## Introduction

Complex-oxide heterostructures have been established as an effective engineering platform offering prospects to create tunable electro-magnetic functionalities, enabled by manipulation of the cooperative interplay between electronic spin, charge, orbital, and lattice degrees of freedom1,2. The stacking of different oxides disturbs the subtle equilibrium among various interactions, leading to a wealth of exotic quantum states, such as two-dimensional electron or hole gas at the interface of two insulating materials such as LaAlO3/SrTiO3 (LAO/STO)3,4, the spontaneous magnetic reversal in La2/3Sr1/3MnO3 films5, a ferromagnetic (FM) interface between nonmagnetic constituents6,7, polar magnetic metal phase in BaTiO3/SrRuO3/BaTiO3 heterostructures8, chiral ferromagnetism in SrRuO3 films9, and strain-induced superconductivity in RuO2 films10. The continued advancements in thin-film synthesis have made possible the fabrication of complex-oxide layers down to extremely thin limits with atomic precision, providing fine control over different lattice structures and paving the pathway to observe unusual quantum states11,12,13,14,15.

The two ABO3 4d-perovskite structure ruthenates CaRuO3 (CRO) and SrRuO3 (SRO), despite having similar structure and electron counting, present unusual contrast in their physical properties. SRO is a strong Stoner metallic ferromagnet16,17; while CRO, though a metal17, lacks long-range magnetic order18,19. Extensive experimental and theoretical studies led to lively debates on the origin of the contrasting behavior, though the most likely explanation is that the impact of replacing Sr with Ca in SRO is indirect. The smaller ionic radius of Ca (2.31 Å versus 2.55 Å for Sr) leads to different octahedral Ru-O-Ru bond angles that result in subtle changes of the Fermi-energy density of states (DOS)20,21,22.

Thin films of CRO and SRO also exhibit distinct properties, depending on temperature, film thickness, substrate strain, and film stoichiometry. Relatively thick CRO films grown on STO (001) have been reported to be metallic23, yet under similar epitaxial strain, an insulating CRO phase can emerge below a certain critical thickness24,25, which depends on growth conditions and is much larger than the critical thickness (2–3 u.c.) for similar behavior by SRO films26,27. At present, the intrinsic critical thickness of stoichiometric CRO films is not known. In addition, theoretical calculations predicted that tensile epitaxial strain can drive CRO to a FM state28, yet experimental confirmation is lacking29. Moreover, cation substitution at Ru sites by defects/dopants has also attracted considerable attentions as a way to induce FM order in CRO, suggesting an extremely fragile ground state30,31,32,33,34,35. Therefore, the delicate nature of incipient ferromagnetism in CRO suggests that one can manipulate CRO thin films in unique ways to obtain unusual, even unexpected electro-magnetic properties.

The present work focuses on ultrathin CRO films, which we perturb by inserting a single SrO layer (thus, mimicking a single-u.c. of SRO14,15 or δ-doping36,37) in the middle of the films, all fabricated with atomic precision. Combining magneto-transport measurements, atomically resolved imaging by scanning transmission electron microscopy (STEM), and electron energy-loss spectroscopy (EELS), along with density-functional-theory (DFT) calculations, we reveal a thickness-dependent metal to insulator transition (MIT) with no sign of long-range magnetic ordering in pristine CRO films. As the thickness reaches 15 or fewer u.c., the films become insulating. However, the insertion of a single SrO layer not only triggers an insulator-to-metal transition in the 15 u.c. CRO films and enhances the conductivity of thicker films, but also drives the studied thin films (15–40 u.c.) toward emergent Griffiths-like phase and unusual ferromagnetism. Atomic-resolution imaging and DFT calculations reveal that SrO-layer insertion preserves the orthorhombic symmetry, and the structural and electronic changes are largely confined near the insertion layer. Our results underline the fragile nature of the magnetic properties and likely the electronic structure of CRO by which a highly localized modification is able to tip the delicate balance for both transport and magnetic ordering in the system.

## Results

### Atomic-scale structure and composition

We have fabricated epitaxial 15-u.c. CRO (CRO15), 20-u.c. CRO (CRO20), and 40-u.c. CRO (CRO40) films on SrTiO3 (001) substrates, and corresponding δ-doped CRO films containing a localized SrO layer nested in the middle, i.e., CRO7-SrO-CRO8, CRO10-SrO-CRO10, and CRO20-SrO-CRO20. Figure 1a shows a schematic of the CRO7-SrO-CRO8 heterostructure while Fig. 1b–d displays the atomically resolved structure of the same system. Our X-ray diffraction data (see Supplementary Information Note 1), and STEM measurements demonstrate that these films are fully strained to the substrate with high crystallinity (see Supplementary Fig. 2). The STEM results confirm microscopically that the heterostructures have a homogeneous SrO layer and coherent interfaces. It is apparent from the STEM image that the CRO7-SrO-CRO8 heterostructure is uniform with coherent and high-quality hetero-interfaces (Fig. 1b–d and Supplementary Fig. 3). In Z-contrast High-angle annular dark-field (HAADF) images, Sr (Z = 38) columns appear brighter than Ca (Z = 20), whereby a uniform and homogeneous single Sr layer is observed clearly in Fig. 1c and Supplementary Figs. 3, 4. Furthermore, the electron energy loss spectroscopy (EELS) elemental maps of Ca (purple) and Sr (green) (Fig. 1e and Supplementary Fig. 4) confirm that Sr is confined within a single layer with minimal if any intermixing, establishing that the nested SrO is a monolayer.

The high-resolution STEM imaging permits us to reveal the structural distortions (see Fig. 2). The orthorhombic (CRO) unit-cell oriented on the cubic STO (001) grows in the [110]O direction. Consequently, either in-phase [001]O or out-of-phase [1–10]O rotation axis can align along the [100] direction of STO; generating two different structural domains with a 90° rotation (referred as A and B, see Supplementary Note 3 for details)38,39. Viewing along the [100] direction of STO substrate, we can acquire projected structures of the film in the [001]O direction from domain A and the [1–10]O direction from domain B, simultaneously. In domain A, the in-phase octahedral rotation axis is along the STO [100], hence allowing the visualization of RuO6 octahedron tilt (Fig. 2a, c). In contrast, for domain B, the direct imaging of octahedral tilt is not possible, but orthorhombicity related A-site cation displacements can be measured as displayed in Fig. 2b, e. The projected octahedral tilt (θ as denoted in Fig. 2c, d) extracted from the ABF images of domain A (Fig. 2a, c) shows that except at the 1st unit-cell near film-substrate interface (θ ≈ 8.4°), the RuO6 tilt angle in the CRO film is constant (θ ≈ 11°); a nearly identical behavior as that of CRO bulk (θ ≈ 11.5°). Hence, the octahedral mismatch is adjusted close to the film-substrate interface, where TiO6 interfacial layers on the STO side undergo significant distortion to accommodate the octahedral mismatch of RuO6-TiO6 (bulk CaRuO3: θ ≈ 11.5° versus SrTiO3: θ ≈ 0°). Additionally, we note that the 15-u.c. undoped CRO film also has θ ≈ 11° (see Supplementary Note 4). Therefore, the octahedral network structure is not altered by the SrO-interlayer insertion. Instead, due to a corner-connectivity constraint, the octahedral geometry is conserved throughout the entire δ-doped heterostructure, i.e., the structure preserves bulk-CRO orthorhombic symmetry.

The A-site cation displacements (xA), a signature of orthorhombicity37,40 were determined quantitatively for individual layers with the domain B imaging (Fig. 2b, e as well as Supplementary Figs. 58). It is seen that the δ-doped heterostructure (see Fig. 2f) shows an averaged Ca-site xA ≈ 0.38 ± 0.07 Å, which matches that of a pristine CRO film (xA ≈ 0.38 ± 0.07 Å, see Supplementary Fig. 8), while slightly smaller than CRO bulk (xA ≈ 0.43 Å, see Fig. 2g). On the other hand, the xA at nested SrO is reduced to 0.26 ± 0.10 Å (see Fig. 2f), but it is significantly larger than that in bulk SrRuO3 (xA ≈ 0.12 Å, see Fig. 2h). These observations suggest a small local structural modification is present in the SrO layer, which is induced by the ionic (Ca/Sr) radius mismatch.

### Electron transport of pristine and δ-doped CaRuO3 films

To understand the δ-doping effect on the electronic properties of CRO films, we have systematically measured the transport behavior of the CRO films with and without SrO insertion. Figure 3a shows the sheet resistance temperature evolution of pristine and δ-doped CRO films for different thicknesses. As shown in Fig. 3a, the thicker pristine CRO40 film exhibits bulk-like metallic transport (dρ/dT > 0) down to ~21 K, followed by a small resistivity upturn (see Supplementary Fig. 9 for details), characterized by weak localization41,42,43,44,45. The intermediate thickness CRO20 film features a metallic behavior at high temperatures, but exhibits a resistivity upturn below ~95 K. Such a robust resistivity upturn at low temperatures is frequently observed in many metallic oxide films, especially close to the verge of a metal–insulator transition41,42,43,44. Finally, the 15 u.c. (CRO15) film is identified to be fully insulating (dρ/dT < 0 at all temperatures), where ρ(T) exhibits variable range hopping (VRH) (see Fig. 3b, c and Supplementary Note 5 for more details). Specifically, the CRO15 transport follows a Mott-type VRH [ln(ρ) T−1/3] above ~25 K (see Fig. 3b), indicating that the transport is governed by disorder-driven Anderson localization46,47,48. At low temperatures, a crossover to Efros-type VRH [ln(ρ) T−1/2] is observed (Fig. 3c), likely suggesting the significance of electron-electron interactions in the strong localization regime49,50,51,52. In contrast to insulating CRO15, the δ-doped film i.e., CRO7-SrO-CRO8 displays improved conductivity holding a room temperature metallicity, though a strong upturn appears below ~ 250 K (see the inset of Fig. 3a). Likewise, the δ-doping consistently lowers the resistivity and resistivity upturn temperatures, as seen in CRO10-SrO-CRO10 and CRO20-SrO-CRO20 (see Fig. 3a).

The δ-doping of CRO films not only triggers the enhancement of conductivity but also induces a pronounced ferromagnetic order revealed by magnetoresistance: $${\rm{MR}} = \left\{ {{\it{\rho }}\left( H \right) - {\it{\rho }}\left( 0 \right)} \right\}/{\it{\rho }}\left( 0 \right)$$, where ρ(H) and ρ(0) are resistivities with and without magnetic field, respectively. The MR in pristine CRO40 and CRO20 is very small, as expected for paramagnetic metallic systems (Fig. 3d). However, the MR is monotonically enhanced with reducing film thickness to CRO15 due to the charge localization. At the same time, a very small, but noticeable MR hysteresis could be observed in CRO15, signifying a weak and possibly short-range ferromagnetic fluctuation phase53,54. Meanwhile, the low-field MR in CRO15 is positive (see blue arrows in Fig. 3d) and becomes negative at higher fields. The positive MR is a sign of electron-electron correlations (EEC) that are robust at low temperatures, consistent with the presence of Efros-type VRH ρ(T) behavior (see Fig. 3c)55,56,57. In contrast, as shown in Fig. 3e, the δ-doping in CRO15 (i.e., CRO7-SrO-CRO8) leads to a clear butterfly-like hysteretic MR, representative of ferromagnetic order14,15,58,59,60,61. In parallel to this, the positive MR detected in pristine CRO15 is also diminished (see Fig. 3d, e), supporting the conjecture that the emergence of ferromagnetic ordering involves modification of electronic correlations35,62. In addition, as shown in Fig. 3e, a distinctive FM-induced hysteretic MR is also spotted in both CRO10-SrO-CRO10 and CRO20-SrO-CRO20 heterostructures, validating the appearance of FM order induced via benign δ-doping of CRO.

### Magnetic characterization

To further reveal the unusual magnetic behavior in the δ-doped films, we performed cryogenic magnetic force microscopy (MFM) studies (see Supplementary Note 6 for more details). The MFM images of the CRO10-SrO-CRO10 in different magnetic fields at 5.5 K are shown in Fig. 4a–h. There is weak bubble-like magnetic contrast (bright-dark pattern) in the zero-field MFM image after the sample was saturated at a positive field (6 T), indicating magnetic inhomogeneity. The magnetic contrast is barely above the noise level of our MFM system. These features suggest that the FM order in the ground state is not fully long-range. With an increasing magnetic field, the dark-bright contrast increases strongly. More bubble-like magnetic contrast emerges at −0.3 to −0.4 T (see Fig. 4b, c), indicating inhomogeneous switching of magnetic order. The field dependence of the magnetic contrast as measured by the root-mean-square (RMS) value of the MFM images (Fig. 4i) shows a sharp peak between 0 T and −1 T. While reaching its maximum value at around −0.3 T, the magnetic contrast is barely visible below −1 T, indicating that the sample is approaching saturation (see Fig. 4d). In accord with the above, the RMS value varies very little below −1 T. A typical MFM image of the sample at saturation is shown by the inset of Fig. 4i. In contrast to the negative ramping, relatively uniform magnetic contrast was observed between −6 and 0 T after saturating the sample at −6 T as in Fig. 4h–e. Consistently, the RMS values of the MFM images do not vary much as shown in Fig. 4i, demonstrating the hysteretic behavior of the magnetic order. Overall, the evolution of the magnetic contrast and their hysteretic behavior provide supporting evidence of unusual ferromagnetism without fully long-range ordering in the sample.

The magnetization as a function of temperature [M(T)] for pristine and δ-doped CRO films is shown in Fig. 4j. All pristine CRO films show a paramagnetic-like signal reminiscent of the STO substrate with no clear signs of a ferromagnetic transition. On other hand, SrO δ-doping in the middle of the CRO films induces a FM order since the M(T) represents a paramagnetic to ferromagnetic transition. However, the M(T) curves in the δ-doped CRO films have a rather unusual T-dependence. At low temperature, they show a non-typical long-range order M(T) line shape with a very weak upturn between 35 and 60 K. Above this temperature range, the magnitude of magnetization increases, but is still relatively weak compared to its sister counterpart, SrRuO3 films63. The presence of ferromagnetism is further corroborated by an anomalous Hall effect (see Supplementary Fig. 13 for details).

Normally, a long-range ordered FM system above TC obeys Curie–Weiss (CW) law; $$\chi = \frac{C}{{T-\theta _{\rm{cw}}}} = \frac{M}{H} \Rightarrow M^{ - 1} \propto \left( {T-\theta _{\rm{cw}}} \right)$$, where C is the CW constant and θcw is the Weiss temperature, so that M−1 is linearly proportional to T above TC. In our case here, a measurement of χ is not feasible due to the extremely thin films, but the T-dependent inverse of magnetization [M−1(T)] can shed light on the unusual CW behavior. As shown in Fig. 4k, the M−1(T) of CRO10-SrO-CRO10 in the paramagnetic state exhibits decent linearity only above a characteristic temperature TG ≈ 60 K, but a sudden downturn occurs below TG. Such a deviation from the CW law in the temperature range TC < T < TG is reminiscent of a Griffiths-phase (GP) phenomenon (TG is referred to as Griffith’s temperature)19,64,65,66,67. The GP is characterized by the coexistence of ferromagnetic entities within the globally paramagnetic phase, causing a non-analytical behavior in magnetic susceptibility with characteristic departure from Curie–Weiss behavior in the vicinity of TC and TG. Such a GP signature has been reported in bulk Ca-doped SrRuO3, where Ca substitution for Sr introduces ferromagnetic spin–spin coupling dilution through Ru–O–Ru bonds, and leads to TC reduction19.

### Density functional theory (DFT) calculations

We have performed DFT calculations on the heterostructure shown schematically in Fig. 5a to gain additional insights into the observed phenomena (see Supplementary Note 8 for details). Analyzing the structural changes due to the δ-doping, we find that the plane-projected octahedral tilt angle θ (Fig. 5b) remains essentially unchanged, whereas in Fig. 5c, a dip in the A-site cation displacement (xA) is consistent with the STEM data of Fig. 2. Additionally, by looking at the RuO2 interlayer spacing (Δ), a significant increase at the place of the δ-layer site occurs paralleling the dip in xA (Fig. 5d). Although not evident in the projected tilt angle (θ) measured by STEM, there is a large change in the 3D octahedral angle (defined as Θ, see Fig. 5e) at the δ-doping layer. Taken together, these results indicate that the insertion of the δ-doping layer causes a highly local modification of the atomic structure confined between the adjacent RuO2 layers.

In Fig. 5f, we show the calculated Ru-projected density of states (DOS) for the pristine CRO thin-film in the layers adjacent to the CaO layer that gets replaced by SrO (blue-shaded region). It is clear that the thin-film is semi-metallic8,22. We assume that such a thin film models CRO15, which according to Fig. 3d, is on the verge of being ferromagnetic (the accuracy of our DFT + U calculations would not allow us to reliably predict at what thickness such a state would exist). In Fig. 5f, we also show the Ru-projected DOS for the δ-doped film in several layers near the SrO plane (see also Supplementary Fig. 15). We note that the DOS in the immediately adjacent (green curves) differs from the others in that it signifies an enhancement of the DOS at the Fermi energy by approximately a factor of 2.

## Discussion

If some form of disorder is present at increasing levels as the film thickness is reduced, the thinnest film may have sufficient disorder to induce Anderson localization in the small number of states at the Fermi energy EF throughout the CRO film. Hence a MIT occurs at a critical thickness. If we then assume that the same level of disorder is present in a doped film as in an undoped film we reason as follows. In films of all thicknesses, a doped film has a larger DOS at EF in the vicinity of the SrO layer than in the corresponding undoped film. Thus, in all doped films, only a fraction of the propagating states in the region of the SrO layer undergo localization, creating a mobility edge, i.e., propagating states remain so, and the MIT is avoided. This effect enhances the conductivity of films above the critical thickness, as observed. For thin films below the critical thickness, the same effect induces metallic behavior in the region of the SrO layer, which is also in agreement with the experimental data since the data cannot tell if the film is conducting throughout or only in the region of the SrO layer. As for the Griffiths-phase-like ferromagnetism in doped CRO films, the above analysis also tells us that there may be sufficient density of propagating states at EF in the SrO region to satisfy the Stoner criterion locally. We can then speculate that nonlocal exchange may trigger a domino effect, which generates patchy ferromagnetism throughout the CRO film. It is not currently practical to perform DFT calculations in large heterostructures using hybrid functionals that include nonlocal exchange and check if the formation of FM patches in the CRO film lowers the total energy. The domino possibility remains to be tested.

In summary, we show that CaRuO3, otherwise being metallic and at the verge of a magnetic critical point, retains its nonmagnetic nature but becomes insulating in thin film form under a critical thickness (15 u.c.). In contrast, δ-doping a single layer of SrO into ultra-thin CRO films results in an unusual ferromagnetism and a transition back to a metallic state while the entire heterostructures preserve the bulk-CRO orthorhombic lattice symmetry. Atomic-resolution imaging along with DFT calculations find that SrO-layer insertion causes highly local structural and electronic changes. The calculated DOS at the Fermi energy shows a noticeable enhancement near the insertion layer, leading to the probable local satisfaction of the Stoner criterion, which in turn may induce patchy ferromagnetism in the entire film by nonlocal exchange interactions. The observations demonstrate the fragility of the emerging magnetic state in CRO, shedding light on the role of A-site cation in electronic and magnetic structure additional to lattice distortion in ruthenates. These findings provide an innovative pathway to understanding the correlated system’s electronic and magnetic nature through heterostructure architecture.

## Methods

### Film growth, X-ray diffraction, and magneto-transport measurements

Pristine and δ-doped CaRuO3 (CRO) films were grown on SrTiO3 (001) substrates by pulsed laser deposition (PLD) at 700 °C with an oxygen pressure of 100 mTorr. The δ-doping of SrO was achieved from SrRuO3 (SRO) target at a growth temperature of 700 °C and oxygen pressure of 100 mTorr. The utilization of an SrRuO3 target ensures the formation of the desired SrO-RuO2 stacking formation. A KrF excimer laser (λ = 248 nm) with a 10 Hz repetition rate and laser energy density ~1 J cm−2 was used. After growth, samples were cooled down at ~11°/min to room temperature in an oxygen atmosphere of 100 mTorr. To monitor the film growth and thickness, the in-situ Reflection high-energy electron diffraction (RHEED) was employed. X-ray diffraction was performed on a PanAlytical X’Pert thin-film diffractometer with Cu Kα−1 radiation with a single-crystal monochromator. The electron transport measurements were performed in a four-probe configuration on Quantum Design Physical Property measurement system (PPMS) in the temperature range of 5–300 K. For the magnetoresistance (MR), the external magnetic field was applied along the film normal. The magnetization was studied by using Quantum design SQUID (superconducting quantum interference device) reciprocating sample option (RSO). For magnetization as a function of temperature M(T) measurements, the samples were first cooled down to 5 K under the 5000 Oe field, and then the data was acquired while warming in presence of 100 Oe field. The data points were smoothed using Locally Weighted Scatterplot Smoothing.

### Scanning transmission electron microscopy (STEM) and electron energy loss spectroscopy (EELS)

The STEM and EELS results were attained using the 200 kV JEOL ARM electron microscope at Brookhaven National Laboratory (BNL) equipped with double aberration correctors, a dual energy-loss spectrometer, and a cold field emission source. Cross-sectional TEM samples were thinned using a focused ion beam with Ga+ ions followed by Ar+ ions milling down to sample thickness of 30 nm. The atomic-resolved STEM images were collected with a 21 mrad convergent angle (30 μm condenser aperture) and a collection angle of 67–275 mrad for HAADF and 11–23 mrad for ABF imaging. The STEM imaging conditions were optimized for simultaneous EELS acquisition with a probe size of 0.8 Å, a convergence semi-angle of 20 mrad, and a collection semi-angle of 88 mrad. EELS spectroscopy images were obtained across the whole film with a step size of 0.2 Å and a dwell time of 0.05 s/pixel. EELS spectra for composition distribution as well as Ru-L and Sr-L edges were acquired with energy dispersion of 1 eV/channel. The EELS spectra background was subtracted using a power-law function, and multiple scattering was removed by a Fourier deconvolution method.

### Magnetic force microscopy (MFM)

The MFM experiments were carried out in a homemade cryogenic magnetic force microscope using commercial piezoresistive cantilevers (spring constant ≈ 3 N/m, resonant frequency ≈ 42 kHz)68. The homemade MFM is interfaced with a Nanonis SPM controller and a commercial phase-lock loop (SPECS). The out-of-plane magnetic field was applied via a superconducting magnet. MFM tips were prepared by depositing a nominally 100 nm Co film onto the bare tips using sputtering. The MFM signal, the change of cantilever resonant frequency, is proportional to the out-of-plane stray field gradient. The sample surface is coated with Pt (15 nm)/Al (2 nm) bilayer to screen the electrostatic interaction.

### Density-functional calculations

DFT calculations were performed using the Vienna ab initio Simulation Package (VASP)69. The projector-augmented wave (PAW) method was used to describe the core-valence electron interactions70,71. For bulk-like unit cells, a plane-wave basis cutoff energy of 600 eV was used and reduced to 450 eV for the heterostructure. The Perdew-Burke-Ernzerhof form of the generalized gradient approximation was employed for the exchange-correlation functional with a Hubbard U (see Supplemental Information Note 8)72,73. For bulk unit cells, the k-point sampling was performed using 8×8×8 Γ-centered grids. For the heterostructure, a 4×4×1 Γ-centered grid was used. The heterostructure considered was terminated with CaO on both sides and consists of 5-layers of CaO on each side of the SrO layer. RuO2 layers have 4 Ru atoms/layer. A vacuum spacing of 15 Å along the z-axis was used to prevent spurious interactions between slabs due to periodic boundary conditions. In all cases, structures were relaxed until atomic forces were converged to be less than 0.02 eV/Å.