Doping dependent intrinsic magnetization in silicon in Ni/Si heterostructures

This investigation delves into the complex interaction at metal-semiconductor interfaces, highlighting the magnetic proximity effect in Ni/Si interfaces through systematic X-ray magnetic circular dichroism (XMCD) studies at Ni and Si edges. We analyzed two Ni/Si heterostructures with differing semiconductor doping, uncovering a magnetic proximity effect manifesting as equilibrium magnetization in the semiconductor substrate induced by the adjacent Ni layer. Our results display distinct magnetization signs corresponding to the doping levels: low-doped samples show parallel alignment to the Ni layer, while high-doped samples align antiparallel, indicating a nuanced interplay of underlying magnetization mechanisms. These findings pinpoint the roles of electron tunneling and exchange splitting modification in the magnetization behavior. The study enriches the understanding of ferromagnetic-semiconductor interface behavior, setting a precedent for the design of advanced spintronic devices that leverage the nuanced magnetic properties of these hybrid systems.

In this context, the present research work is focused on this Ni/Si 3 N 4 /Si heterostructure, employing X-ray magnetic circular dichroism (XMCD) to probe the magnetic properties of this interface.The XMCD technique offers the unique advantage of being able to distinguish unambiguously the local magnetism via individual core-level excitations, providing valuable insights into the underlying mechanisms responsible for the observed magnetic behavior.However, although XMCD is a standard technique to study metallic magnetic systems, limited data is present for semiconductor materials, as for example the Si L 2,3 , which is investigated only in few Si-based Heusler alloys 12,13 .The approach in this paper allows for the unequivocal identification of local magnetism on both Ni and the proximal layer of the semiconductor substrate.By examining two samples with quite different semiconductor dopings by means of total electron yield (TEY) and reflectivity techniques, uncovers the presence of induced spin polarization in silicon at equilibrium, potentially arising from the accumulation layer region.Strikingly, the magnetic state in silicon display a duality-opposite directions to different doping levels, unveiling a complex and captivating character of spin interactions The exceptional interface quality of our samples, as corroborated by the findings from high-resolution transmission electron microscopy (HRTEM) investigations presented in a separate publication 14 , precludes the possibility that the observed signal emanates from silicide formations.Further, the contribution from Ni silicides can be ruled out, as they are expected to be nonmagnetic from literature 15,16 .This finding is particularly noteworthy as it suggests the existence of a direct magnetic coupling between the ferromagnetic layer and the underlying semiconductor, which has significant implications for the field of spintronics.

Experimental
Two Ag/Ni/Si 3 N 4 /Si[111] hetero-structures differing only for the doping concentration of the Si substratenamely low doped (LD), with resistivity 10 cm (N d ∼ 1.5e +15 cm −317 ) and high doped (HD), with resistivity 0.005 cm (N d ∼ 2.1e +19 cm −317 ), both p-type with B dopant acceptors-were grown at the VUV-Photoemission beamline (Elettra Sincrotrone Trieste).The silicon substrates were passivated with nitride in order to reduce the formation of silicides, resulting in the formation of a crystalline bilayer of Si 3 N 4 , of subnanometric thickness 14 .The presence of a finite amount of Ni silicides in the Si substrate is restricted within 3 nm from the Si 3 N 4 layer into the Si substrate 14 .Subsequently, 7 nm of Ni were deposited at liquid nitrogen to form epitaxial layers 20 .Finally, a silver capping layer of 2 nm was grown to avoid the oxidation of the Ni film.It is possible to estimate the width of the accumulation layer for the two samples according to Ref. 4 as 520 nm for LD and 6 nm for HD.
The XMCD measurements were carried out at the CiPo beamline 21 at Elettra Sincrotrone Trieste.The samples were positioned at an incidence angle of 45 • , enabling the simultaneous acquisition of both the TEY and the reflectivity signals.The acquired data were subsequently normalized to the intensity I 0 of the incident radiation, as determined by the photocurrent measured from the gold coating of the focussing toroidal mirror positioned immediately before to the sample.The applied magnetic field B, with its direction parallel to the k-vector of the incoming synchrotron radiation, aligns the magnetization M of the Ni film along the line of intersection between the sample surface and the plane of incidence.The saturating external field during the experiment was set to 200 mT.Element sensitivity to nickel and silicon is achieved by resonantly tuning the photon energy at the Ni M 2,3 edge 22 and the Si L 2,3 edge 12 , which are 35 eV apart.Throughout the entire range of measurements (50-110 eV), the degree of polarization for the delivered circularly polarized synchrotron radiation is maintained at 90% , the resolving power being 8100.All measurements were conducted at room temperature.
The TEY generated from the photoabsorption of the circularly polarized radiation was obtained by means of the drain current from the sample measured with a Keithley 6512.The reflection from the sample was instead collected by using an AXUV100G silicon diode whose current was measured by means of an Agilent 34401A multimeter.The signal intensity at each energy point of any spectrum was the result of averaging 5 measurements at an integration time of 300 ms.Then, a baseline was removed on the pre-edge plateau for each resulting traces by means of a linear fitting, and subsequently the spectra were normalized to a region above the edge.Finally, the XMCD signals were calculated as the difference of the spectra taken at opposite fields (helicities) while mantaining the helicity (field) fixed.
Additional static magnetic measurements were conducted at the MagneDyn end-station 23 utilizing the externally seeded EUV free-electron laser (FEL) FERMI 24 at Elettra Sincrotrone Trieste.Specifically, resonant magneto-optic Kerr effect (RMOKE) magnetic hysteresis measurements were obtained with the probe resonantly tuned at the Ni M 2,3 edge and at the Si L 2,3 edge.The details on the experimental setup and on the measurements can be found in other sources 11,25 .Additionally, the same interface has been characterized by HRTEM, revealing that the presence of silicides at the interface was kept under control during the sample growth 14 .

Results
Figure 1 displays the reflectivity and TEY signals (red and blue curves, respectively) taken a the Ni M 2,3 edges (panel a), as well as the Si L 2,3 edge (panel b).At the Ni edge (Fig. 1a), both reflectivity and TEY lineshapes display a clear increase at approximately 66 eV.
On the other hand, while the reflectivity line shape shows a clear resonance signal at the Si L 2,3 threshold (Fig. 1b), this is not the case for TEY.Consequently, the corresponding XMCD signal is much more evident in the reflectivity signal.This can be rationalised by considering that the probing depth of reflectivity is much more bulk-sensitive than that of the TEY 26 .
Hence, even though the magnetic signal is present in both TEY and reflectivity, the subsequent discussion is solely focused on the reflectivity measurements.
The Si L 2,3 absorption edge corresponds to an excitation from the 2p inner shell to a final state associated with the minimum of the conduction band 27 at a threshold of 99.8 eV.The 2p inner shell is split by a spin-orbit interaction of 0.61 eV, with a statistical intensity ratio of 2:1 between the L 2 and L 3 components.9][30] , a clear determination of the origin of the peaks in the line-shape reflectivity spectra at the Si L 2,3 edge can be made.The initial edge signal, which encompasses a pre-edge at 99 eV, a primary peak at 100 eV, and a post-edge feature at 102 eV, can be ascribed to Si 0 oxidation state.In the higher energy domain, specifically within the 104-110 eV range, a secondary peak emerges due to the presence of Si 4+ nitridation state, which derives from the Si 3 N 4 layer 31,32 .It is noteworthy that the established Ni silicides absorption edge position resides within 0.1-0.3eV above the Si absorption edge 33,34 .
In contrast, the scenario at the Ni M 2,3 edge is considerably more straightforward, as the M 2 and M 3 peaks at positions 65.3 and 66.9 eV 35,36 merge into a single peak.In this context, the transition responsible for generating the XMCD signal takes place from p-states to d-states, while the transition into s-states can be disregarded.
Figure 2 displays the XMCD reflectivity signals collected at the Ni M 2,3 edge (67 eV) and the Si L 2,3 edge (100 eV).In Fig. 2a the XMCD signal at the Ni edge shows a single almost-symmetric peak at 66.5 eV for both the LD (squares) and HD (triangles) samples, as the two metallic films have the same thickness and magnetic state.In Fig. 2b the XMCD reflectivity collected both at opposite fields at fixed helicity (blue) and at opposite helicities at fixed field (red) at the Si edge for the LD sample is shown.The signal displays a single negative peak, rising from zero at 99 eV to the maximum amplitude at 100 eV and slowly decaying again to zero above 104 eV. Figure 2c shows similarly the XMCD reflectivity for HD.As it is known that the sample aligns the metallic film magnetization along the surface and in the same direction of the external magnetic field, it can be easily deduced that the substrate magnetization of LD is "ferromagnetic-like", whereas HD behaves antiferromagnetically, meaning that the Si magnetization is opposed to that of Ni.Excluding the sign, the shapes of both XMCD reflectivity and RMOKE hysteresis (see Supplemental I) of LD and HD are comparable.

Discussion
Silicon is inherently a weakly diamagnetic material, and as such, an XMCD signal at any absorption Si edge is not typically expected.However, the observations reported in Fig. 2b and c-as well as in Supplemental I-reveal a distinct magnetic signal in the present Ni/Si interfaces.In exploring the origins of magnetism in silicon, we consider two mechanisms linked to the magnetic proximity effect from a neighboring magnetized nickel layer.These mechanisms are visualized in Fig. 3a and b.
The first mechanism involves the tunneling of thermal electrons from Ni to Si thourgh the interlayer.At equilibrium within the metallic layer, spin-minority and majority electrons experience differing exchange interactions with the predominantly spin-majority polarized electron background.As a consequence, spin Ni M 2 at 66.9 eV ( β ), Si L 3 at 99.2 eV ( γ ), Si L 2 at 99.8 eV ( δ ), and the delta Si 2p at 101.5 eV ( ǫ ) from Lucovsky et al. 31 , and Si 3 N 4 at 104.1 eV ( ζ ) and 104.9 eV ( η ) from Leitch et al. 32 .Black dashed lines mark the energies of RMOKE hysteresis measurements (see Supplemental I).majority scattering times and mean free paths are greater than the corresponding values for minority electrons.This difference causes the thermal electrons that reach the Ni/Si interface to carry a predominance of one spin type over the other, introducing spin polarization into the semiconductor through a tunneling current.An estimate of the weighted tunneling probability across the interlayer's potential barrier, with a thickness of 0.7 nm, along with the details of the calculations and the parameters employed, is presented in the Supplemental Materials.
At zero applied bias, the semiconductor must return an equal number of electrons to the metal to maintain electrical balance, resulting in no net charge flow.However, this exchange is not spin-neutral, leading to an excess of one spin type in the silicon layer, as detailed in Fig. 3a, potentially giving rise to a net magnetic effect in the silicon 37 .
A second possible source of magnetism (see Fig. 3b for a visual representation) in silicon may be attributed to the proximal magnetic field, which induces a spin polarization in the conduction electrons within the Schottky barrier accumulation layer.The Si 3 N 4 interlayer serves as an insulator, yet its thinness means the sample behaves similarly to a sharp metal/silicon interface.This interface generates a Schottky barrier, the height of which ( SB ) is + 0.02 eV and scales linearly with the insulator thickness, thus avoiding Fermi level pinning 38 .The thickness of the accumulation layer varies, extending from approximately 520 nm in the LD sample to about 6 nm in the HD sample.In both instances, the proximity of the ferromagnetic Ni layer creates an additional magnetic field which results in exchange splitting within the accumulation layer of the Si, leading to a net spin polarization in the accumulation layer.The fact that the two samples show opposite magnetization directions is noteworthy and suggests that the effects responsible for magnetism might be competing with each other.
Further, the role of silicides can be ruled out, as the known phases of nickel silicides are nonmagnetic 15,16 , and their presence is mitigated by the growth technique (see also Ref. 14 ).
To provide greater clarity to the observed effect, it is useful to try to estimate the components of the magnetization in Si.As stated above, the theoretical XMCD transition from a L 2,3 edge involves the core level 2p of the www.nature.com/scientificreports/chemical species.In the present case of silicon, further simplifications can be employed; the transition can in fact be considered probing only the empty s-band, as the contribution from the d-band to the conduction band arises solely at higher energies.Accordingly, in the range 0-3 eV above the absorption edge any contribution other than from a s-band can be neglected 39 .The theoretical XMCD signal is in general comprised of three terms: the orbital angular momentum L z , the spin angular momentum S z and the magnetic dipole momentum T z .However, as the L 2,3 transition arises from a p-to a s-band, further simplifications may be applied.The final state in fact doesn't allow a nonzero angular momentum, as well as the magnetic dipole momentum 40 , if any contribution arising from surfaces and interfaces is excluded.As a result, the spin sum rule from the initial filled band c to the final band l with occupation n can be written as 41,42 where the labels c and l refer to the initial filled core level and the final h-hole filled level respectively and the energy ranges j + and j − pertain to the transition to a state with final moment c + 1/2 , or L 3 , and c − 1/2 or L 2 , respectively.Since the initial and the final states are a p-band (c = 1) and a s-band (l = 0), whereas the holes h can be determined as 4l + 2 − n (n being the number of electrons in the band), the expression can be further reduced to where A 3 and A 2 are the XMCD asymmetries integrated on the L 3 and L 2 edges respectively and A the reflectivity edge integrated across the whole L 2,3 edge.
To apply the spin selection rule, it is necessary to unambiguously separate the two absorption edges.However, according to the literature, this is not possible when the edges overlap, as occurs at the M 2,3 edge for magnetic transition metals, as well as at the Si L 2,3 edge.Despite this challenge, the XMCD signal in reflection at the Si L 2,3 edge displays a clear step where the contribution from the L 2 edge begins to increase.Based on the assumptions outlined in the previous paragraph, the L 3 and L 2 contributions to the total XMCD signal were estimated.The XMCD signal was fitted with two step-functions separated by the Si spin-orbit splitting of 0.61 eV and each aligned at higher energies with the same exponential decay, which accounts for the reduced magnetic sensitivity as one moves away from the Si edge.Subsequently, the amplitudes of the two components were normalized to the mean reflectivity signal in the range up to 3 eV above the edge.The normalized values for the L 3 and L 2 XMCD components can be found in Table 1.From these values it is possible to extract the spin angular momentum S z for LD and HD, which are respectively − 0.0295 ± 0.0002 µ B and + 0.0174 ± 0.0005 µ B .These values are comparable to the spin magnetic moment measured at Si L-edge on Si-based Heusler alloys 12,13 .
The spin and orbital angular momentum in Ni can be obtained by theoretical and experimental literature data taken at the Ni L-edges.The values of the measured magnetic moments deviate considerably from the bulk (1) values only for films of 2 ML or less 43 .As in the present case the thickness of the Ni film is far greater than 2 ML, it is possible to fairly estimate the magnetic moments as the bulk values ones 44 , that is S z(Ni) = 0.47 µ B and L z(Ni) = 0.05 µ B (the case of a nanocrystalline Ni sample has been considered, which seems a fair assumption based on the HRTEM data).
Our finding illustrate the feasibility of observing extremely weak induced magnetic moments in heterostructures.Further, by evaluating the induced magnetic moment it can also provide acceptance to the abovementioned mechanisms.

Conclusions
In this work, the sistematic investigations of the XMCD signals at the Ni M 2,3 and Si L 2,3 edges in two distinct Ni/Si interfaces were carried out.The samples, differentiated solely by the doping level of the substrate, demonstrate a nonzero magnetization of the silicon substrate due to the magnetic proximity effect from the Ni film.Remarkably, the sign of the magnetization in the two cases is found to be opposite; the low-doped sample aligns parallel to the magnetic film, while the high-doped sample aligns antiparallel.
This observed discrepancy in magnetization states suggests the presence of an intricate competition among various mechanisms responsible for the magnetization reversal.The two plausible mechanisms that could give rise to the magnetization are put forward: either through the tunnelling of spin-polarized electrons from the Ni magnetic layer or due to the modification of the exchange splitting of electrons in the silicon accumulation layer, induced by the effective magnetic field.
To fully elucidate the behaviour of the substrate in these systems and the role of the magnetic proximity effect, further theoretical investigations are warranted.The insights gained from this study contribute to the comprehension of the complex interplay between ferromagnetic materials and semiconductors at the interface.This knowledge paves the way for the development of innovative spintronic devices that harness the unique properties of these hybrid systems.Table 1.XMCD L 2 and L 3 components of the fits for LD and HD normalized per the mean reflectivity edge A in the range 0-3 eV above the Si L 2,3 edge.

Figure 2 .
Figure 2. XMCD signals collected from the Ni/Si heterostructures.(a) XMCD signal in reflectivity at the Ni M 2,3 edge on LD (squares) and HD (triangles); the complementary behaviour confirm the magnetic nature of the metallic film for both the samples.Data are compared to the theoretical expectation (black curve) taken from Ref. 36 .(b) XMCD signal in reflectivity at the Si L 2,3 edge on LD collected with the same helicity at opposite fields (blue) and viceversa (red); both the signals reveal a single peak at the Si edge position.(c) XMCD signal on HD; both the XMCD peaks at the Si L 2,3 edge are reversed in sign.

Figure 3 .
Figure 3.This diagram illustrates the characteristic band structure of a metal/interlayer/p-Si interface where the interlayer dictates band alignment through the metal work function and silicon electron affinity difference.The bending of Si's conduction band near the interface leads to a charge accumulation zone (highlighted in red).(a)In the first scenario, spin-polarized tunneling current j T from nickel propagates into the accumulation zone.Without an external electric field, the current from nickel is counterbalanced by a similar tunneling current from the Si accumulation zone to Ni.The spin imbalance of these currents results in electron spin polarization within the accumulation zone and the resulting magnetization profile M Si .(b) In the second scenario, the magnetic field proximity generated by the nickel layer's magnetization M Ni alters the electron energy distribution in the accumulation zone by a term equivalent to the dipolar interaction between electron spin and the magnetic field magnitude B, assumed to be µ B × B .Consequently, an asymmetry in the populations of spin-up and spin-down electrons in the accumulation zone leads to a net magnetization at the silicon interface's accumulation zone.In either cases, this interface magnetization is the origin of the observed Kerr signal at the Si L 2,3 threshold.