Ferromagnetism of Mn x Si 1x ( x ∼ 0 . 5 ) films grown in the shadow geometry by pulsed laser deposition method

The results of a comprehensive study of magnetic, magneto-transport and structural properties of nonstoichiometric MnxSi1-x (x ≈ 0.51-0.52) films grown by the Pulsed Laser Deposition (PLD) technique onto Al2O3(0001) single crystal substrates at T = 340°C are present. A highlight of used PLD method is the non-conventional (“shadow”) geometry with Kr as a scattering gas during the sample growth. It is found that the films exhibit high-temperature (HT) ferromagnetism (FM) with the Curie temperature TC ∼ 370 K accompanied by positive sign anomalous Hall effect (AHE); they also reveal the polycrystalline structure with unusual distribution of grains in size and shape. It is established that HT FM order is originated from the bottom interfacial self-organizing nanocrystalline layer. The upper layer adopted columnar structure with the lateral grain size ≥50 nm, possesses low temperature (LT) type of FM order with Tc ≈ 46 K and contributes essentially to the magnetization at T ≤ 50 K. Under these conditions, AHE ...


I. INTRODUCTION
Mn x Si 1-x (x≈0.5)2][3][4][5][6][7] The perfect single crystal ε-MnSi with B20-type of structure possesses at low temperatures (≤ 30 K) intriguing magnetic and transport phenomena caused by formation of new magnetic quasiparticles -skyrmions (see Ref. 6 and references therein).On the other hand, the Mn x Si 1-x (x≈0.5)thin layers grown on Si(001) or Al 2 O 3 (0001) substrates a E-mail: vvrylkov@mail.rub E-mail: tuvictor@mail.ru3][4] This fact is in contrast to the case of bulk ε-MnSi single crystal, where only the low-temperature (LT) FM was reported with T C ≈ 30 K. 8,9 The HT FM order at x 0.506 (that just corresponds to the single crystal ε-MnSi belonging to berthollides 9,10 ) was observed in the Mn x Si 1-x /Si(001) structures but at enough small Mn x Si 1-x film thickness less than one ε-MnSi monolayer. 2,11This order is explained by the formation of c-MnSi phase with B2-like (CsCl) crystal structure stabilized with tetragonal distortion due to favorable lattice mismatch between the film and substrate. 1Recently we reported the HT FM appearance with T C ≈ 330 K in 70 nm thick Mn x Si 1-x (x ≈ 0.52-0.55)films grown on the Al 2 O 3 (0001) substrates by pulsed laser deposition (PLD) technique. 3,4We argued that the observed HT FM has a defect-induced nature: it is due to formation of local magnetic moments on the Si vacancies inside the MnSi matrix and the strong exchange coupling between these moments mediated by spin fluctuations of itinerant carriers. 12The Mn x Si 1-x films in 3,4 were deposited at a relatively slow deposition rate (∼2 nm/min) using PLD method in a conventional "direct" geometry (DG) when the surface of Al 2 O 3 (0001) substrate is exposed to the Mn-Si laser plume.Accordingly to atomic-force microscopy (AFM) measurements, the structure of thus grown films is mosaic, with the crystallite size ∼0.5-1µm.
In this work we present new results of a comprehensive study of structural, magnetic and magneto-transport properties of the Mn x Si 1-x (x ≈ 0.52) polycrystalline films grown by PLD technique employing unconventional "shadow" geometry (SG) with Kr as a buffer gas. 13As compared to the conventional "direct" geometry (DG) of Ref. 3 and 4, in the SG method the effective scattering of ablated particles in the buffer gas results in the lower energy of the depositing atoms as well as very high deposition rate. 13We found that SG grown Mn x Si 1-x (x ≈ 0.5) films have two magnetic phases: HT FM phase with T C ≈ 370 K and LT FM phase with T C ≈ 46 K.At the same time, the anomalous Hall effect (AHE) changes its sign from the positive to negative one at the temperature below 30 K. We explain obtained experimental results by the interplay of two effects: 1) self-organization of polycrystalline film leading to the formation of two layers in which the crystallites strongly differ in size and shape; 2) peculiarities of defect-induced FM ordering in such a system.

II. SAMPLES AND EXPERIMENTAL DETAILS
The SG grown Mn x Si 1-x thin films were deposited in Kr atmosphere (∼10 −2 mbar) onto the α-Al 2 O 3 (0001) substrates 10x15 mm 2 in size using the single crystal MnSi target. 13The substrate temperature during the deposition (340 • C) was the same as for previous DG deposited films, while the deposition rate was higher (≥ 7 nm/min).The Rutherford backscattering spectrometry (RBS) was used to determine the film composition and thickness. 13The film thickness d depends on the distance L to the target; the value d decreases from 270 to 70 nm with the increase of L at the length δL≈15 mm.The Mn content at the same deposited area increases from 0.506 up to 0.517.The Mn content at the same deposited area increases from 0.506 up to 0.517, but most strongly the Mn content and film thickness change at the substrate edge located closer to the target. 13When the film thickness decreases from 160 to 70 nm (δL≈10 mm), the film composition slightly changes with L (x ≈ 0.514-0.517).To investigate the effect of the film composition and deposition rate on the structural, magnetic and magneto-transport properties, the as grown sample was cut into seven 2x10 mm 2 stripes with different thicknesses.
The structural properties of Mn x Si 1−x /α-Al 2 O 3 samples were investigated by X-ray diffraction (XRD) measurements using a Rigaku SmartLab diffractometer.To elucidate the microscopic structure of Mn-Si films, they were further investigated by scanning transmission electron microscopy (STEM) using TITAN 80-300 TEM/STEM instrument (FEI, US) operating at an accelerating voltage of U=300 kV, equipped with Cs-probe corrector, high-angle annular dark-field detector (HAADF) (Fischione, US) and energy dispersive X-ray (EDX) microanalysis spectrometer (EDAX, US).The Mn x Si 1−x /α-Al 2 O 3 samples with the film thickness of 250 nm (x ≈ 0.51) and 100 nm (x ≈ 0.516) were studied.The cross-sections of the films were prepared by the mechanical polishing of sandwiched pieces followed by Ar + ion-beam milling until perforation in Gatan PIPS (Gatan, US).The temperature dependences of saturation magnetization and the magnetic hysteresis of the SG grown Mn x Si 1-x films 2x1.5 mm 2 in size were measured by superconducting quantum interference device MPMS-3 (SQUID-VSM) magnetometer between 5 and 400 K at in plane magnetic fields µ 0 H till 1.5 T. The uncertainty in measurements of coercivity was about 5 Oe.
The Hall effect and conductivity were studied in the 2x8 mm 2 stripes of Mn x Si 1-x films in the double Hall bar geometry.Contacts were fabricated by the soldering indium with the distance between potential probes l≈2.5 mm.Details of Hall effect measurements were described in Refs. 3 and 4. We used the same procedure and measured lateral resistance R xy at various polarities of magnetic field B at the "downward" and "upward" scanning directions of B; then expanded obtained function R xy (B) in odd and even components.Such an approach makes it possible to extract Hall component from R xy (B) with possible hysteresis in the behavior of the Hall resistance R H and to suppress the parasitic contribution of the magnetoresistance to R xy as well as to distinguish possible even contributions of the incoherent mesoscopic effect or the planar Hall effect (for details see Refs. 14 and 15).

III. STRUCTURE MEASUREMENTS
The results of XRD measurements of as grown Mn x Si 1-x /Al 2 O 3 (0001) samples 10x15 mm 2 in size (before cutting) are shown in Fig. 1.The angular range 2θ = 30-70 • contains several peaks, which are all attributed to ε-MnSi phase with B20 structure.An additional intense diffraction peak observed at 2θ = 64.5 • does not belong to ε-MnSi and could point at (200) plane diffraction of c-MnSi phase (similarly to c-FeSi phase in Ref. 16).However, further analysis of XRD rocking curve reveals that this peak originated from a quasi-forbidden reflection (0009) of Al 2 O 3 substrate and appears as a result of multiple reflections (so-called multi-wave diffraction, see insert to Fig. 1).
The structural perfection of the film is described by such an integral characteristic as the FWHM of the peak in the rocking curve (FWHMω).FWHMω value for the single-crystalline films should lie in the range between 64 seconds of arc and 245 seconds of arc for the samples under the study with layer thicknesses between 70 nm and 270 nm.At the same time at fig. 1 FWHMω parameter at 2θ = 44, 43 • is approximately 550 seconds of arc.Such a broad peak is a signature of a pronounced mosaicity of the film structure as well as of a presence of structural defects in PLD grown ε-MnSi films.
The low magnification bright field (BF) TEM image of Mn x Si 1-x /α-Al 2 O 3 with the film thickness of d ≈ 250 nm is presented in Fig. 2(a).The Mn x Si 1-x film exhibited columnar microstructure with the lateral grain sizes of about 50 nm.The electron diffraction (not shown here) and Fourier analysis of High Resolution (HR) TEM images (Fig. 2  demonstrated that the grains in the upper Mn x Si 1-x layer adopted the B20 crystal structure type and that is consistent with the XRD data.The HAADF STEM images of the Mn x Si 1−x /α-Al 2 O 3 interfaces of the samples with d ≈ 250 and 100 nm, are presented in Fig 2(c) and Fig. 2(d), correspondingly.These images revealed the presence of thin layer in the Mn x Si 1-x film adjacent to the interface with different morphology: the Mn x Si 1-x particles adopted equi-axed or dome shape with the size of 4-10 nm.The thickness of that layer was of 10 nm.The formation of the layer could be caused by different crystal structure and large crystal lattice mismatch.The Mn x Si 1-x crystal lattice is characterized by cubic B20 structure type (Space group P2 1 3 #198 ["International tables for crystallography" Volume A: Space-Group Symmetry Editor T. Hahn Springer Fifth Edition 2002] with the lattice constant a ≈ 4.56 Å. Sapphire (α-Al 2 O 3 ) belongs to the space group R3 c and although being rhombohedral, it is commonly described in terms of hexagonal Miller-Bravais indices with lattice constants a = 4.7589 Å, c = 12.991 Å.The orientation of α-Al 2 O 3 substrate was [0001], which is sixfold and in the sake of the symmetry it could be proposed the growth of cubic Mn x Si 1−x film in [111] direction.In that case the mismatch between {1120} α-Al2O3 with d = 2.38 Å and {111} MnSi with d = 2.63 Å is close to 10%, which is huge.The lattice mismatch released through the growth of small grains at the interface in different orientation and these grains form a layer with the thickness of about 10 nm.
The typical HR TEM image of the 100 nm SG grown Si 1-x Mn x /Al 2 O 3 (0001) sample is shown in Fig. 3.The close inspection of the HR TEM images of the interface area (Fig. 3(a)) with small grains and analysis of Fast Fourier Transform (Fig. 3(b)-3(d)) indicated that these grains adopted B20 crystal structure, similar to the upper layer.The interface between the bottom and upper layer of the Mn x Si 1-x film is uneven and blurred, but could be revealed better by HAADF STEM imaging (Fig. 2(c) and 2(d)).
Note also that diluted Mn x Si 1-x (x < 0.04) alloys containing Mn-rich nanocolumns were grown by molecular beam epitaxy (MBE) technique in. 17,18No essential manifestations of HT FM caused by these nanocolumns were revealed in Refs.17 and 18. I.e. the situation in this case is opposite to Ge-Mn alloys with nanocolumns structure where above room temperature FM was observed. 19use of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions.IP: 93.180.49.165On: Thu, 18 Feb 2016 09:13:02

IV. MAGNETIC AND MAGNETO-TRANSPORT MEASUREMENTS
The temperature dependence of saturation magnetization M s (T) of three Mn x Si 1-x samples 1-3 (x ≈ 0.517, 0.516 and 0.514) with the thicknesses d ≈ 70, 90 and 160 nm, respectively, is presented in Fig. 4. The applied field was µ 0 H = 1 T. The obtained data of Fig. 4 revealed a presence of two ferromagnetic phases: a HT phase with T C ≈ 370 K and a LT phase with T C ≈ 46 K.The relative contribution of the LT FM phase clearly increases with the increase of the film thickness.Such behavior is in contrast to that of DG grown Mn x Si 1-x films (Fig. 5).When x ≈ 0.52, the decrease of M s (T) in the temperature range T = 10-100 K does not exceed 6% and fits well to the Bloch law.Moreover, the M s (T) value does not increase significantly with lowering T even in case of HT FM degradation, as observed in DG films with the Mn content x ≥ 0.53 (Fig. 5, see also Ref. 3).
Fig. 6 shows the magnetization vs. magnetic field M(H) dependence for the sample 1 (x ≈ 0.517, d ≈ 70 nm) at T = 5, 100 and 300 K.The open hysteresis loops are clearly visible at temperature below 100 K (see right inset), which is not observed in bulk ε-MnSi single crystal.Left inset in Fig. 5 shows the temperature dependence of coercivity -even at room temperature the coercivity is about 20 Oe.The magnetization saturates in the magnetic field µ 0 H ≈ 0.6 T at low temperature (T = 5 K) and then linearly increases like in the case of ε-MnSi single crystal. 9,20At room temperature the saturation field value decreases till µ 0 H ≈ 0.2 T.
It is curiously to note that at T > 46 K the "surface density" of magnetic moment J m /A of the HT FM phase (i.e. the total magnetic moment J m normalized to the film surface A; see inset to Fig. 1) does not depend practically on the film thickness.This fact clearly indicates that the HT FM phase (T Ch ≈ 370 K) is formed mainly in the interfacial layer directly grown on the substrate with a fixed effective thickness d 1 , while the LT FM phase (T Cl ≈ 46 K) is formed in the upper layer with a variable thickness d 2 = (d − d 1 ).So, the magnetometry data allude to a presence of two FM layers with different effective thicknesses, magnetic moments and Curie temperatures in our films.Hereinafter we will imply the value of d 1 = J m /A•M sh as an effective thickness, where M sh is the saturation magnetization of HT phase.In our case it means that d 1 ≈ const when M sh ≈ const.We will also use the term "two-layer system" only as a quite symbolic, to emphasize the relative dominance of columnar microstructure of the B20 phase in the LT upper layer of Si-Mn film.Obviously, partial penetration of this phase into the HT interfacial layer is possible, leading to an absence of clear geometrical boundary between two layers.
The Hall effect provides rich information on the correlation between magnetic and transport properties of Mn-Si system under investigation.Let us recall that in "ordinary" FM material, the Hall resistance R H contains two components following the expression 21 : where ρ H is the total Hall resistivity, ρ n H and ρ a H are the normal and anomalous components of the Hall resistivity, respectively, d is the thickness of FM material, R 0 is the normal Hall effect constant related to the Lorentz force, B is magnetic induction, R s ∝ (ρ xx ) α is the anomalous Hall effect (AHE) constant related to the spin-orbit interaction in FM material, M is the magnetization.For a "skew-scattering" driven mechanism of AHE, α = 1, and for "intrinsic" and "side-jump" mechanisms of AHE, index α = 2. 21 Usually, at the temperature T ≤ T C and for the magnetic field corresponding to the saturation magnetization, the second term in Eq.( 1) dominates, i.e. ρ n H << ρ a H .Note that in the case of ε-MnSi single crystal, the third term may also appear in Eq.( 1) due to skyrmions formation 22 (so-called component of the topological Hall effect), but in our system we presume that skyrmions are destroyed due to the scattering on the structural and magnetic disorder in the Mn x Si 1−x alloy.Fig. 7 demonstrates the magnetic field dependence of ρ H (B), as measured for the sample 1 (d ≈ 70 nm, x ≈ 0.517) at the temperature range T = 5-160 K.One can see that the anomalous component ρ a H in the saturation regime (at B ≥ 1 T) decreases up to 10 times as the temperature decreases from 160 K to 5 K.One can notice that in case of the DG grown film the value of ρ a H in the same temperature range is either nearly constant (for x ≈ 0.52) or increases as the temperature Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions.IP: 93.180.49.165On: Thu, 18 Feb 2016 09:13:02 lowers (up to 2 times for x ≈ 0.55, see Fig. 4(a) from Ref. 3).The unusual behavior of ρ H (B) in the SG grown film can be explained in the frame of effective "two-layer system", i.e. as a partial compensation of the positive Hall emf from the bottom HT FM layer and the negative Hall emf from the upper LT FM layer (see inset to Fig. 7).To justify this explanation we have to suggest that in the upper layer, the effect of LT FM order on the Hall transport is similar to the case of bulk ε-MnSi, where AHE has the negative sign. 20,22At the same time, we have to postulate that in the interfacial layer, the effect of the HT FM order on the Hall transport is similar to the case of DG films, 3 where the AHE of positive sign was reported 3 (the AHE of positive sign is observed also in amorphous Mn x Si 1-x alloys. 7,23) Evidently, in the two-layer SG grown film a partial compensation of negative and positive contributions ρ H (B) should be more pronounced at temperatures below the Curie temperature of the LT FM layer (T Cl ≈ 46 K); this compensation becomes more efficient with the film thickness increasing.
The temperature dependence of ρ H (T) of the thicker sample 2 (d ≈ 90 nm, x ≈ 0.516) measured at B = 1.2 T is presented in Fig. 8(a).One can see that below T ≈ 50 K the ρ H (T) function falls down and then changes its sign to the opposite below T ≈ 30 K. At T = 40 K a small observed hysteresis of ρ H (B) curve has the normal form like for sample 1 at T = 5 K (see inset in Fig. 8).On the other hand at the temperatures T ≤ 10 K, the hysteresis loop ρ H (B) acquires unusual shape (Fig. 8(b)).Obviously, this is the result of superposition of two AHE components: the first one is hysteretic and provided by HT FM layer,ρ a H 1 > 0, while the second one is non-hysteretic and provided by the LT FM layer, ρ a H 2 < 0. Notice, that due to the larger values of thickness and conductivity of the LT FM layer, its contribution to the Hall resistance can be larger in absolute value than that from the HT FM layer (see Eq. ( 4) below).For both samples with d ≈ 70 and 90 nm the absolute value of Hall resistivity drop is about 10 times at temperature lowering from ∼100 to 10 K. Therefore the crossover from the positive AHE to negative one at low temperatures (∼10 K) comes in our case at a critical film thickness of about 80 nm.
The positive sign of ρ a H 1 component is not surprising and testifies to a similarity of structural, magnetic and transport properties of the interfacial HT FM layer and DG grown Mn x Si 1-x films.The negative sign of ρ a H 2 may be attributed to a similarity of the properties of the upper LT FM layer and ε-MnSi, where ρ a H is negative. 20,22It is also important to note that normal Hall effect in ε-MnSi is positive; 20,22 therefore, the linear behavior of the ρ H (B) dependence in fields the B ≥ 0.7 T corresponds to the hole type of conductivity (see Fig. 8(b)).
In addition, introduced two-layer model is confirmed by results of Hall effect investigations in the thick sample 3 (d ≈ 160 nm, x ≈ 0.514).In this case it is necessary to expect the dominating contribution to Hall effect from the upper LT layer at low temperatures T < T Cl ≈ 46 K.It is really observed (see Fig. 9).At T = 23 and 10 K AHE is the negative and does not contain the hysteresis in field behavior; the ρ a H value falls on absolute value with temperature lowering reaching value of the order of 10 −2 µΩ•cm as in case of ε-MnSi 20 (in case of ε-MnSi the | ρ a H | value is twice smaller).However, at temperatures above Curie temperature T Cl ≈ 46 K the transition to the positive AHE is observed.At T = 54 K the value of ρ a H is positive and very small, less than 10 −2 µΩ•cm (Fig. 9).The observation of positive AHE means that the HT phase in interfacial layer is continuous and forms the infinite cluster. 14n order to analyze better the results of Hall effect measurements in the "two-layer system", we have also studied the temperature dependence of longitudinal resistance R(T) for grown SG films.In Fig. 10, the normalized temperature dependences R(T) = R SG (T) and R(T) = R DG (T) (taken from 3 ) are shown, respectively, for DG (d ≈ 70 nm; x ∼ 0.52) and SG (d ≈ 70 and 160 nm; x ∼ 0.52) grown Mn x Si 1-x films, in comparison with R(T) = R SC (T) for ε-MnSi single crystal (taken from 24 ).From the data presented in Fig. 10 it follows that resistance R(T) drops more strongly with temperature decreasing than the thick SG grown film: f (11.5K)=R(11.5K)/R(290K)≈ 0.29 and 0.21 (corresponds R ≈ 6.03 and 2.15 Ω at 11.5K) for samples with d ≈ 70 and d ≈ 160 nm, respectively.(Note that in our case the resistance reaches of approximately residual value at T ≤ 12 K).The resistance decreasing for perfect epitaxial ε-MnSi films is much stronger and FIG. 9. Resistivity of the Hall effect ρ H (B) versus magnetic field for SG grown sample 1 (d ≈ 160 nm; x ≈ 0.514) at different temperatures.Circles and triangles of curves ρ H (B) correspond to the "upward" and "downward" scanning directions of B. reaches f ≈ 0.03. 6Nevertheless, the attention should be paid to the similarity between R SG (T) and R SC (T) and its drastic difference from R DG (T) (Fig. 9).

V. DISCUSSION
The results of TEM investigation unambiguously demonstrated the two-layer structure of Mn x Si 1-x (x ≈ 0.51-052) films, apparently due to the peculiarity of the SG growth process as well as sufficiently large mismatch (≈ 10%) between the α-Al 2 O 3 substrate and Mn x Si 1-x (x ≈ 0.5) film with B20 structure.The important difference between two layers is the morphology, namely the grain sizes and grain shape.The bottom interfacial HT FM layer, which was deposited directly on the substrate surface is composed of randomly oriented equi-axed or dome shape grains with the average size of 5 nm.The thickness of the layer is about 10 nm.The grains in the upper layer adopted columnar morphology with the diameter of 60-150 nm and propagated to the film surface.Generally, the microstructure of the thick (250 nm) and thin films (100 nm) are similar: bottom Mn x Si 1-x layer adjacent to the interface and top layer.Below we propose the consideration of the magnetic and transport properties of Mn x Si 1-x films (x ≈ 0.51-0.52)based on that two-layer film morphology or "two-layer system" approximation (see above).
First of all, we have to estimate the value of effective magnetic moment on Mn atom in both layers, suggesting that the density of Mn x Si 1-x (x ≈ 0.51-0.52)alloy is equal to that of the bulk ε-MnSi single crystal, i.e. ≈ 5.82 g/cm 3 . 25The HT FM and LT FM phase contributions to the total magnetization of the film can be found using the simplified Brillouin function fit for M s (T): In our case, n = 1.5 leads to the best fit of experimental M s (T) data (Fig. 1).Using Eq. ( 2), we have found for the samples with x ≈ (0.51-0.52) the effective magnetic moments m = (1.3-1.75)µ B / Mn and (0.43-0.52) µ B /Mn for for HT and LT FM phase, respectively (magnetic moments demonstrate a little increase with decreasing the film thickness).
The effective magnetic moment of the interfacial HT FM layer in Mn x Si 1-x films (x ≈ 0.51-0.52)grown in the SG significantly exceeds the magnetic moment of MnSi single crystal, m ≈ 0.4 µ B /Mn. 9 It is also higher as compared to the case Mn x Si 1-x film grown in DG (x ≈ 0.52, T C ≈ 330K), where the effective magnetic moment is m ≈1.1 µ B /Mn. 3 These facts do not leave doubt about existence of defect-induced local magnetic moments in the HT FM phase, which are formed due to the same mechanism as in DG grown nonstoichiometric Mn x Si 1-x (x ≈ 0.52) alloys.The origin of this mechanism, following Ref.vacancy.Due to a strong hybridization between 3d-electron states of Mn and 3(s,p)-electron states of Si this variation leads to the corresponding local redistribution of charge and spin densities near the Si vacancy, which is thereby responsible for the formation of a complex defect with local magnetic moment ∼ (2.0-3.5)µB /Mn and effective (average) magnetic moment ∼ (1.2-1.75)µB /Mn.
The effective magnetic moment of the upper LT FM layer is in good agreement with the magnetic moment of single crystalline ε-MnSi; this fact may be naturally interpreted as an absence of local magnetic moments in the upper LT FM layer.At first glance, this conclusion is surprising, since according to the results of TEM studies and Rutherford backscattering analysis 13 the composition of the film is homogeneous across the film thickness, i.e.LT FM phase contains the same excess amount of Mn atoms as in HT FM phase.Therefore, we have to suggest that most part of Mn containing defects in the upper LT FM layer is in a weak-magnetic or non-magnetic ("magnetically dead") configuration.Following Ref. 3 and 4, as an example of such the configuration we can imagine an interstitial Mn atom introduced into the MnSi matrix.The calculated magnetic moment on this Mn atom is extremely small (∼ 0.09µ B /Mn) and the effective (average) magnetic moment is ∼ 0.34µ B /Mn for Mn x Si 1-x (x ≈ 0.52) film.
To explain magnetic data we suppose that due to the specificity of the SG method the Si vacancies mainly arise in the interfacial layer of the film.The nanocrystallite boundaries in this layer form a vast network; they eventually can work as the gettering regions for Si vacancies and, consequently, for local magnetic moments on these vacancies.So, following our supposal, nanocrystallite boundaries play the key role in the magnetic properties of HT FM layer, acting as a magnetic envelope of the nanometer scale non-magnetic crystallite.Early in Ref. 12 in the frame of the spin-fluctuation model of FM ordering, we have analyzed the role of dimension effects in granular dilute Si-Mn alloys.We considered the precipitate nanoparticles of MnSi 1.7 type in the Si matrix and estimated variation of the Curie temperature as a function of the shape and size of these precipitates.Similar analysis can be effectuated for the case of Mn x Si 1-x (x ∼ 0.5) alloys.For a spherical crystallite of weak itinerant FM with the small radius r 0 << ζ, where ζ is FM correlation length, encircled by an envelope with defect-induced local magnetic moments S having the surface density σ 0 << a −2 , where a is the lattice parameter, we can roughly estimate the Curie temperature T C as k B T C ∼ J S(W/v F Q SF ) 1/2 (a/r 0 ) 1/2 (σ 0 a 2 ) 1/2 . ( Here J is exchange interaction potential between the local moment on the defect and itinerant electron spin, W is itinerant electron bandwidth, v F is the Fermi velocity, Q SF is spin-fluctuation cutoff wave vector.At JS ∼ 0.1 eV, W/v F Q SF ∼ 10, a/r 0 ∼ 10 -1 , σ 0 a 2 ∼ 10 -1 ÷ 10 -2 we have T C ∼ 100 ÷ 400 K that is not far from above obtained experimental results.
Finally, note that the shape of Mn-rich precipitates can also play a crucial role in the formation of HT FM order.For example, the influence of isovalent Pb surfactant on the growing process of dilute Si-Mn thin films prepared by MBE has been investigated in Ref. 18.It was found that Pb surfactant initiates the formation of nanorod-type ferromagnetic precipitates that lie in the film plane and have T C above room temperature, while the growing without Pb surfactant creates paramagnetic nanocolumns.
Let us now consider the transport data.As the temperature decreases from 300 to 5 K, the R DG (T) curve in Fig. 10 demonstrates a relatively slow (about 1.3 times) temperature decreasing.It was also shown in Ref. 3 that, contrary to the case of ε-MnSi single crystal, for the DG films the carrier mobility strongly increases (about fifteen times at 60 K), but the carrier concentration drastically decreases (about twenty five times at 100 K).Thus, R DG (T) behavior is driven by an interplay of these two effects and as a result, the value R DG (T) for Mn x Si 1-x (x ≈ 0.52) film below ∼ 40 K significantly exceeds R SC (T) for ε-MnSi, where R SC (T) falls down dramatically. 24he physical origin of this remarkable phenomenon of simultaneous increase of carrier mobility and decrease of carrier concentration at the doping of single crystal ε-MnSi with additional Mn atoms is not yet clear.A possible (but certainly open to discussions) reason qualitatively explaining experimental data has been proposed in Ref. 3. It presumes that: 1) the Mn doping induces the carrier localization on the defect center (e.g., the above discussed Si vacancy) in the MnSi matrix; 2) this doping also destroys collective (spin-polaron or Kondo type) resonance, probably existing in ε-MnSi single crystal. 24The combination of these two effects obviously leads to the simultaneous decrease FIG. 1.The results of X-ray diffractometry for SG Si 1-x Mn x /Al 2 O 3 (0001) structure.Insert shows quasi-forbidden reflection (0009) from Al 2 O 3 substrate.

FIG. 2 .
FIG. 2. (a) Low magnification cross-section bright field TEM image of 250 nm SG grown Si 1-x Mn x /Al 2 O 3 (0001) sample.Note the columnar structure of the top layer mean lateral grain size of 50 nm.(b) The HR TEM image of the columnar grain with FFT spectra in the inset.The FFT spectra indicated that the Si 1-x Mn x grain adopted B20 crystal structure observed in [212] zone axis.The HR TEM image was obtained from the middle part of the grain.(c) The enlarged HAADF STEM image of the interface area of the 250 nm SG grown Si 1-x Mn x /Al 2 O 3 (0001) sample.The 10 nm layer at the interface have the contrast differs from the upper part of the film.(d) The interface area of the 100 nm SG grown Si 1-x Mn x /Al 2 O 3 (0001) sample.

FIG. 4 .
FIG.4.Temperature dependence of saturation magnetization M s for Mn x Si 1-x films with different thickness and close Mn content (x ≈ 0.516) grown in shadow geometry.The insert shows the temperature dependence of magnetic moment J m normalized by film square A. (For sample with d = 70 nm the J m (T )/A curve practically coincides with one for sample with d = 90 nm and is not shown on the insert).Solid lines are fitting dependencies of M s (T ) with using equation (2).

FIG. 6 .
FIG. 6. Magnetization versus magnetic field for SG grown sample 1 (d ≈ 70 nm; x ≈ 0.517) at different temperatures.The left inset shows the temperature dependence of coercivity, the right inset shows the enlarged view of central part of M(H ) dependences.

FIG. 7 .
FIG. 7. Resistivity of the Hall effect versus magnetic field for SG grown sample 1 (d ≈ 70 nm; x ≈ 0.517) at different temperatures.The inset shows the schematic drawing of Mn x Si 1-x /Al 2 O 3 structure.

FIG. 8 .
FIG. 8. (a) Temperature dependence of the Hall resistivity for SG grown sample 2 (d ≈ 90 nm; x ≈ 0.516) measured at B = 1.2 T. (b) Resistivity of the Hall effect ρ H (B) versus magnetic field for sample 2 at T = 9 K.The inset demonstrates ρ H (B) dependence at T = 40 K. Arrows show the "upward" and "downward" scanning directions of B.