroscopy techniques. Therefore, a technique that is non-destructive, spin- and site-specific, and directly probes surface magnetic and electronic properties without charging problems is highly demanded.

In this Article, we report the emergence of novel, emergent room-temperature surface magnetic ordering and surface and subsurface electronic dipole layers (or surface-like electronic dipole layers) with strong surface magneto-electronic coupling through many-body upper Mott-Hubbard band (UHB) in 2D Spin = 1/2 Mott-Insulator La₂CuO₄ ultrathin film. We map layer-by-layer magnetic and electronic structures in energy and real (reciprocal) spaces from the surface to all subsurface layers using newly-developed non-destructive element-specific with highly surface-sensitive experimental techniques, namely a new grazing-incident-angle resonant Soft X-ray and Magnetic Scattering (GA-RSXMS), a new grazing-incident-angle X-ray absorption spectroscopy (GA-XAS), and the newly-developed grazing-incident-angle-resonant soft X-ray scattering (GA-RSXS).

We prepare epitaxially ~ 4 unit cell (uc) La₂CuO₄ ultrathin film on LaAlO₃ using ultra-high vacuum molecular beam epitaxy pulsed laser deposition (UHV MBE PLD). We design all main experiments in UHV conditions (1 – 3 × 10⁻⁹mbar) to ensure the cleanliness of the surface. Our UHV MBE PLD is equipped with in situ reflection high-energy electron diffraction (in situ RHEED) to measure real-time epitaxial film growth (Supplementary Information Fig. S1) and in situ X-ray and ultraviolet photoemission spectroscopies. The surface of the film is measured using atomic force microscopy (AFM), while the crystal structure and orientation of La₂CuO₄/LaAlO₃ ultra-film are measured using high-resolution synchrotron radiation X-ray diffraction (Supplementary Information Figs. S1 and S2). The GA-RSXMS, GA-XAS, and GA-RSXS measurements are performed in a unique UHV 5-circle diffractometer at the soft X-ray ultraviolet (SUV) beamline at the Singapore Synchrotron Light Source (SSLS)²². Experimental geometry set-up and schematic of electronic and spin transitions of these techniques are discussed in the Supplementary Note. 1, Supplementary Table. S1, and Supplementary Fig. S3–S5. For GA-RSXMS, GA-RSXS, and GA-XAS measurements, the experiments are performed as follows. Right after the films are grown, we transfer quickly and keep the samples in the UHV chamber until all GA-RSXMS, GA-RSXS, and GA-XAS measurements are completed. To check the reproducibility and stability, we make measurements at different times and spots within the same sample. Even after several months, the results are reproducible, revealing that no changes, no contaminants, and no new phases are observed, and the stoichiometry of the sample remains. Furthermore, the temperature-hysteresis loop at surface-UHB reveals the reversible loop, indicating that the surface sample response to heating and cooling is stable and shows no degradation of properties. Details of the experimental techniques and various other characterizations are in the Materials and Methods section and Supplementary Information.

Our new strategy is the following. Magnetic and electronic structures of UHB at the CuO₂ surface and subsurface (or underneath) CuO₂ layers of La₂CuO₄ ultra-thin film are directly probed and mapped using A-RSXMS, GA-RSXS, and GA-XAS at Cu L_3,2 and O K edges. At Cu L_3,2 edges (Cu 2p_j → 3 d, with j = 3/2 and 1/2 for Cu L₃ and Cu L₂, respectively), the UHB is directly revealed via Cu 2p_j→UHB (Cu ${3d}_{x^2-y^2}$) transition probing spin and electronic orderings at the Cu site. At O K edge (O 1 s → 2p), the UHB is observed via O 1 s → O 2p_xy hybridized with UHB (Cu ${3d}_{x^2-y^2}$) revealing spin and electronic orderings of Cu within an oxygen environment. By tuning the angle of incidence from grazing-incident-angle to high-incident-angle in RSXMS, RSXS, and XAS, we map magnetic and electronic structures layer-by-layer from the surface to all subsurface CuO₂ layers, which were never previously explored. The RSXS measurement is performed in reflectivity mode using a linearly polarized photon (LnP), denoted as R_LnP($\hslash \omega$,θ). The RSXMS measurements are performed in reflectivity magnetic dichroism mode using circularly polarized photons. The relationship between reflectivity magnetic dichroism, and reflected circularly polarized photons is expressed as:

$$R_{MCD}\left(\hslash \omega ,\mathrm{\theta }\right)\equiv R_{LCP}\left(\hslash \omega ,\mathrm{\theta }\right)-R_{RCP}\left(\hslash \omega ,\mathrm{\theta }\right),$$ 1

where, R_MCD($\hslash \omega$,θ), R_LCP($\hslash \omega$,θ), R_RCP($\hslash \omega$,θ), $\hslash \omega$^,$\theta$, LCP, and RCP are defined as reflectivity magnetic dichroism, reflectivity from a left circularly polarized photon, reflectivity from a right circularly polarized photon, photon energy, angle of incidence, left-circularly polarized photon, and right-circularly polarized photon, respectively. The XAS is performed in total electron yield mode (TEY) and normalized to the tabulated value, resulting in the extinction coefficient K and refractive index $n$ (see also Materials and “Methods”)^22–24.

Results

Our main observation is the emergent surface magnetic ordering and surface-like electronic dipole layers at room temperature in S = 1/2 ultra-thin La₂CuO₄ film. We start our discussion with surface magnetic ordering. To reveal the surface magnetic ordering, we perform GA-RSXMS measurements at Cu L_3,2 edges as shown in Fig. 1. We observe significant R_MCD($\hslash \omega$~ 931,θ) at 300 K and in the range of θ from 2° to 4.7° (Fig. 1a). The R_MCD($\hslash \omega$~ 931,θ) strength decreases beyond 4.7° and becomes infinitesimally small near the angle of incidence 14° and above. The photon penetration depth of our film from 2° to 4.7° is 19 Å ± 10 Å to 38 Å ± 10 Å, which are around 2-3 top CuO₂ layers of La₂CuO₄ ultra-thin film, while our La₂CuO₄ film is 52 Å thick (Supplementary Fig. S6). Therefore, the grazing-incident-angle, even up to 4.7° is dominated by the surface. Such a strong R_MCD at resonance occurs due to the matrix element of magnetic scattering, where the RSXMS signal has momentum transfer, Q ≠ 0 and is orders of magnitude higher compared to that of the X-ray magnetic circular dichroism (XMCD)²³, which has Q = 0. This makes GA-RSXMS very sensitive to surface magnetic orderings and even weak magnetic signals.

Fig. 1. Temperature-dependent grazing-incident-angle resonant soft x-ray magnetic scattering (GA-RSXMS) at Cu L₃ (upper Hubbard band).

a Room temperature GA-RSXMS using left and right circularly polarized light (LCP and RCP), R_CP($\hslash \omega$,θ), for 3°< θ < 20° at Cu L₃. The inset displays R_CP($\hslash \omega$,θ) for the full θ range, 3°< θ < 88°. b Temperature-dependent reflectivity magnetic dichroism of RSXMS, R_MCD($\hslash \omega$,θ) ≡ R_LCP($\hslash \omega$,θ) - R_RCP($\hslash \omega$,θ), at Cu L₃ for 3°<θ < 20°. The inset shows R_MCD($\hslash \omega$,θ) for the full θ range, 3°<θ < 88°, with the splitting of the angular region into five regions (I- 3°<$\theta <$7°, II- 7°<$\theta <$13°, III- 13°<$\theta <$19°, IV- 19°<$\theta <$67° and V- 67°<$\theta <$88°).

Based on photon penetration depth, RSXMS, and RSXS spectra are divided into five distinct regions, each with its own unique characteristics, as shown in the inset of Figs. 1b and 2a, respectively. Region I is sensitive to surface properties. Regions II to IV encompass contributions from both surface and bulk properties. Region V represents the (002) Bragg peak. The relationship between photon penetration depth ($L_p$) and θ is shown in Supplementary Note 2 and Supplementary Fig. S6. Noted that we define the underlying layers as bulk-like, distinguishing them from the real bulk system.

Fig. 2. Grazing-incident-angle Resonant soft x-ray scattering (GA-RSXS), resonance profile.

(RP($\hslash \omega$)), and grazing-incident-angle X-ray absorption spectroscopy (XAS) across Cu L_3,2 edges as a function of temperature for 4 uc La₂CuO₄/LaAlO₃ ultrathin film. a The GA-RSXS in reflectivity mode (3° < θ < 20°) using linearly polarized light R_LnP($\hslash \omega$,θ) for three temperatures (320 K, 300 K, and 37 K) at Cu L₃ (931 eV) normalized with respect to room temperature off-resonant energy (920 eV). The inset shows normalized reflectivity for the full θ range (3° <θ < 88°) with the splitting of the angular region into five regions (I- 3°<$\theta <$7°, II- 7°<$\theta <$13°, III- 13°<$\theta <$19°, IV- 19°<$\theta <$67° and V- 67°<$\theta <$88°) (detail in the text). b Resonance profile (RP($\hslash \omega$)) for the region I for three temperatures (320 K, 300 K, and 37 K) across Cu L₃ (in the left y-axis) and extinction coefficient, K($\hslash \omega$,θ) at Cu L₃ measured via XAS (in the right y-axis) at θ ~ 20° and temperature~ 320 K. The inset shows the RP($\hslash \omega$) and K($\hslash \omega$,θ) for the full photon energy range across Cu L_2,3 edges. Error bars denote the uncertainty in the measured reflected intensity at a given photon energy. X-ray absorption spectra as a function of temperature across Cu L_2,3 edges with an angle of incidence (θ) (c) 6° (or GA-XAS) (d) 20°.

Figure 1b shows temperature-dependent R_MCD($\hslash \omega$,θ) with varying θ. The inset of Fig. 1b shows the full range of θ, which is divided into the five regions based on photon penetration depth. The R_MCD( ~ 931 eV,~ 4.7°) is the highest at 300 K. It decreases by a factor of six upon increasing the temperature to 320 K, and decreases with cooling below 300 K, and diminishes at 200 K and 37 K. We observe weak R_MCD($\hslash \omega$,θ) in Region II for all temperatures, supporting the strong magnetic ordering arises from the surface and weak bulk sub-layer magnetism. In contrast, regions III to V show significantly weak R_MCD($\hslash \omega$,θ) and exhibit the onset of anti-ferromagnetism in the sub-layers akin to bulk La₂CuO₄.

To rule out other possible low-angle effects, we compare the R_MCD($\hslash \omega$,θ) at resonance with off-resonance energy (see Supplementary Note. 3 and Supplementary Fig. S9). During GA-RSXMS measurements, we only change the polarization from left circularly (R_LCP($\hslash \omega$,θ)) to right circularly (R_RCP($\hslash \omega$,θ)) polarizations. Therefore, R_MCD($\hslash \omega$,θ) is only sensitive to spin ordering or magnetism, while other low-angle phenomena, such as fringes from thin films and birefringence, remain zero or negligible in the R_MCD($\hslash \omega$,θ) signal. Intriguingly, we observe nearly a factor of ~4 enhancement in R_MCD($\hslash \omega$,θ) at the maximum of the absorption compared to at the edge of the absorption (see also Supplementary Note 4 and Supplementary Fig. S10). Furthermore, significant dichroism still occurs as large as ~ 12°. Therefore, the magnetic ordering at a low angle arises from the sample’s intrinsic magnetism at resonance.

Figure 2a displays R_LnP($\hslash \omega$,θ) for $3^{\circ }<\theta <20^{\circ }$. The R_LnP($\hslash \omega$,θ) measurement is conducted as a function of temperature with a linearly polarized photon, where the electric field, E || CuO₂-layer. Varying $\theta$ or $\hslash \omega$ results in a momentum transfer Q_HKL along (00 L), where H, K, and L refer to intercept along the a-axis, b-axis, and c-axis in reciprocal lattice units (r.l.u.), respectively. The R_LnP($\hslash \omega$,θ) is measured at the Cu L₃ edge with resonant photon energy, $\hslash \omega$ ~ 931 eV (UHB within Cu²⁺ configuration) for three temperatures (320 K, 300 K, and 37 K). We observe a new phenomenon of anomalously changing of R_LnP($\hslash \omega$,θ) as a function of temperature, $\hslash \omega ,$ and θ. Interestingly, R_LnP(~ 931 eV,~ 4.7°) shows a new peak at 300 K. This peak is higher at 320 K and significantly reduced at 37 K. Based on resonance profiles as shown in Fig. 2b and XAS as shown in Fig. 2c, d, the anomalous reflection at R_LnP(~ 931 eV,~ 4.7°) reveals the presence of an electronic dipole-like ordering between surface and subsurface layers or named surface-like electronic dipole layers. The surface-like electronic dipole layers occur between the 2 - 3 top CuO₂ layers of La₂CuO₄ ultra-thin film (see Supplementary Note 5 and Supplementary Fig. S11). Below the surface, the CuO₂ layers behave similar to that of bulk La₂CuO₄ as discussed above. As discussed later, at 300 K, the surface CuO₂ layer contains a mixture of Cu²⁺ (S = 1/2) and Cu¹⁺-like (S = 0), and the CuO₂ sub-layers contain Cu²⁺ (S = 1/2) and an additional hole, yielding electronic polarization along the c-direction. For θ > 14°, which is probing CuO₂ layers of the entire film, R_LnP(~ 931 eV, θ > 14°) is significantly reduced and shows nearly temperature-independent. This further supports that the surface electronic structure is unique and different from the bulk electronic structure. Furthermore, at off-resonant photon energy, R_LnP(~ 920 eV,~ 4.7°), which has a bulk-like photon penetration depth of 70 ± 10 Å, is significantly weak. This further supports that R_LnP(~ 931 eV,~ 4.7°) at 300 K is directly related to the surface-like electronic ordering of UHB.

By employing RSXS and RSXMS over the full range θ, we observe the contrast between surface and bulk R_LnP($\hslash \omega$,θ) as a function of temperature, $\hslash \omega ,$ and θ. The reflectivity across the broader θ range, from 3° to 88° is shown in the inset of Fig. 2a. At a high θ ~ 80° (region V), we observe (002) Bragg peak feasible at resonant Cu L₃ edge and very weak at off-resonance (see Supplementary Fig. S12) measured using RSXS. This reveals that at resonance UHB, the intensity of (002) Bragg peak is dominated by the electronic ordering of UHB in CuO₂ layers of the entire La₂CuO₄ film and is also affected by the surface-like electronic dipole layers of UHB. Note that the photon penetration depth of R_LnP(~ 931 eV,~ 80°) is ~ 891 ± 10 Å (Supplementary Fig. S6). The intensity from lattice ordering is less significant due to the scattering matrix element^23,24. Upon cooling from 320 K to 300 K, the intensity of the (002) Bragg peak is enhanced significantly, supporting the creation of surface-like electronic dipole layers (as further discussed later).

To reveal the origin of the dramatic changes in surface reflectivity, we measure the resonance profile, RP($\hslash \omega$) of R_LnP($\hslash \omega$,θ) at region I (Fig. 2b). The details of the resonance profile are in the Methods. We take RP($\hslash \omega$) for three different temperatures of 320 K, 300 K, and 37 K to be consistent with R_LnP($\hslash \omega$,θ) shown in Fig. 2a. The RSXS and RSXMS at Cu L_3,2 edges directly detect and distinguish between the presence of Cu²⁺ (~ 931 eV) and Cu¹⁺-like (~ 931.9 eV)²³. Figure 2b shows the RP($\hslash \omega$) for region I and the extinction coefficient, K($\hslash \omega$,θ) measured from XAS. The RP($\hslash \omega$) for other regions, II, III, IV, and V are shown in Supplementary Fig. S14. At 320 K, K($\hslash \omega$,θ = 20°) shows two main peaks, Cu L₃ (∼ 931 eV) and Cu L₂ (953.1 eV) edges (shown in the inset of Fig. 2b), revealing the presence of Cu²⁺ in the CuO₂ layers of cuprates²³. The RP($\hslash \omega$) resonates at Cu²⁺ and shows a significant intensity from Cu¹⁺-like, unraveling that the anomalously high reflectivity at low-θ is due to Cu²⁺ at the surface (c.f. Fig. 2b). Upon cooling, the RP($\hslash \omega$) changes abruptly. At 300 K, surprisingly it shows enhancement from both Cu²⁺ and Cu¹⁺-like, while generally, the resonance profile of Cu²⁺ at 300 K reduces compared to that of the resonance profile at 320 K, which is consistent with surface reflectivity (c.f. Fig. 2a). This reveals new electronic dipole layers consisting of the surface CuO₂ layer, which has a strong mixture of Cu²⁺ and Cu¹⁺-like, and the underneath CuO₂ layer, which has Cu²⁺, resulting in an electronic polarization along the c-direction. At 37 K, we observe an infinitesimally small contribution of R_LnP($\hslash \omega$,θ) in RP($\hslash \omega$). This shows that most Cu²⁺ transforms into Cu¹⁺ 3 d¹⁰-like, where Cu 2p → 3d transition is somewhat forbidden due to X-ray dipole selection rules. Clearly, upon cooling, the charge state of Cu at the surface exhibits a change from mostly Cu²⁺ (3d⁹) at 320 K to a mixture of Cu²⁺ and Cu¹⁺-like at 300 K and then to mostly Cu¹⁺ (3d¹⁰)-like at 37 K, while underneath CuO₂ layers, remain mostly Cu²⁺ with additional hole due to charge migration from the surface (see discussion below).

Figure 2c, d show the temperature-dependent extinction coefficient, K($\hslash \omega$,θ) measured through XAS at Cu L_3,2 edges for θ = 6°, primarily probing the surface, and for θ = 20°, primarily probing the entire film, respectively. Interestingly, temperature-dependent K($\hslash \omega$,θ) shows an opposite trend between θ = 6° and θ = 20°. The effective photon penetration depth of K($\hslash \omega$∼ 931 eV,θ) for θ ~ 6° and 20° is ~ 40 ± 10 Å and 160 ± 10 Å, respectively (Supplementary Fig. S6). The XAS shows two peaks, at 931 eV and 953.1 eV, which reveal UHB of Cu²⁺ $\left({3d}_{x^2-y^2}\right)$ in CuO₂-layers (see discussion above). The K($\hslash \omega$,θ = 6°) shows a decrease, revealing the decrease of UHB at the surface as the temperature decreases from 320 K to 300 K, followed by the disappearance of UHB at 37 K. This reveals that holes are migrating from the surface to the sublayers. The valence state of Cu at the surface significantly changes, i.e., from mostly Cu²⁺ at 320 K to a strong mixture of Cu²⁺ and Cu¹⁺-like at 300 K, and eventually mostly Cu¹⁺-like at 37 K (see further discussion below and Supplementary Fig. S8). In contrast, K($\hslash \omega$,θ = 20°) increases as the temperature decreases from 320 K to 37 K, revealing that additional holes are migrated into the sublayers. Combining temperature-dependent RP($\hslash \omega$), K($\hslash \omega$,θ = 6°) and K($\hslash \omega$,θ = 20°) reveals that upon cooling, holes are migrating from the CuO₂ surface to CuO₂ sub-layers. Such hole migration yields the creation of Cu¹⁺-like on the surface and changes the valence state of Cu differently between the surface and sub-layers. Note that the XAS at Cu L₃ keeps increasing at lower angles and high temperatures, revealing that they are not affected by saturation (see Supplementary Note. 3 and Supplementary Fig. S15).

The surface-like electronic dipole layers and hole migration (from the surface into the sub-layers) also affect the (002) Bragg peak, as shown in the RP($\hslash \omega$) of region V (c.f. Supplementary Fig. S14d). At 320 K, RP($\hslash$ω) follows XAS at Cu L_3,2 and as the temperature decreases the RP($\hslash \omega$) significantly increases and shifts toward Cu L₃’ (931.9 eV). Following the matrix element of scattering²³, the significant enhancement of the intensity of the (002) Bragg peak and the shift are due to the hole migration into the sub-layers and the formation of surface-like electronic dipole layers. This also further supports the anomalous R_LnP($\hslash \omega$,θ) in region I. It is worth noting that the temperature behavior of the (002) Bragg peak is opposite to Templeton-Templeton scattering²⁵. In the Templeton-Templeton scattering, the RP($\hslash \omega$) of the forbidden Bragg peak would follow polarization anisotropy of anomalous X-ray scattering or absorption. In contrast, RP($\hslash \omega$) of (002) Bragg peak and K($\hslash \omega$, θ) at Cu L₃ shows the opposite. First, upon cooling, the surface K($\hslash \omega$, θ=6°) decreases (c.f. Fig. 2c), while the RP($\hslash \omega$) of (002) Bragg peak increases (c.f. Supplementary Fig. S14d). Second, at a high temperature of 320 K, the RP($\hslash \omega$) of the (002) Bragg peak enhances at Cu²⁺, while at a low temperature, 37 K, it enhances at both Cu²⁺ and Cu¹⁺-like. This reveals that the surface-like electronic dipole plays a significant role in increasing the (002) Bragg peak. Altogether, R_LnP($\hslash \omega$,θ), RP($\hslash \omega$) and K($\hslash \omega ,\mathrm{\theta }$) at region I reveal surface-like electronic dipole layers consisting of a strong mixture of Cu²⁺ and Cu¹⁺-like at the CuO₂ surface and Cu²⁺ with additional hole (or Cu²⁺L-like, with L is ligand hole) in CuO₂ sub-layers.

We would also like to highlight the following observations and comparisons. First, it is worth noting that the shape of the Bragg peak is qualitatively similar when the photon energy changes (Supplementary Fig. S13). Therefore, the enhancements are due to the resonance effect of Cu²⁺ and Cu¹⁺-like (or surface-like electronic dipole layers of UHB), while the interference process between the Bragg peak and absorption is negligible. Second, we compare XAS at the Cu L₃ edge for our 4 uc La₂CuO₄ film at θ = 20° with bulk La₂CuO₄ from ref. ²⁶ and strain La₂CuO₄ film from ref. ²⁷ our La₂CuO₄ film behaves similar to bulk La₂CuO₄ (Supplementary Fig. S7).

Figure 3a displays the R_LnP($\hslash \omega$,θ) as a function of temperature across the O K edge at three different photon energies, i.e., $\hslash \omega$ ∼ 530.1 eV (UHB in the oxygen environment), $\hslash \omega$ ∼ 532.1 eV, and $\hslash \omega$ ∼ 536.1 eV. At 320 K and $\hslash \omega$ ∼ 530.1 eV, in region I, R_LnP($\hslash \omega$∼ 530 · 1 eV,θ∼ 5.7°) shows a peak, which slightly decreases as the temperature is reduced to 300 K and eventually vanishes at 37 K. This trend of temperature-dependent R_LnP($\hslash \omega$∼530 · 1 eV,θ∼ 5.7°) is similar to that of R_LnP(~931 eV,~ 4.7°), supporting that they come from the same origin. The R_LnP($\hslash \omega$∼530 · 1 eV,θ∼ 5.7°) reveals the importance of oxygen in determining surface-like electronic ordering in the CuO₂ layers. The peak at ~ 532.1 eV and ~ 536.1 eV is due to the transition from O 1 s → O 2p_xy hybridized with $e_{g\downarrow }\left({3d}_{{3z}^2-r^2}\right)$ in CuO₂-layer and O1s → apical O 2p_z hybridized with La 5 d in LaO-layer, respectively^3,4. We, therefore, assign them as oxygen in the CuO₂-layer and apical oxygen, respectively. At a temperature of 320 K and in the region I, both R_LnP($\hslash \omega$∼ 532 · 1 eV,θ∼5.7°) and R_LnP($\hslash \omega$∼ 536 · 1 eV,θ∼ 5°) shows a peak and it diminishes upon cooling down to 300 K and completely vanishes at 37 K. This reveals that oxygen in CuO₂-layer and apical oxygen are migrating moving away (or migrating) from the surface toward sub-layers upon cooling. On the contrary, bulk-like region III shows no considerable variation in R_LnP($\hslash \omega$,θ) as a function of temperature for all three photon energies. We observe temperature-dependent R_LnP($\hslash \omega$,θ) in region II, revealing that the surface still contributes, in addition to the bulk.

Fig. 3. Grazing-incident-angle Resonant soft x-ray scattering (GA-RSXS) and resonance profile across O K edge as a function of temperature for 4 uc La₂CuO₄/LaAlO₃ ultrathin film.

a The GA-RSXS in reflectivity mode (R_LnP($\hslash \omega$,θ)) at three photon energies, $\hslash \omega$ ~ 530.1 eV (UHB, shown with dashed-dotted lines), $\hslash \omega$ ~ 532.1 eV (shown with solid lines) and $\hslash \omega$ ~ 536.1 eV (shown with dashed lines) for three temperatures (320 K, 300 K, and 37 K). It is divided into three regions (I-3° < θ < 7°, II-7° < θ < 21° and III-21° < θ < 45°). b Normalized Resonance profile (RP_norm.($\hslash \omega$)), normalized with off-resonant) for the region I for three temperatures (320 K, 300 K, and 37 K) across O K edge (in the left y-axis) and extinction coefficient, K($\hslash \omega$,θ) at O K measured via XAS (in the right y-axis) at θ ~ 20° and temperature~320 K. The inset shows the RP($\hslash \omega$) and K($\hslash \omega$,θ) for UHB across O K edges. Error bars denote the uncertainty in the measured reflected intensity at a given photon energy.

Figure 3b illustrates the resonance profile $RP\left(\hslash \omega \right)$ across O K edge for various temperatures in region I and K($\hslash \omega$,θ) as a reference. Interestingly, upon cooling down to 300 K, $RP\left(\hslash \omega \right)$ of UHB remains the same, while $RP\left(\hslash \omega \right)$ at $\hslash \omega$~ 532.1 eV and $\hslash \omega$~ 536.1 eV change significantly. At 37 K, the $RP\left(\hslash \omega \right)$ decreases significantly, in other words, having almost negligible reflectivity at all photon energies. Region III exhibits negligible reflectivity at all temperatures (Fig. 3a). Based on RSXMS, RSXS, and XAS, we obtain emergent magnetic and electronic phase diagrams of the surface and sub-layers of La₂CuO₄ ultra-thin film.

We measure and identify distinct magnetic orderings from R_MCD($\hslash \omega$,θ) at Cu L₃ of the surface (region I) and the entire film (region V) as a function of temperature (Fig. 4a). To qualitatively obtain the magnetic strength corresponding to surface and bulk, we integrate R_MCD(θ) strength at each region (regions I and V). Note that in our experimental set-up, R_MCD(θ) is measured without applying the magnetic field; therefore, the magnetic scattering dichroism obtained is a remnant, intrinsic magnetism from the sample. Surprisingly, we find that the R_MCD(θ) strength in region I shows a remarkable increase at 300 K, revealing an extremely strong surface magnetic ordering. As the temperature increases to 320 K, the R_MCD(θ) strength decreases by a factor of six, assigned to surface anti-ferromagnetic-like ordering. Upon cooling below 300 K, it drops dramatically and then further decreases monotonically until 200 K. Further cooling, it ultimately suppresses to zero, named weak surface magnetic ordering and no surface magnetic ordering, respectively (see Supplementary Note 6 and Supplementary Fig. S16). Conversely, in region V, the R_MCD($\hslash \omega$,θ) strength is relatively stronger at lower temperatures till 200 K and decreases monotonically at higher temperatures (see details in Supplementary Note 6 and Supplementary Fig. S17).

Fig. 4. Emergent surface magnetic and surface electronic dipole-like ordering phase diagram.

a Temperature-dependent R_MCD($\hslash \omega$,θ) for region V (bulk) and region I (surface) at Cu L₃. Based on experimental results, the surface magnetic structure is divided into four phases. The first phase is non-magnetic nature, the second phase is weak surface magnetic ordering, the third phase is strong surface magnetic ordering, and the fourth phase is paramagnetic nature. Error bars denote the uncertainty in the measured reflectivity magnetic dichroism at a given photon energy. b Temperature hysteresis for resonant soft X-ray scattering, R_LnP($\hslash \omega$,θ), at $\hslash \omega$ ~ 530.1 eV (UHB of O K edge) and $\hslash \omega$ ~ 931 eV (UHB of Cu L₃). Similar to R_MCD($\hslash \omega$,θ) strength, it is also divided into four phases. The first phase shows the surface Cu¹⁺-like, the second and third phases present a mixture of Cu²⁺ and Cu¹⁺-like (surface-like electronic dipole layers), and the fourth (above ~ 330 K) presents Cu²⁺ at the surface. Combining (a) and (b), the system exhibits emergent strong surface magnetic ordering and surface-like electronic dipole layers with strong magneto-electronic coupling via UHB at 300 K. Error bars denote the uncertainty in the measured reflected intensity as a function of temperature.

To reveal the effects of the holes and oxygen migrations on the surface-like electronic dipole layers as a function of temperature, we conduct temperature hysteresis (heating-cooling cycle) of R_LnP($\hslash \omega$= UHB,θ = 6°), both during warming up from 37 K to 330 K and during cooling down (Fig. 4b and Supplementary Note. 7). The temperature hysteresis R_LnP($\hslash \omega$= UHB,θ = 6°) is performed at both ~ 931 eV (UHB of Cu L₃ edge) and ~ 530.1 eV (UHB of O K edge), which are related to holes and oxygen ion migrations, respectively. Surprisingly, we observe strong hysteresis at $\hslash \omega$ ∼ 530.1 eV and still feasible hysteresis at $\hslash \omega$ ∼ 931 eV. As temperature increases, R_LnP($\hslash \omega$,θ = 6°) at both UHB follows the same trend, with an onset transition occurring ~ 200 K. Prior to 200 K, R_LnP($\hslash \omega$,θ) is zero at both photon energies, and subsequently, as the temperature rises above 200 K, R_LnP($\hslash \omega$,θ) increases gradually with the increase in temperature till 330 K and decreases on cooling down, resulting in R_LnP($\hslash \omega$,θ = 6°) temperature hysteresis. Notably, upon cooling, R_LnP($\hslash \omega$= 931 eV, θ = 6°) decreases at a faster rate compared to R_LnP($\hslash \omega$= 530 · 1 eV, θ = 6°). Details of fitting and calculation on the transition rate of Cu²⁺ and Cu¹⁺-like based on R_LnP($\hslash \omega$,θ = 6°) temperature hysteresis for both the UHB of Cu L₃ edge and O K edge are shown in Supplementary Note. 7 (Supplementary Figs. S18–20). Note that the temperature hysteresis R_LnP($\hslash \omega$,θ = 6°) at the O K edge has been performed a few times, which are reproducible.

To have a deeper understanding of the surface magnetic and electronic structures, we construct a four-unit cells (4 uc) model of La₂CuO₄ and perform density functional theory (DFT) with Hubbard U to calculate the projected density of states (PDOS) and magnetic moments (Fig. 5a, b and Supplementary Figs. S21–23). The details of the theoretical calculations are shown in Materials and Methods and Supplementary Figs. S21–23. The relaxed crystal structure results in a surface reconstruction in which the length of the c-axis is extended by 2.56% (13.56 Å), whereas the Cu-O-Cu bond angle is 151.42° at the surface. To induce a ferromagnetic configuration, the total magnetization is constrained to be 1 ${\mu }_B$/unit cell. This results in a ferromagnetic ground state, where magnetic moments of the Cu atoms in each layer are observed. In Fig. 5a, the collinear FM DFT calculations show a large enhancement of the magnetic moments at the surface, both in the unrelaxed (c-axis = 0) and relaxed surface atoms (c-axis = 46.16 - 53.28 Å). Meanwhile, the magnetic moments of bulk-like La₂CuO₄ are small. This surface magnetic enhancement agrees with GA-RSXMS.

Fig. 5. Magnetic moment, projected density of states (PDOS) and illustration of surface magnetic ordering and surface charge dipole layers as well as ion and charge migrations mechanism as a function of temperature.

a Magnetic Moment of Cu atom in La₂CuO₄ as a function of c-axis. The inset shows the crystal structure of 4 uc La₂CuO₄. b PDOS of Cu 3 d for bulk-like La₂CuO₄ (Cu atoms located below the surface) and surface La₂CuO₄. c Schematic illustration for surface magnetic ordering and surface-like electronic dipole layers as a function of temperature at (A) 320 K, (B) 300 K (during cooling), (C) 37 K, and (D) 300 K (during heating) in 4 uc La₂CuO₄/LaAlO₃ thin film. A, B, C, and D are defined in the temperature hysteresis of Fig. 4c. The red sphere represents O^2-, the black sphere with a spin represents Cu²⁺, the black sphere without spin represents Cu¹⁺-like, the black sphere with a black dashed boundary shows Cu¹⁺-like with the charge migration (h⁺), and the red dashed circle showing missing O (details are shown in Supplementary Fig. S17). Brown arrows (curved) in the clockwise direction represent the change in spin and electronic dipole layers with temperature. P represents the electronic polarization between the surface CuO₂ layer and CuO₂ sub-layers along the c-axis direction (as shown with the green arrow). We do not show the LaO layer to simplify the unit cell and to focus the explanation on the surface-like electronic dipole layers indicated by the blue and red layers. The top (surface) CuO₂ layer comprises mixed Cu²⁺ and Cu¹⁺-like states, and the CuO₂ sub-layers are in the Cu²⁺ state. The CuO₂ plane at the bottom is shown in green color, representing the antiferromagnetic spin structure with a Cu²⁺ state. In the schematic, MO- Magnetic ordering, AFM- anti-ferromagnetic, and c- c-axis lattice parameter.

To further explore the surface electronic structure, we calculate the spin-dependent projected density of states (PDOS) for Cu 3 d and O 2p orbitals for surface and bulk atoms (Fig. 5b and Supplementary Fig. S22). We observe that the surface electronic structure of La₂CuO₄ is indeed different from the bulk, especially near the Fermi level. Both Cu 3 d and O 2p surface atoms show significant broadening, creating new spin-polarized mid-gap states localized at the surface. By examining Cu 3 d orbitals, we can observe the origin of the surface spin-polarized mid-gap states. The PDOS bulk La₂CuO₄, i.e., Cu 3 d orbitals located below the relaxed surface, show states that are separated by a band gap. These states are dominated by Cu²⁺ and behave like the antiferromagnetic ground state of La₂CuO₄. Interestingly, the surface Cu 3 d shows spin-polarized and localized midgap states. The surface spin-polarized mid-gap states are due to the mixture of Cu²⁺ and Cu¹⁺-like and the symmetry broken, hosting the surface electronic dipole layers as well as surface magnetic ordering as observed in GA-RSXS and GA-RSXMS.

Discussion

Based on our experimental data supported with theoretical calculations, we draw the schematic of spin and electronic structures from the surface into sub-layers of S = 1/2 ultra-thin La₂CuO₄ film as a function of temperature (Fig. 5c and Supplementary Fig. S24 for details). At 300 K, the co-existence of surface magnetic ordering and surface-like electronic dipole layers emerges through many-body UHB. The electronic dipole-like layers consist of two different CuO₂ layers, i.e., (1) the surface CuO₂ layer, which has a strong mixture of Cu²⁺ and Cu¹⁺-like, and (2) the underneath CuO₂ layer, which has Cu²⁺ with an additional hole, resulting in the creation of a charge dipole along the c-direction depicted as P. When only Cu²⁺ (S = 1/2 at 320 K) or Cu¹⁺-like (S = 0 at 37 K) at the surface of the CuO₂ layer is observed, magnetic ordering significantly weakens. The movement of holes and oxygen results in broken inversion symmetry and the emergence of surface magnetic ordering, which further leads to the onset of surface-like electronic dipole layers (as further discussed below). Interestingly, RP($\hslash \omega$) and R_LnP($\hslash \omega$,θ=5°) at 536.1 eV, which track the apical oxygen (or oxygen in La-O layer), show a prominent peak at 320 K and reduce drastically at 300 K (Fig. 3a and b), revealing the movement of apical oxygen from the surface to sub-layers (Supplementary Fig. S24). Note that interstitial and staging of oxygen have been observed in La₂CuO_4+y with an oxygen excess system, supporting that the oxygen moves into sub-layers^28–30. Similarly, RP($\hslash \omega$) and R_LnP($\hslash \omega$, θ = 5 · 7°) at 532.1 eV, which probe O in CuO₂-layer, show a significant reduction in reflectivity on lowering the temperature from 320 K to 300 K (Fig. 3a and b), showing the movement of CuO₂-layer oxygen into sub-layers (as shown in schematic Fig. 5c and Supplementary Fig. S24). The GA-RSXS at UHB ( ~ 530.1 eV), both RP($\hslash \omega$) and R_LnP($\hslash \omega$, θ = 5 · 7°) remain the same as a function of temperature, signifying that the system maintains charge transfer at 300 K (Fig. 3a and b). The movement of holes and oxygen in the apical and CuO₂-layer from the surface results in the mixture of Cu²⁺ and Cu¹⁺-like, generating surface-like electronic dipole layers with electronic polarization along the c-direction (Fig. 5c).

The R_MCD($\hslash \omega ,\theta$) strength of UHB at Cu L₃ edge in GA-RSXMS exhibits an enormous increase in surface magnetic ordering at room temperature (c.f. Figure 4a). Supported by theoretical calculations, we ascribe the magnetic transition at 300 K as a complex, non-collinear magnetic ordering due to the mixture of Cu²⁺ (S = 1/2) and Cu^1+-like (S = 0) in the surface CuO₂-layer (Fig. 5c). Based on R_MCD($\hslash \omega ,\theta$) strength (Fig. 4a), we infer the presence of robust surface magnetic ordering at 300 K, and albeit weaker, but still noticeable magnetic ordering at 320 K, indicating that the Néel temperature likely exceeds 320 K. At temperatures higher than the Néel temperature (T_N)⁵, Cu²⁺ spins in La₂CuO₄ are arranged in the paramagnetic phase. As the temperature is lowered to the Néel temperature, an anti-ferromagnetic transition occurs, causing Cu²⁺ in the CuO₂-layers to develop a long-range anti-parallel spin order⁵. On going down to 320 K (below Neel temperature), the Cu²⁺ dominates at the surface, resulting in a weak magnetic ordering that suggests the onset of weak competing magnetic interactions between adjacent Cu²⁺ spins, leading to spin canting. Upon cooling down to 300 K, we argue that a mixture of Cu²⁺ (S = 1/2) and Cu¹⁺-like (S = 0) results in a strong competing magnetic interaction between antiferromagnetic and ferromagnetic, causing spin frustration between adjacent Cu²⁺ (S = 1/2) spins and resulting in a somewhat non-collinear spin structure. Note that the interplay of Cu²⁺ and Cu¹⁺ has been shown to play an important role in the multiferroic LiCu₂O₂ (ref. ³⁰), and a somewhat similar but more complex phenomenon may occur at the surface of La₂CuO₄. Upon cooling to 200 K and beyond, surface magnetism in the La₂CuO₄ significantly reduced (c.f. Figs. 1b, 4a). This is due to the presence of a majority of non-magnetic Cu¹⁺-like (S = 0) at the surface, in which, unlike Cu²⁺ (3d⁹), the Cu¹⁺(3d¹⁰)-like does not have any unpaired d electrons and therefore does not contribute to the observed magnetism³¹.

We next investigate the temperature hysteresis of UHB using GA-RSXS at Cu L₃ and O K edges (Fig. 4b). The many-body UHB of La₂CuO₄ ultra-thin film is shown to occur in the CuO₂-layer, and we observe copper atoms undergo changes in the valence state for varying temperatures, and the hole (charge) and oxygen moving out of and into the surface (Fig. 5c). At the UHB of Cu L₃ edge, the observation of GA-RSXS temperature hysteresis provides insights into different valence states of Cu in UHB. Upon cooling, Cu²⁺ is reduced to Cu¹⁺-like, resulting in a decrease of R_LnP($\hslash \omega$,θ). Upon heating, Cu¹⁺-like changes its valence state to form Cu²⁺, increasing the R_LnP($\hslash \omega$,θ). Interestingly, this increase in R_LnP($\hslash \omega$,θ) do not follow the same path (or have different rates) upon subsequent cooling, resulting in a hysteresis loop in the GA-RSXS measurements, where R_LnP($\hslash \omega$,θ) remains higher even upon cooling until a certain temperature is reached. This behavior shows the presence of Cu²⁺ that has not fully reduced back to Cu¹⁺-like upon cooling.

At the UHB of O K edge, GA-RSXS temperature hysteresis provides insights into UHB in the oxygen environment. Interestingly, it shows a broader hysteresis as compared to that of GA-RSXS at UHB of Cu L₃. This reveals that the dynamic behavior of UHB is associated with oxygen environments. Therefore, the interplay of the migration of holes and oxygen plays an important role in determining the temperature hysteresis of UHB during heating and cooling cycles.

We next construct the correlation between surface magnetic ordering, surface-like electronic dipole layers, and migration of hole and oxygen across three distinct temperatures 320 K, 300 K, and 37 K, encompassing both heating and cooling processes (Fig. 5c). At 320 K, Fig. 4a reveals a discernible yet weak magnetic ordering, while Fig. 4b shows the presence of Cu²⁺ at the surface as shown in Fig. 5c (A). This is the state where the presence of canted spins arises from the broken symmetry at the surface of the ultra-thin film, resulting in weak magnetic dichroism (marked as A in Fig. 5c).

Upon cooling down to 300 K, the system has the following conditions: (1) the UHB at the surface remains as revealed by RP($\hslash \omega$) of GA-RSXS at ~ 530.1 eV (c.f. Fig. 3b); (2) The pronounced surface magnetic ordering emerges revealed by GA-RSXMS (c.f. Figs. 1a and 4a); (3) The surface-like electronic dipole of a mixture Cu²⁺ and Cu¹⁺-like occurs revealed by GA-RSXS (c.f. Fig. 2a, b) and GA-XAS (c.f. Fig. 2c, d and see also marked as B in Fig. 5c); (4) The activation energy for Cu²⁺ → Cu¹⁺-like at UHB of Cu L₃ edge is similar to the activation energy at UHB of O K edge (Supplementary Table S2); and (5) the migration of holes and oxygens mainly in apical from the surface into sub-layers revealed by XAS at grazing- and high-incident angles of Cu L_3,2 edges (c.f. Fig. 2c, d) and RP($\hslash \omega$) at O K edge (c.f. Fig. 3). Therefore, this is the state, where the surface UHB exhibits both strong surface magnetic ordering and surface-like electronic dipole layers. The interplay of the mixture of Cu²⁺ and Cu¹⁺-like and charge transfer (or hole (h⁺) migration), accompanied by O^2- (apical oxygen) migration from surface to sub-layers, determines the surface magnetic and electronic orderings (Fig. 5c (B)). Note that it is relatively easy for the apical oxygen to move as compared to O in-CuO₂ layer^32,33.

Further cooling down to 37 K induces a significant reduction in magnetic ordering seen from GA-RSXMS (Fig. 4a) and surface-like electronic dipole layers in GA-RSXS intensity (Fig. 4b), due to the fact that the surface primarily consists of a Cu¹⁺-like state. This reveals that holes and O^2- (apical and CuO₂-layer) further migrate from the surface to sub-layers of the crystal lattice [Fig. 5c (C)]. Subsequently, upon raising the temperature back to 300 K, the movement of holes occurs from sub-layers to the surface as depicted in D (Fig. 5c). Further increase in temperature to 320 K, we get back to the initial state with Cu²⁺ prevailing at the surface. Based on temperature hysteresis data, we find that the data are highly reproducible; therefore, the surface of La₂CuO₄ is an active layer (see details in Supplementary Note 8).

It is worth highlighting other unique strengths of GA-RSXMS and GA-RSXS to directly map real and energy spaces layer-by-layer and resolve magnetic and electronic structures from the surface to sub-layers generally. We also show the difficulty of detecting surface properties using bulk-type experimental geometry of RSXS measurements (c.f. Supplementary Fig. S14c and inset of Fig. 2a). The RP($\hslash \omega$) of RSXS in region IV, which is probing bulk properties, reveals that even RSXS cannot detect the surface states. This further supports the main challenge of using conventional bulk measurements to measure surface states, and thus GA-RSXMS and GA-RSXS are powerful and unique to probe surface properties even in ultra-thin films.

Methods

Sample preparation

La₂CuO₄ ultra-thin films are prepared epitaxially on 1 cm × 1 cm LaAlO₃(001) substrates using a custom-made ultrahigh vacuum molecular beam epitaxy pulsed laser deposition (UHV-MBE PLD) system. The growth process involved the utilization of a solid-state ablation Nd:YAG laser with an output wavelength of 266 nm and growth monitoring using in situ reflection high-energy electron diffraction (in situ RHEED). The LaAlO₃ (001) substrate is rinsed in isopropanol and blown-dried in the air before being loaded into the UHV-MBE PLD system with a base pressure of 5 × 10⁻⁹ Torr. The substrate is first outgassed in a vacuum at 310 °C for 45 mins before being annealed at 750 °C for 60 mins under 50 mTorr O₂ to obtain a clean LaAlO₃ (001) surface as verified using in situ RHEED as depicted in Supplementary Fig. S1. The La₂CuO₄ film is then pulsed laser deposited onto LaAlO₃ (001) substrate at 750 °C under 50 mTorr O₂. Subsequently, the sample underwent an additional annealing step at 750 °C under 300 Torr O₂ for another 60 mins. The pulsed laser utilizes an energy of 3.25 J cm⁻². Prior to the deposition, the La₂CuO₄ target is pre-ablated at 10 Hz with 2000 pulses.

Resonant Soft X-ray and Magnetic Scattering (RSXMS)

Resonant soft X-ray and magnetic scattering (RSXMS) are performed at the Soft X-ray Ultraviolet (SUV) beamline, Singapore Synchrotron Light Source (SSLS), Singapore^22,23. The RSXMS is an element-sensitive, non-destructive, high-energy resolution, and polarization-sensitive experimental technique (Supplementary Fig. S5). Depending on the scattering geometry (or angles), the probing depth varies from a few to a hundred nanometers, therefore, we can map magnetic and electronic structures making it powerful to probe spin, charge, and orbital modulations from surface to sublayers as well as buried interfaces. The scattering chamber consists of an ultrahigh vacuum (UHV) 6-circle diffractometer with a based pressure of 10^-9mbar. The beamline covers a broad energy range from ultraviolet photons ( ~ 3.5 eV) to soft X-ray photons (~ 1500 eV). The X-ray scattering intensity is measured for linearly polarized light (LnP) with a degree of polarization ~ 95% for RSXS measurement and using left and right circularly polarized X-rays, (LCP and RCP, respectively) with a degree of circular polarization ~ 80% for RSXMS measurements. The reflectivity magnetic dichroism, R_MCD($\hslash \omega$,θ), is calculated by taking the difference between R_LCP($\hslash \omega$,θ) and R_RCP($\hslash \omega$,θ) as shown in Eq. 1. Note that in our previous study, we observe a strong magnetic dichroism in low-dimensional Au/La_1.80Ba_0.20CuO₄/LaAlO₃ films with 80% circular polarization, revealing in-plane and out-of-plane ferromagnetism using resonant soft X-ray and magnetic scattering (RSXMS)²². The RSXMS intensity is ~ 50 times stronger than X-ray magnetic circular dichroism (XMCD), enabling it to measure infinitesimally small magnetic signals in the materials. The X-ray scattering intensity is measured by tuning X-ray energy to the O K edge and Cu L_2,3 edges and then scattered photons are collected for varying scattering angles using a photodiode to get the total fluorescence yield (TFY) from the sample. The collected spectra have been normalized to the incident X-ray photon intensity first and then with respect to off-resonance energy.

Resonance Profile (RP($\hslash \omega$,θ))

The RP($\hslash \omega$,θ) spectra is a result of measuring the X-ray scattering intensity, using reflectivity mode, at different energies across the O K edge and Cu L_2,3 edges while varying θ/2θ (Figs. 2b, 3b, and Supplementary Fig. S14). The measurement is conducted using linearly polarized light simultaneously in both TFY and TEY modes. The obtained X-ray scattering intensity spectra with varying angles are divided into several regions for analysis of surface-to-bulk-like properties. The RP($\hslash \omega$) is calculated by integrating X-ray scattering intensity (Reflectivity) over an angular range from ${\theta }_1$ to ${\theta }_2$ for each region and is expressed as:

$$RP\left(\hslash \omega \right)={\int }_{{\theta }_1}^{{\theta }_2}{R}_{LnP}\left(\hslash \omega ,\theta \right)d\theta$$ 2

Similarly, it is obtained for all photon energies. It has been calculated for three different temperatures (320 K, 300 K, and 37 K).

X-Ray absorption spectroscopy (XAS)

The X-ray absorption spectroscopy (XAS) spectra (Supplementary Fig. S3) are collected at the Soft X-ray Ultraviolet (SUV) beamline, Singapore Synchrotron Light Source (SSLS), Singapore²². The XAS is a non-destructive, element-specific, high-energy resolution and offers sensitivity to the local environment. The XAS measurements are taken in total electron yield mode (TEY), and the incident photon energy is varied to follow RSXS and RSXMS (see above). In a very grazing incidence geometry, the sensitivity of XAS is enhanced on the surface region of the material as we probe the electronic and structural properties of the top few nanometers (Supplementary Fig. S3). The measurements are conducted using linearly- and/or circularly polarized X-ray photons. The XAS spectra are normalized to the incident X-ray photon intensity and X-ray tabulated value to get the complex refractive index:

$$N\left(\hslash \omega ,\theta \right)=\left(1-\delta \left(\hslash \omega ,\theta \right)\right)+iK\left(\hslash \omega ,\theta \right)$$ 3

where K is the extinction coefficient and $n=\left(1-\delta \left(\hslash \omega ,\theta \right)\right)$ is the refractive index, and they are obtained through Kramer-Kronig Transformation (KKT)^22,23,34. The collected spectra are normalized to the incident X-ray photon intensity, followed by background subtraction. Based on our wide scan of XAS, our thin film consists of La, Cu, and O. To show reproducibility, we perform XAS on different days (Supplementary Fig. S25).

Reflection high-energy electron diffraction (RHEED), X-ray diffraction (XRD), and atomic force microscopy (AFM)

Figure S1 presents the results of the reflection of in situ high-energy electron diffraction (RHEED) (Supplementary Fig. S1a–d), RHEED intensity oscillations during the growth of the sample in pulsed laser deposition (Supplementary Fig. S1e) and high-resolution X-ray diffraction (HR-XRD) (Supplementary Fig. S1f) obtained from the growth and characterizations of 4 uc La₂CuO₄/LaAlO₃ (001). The sample is prepared under ultrahigh vacuum conditions using PLD-MBE. The in situ RHEED intensity oscillations (Supplementary Fig. S1e) together with the in situ RHEED pattern at azimuth angle 45° and 90° exhibiting the same (1 × 1) surface symmetry pattern before and after the growth of La₂CuO₄ on LaAlO₃ (001) with streak pattern, indicate two-dimensional (2D) layer-by-layer epitaxial growth during in-situ pulsed laser deposition (Supplementary Fig. S1a–d). The XRD θ − 2θ scans show strong diffraction patterns corresponding to the La₂CuO₄ film and LaAlO₃ substrate peaks. The crystal structure analysis using a four-circle X-ray diffractometer shows a pseudo-tetragonal crystal structure with the c-axis normal to the substrate surface. The LaAlO₃ (001) and (002) substrate peaks are at 23.51° and 47.92°, while La₂CuO₄ (004), (006), and (008) film peaks are at 26.67°, 41.03°, and 55.65°, respectively (Supplementary Fig. S1f). The a-, b- and c-axis lattice parameters of the La₂CuO₄ film are found to be ~ 0.38, ~ 0.38, and 1.32 nm, respectively, suggesting the ultrathin film is fully strained with the substrate. These results collectively show successful epitaxial growth of the La₂CuO₄ film on LaAlO₃ (001) substrate characterized by the following relationship {La₂CuO₄ (001)//LaAlO₃ (001) and La₂CuO₄  <  001  >  //LaAlO₃  <  001 > }. Kiessig fringes are also observed in the XRD θ − 2θ scans, and based on the analysis of the fringes associated with La₂CuO₄ (006), the epitaxial La₂CuO₄ film thickness is determined to be ~ 5.2  ±  0.5 nm, which is equivalent to 4uc of La₂CuO₄. We calculate the thickness of La₂CuO₄ thin film from XRD using the formula below:

$$Thickness\left(nm\right)=\frac{\lambda \left(n_1-n_2\right)\left(nm\right)}{2*\left(sin{\theta }_1-sin{\theta }_2\right)}$$ 4

where $\lambda$ is the wavelength of Cu-Kα X-ray source (0.154 nm), $n_1$ and $n_2$ are two adjacent maxima in the oscillations such that $n_1-n_2$ = 1. The angles ${\theta }_1$ and ${\theta }_2$ are the corresponding adjacent angles. The thickness is found to be ~ 5.2  ±  0.5 nm. At this thickness, the surface has a root mean square (rms) roughness of ~ 0.3 nm, which is comparable to the initial rms surface roughness of LaAlO₃. The clean LaAlO₃ (001) surface appears smooth with a surface roughness of ~0.1 nm. The surface morphology for La₂CuO₄-thin film obtained from atomic force microscopy (AFM) is shown in Fig. S2.

Density functional theory (DFT)

We perform DFT calculations for the La₂CuO₄ thin film. We construct a 4-unit cell (4 uc) model of La₂CuO₄ to calculate the projected density of states and magnetic moments. The model is shown in Supplementary Fig. S21, where a 1 × 1 × 4 La₂CuO₄ supercell is calculated using the Quantum Espresso simulation package³⁵. Spin-dependent generalized gradient approximation³⁶ (GGA) with Hubbard U (GGA + U) is used with SG15 Optimized Norm Conserving Vanderbilt (ONCV) with frozen-core Projected Augmented Wave (PAW) pseudopotentials^37–39. The Hubbard U values are set as $U_{eff,La}=11$ eV and $U_{eff,Cu}=7$ eV, as conducted by previous theoretical works⁴⁰. The lattice parameters are a = b = 3.7899 $\ddot{\mathrm{A}}$ and c = 13.221 $\ddot{\mathrm{A}}$, respectively, which are obtained from high-resolution synchrotron-XRD measurement at the Singapore synchrotron light source (SSLS). To avoid interaction between neighboring structures, 25 Å of vacuum is inserted. The structure relaxation uses a Monkhorst-Pack k-point grid of $2\times 2\times 1$, where the xy-positions of all atoms are kept stationary, whilst the z-positions are allowed to relax only for the top two-unit cells (surfaces). The fixed lattice parameters in the ab-axes replicate the 4 μc thin film observed experimentally and verified through the Synchrotron-XRD. The relaxation is conducted until the forces on each atom are less than 0.02 eV/ Å. The self-consistent calculations and non-self-consistent calculations are conducted with $5\times 5\times 1$ and $10\times 10\times 1$ Monkhorst pack k-point grid, respectively. The cutoff energy for the plane wave basis is set at 50 Ry (~ 680 eV), and the kinetic energy cutoff is set at 200 Ry. To induce a ferromagnetic configuration, the total magnetisation is constrained to be 1 ${\mu }_B$ /unit cell. The spin-dependent projected density of states (spin-PDOS) and charge density plots are calculated using the projwfc.x and pp.x programs, respectively, provided in the Quantum Espresso package.

Author contributions

B.L.O., E.S.T., and A.R. grew samples and performed in-situ RHEED and AFM measurements. A.J., C.D., and A.R. performed RSXMS, RSXS, and XAS measurements. B.L.O., E.S.T., M.S., and A.R. performed XRD measurements. A.J., E.S.T., and A.R. analyzed data comprehensively and wrote the manuscript with inputs from C.D., B.L.O., A.D.F., K.J., M.A.N., S.P.J., X.C., T.J.W., and M.B.H.B. A.R. proposed the idea, designed GA-RSMXS, GA-RSXS, and integrated UHV-MBE-PLD with in-situ RHEED and led the project. All authors have approved the final version of the manuscript.

Peer review

Peer review information

Nature Communications thanks Angelo Di Bernardo and Jonathan Pelliciari for their contribution to the peer review of this work. A peer review file is available.

Data availability

All data in the main article and supplementary information are available on request.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-69457-2.