Quantifying the critical thickness of electron hybridization in spintronics materials

In the rapidly growing field of spintronics, simultaneous control of electronic and magnetic properties is essential, and the perspective of building novel phases is directly linked to the control of tuning parameters, for example, thickness and doping. Looking at the relevant effects in interface-driven spintronics, the reduced symmetry at a surface and interface corresponds to a severe modification of the overlap of electron orbitals, that is, to a change of electron hybridization. Here we report a chemically and magnetically sensitive depth-dependent analysis of two paradigmatic systems, namely La1−xSrxMnO3 and (Ga,Mn)As. Supported by cluster calculations, we find a crossover between surface and bulk in the electron hybridization/correlation and we identify a spectroscopic fingerprint of bulk metallic character and ferromagnetism versus depth. The critical thickness and the gradient of hybridization are measured, setting an intrinsic limit of 3 and 10 unit cells from the surface, respectively, for (Ga,Mn)As and La1−xSrxMnO3, for fully restoring bulk properties.

Due to the complex interaction between charge, orbital and magnetic orders in manganites, all of them effectively influence the double-exchange transport mechanism. As a result, the resistivity of the film and its Curie temperature directly depend upon film quality. MBE-grown LSMO films with thickness more than 5 nm have no in-plane anisotropy in electrical and magnetic properties. Resistivity of optimally doped LSMO 100 u.c. thick film reaches the value of 70 µΩ cm ( Supplementary Fig. 5) and Curie temperature can be estimated as 345 ± 5 K (defined as the derivative maximum), while for bulk crystal of the same doping level Curie temperature reaches 370 K and resistivity approaches 100 µΩ cm [2]. Squared hysteresis loops with a coercive field of about 9 Oersted were measured by magneto optical Kerr effect (MOKE).
Films have a flat surface with clearly visible (by AFM) regular terraces 0.4 nm high (up to 20 u.c. of thickness) ( Supplementary Fig. 6), confirming previous reports [3][4][5]. RHEED pattern shows half-order diffraction peaks corresponding to oxygen octahedral around Mn atom distortion.

Supplementary Note 2: Structural and magnetic characterization of (Ga,Mn)As thin films
Ferromagnetic (Ga,Mn)As films (Mn doping level between 5% and 13%) were grown by molecular beam epitaxy using a modified Veeco Gen II system, following a well established procedure described in Ref. [6]. Thickness ranging between 20 and 300 nm were grown.
Details on the nominal thickness of the samples and the exact growth temperature are given in Supplementary Table 1.

The nominal Mn concentration was determined by secondary ion mass spectroscopy (SIMS)
measurements. The absolute Ga deposition rate was determined by RHEED oscillations on GaAs(001). Details on the sample growth and the used MBE system are given in ref. [6].
The magnetic properties of the samples were studied using superconducting quantum interference device (SQUID) magnetometry and by MOKE over a wide temperature range (10 < T < 300 K). The Curie temperature TC measured with SQUID is obtained from the same piece of (GaMn)As measured with HAXPES. To extract TC, from the SQUID data, the magnetization was saturated in high field and subsequently the temperature dependent magnetization m(T) was measured in a field of 100 Oe. TC was taken as the inflection point of the measured m(T) curve. Supplementary Fig. 7 shows typical results for 6% and 12% Mn doped films with different thickness. Post-annealing of the sample has been purposely avoided, in order to exclude MnAs cluster segregation on the surface.

Supplementary Note 3: Contamination and HAXPES
Reliability of HAXPES results are strictly connected to a careful control of contamination.
Results shown in Fig. 1 and Fig. 2

(GA,Mn)As
For AFM analysis, samples for the same batch were cut in two pieces. One piece was untreated; the other piece was chemically etched following the established procedure for removing spurious contamination from the surface. Samples used for HAXPES and spectroscopy characterization are etched ones. Details of chemical etching procedure are found in ref. [7]. In both cases, samples were washed by ultra-pure water, dried under nitrogen flux and measured in air within about 10 minutes. Root mean squared area roughness values were determined by averaging at least three different 3x3 μm 2 and 10 x10 µm 2 areas using the standard deviation of these measures as the uncertainty. Supplementary  Fig. 9 reports results of the untreated sample. The distribution of outgrowths (size ranging between 100 and 500 nm, thickness ranging between 3 and 12 nm) is not homogeneous. The RMS roughness is 1.05± 0.20 nm which reduces to 0.4 ± 0.10 nm if measured in between the outgrowths.
Supplementary Fig. 1 shows AFM images of the sample after chemical etching. Note after etching the number of outgrowths (size between 100 and 200 nm with a thickness between 3 and 10 nm) were strongly reduced with respect to the untreated. The RMS roughness of etched sample is 1.51± 0.25 nm and is less sensitive to the presence of the outgrowths. The RMS roughness measured in between the outgrowths is 1.21 ± 0.15 nm.

LSMO
Root mean squared area roughness values were determined, after AFM measurements, by averaging at least three different 5x5 μm 2 and 50 x50 µm 2 areas. Sample shows parallel grooves 15 µm spaced with some small outgrowths (< 5 nm thick) rarely present. The measured roughness for thin films with thicknesses above 40 u.c. is 0.60±0.15 nm (0.32 ±0.10 nm if measured in between the grooves). The small modulation appearing in Supplementary   Fig. 11 (5x5 µm 2 image) is due to the terraces of the substrate and it does not influences the mean roughness.

Supplementary Note 5: Peak Fitting procedure
In order to estimate the contribution of the extra-peak to the total photoemission signal, a fitting procedure of the lineshapes is required: since the extra-peak in the Mn 2p1/2 component is not very well resolved, we restricted our analysis to the case of the Mn 2p3/2.
The lineshape is the result of the superposition of various peaks associated to different oxidation states, which in turn are mixed by hybridisation and display a multiplet structure, which in the experimental spectra is not resolved.
We started our analysis from the spectrum acquired at 5940 eV which displays the most intense extra-peak. We succeeded in reproducing the extra-peak only by using a Gaussian.
We managed to account for the rest of the lineshape by using five Gaussian lines (see Supplementary Fig. 13). We left the parameters of the peaks free when passing from a photon energy to another as reported in Supplementary Tab. 2. As detailed in Supplementary Fig. 13, Peak 1 represents the extra-peak, while Peak 2 -6 reproduce the rest of the Mn 2p3/2 lineshape. The background was fitted by using a Tougaard-type line.
The standard deviation around zero of the residuals (difference between the data and the fit) was in most of the cases <0.15% and always <0.2%.
We applied a similar approach to the case of the fitting of the Mn 2p3/2 measured from the La0.67Sr0.33MnO3 spectra in the metallic phase (T = 200 K). In this case when fitting the lineshapes, other than the evaluation of the integral background, a major source of uncertainty derived from the determination of the area of the satellite peak at 1000 eV, where the feature it is not resolved. As for the case of Ga0.87Mn0.13As sample, the fitting parameters have been left free to move. The parameters obtained from the fitting procedure are shown in Supplementary Tab. 3. The standard deviation around zero of the residuals was always <0.5%.

Supplementary Note 6: X-ray penetration depth in HAXPES
The grazing incidence geometry is a relevant parameter affecting HAXPES measurements, as when the low incidence angle geometry is exploited, the x-ray penetration depth might decrease markedly to values of the same order as the photoelectron escape depth [8]. For fixed grazing incidence angle, this effect is more relevant for the soft rather than the hard xray photon energies. However, we show here that in our experiment the penetration depth of the incident x-ray is always larger than the Mn2p photoelectron escape depth by about one order of magnitude. This result comes out through comparing the attenuation length of the incident x-rays and the Mn 2p photoelectrons for each excitation energy adopted in our experiment. We remind here that the propagation of the incident X-rays across the solid is characterized by the attenuation length (λX), namely the depth into the material measured along the surface normal where the intensity of x-rays falls to 1/e of its value at the surface.
Accordingly to Ref. [9], we have estimated the values of λX as a function of the grazing incidence angle of the x-ray beam for all the photon energies adopted in our experiment, as shown in Supplementary Fig. 14 for both materials, using the optical constants available in Ref.
[10]. For the 3-degrees grazing incidence geometry, λX ranges from about 8-9 nm to more than 200 nm passing from 800 eV to about 6 keV, respectively. These values are compared in Supplementary Fig. 15 to the correspondent electron attenuation length λeof the Mn 2p photoelectrons calculated with the TPP-2M formula. [11,12] The kinetic energy of the Mn 2p photoelectrons, assuming a Binding Energy of 640 eV, ranges from about 140 eV (for hν = 800 eV) to 5300 eV (for hν = 5940 eV), thus spanning the so-called "universal curve" of λefrom around the minimum to the larger values of the right branch of the curve, respectively. The take-off angle of detection of the photoelectrons is about 3-degrees off the normal to the surface, hence our experimental geometry maximizes the bulk sensitivity and makes angular effects on λenegligible. The results of Supplementary Fig. 15 demonstrate that for the Mn 2p photoelectrons the condition λX >> λeis largely fulfilled for all the photon energies adopted in our experiment. We can therefore conclude that the penetration depth of the X-rays is always larger than the photoelectron escape depth, thus ensuring about the consistency of our measurements over the whole interval of photon excitation energies.