Enhanced electron-electron correlations in nanometric SrRuO 3 epitaxial films

Epitaxial and fully strained SrRuO 3 thin films have been grown on SrTiO 3(100). At initial stages the growth mode is three-dimensional~3D-!like, leading to a finger-shaped structure aligned with the substrate steps and that eventually evolves into a 2D step-flow growth. We study the impact that the defect structure associated with this unique growth mode transition has on the electronic properties of the films. Detailed analysis of the transport properties of nanometric films reveals that microstructural disorder promotes a shortening of the carrier mean free path. Remarkably enough, at low temperatures, this results in a reinforcement of quantum corrections to the conductivity as predicted by recent models of disordered, strongly correlated electronic systems. This finding may provide a simple explanation for the commonly observed—in conducting oxidesresistivity minima at low temperature. Simultaneously, the ferromagnetic transition occurring at about 140 K, becomes broader as film thickness decreases down to nanometric range. The relevance of these results for the understanding of the electronic properties of disordered electronic systems and for the technological applications of SrRuO3—and other ferromagnetic and metallic oxides—is stressed.


I. INTRODUCTION
The development of devices based on thin films is an active area of research.In particular, magnetic tunneling junctions with ferromagnetic oxide electrodes are interesting due to their promising technological applications.Successful fabrication of heterostructures requires to have a deep understanding of the effects related with the interfaces between layers.These effects may manifest itself in a variety of phenomena, including vacancies, structural disorder or phase segregation, and may be relevant to the transport and magnetic properties and thus, have a straightforward impact on the performance of the devices.Indeed, it has been recently demonstrated that the interface microstructure limits the spin-injection efficiency across heteroepitaxial interfaces in ZnMnSe/AlGaAs-GaAs spin-polarized light emitting diodes. 1 Manganite-based tunnel junctions such as La 2/3 Sr 1/3 MnO 3 /SrTiO 3 /La 2/3 Sr 1/3 MnO 3 , also display a dramatic suppression of their performance at temperatures well below the Curie temperature.It has been proposed that this effect originates from complex electronic inhomogeneities existing at the interfaces of these heterostructures. 2 The extreme tendency of manganites towards electronic phase separation is intimately related to the double exchange mechanism of ferromagnetic coupling and the existence of strong electron-phonon coupling.
On the other hand, understanding of the impact of disorder in the electronic properties of strongly correlated systems is an important issue, since metallic oxides involving 3d or 4d metal transition ions are commonly used in heterostructures and, as will be shown below, microstructural disorder close to interfaces plays a major role.
In this paper we will focus on these important issues by exploring in detail the magnetotransport properties of epitaxial SrRuO 3 thin films as a function of thickness (4 nmϽt Ͻ320 nm).SrRuO 3 is a promising material for using in technological applications. 3It is a metallic ferromagnet, whose ferromagnetism is tied to the conduction electrons lying in a * narrow band formed by the overlap of Ru t 2g orbitals with the O 2p orbitals. 4,5The itinerant character of magnetism in SrRuO 3 is well founded both theoretically and experimentally, 4 -6 and it has been proposed that the nature of the magnetic coupling in this compound should be more robust against interface effects when compared to doubleexchange ferromagnets such as manganites. 7Small distorsions induced in the lattice reverts in a narrowing of the * band that affect in a significant way its magnetic properties.In fact, substitution of Sr cations by other cations leads to the formation of non magnetic compounds such as CaRuO 3 or BaRuO 3 , with crystalline structures differing slightly from that of SrRuO 3 , due to slight tilts and rotations of the RuO 6 octahedra. 8This fact indicates that strain-induced effects arising from the film-substrate interactions could be relevant for the magnetotransport properties of SrRuO 3 films.On the other hand, the existence of strong electronic correlations in SrRuO 3 has been experimentally confirmed either from specific heat measurements, 4 low-temperature transport behavior, 9 or photoemission spectra, 10 among others; it has also been found that the Fermi-liquid state is remarkably sensitive to disorder and breaks down at a very low temperature (Tϳ10 K), further confirming the significance of the electronic correlations. 11Therefore, SrRuO 3 appears as an ideal candidate to explore the role of the growth-induced disorder on the transport properties of strongly correlated ferromagnetic oxides, a key issue in the field of spintronics.
3][14][15][16][17][18][19][20][21][22][23] In addition, there is some information about the early stages of growth in SrRuO 3 films, 14,21 but its correlation with physical properties is still lacking.The microstructure of films at nanometer scale, i.e., close to the interfaces, is closely related to the growth mechanism and may have a significant impact on the electronic properties of the film.Therefore it is necessary to undertake a thorough study on the thickness dependence of the magnetotransport properties in nanometric thin films.To the best of our knowledge, this study has only been performed on SrRuO 3 /SrTiO 3 superlattices, 12,13 but not in single films.In superlattices, a decrease of the Curie temperature was found as SrRuO 3 layer thickness decreases and this fact is attributed to a lowdimensional effect.Furthermore, the enhancement of the resistivity when reducing the SrRuO 3 layer thickness was attributed to scattering of conduction electrons at the SrRuO 3 -SrTiO 3 interfaces. 12n this paper we report on structural and transport measurements for epitaxial SrRuO 3 thin films grown on SrTiO 3 ͑100͒ substrates.We will show below that the initial growth mode found in our films leads to a self-arranged pattern of defective regions that induces an in-plane anisotropy of the electrical transport.We present experimental procedures to reduce these defects and to control the density of the defective regions.We shall take advantage of the controlled presence of microstructurally disordered regions to study in detail the quantum corrections to the conductivity occurring at low temperature.We will show that this is intimately connected to the density of defects.
Finally, we will address the thickness dependence of the magnetic transition.We will show that the onset of ferromagnetism remains essentially constant down to tϷ6 nm and thus is not determined by dimensional effects.However, the ferromagnetic transition becomes broader as the thickness of the films is reduced, likely as a result of microstructural defects originating from the film growth.

II. EXPERIMENTAL
SrRuO 3 thin films were grown on SrTiO 3 (100) substrates by pulsed laser deposition with a KrF excimer laser ( ϭ248 nm), with a pulse duration of 34 ns and a repetition rate of 10 Hz.The laser beam was focused to a fluence around 2 J/cm 2 and directed at an angle of 45°on a rotating target of stoichiometric SrRuO 3 .The substrate was placed parallel to the target at a distance of about 5 cm.The films were deposited at 750 °C and under an oxygen pressure of 0.1 mbar.When the laser was switched off, the oxygen pressure was slowly increased whereas the substrate was cooled down, reaching values of about tens of mbar during all the cooling.The films grown in this way will be labeled henceforth as series A films.No treatment of the substrates had been undertaken, prior to film deposition, to favor a particular atomic termination or to promote eventual surface reconstruction.However, atomic force microscopy ͑AFM͒ images revealed that as-received substrates, after heated to a temperature identical to that used for thin film deposition, display a clear miscut-originated terraces and steps topography.
Using these conditions a series of films of different thickness were prepared by changing the number of laser pulses. 23he thickness ͑t͒ of the films, ranging from 4 to 320 nm, was measured by using either a stylus profilometer or x-ray reflectometry, and the structural quality and lattice parameters were investigated by using x-ray diffraction ͑XRD͒ measurements in a four-circle diffractometer using Cu K ␣ radiation.AFM working in tapping mode was used for surface characterization.Transport measurements were performed with the four-probe method, with contacts made on previously deposited Au, in a PPMS system ͑Quantum Design͒.

III. RESULTS I: MICROSTRUCTURE AND ELECTRICAL ANISOTROPY
Reciprocal space maps were performed for the ͑204͒ reflection.From these measurements, shown in Fig. 1, several conclusions can be drawn.First, all the films show an inplane lattice parameter very close to the lattice constant of the substrate.Indeed, the data indicate that the in-plane lattice parameter of the films are a 0 Ϸ3.91 Å, while the SrTiO 3 is a cubic perovskite with a 0 ϭ3.905Å.It is remarkable that all films (4 nmрtр320 nm) are found to be fully strained.Second, the out-of-plane lattice parameter is cϷ3.96Å for all the films, so the unit cell is slightly compressed in volume ͑ϳ0.2%͒ with respect to the values of bulk SrRuO 3 ͑pseudocubic, a 0 Ϸ3.93 Å).No significant variation of these lattice parameters with thickness is observed.Therefore, the SrRuO 3 unit cell of these films is always compressively strained in the plane of the film and undergoes a tensile stress in the out-of-plane direction.These data are similar to those reported by other authors, signalling a biaxial stress. 15On the other hand, the rocking curves, measured around the ͑002͒ reflection, are about ⌬ϭ0.09°wide ͑half-width at half maximum͒, irrespectively on the film thickness, demonstrating the good crystallinity of the films.This property can be also deduced from the shape of the reciprocal lattice peaks, in which the splitting due to K ␣1 and K ␣2 radiation is observable.Moreover, the scans, measured around the ͑022͒ reflection, indicate a good in-plane epitaxy.
The evolution of the surface morphology is summarized with the AFM images shown in Fig. 2. At early stages of growth ͓tϷ4 nm, Fig. 2͑a͔͒ a fingerlike pattern formed by three-dimensional elongated islands following the ͓100͔ direction of the substrate is developed.At intermediate values of thickness ͓tϷ8 nm, Fig. 2͑b͔͒ there is a coalescence of these islands.The islands are well connected, although a number of holes, with a maximum depth of ϳ5 nm, remain visible on the film surface.The most noticeable is that a structure of terraces starts to develop, and thicker films ͓Fig.2͑c͔͒ show a well-defined structure of terraces and steps, which typically have one unit-cell height.The terraces are smooth, and a very low roughness ͑root mean square value͒ of 0.13 nm is determined on a 1ϫ1 m 2 image.The terraces have the same direction and width that those observed ͑not shown͒ on the substrates ͑miscut angle Ͻ0.2°͒.This fact, and the low number of two-dimensional islands, suggests that the growth mode is step flow.The observed transition from a 3D to a 2D growth mode is surprising, and it will be described elsewhere. 24his remarkable transition, whereby a 2D step flow occurs at thickness around 10 nm subsequent to a 3D fingerpatterned growth at first stages, might have some consequences on the transport properties of the specimens.Indeed, a striking effect is observed in the resistivity.Electrical currents were injected in two orthogonal directions, and the respective measured resistivities are designated as ʈ and Ќ .These directions were chosen so that they were aligned along and normal to a ͓100͔ direction of the substrate.As illustrated in Figs.3͑a͒-3͑c͒ the resistivity displays the typical metallic behavior of SrRuO 3 .For the thickest film FIG. 2. ͑Color online͒ AFM surface images for films with ͑a͒ tϭ4 nm, ͑b͒ tϭ8 nm, and ͑c͒ tϭ40 nm.FIG. 3. Plot of the Ќ -T and ʈ -T curves for three films of series A ͓͑a͒ tϭ320, ͑b͒ tϭ40 nm, ͑c͒ tϭ8 nm], showing the inplane transport anisotropy.On the contrary, in films of series B either cooled in Ar ͑d͒ or in O 2 ͑e͒ this anisotropy vanishes.
(tϷ320 nm) we measured (300 K)Ϸ240 ⍀ cm, similar to previously reported values for epitaxial films and single crystals.Due to the peculiar growth mechanism, the thickness of the thinner films is not well defined.In spite of this, nominal values, determined from the number of laser pulses, have been used to compute the resistivities and these values are used throughout.
From the measurements plotted in Figs.3͑a͒-3͑c͒ one can conclude that ͑i͒ at any temperature, increases when reducing the thickness and ͑ii͒ a clear anisotropy is observed, with ʈ Ͻ Ќ which reduces when increasing the film thickness.In the light of the peculiar growth mechanism occurring in these films, it is reasonable to correlate ʈ with current injection along the ͓100͔-aligned finger-shaped 3D islands observed in the AFM images, whereas Ќ corresponds to current that is essentially perpendicular to them.One must draw attention to the fact that the tϭ40 nm film ͓Fig.3͑c͔͒ still shows a prominent in-plane resistivity anisotropy, in spite of having a very regular surface morphology.
The experimental data coming from the AFM images combined with the observed ( ʈ , Ќ ) anisotropy, convincingly suggest that a well patterned structural and a concomitant electronic disorder appear in films of series A. The fact that the anisotropy progressively is wiped out as the thickness is increased indicates that this disorder is more prominent near the film-substrate interface.This is not surprising, if one considers the growth mechanism just discussed.
Before reaching the 2D growth, there is coalescence of the finger-shaped islands.At the edges where these grains merge together there could be some oxygen content depletion as a part of microstructural disorder that could allow some strain relief.With the aim of checking whether our films were oxygen deficient, we prepared films grown in the same conditions as those of series A, but once the growth had finished, the samples were cooled down to room temperature in an oxygen rich atmosphere, by introducing a pressure of 1 bar inside the chamber at a temperature of 530 °C.Note that in this way we also changed the cooling rate with respect to films of series A. These films are labeled hereafter as films of series B. X-ray diffraction data showed no difference in the structural parameters with respect to films of series A.
The in situ annealing described above for films of series B resulted in a suppression of the ( ʈ , Ќ ) anisotropy, as is seen in Fig. 3͑e͒.With the purpose of exploring further and eventually confirming whether the remarkable features appearing in the transport properties of films of series A could be attributed to a lack of oxygen at the grain boundaries, we performed some ex situ annealings in oxygen ( P O2 ϭ1 bar, 45 min, 500 °C͒ on series A films, reproducing similar conditions found in the in situ annealing of films of series B. However, attempts to oxygenate the films of series A were unsuccessful since the anisotropy of the transport properties remained.Consequently, we conclude that the in-plane transport anisotropy is closely related to microstructurally disordered, but likely well-oxygenated regions, formed at grain boundaries.
It has been recently observed, by using x-ray synchrotron radiation 25 that SrRuO 3 undergoes a series of phase transfor-mations ͑polymorphism͒, going from an orthorhombic Pnma structure at room temperature, changing continuously to Imma at about 685 K, then changing discontinuously to tetragonal I4/mcm at about 825 K, and finally, changing continuously to a cubic structure at 950 K.This result provides a very simple and natural way to rationalize the present experimental observation.The different phases of SrRuO 3 differ essentially in the tilt of the RuO 6 octahedra and, therefore, on the Ru 4dϪO 2p bandwidth and then on their transport properties.The residual stress at the grain boundaries may promote the local presence of some particular phase of the polymorphic family, which certainly are unobservable by conventional x-ray diffraction, and the electrical transport around and close the step edges may be rather different.As the tetragonal to orthorhombic transition is a first order one, 25 the cooling rate should be very relevant to determine its relative concentration.With the purpose of having a deeper insight in the possible role of the cooling rate, we performed an additional experiment preparing a film of series B, but substituting oxygen by argon; namely, once the growth had finished, an argon pressure of 1 bar was introduced inside the chamber at a temperature of 530 °C.Thus, we keep a similar cooling rate than in series B but in an oxygen-free atmosphere.As shown in Fig. 3͑d͒, this annealing lead to films with no anisotropy at all, thus supporting the view according to which the cooling rate has a key role in the observed anisotropic behavior.This argument illustrates that the existence of the complex phase transformation in SrRuO 3 upon cooling has a profound impact on the transport properties.
The observed microstructural disorder has important consequences on the magnetotransport properties: on one hand, there is a conductivity depression at the lowest temperature signalled by the appearance of minima in the resistivity and, FIG. 4. The low-temperature (5 KрTр30 K) resistivity is plotted for the films: ͑a͒ 8 nm series A ( Ќ ), ͑b͒ 8 nm series A ( ʈ ), and ͑c͒ 6 nm series B. The temperatures at which the minima appear are indicated, as well as the fittings to the expression ͑3͒ ͑solid lines͒.
on the other hand, the ferromagnetic transition becomes broader.Both effects are enhanced as disorder increases.In the following we will discuss in detail both issues.

IV. RESULTS II: LOW-TEMPERATURE ELECTRICAL TRANSPORT
With the aim of determining the effect of microstructural disorder on the electronic properties, we take advantage of the controlled presence of defective regions by using the low-temperature transport data in the thinner films.We use the data collected for the tϭ8 nm of series A ͑both ʈ and Ќ ) and those of ʈ of the tϭ6 nm film of series B. Detailed inspection of the low-temperature region of the resistivitytemperature curves reveals the existence of minima in resistivity appearing at Tр20 K.In Fig. 4 the temperature dependence of the resistivity is plotted for the film 8 nm thick ͑series A͒ for both ʈ and Ќ ͑inset͒ and for the film 6 nm thick ͑series B͒.The temperatures at which the minima appear are also indicated.Note that Ќ of the 8 nm film shows a minimum at about 20 K, whereas for ʈ the minimum is at about 8 K, and for the 6 nm film it is at 6.5 K.This means that disorder is more prominent in the first case, while for the two latter it is weaker.One can discard the Kondo effect, associated with the scattering of the conduction electrons by isolated localized magnetic impurities as a possible source for the formation of the resistivity minima.Indeed the formation of localized magnetic moments in SrRuO 3 is not likely to occur, as it is a metallic itinerant ferromagnet whose magnetism is tied to the conduction electrons lying in a narrow * band.The narrowing of this conduction band, that is attained, for instance, by inducing distorsions in the crystalline structure by substitution of Sr cations by other cations, leads to the formation of nonmagnetic compounds, such as CaRuO 3 or BaRuO 3 . 26On the other hand, as observed in Fig. 5 for the film with tϭ8 nm ͑series A͒, the application of a field of 5 T induces only a small magnetoresistance but does not remove the minima signalling its nonmagnetic origin.Therefore, in agreement with Lo ´pez de la Torre et al., 9 we conclude that the Kondo effect is not likely to be the source of the low-temperature minima commonly observed in SrRuO 3 thin films. 27An alternative nonmagnetic mechanism leading to resistivity minima could be disorder induced localization, either through weak localization or by electroelectron enhanced interactions. 28 -30In order to elucidate the possible relevance of these mechanisms, we have done a careful analysis of the temperature dependence of the lowtemperature resistivity.
Following Altshuser and Aronov 29 and Abrikosov, 30 we consider a model including quantum corrections to the conductivity in 3D systems.Within this framework, the lowtemperature dependence of the conductivity can be described by where the first term is the usual temperature independent elastic scattering from defects, and the second is related to quantum corrections from e Ϫ -e Ϫ interactions.As shown by Abrikosov, these corrections can be estimated by using the expression 30 where ϷE F ͑the Fermi energy͒, F is the electronic Fermi wavelength, and l is the mean free path.Knowing that E F Ϸ2 eV, m*Ϸ3.7m e ͑see Ref. 4͒, we can estimate F Ϸ4.5 Å.The mean free path l is estimated from ϭne 2 /m*ϭne 2 l F /h, with nϷ2ϫ10 22 cm Ϫ3 ͑Ref.20͒.
For our samples, Ϸ2ϫ10 3 ⍀ Ϫ1 cm Ϫ1 at 5 K, so the mean free path is lϷ5 -6 Å at low temperature, so we have k F l Ϸ(2/ F )lϷO(1) in our films.Therefore, we expect the quantum corrections to the conductivity given by Eq. ͑2͒, to be relevant at low temperature.
Assuming that the Mathiessen's rule holds, and in order to account for higher order scattering mechanisms and to extend analytical description to higher temperatures, an additional T 2 term should be included.Accordingly the resistivity data has been fitted to Results of fittings to the expression ϭ͓1/( 0 ϩaT 1/2 )͔ϩbT 2 in the range 5 KрTр30 K for a thin film of series A with tϭ8 nm ͑fittings corresponding to Ќ and ʈ ) and for a thin film of series B with tϭ6 nm.The temperatures at which the -T curves reach a minimum (T min ) are also indicated.
As evidenced by the solid lines through the experimental data, Eq. ͑3͒ allows obtaining excellent fits of (T) in a wide (5 KрTр30 K) temperature range ͑Fig.4͒.The results of our fits are summarized in Table I.The T 2 term in Eq. ͑3͒, is usually ascribed to electron-electron scattering taking into account Pauli's exclusion principle.The b coefficient can be evaluated by using 30 bϳ m*k B From this expression we estimate bϷ4 ϫ10 Ϫ12 ⍀ cm K Ϫ2 , that is 3-4 orders of magnitude smaller than our measured value (bϷ2 -3ϫ10 Ϫ8 ⍀ cm K Ϫ2 ).This important discrepancy was already noted by Klein et al. 20 ͑see also Fig. 2 of Ref. 11, for measurements on single crys-tals͒ and remains poorly understood.
More important within the context of this paper, is that the coefficient a of the T 1/2 term is enhanced when the disorder increases ͑see Table I͒, as predicted by expression ͑2͒.Indeed, as the zero-temperature conductivity 0 is a measure of the degree of disorder, it is found that there is a clear correlation between the increasing relevance of quantum suppression of conductivity at low temperature and disorder.This is illustrated in Fig. 6͑a͒, where we plot a vs 0 ͑closed symbols͒.
From Eqs. ͑1͒ and ͑2͒ it follows that Therefore a linear dependence of a vs 0 Ϫ1/2 is expected.As illustrated by Fig. 6͑b͒ ͑closed symbols͒, this is just the observed behavior.Data analysis can be cross checked by evaluating the Fermi wavelength from the measured slope in Fig. 6͑b͒.We find F Ϸ2 Å, which is in good agreement with estimates given above.
It could be argued that a 3D limit could not be appropiate to describe the physics of nanometric thin films ͑recall that the thickness of the films under discussion is of about 6 -8 nm͒.We shall not discuss here which description is most appropriate, but we will emphasize that in a 2D weaklocalization model, the low-temperature quantum corrections to the conductivity are described by 28 -30 ϭ 0 ϩaЈ ln TϩbT 2 .͑6͒ If use is made of Eq. ͑6͒ to describe the experimental data, good fits can also be obtained.The important message however, is that also in this framework, the coefficient aЈ still displays a close relationship with the degree of disorder.Therefore the same conclusions can be drawn; i.e., quantum interference effects are always enhanced as disorder increases; no matter the model is used to analyze the data.Quantum corrections from electron-electron interactions are at the origin of the resistivity minima commonly observed in SRO thin films.

V. RESULTS III: FERROMAGNETIC TRANSITION
Finally we address the key issue of the magnetic transition and its dependence on thickness and, thus, the influence of disorder.In bulk SrRuO 3 specimens, the Curie temperature is T C ͑Ϸ160 K͒, and the magnetic transition is charac-FIG.6.The coefficient a of the quantum correction T 1/2 term is plotted against the residual conductivity 0 ͑left͒ and versus 0 Ϫ1/2 ͑right͒.
Solid symbols correspond to ʈ and Ќ of the 8 nm thick film ͑series A͒ and of the tϭ6 nm film ͑series B͒ fully described in the text.Open symbols correspond to measurements performed on two additional tϭ6 nm thin films grown on vicinal ͑᭝͒ and on exact ͑᭺͒ SrTiO 3 substrates.FIG. 7. The paramagnetic to ferromagnetic phase transition can be probed by plotting the d/dT curves against the temperature.The onset of ferromagnetism (T C ) is seen to be at ϳ150 K for all the samples ͑indicated by a vertical dotted line͒.Nevertheless, as the thickness decreases, a shift to lower temperatures is seen for the peak (T C *), together with a broadening of the transition, both in series A ͑top pannel͒ and B ͑bottom pannel͒.
terized by a peak in the derivative d/dT at T C * . 20In our films, we observe ͑see Fig. 7͒ that the onset of ferromagnetic correlations-signalled by the rising of d/dT-remains nearly constant at ϳ150 K and that T C * ͑see Fig. 8͒ is pro- gressively shifted towards a lower temperature as the thickness decreases: T C *ϳ(127-110) K for films of series A, whereas for films of series B T C * is somewhat higher: ϳ͑132-118͒ K. Two conclusions are evident from the experimental data: ͑i͒ for all films we found that the measured T C * is substantially lower than the bulk value and ͑ii͒ T C * depends on thickness 22,23 while T C does not.
It is well known that the Curie temperature of SrRuO 3 decreases under hydrostatic pressures, 31 as a result of the induced modification of the overlapping of the Ru 4d and O 2 p orbitals.In the present case, however, we must stress that the films have identical in-plane cell parameters, so the substantial shift of T C * towards lower values as thickness de- creases cannot be explained by an alteration of the cell parameters but likely it is related to the microstructural disorder concomitant to the island growth process observed at early stages of film growth.As mentioned above, the magnetic properties of the ruthenates are strongly sensitive to small distortions of the unit cell, consisting of tilts and rotations of the RuO 6 octahedra. 8Consequently, the hypothetical stabilization of a distinct polymorphic SrRuO 3 phase near the grain edges may lead to a local weakening of the ferromagnetic coupling whereas the rest of the system is relatively unaffected.Interestingly enough is to point out that the onset of ferromagnetism, as indicated in Fig. 7, appears in all films at TϷ150 K, so that there are always regions relatively undistorted where the ferromagnetic correlations appear at this temperature, and these regions are more significant as the thickness increases, i.e., when disorder decreases.When the thickness decreases the broadening of the d/dT curve reflects the broadening of the transition and a decrease of T C * results.

VI. CONCLUSIONS
The evolution of the magnetotransport properties in nanometric epitaxial SrRuO 3 thin films grown on SrTiO 3 sub-strates has been analyzed.3D growth occurs at the first stages, eventually evolving to a 2D step flow growth.The initial growth leads to the formation of finger-shaped 3D elongated growth islands aligned to the substrate steps that coalesce at a critical thickness of t around 10 nm.This peculiar behavior leads to a dramatic in-plane anisotropy of the resistivity, even in films with a very regular surface.We argue that the presence of defective regions, occurring where the growth islands merge, is at the origin of the observed anisotropy.We suggest that the existence of the complex phase transformation in SrRuO 3 upon cooling is at the origin of these remarkable transport properties.In addition, we have presented experimental procedures to reduce these defects.The presence of microstructural disorder leads also to a reduction of the residual conductivity and thus the mean free path of carriers shrinks.We have shown that this promotes a reinforcement of the electron-electron correlations that can be understood on the framework of current ideas of effects of disorder in strongly correlated electronic systems.Accordingly, we have shown that the electron-electron correlations clearly correlate with the degree of disorder and thus they become prominent in nanometric thin films.Finally, the broadening and shift towards lower temperatures of the kink in the resistivity curves ͑that signals the Curie temperature͒ are also found to be intimately related with disorder and are more relevant when film thickness is reduced.In spite of this, the onset of ferromagnetic correlations remains fixed at a constant temperature.
The results reported here illustrate the extreme sensitivity of strongly correlated systems to disorder and thus to the initial stages of film growth.The fact that the mean free path l is close to the electronic Fermi wavelength F is at the origin of the enhancement of quantum corrections at low temperature.Given that SrRuO 3 is an attractive oxide being used already in some applications and being considered as a candidate for technological developments, the present findings may have a deep relevance in the fabrication of multilayered technological devices, such as magnetic tunneling or ferroelectric junctions and to overcome the difficulties pointed out above.
After submission of this paper, we have performed some further measurements that reinforce the main lines here outlined.According to the experimental work of other authors, the vicinality of the SrTiO 3 substrates has a strong influence on the growth of SrRuO 3 thin films. 16,27In agreement with these findings, we are able to control the degree of microstructural disorder of the SrRuO 3 thin films by growing them on miscut SrTiO 3 substrates.We have grown two films with tϭ6 nm in the same conditions but on different substrates, one with a nominal zero-miscut angle, and the other with a miscut angle of 2°. 32The experimental results reveal the expected behavior, i.e., the film grown on the vicinal substrate has a lower degree of disorder as indicated by the lower temperature at which the resistivity minima appear.Indeed, for this film, no resistivity minimum is observed at Tу5 K when current is injected along the substrate steps.Therefore, this procedure has allowed us to add three new points to Figs. 6͑a͒ and 6͑b͒, marked as open circle symbols.We observe that these new points follow the trend found in the previous experiments ͑closed circle symbols͒, i.e., they follow the same a vs 0 Ϫ1/2 and a vs 0 laws as the previous ones, and this fact corroborates the findings showed in the present paper.

FIG. 1 .
FIG. 1. Reciprocal space maps for different samples at the ͑204͒ reflection: ͑a͒ 40 nm, ͑b͒ 80 nm, ͑c͒ 320 nm.Arrows in ͑b͒ indicate the splitting of the peak due to K ␣1 and K ␣2 radiation.

FIG. 8 .
FIG. 8.The variation of T C * with thickness is plotted for series A ͓T C *(A)͔ and series B ͓T C *(B)͔.