Out-of-Plane Magnetic Anisotropy in Ordered Ensembles of Fe y N Nanocrystals Embedded in GaN
A. Navarro-Quezada, K. Gas, T. Truglas, V. Bauernfeind, M. Matzer, D. Kreil, A. Ney, H. Groiss, M. Sawicki, A. Bonanni
OOut-of-Plane Magnetic Anisotropy in Ordered Ensembles of Fe y NNanocrystals Embedded in GaN
A. Navarro-Quezada, ∗ K. Gas, T. Truglas, V. Bauernfeind, M.Matzer, D. Kreil, A. Ney, H. Groiss, M. Sawicki, and A. Bonanni Institute of Semiconductor and Solid-State Physics,Johannes Kepler University Linz, Altenberger Str. 69, 4040 Linz, Austria Institute of Physics, Polish Academy of Sciences,Aleja Lotnikow 32/46, PL-02668 Warsaw, Poland Christian Doppler Laboratory for Nanoscale Phase Transformations,Center for Surface and Nanoanalytics, Johannes Kepler University Linz,Altenberger Str. 69, 4040 Linz, Austria Institute of Theoretical Physics, Johannes Kepler University Linz,Altenberger Str. 69, 4040 Linz, Austria (Dated: July 27, 2020)
Abstract
Phase-separated semiconductors containing magnetic nanostructures are relevant systems forthe realization of high-density recording media. Here, the controlled strain engineering of Ga δ FeNlayers with Fe y N embedded nanocrystals (NCs) via Al x Ga − x N buffers with different Al concen-tration 0 < x Al <
41% is presented. Through the addition of Al to the buffer, the formation ofpredominantly prolate-shaped ε -Fe N NCs takes place. Already at an Al concentration x Al ≈ γ ’-Ga y Fe − y N nanocrystals in the layer on the x Al = 0% buffer lies in-plane, the easy axis of the ε -Fe N NCs in all samples with Al x Ga − x N buffers coincides with the[0001] growth direction, leading to a sizeable out-of-plane magnetic anisotropy and opening wideperspectives for perpendicular recording based on nitride-based magnetic nanocrystals. ∗ [email protected] a r X i v : . [ c ond - m a t . m t r l - s c i ] J u l . INTRODUCTION Iron nitrides (Fe y N) have been widely studied for half a century due to their outstandingphysical properties [1–7] and their application in magnetic recording media [4]. Particularlyrelevant are the high spin polarization and high Curie temperature ( T C ) ferromagnetic com-pounds ε -Fe N with reported T C = 575 K [5], and γ ’-Fe N with T C = 767 K [6–8]. Theirimplementation in combination with GaN into heterostructures is expected to serve for spininjection devices [9–11].In this respect, the controlled fabrication of planar arrays of ferromagnetic γ ’-Ga y Fe − y Nnanocrystals (NCs) embedded in a GaN matrix resulting from the epitaxy of Ga δ FeN lay-ers, and whose size, shape and density can be adjusted through the fabrication condi-tions [12, 13], becomes appealing for the realization of spin injection. The incorporationof Ga ions into the γ ’-Ga y Fe − y N NCs is expected to allow tuning the magnetic propertiesof the embedded NCs from ferromagnetic to ferrimagnetic [14] and weakly antiferromag-netic [15], opening wide perspectives for the implementation of these material systems intothe field of antiferromagnetic spintronics [16]. The structural, magnetic and transport prop-erties of thin Ga δ FeN layers deposited onto GaN buffers grown on c -sapphire (Al O ) havebeen already studied in detail [12, 13, 17–19]. It was demonstrated that in Ga δ FeN lay-ers, the face-centered cubic γ ’-Ga y Fe − y N nanocrystals have a preferential epitaxial relation[001] NC (cid:107) [0001] GaN and (cid:104) (cid:105) NC (cid:107) (cid:104) (cid:105) GaN , with a minimal fraction of NCs aligned accord-ing to (cid:104) (cid:105) NC (cid:107)(cid:104) (cid:105) GaN and adjusting to the hexagonal symmetry of the matrix. Co-dopingwith Mn leads to the reduction of the NCs size and to a quenching of the overall superpara-magnetic character of the layers [18]. Recently, in ordered γ ’-Ga y Fe − y N nanocrystal arraysembedded in GaN, the transport of a spin-polarized current at temperatures below 10 Kand an anisotropic magnetoresistance at room-temperature [19] larger than that previouslyobserved for γ ’-Fe N thin layers [20], were observed.Further control over these embedded magnetic NCs can be achieved with the modificationof their magnetic anisotropy through stress, by incorporating Al into the GaN buffer. Thestrain energies and piezoelectric effects at the GaN/Al x Ga − x N interface are expected to alterthe formation energies and thermodynamic equilibrium conditions of the nanocrystals. Inthis way, size and shape engineering and the modification of the magnetic anisotropy energyare expected to generate a switchable out-of-plane magnetic anisotropy in the nanocrystals.2n this work, the effect of strain, induced by adding Al to the GaN buffer—i.e., inGa δ FeN/Al x Ga − x N (0 < x Al < δ FeN thin layers is investigated. It isobserved that already 5% of Al added to the GaN buffer layer modifies not only the structuralproperties—phase, shape, size and orientation—of the NCs in comparison to those grown ona pure GaN buffer, but it also leads to a sizeable out-of-plane magnetic anisotropy. Throughthe addition of Al into the buffer layer, additionally to the γ ’-Ga y Fe − y N NCs, the forma-tion of ε -Fe N NCs is promoted. The crystallographic orientation and the distribution ofthe two phases in the GaN matrix point at the formation of ordered hexagonal ε -Fe N NCselongated along the growth direction as the origin of the observed magnetic anisotropy.
II. EXPERIMENTAL DETAILS
The layers considered in this work are grown in a metalorganic vapor phase epitaxy(MOVPE) Aixtron 200X horizontal reactor system (Aixtron, Achen, Germany) on c -plane[0001] Al O substrates using trimethylgallium (TMGa), trimethylaluminium (TMAl), am-monia (NH ) and ferrocene (Cp Fe) as precursors. The 1 µ m Al x Ga − x N buffers are de-posited at 1000 ◦ C on a 50 nm low-temperature (540 ◦ C) Al x Ga − x N nucleation layer annealedat 1000 ◦ C. The Al concentration x Al is varied between 0% and 41% over the sample seriesby adjusting the Ga/Al ratio for the growth of the buffer layer.After deposition of the Al x Ga − x N buffers, a 60 nm thick Ga δ FeN layer is grown at 810 ◦ Cfollowing the δ -like procedure described in detail in Ref. [12] for Ga δ FeN fabricated onto GaN.The Ga δ FeN layers are covered by a nominally 20 nm thin GaN capping layer to avoid thesegregation to the sample surface of α -Fe upon cooling [19, 21]. A schematic representationof the samples is reproduced in Figure 1a.Information on the layers’ structure, on x Al and on the nanocrystals’ phases is obtained byhigh-resolution X-ray diffraction (HRXRD) carried out in a PANalytical XPert Pro MaterialResearch Diffractometer (Malvern Panalytical, Nrnberg, Germany). The measurements havebeen performed in a configuration that includes a hybrid monochromator equipped with a0.25 ◦ divergence slit, a PixCel detector using 19 channels for detection and a 11.2 mmanti-scatter slit. Rocking-curves acquired along the [0001] growth direction are employedto analyze the overall layer structure and the nanocrystals crystallographic phase. From3 l Ga N buffer x 1-x GaN capGa d FeN Al O
200 nm [ ] x = 0% Al
40 nm [ ] x = 0% Al
200 nm [ ] x = 41% Al
40 nm [ ] x = 41% Al
200 nm x = 41% Al
200 nm x = 0% Al A l G a N . . G a d F e N G a N (b) (c) (d)(e) (f) (g)(a) G a d F e N FIG. 1. ( a ): Architecture of the investigated samples. Cross-section TEM micrographs of the sam-ples grown ( b , c ): on GaN, and ( e , f ): on Al . Ga . N buffers, showing the embedded nanocrystalsdistributed in the Ga δ FeN layer. ( d , g ): Plan-view TEM images of the two samples, revealing anincreased dislocation network for the layer grown on the Al . Ga . N buffer with respect to thelayer grown on GaN. the integral breadth β of the (000 l ) symmetric and of the (20¯24) asymmetric diffractionplanes, an estimation of the dislocation density in the Al x Ga − x N buffer layers is obtainedaccording to the procedure described by Moram et al. [22]. Reciprocal space maps (RSM)of the asymmetric (10¯15) diffraction plane allow obtaining directly the in-plane a and out-of-plane c lattice parameters of the Al x Ga − x N buffer and of the Ga δ FeN layers, as well asinformation on the strain state of the Ga δ FeN layers. The x Al is then calculated from thelattice parameters by applying the Vegards law [23].The structural characterization has been completed by transmission electron microscopy(TEM) imaging using a JEOL JEM-2200FS TEM microscope (Jeol, Tokyo, Japan) operatedat 200 kV in high-resolution imaging (HRTEM) mode. The TEM specimens are preparedin cross-section and plan-view by a conventional procedure including mechanical polishingfollowed by Ar + milling. The prepared samples are plasma cleaned before being insertedinto the TEM. The elemental analysis is performed via energy dispersive X-ray spectroscopy(EDX) of the specimens while measuring the samples in scanning TEM mode (STEM).The magnetic properties are investigated in a Quantum Design superconducting quan-4um interference device (SQUID) MPMS-XL magnetometer (Quantum Design, Darmstadt,Germany) equipped with a low field option at magnetic fields H up to 70 kOe in the temper-ature range between 2 K and 400 K. The samples are measured in perpendicular and in-planeorientation. The dominant diamagnetic response of the sapphire substrate is compensatedby employing a recently developed method for the in situ compensation of the substratesignals in integral magnetometers [24]. For the magnetothermal properties, measurementsare performed at weak static magnetic fields following the typically employed sequence ofmeasurements: zero-field-cooled (ZFC), field-cooled (FC), and at remanence (TRM). BothZFC and FC measurements are carried out at H = 100 Oe. Moreover, since the experimentalmagnetic signals are in the order of 10 − emu, all magnetic measurements are carried out bystrictly observing an experimental protocol for minute signals [25] elaborated to eliminateartifacts and to overcome limitations associated with integral SQUID magnetometry [26]. III. RESULTS AND DISCUSSIONA. Structural properties
The main structural differences between the Ga δ FeN layers grown on GaN and thosedeposited on the Al x Ga − x N buffers are summarized in Figure 1, where the overall sam-ple structure, including TEM cross-section and plan-view images for the reference sample( x Al = 0%) and for the sample with the highest Al concentration x Al = 41% are reported.A comparison between the overview cross-section images presented in Figure 1b,e revealsa dislocation density in the Al . Ga . N buffer larger than the one in GaN, affecting thenanocrystal distribution in the Ga δ FeN overlayer. As a consequence, the NCs are not all lo-calized in one plane like those embedded in the layer grown on GaN, as demonstrated in theTEM micrographs reproduced in Figure 1c,f. It is further observed that the majority of theNCs in the Ga δ FeN/Al . Ga . N sample form at the end of dislocations propagating fromthe buffer, in contrast to the NCs in the layer grown on GaN, which are embedded in theGa δ FeN matrix volume. This is visualized in the plan-view images presented in Figure 1d,g,where NCs with a round-shaped contour, distributed homogeneously in the plane with anaverage distance of (20–100) nm between nanocrystals, are observed. The NCs density in-creases from (5.0 ± × NCs/cm for the reference sample to (5.0 ± × NCs/cm c) (d)(b)
34 35 36 Ga d FeN Al x Ga N (0002) 41%0%22%10%5% q-w (deg) x Al (a)
34 38 42 46 50 e - F e N Al O (0006) i n t en s i t y ( a r b . ) Al x Ga N (0002) g q-w (deg) un i t s x Al - G a F e N y - y G a d F e N - Q ( A ) z Al Ga N Ga d FeN(1015) x = 5 % -1 Q (A ) x Al Ga N Ga d FeN (1015) x = 41 % -1 Q (A ) x FIG. 2. ( a ) Radial 2 θ - ω scans collected along the [0001] growth direction with the diffraction peaksidentified for the Al x Ga − x N buffer, the Ga δ FeN layers and the embedded nanocrystal phases [27].( b ) Close-up of the (0002) diffraction peaks of the Al x Ga − x N buffer and of the Ga δ FeN layers.( c , d ) Reciprocal space maps of the (10¯15) diffraction plane for the samples containing 5% and 41%Al in the buffer, respectively. for the sample grown on the Al . Ga . N buffer. Besides an increased NC density, there isa complex dislocation network connecting the NCs observed for the Ga δ FeN layer grown onthe Al . Ga . N buffer.The nanocrystal phases are established from the HRXRD 2 θ - ω scans collected along the[0001] growth direction and reported in Figure 2a for all samples. Besides the diffractionpeaks from the Ga δ FeN layer, from the Al x Ga − x N (0 < x Al < O substrate, two additional diffraction peaks located around (41.28 ± ◦ and(47.72 ± ◦ are observed for all samples with Al in the buffer. The first diffraction peak isattributed to the (0002) plane of the hexagonal ε -Fe N phase, while the second one originsfrom the (200) plane of the fcc γ ’-Ga y Fe − y N phase. The calculated lattice parameters forthe two Fe y N phases are (0.437 ± ± ABLE I. List of investigated samples and their relevant parameters: Al concentration x Al in thebuffer; R % degree of relaxation; out-of-plane (cid:15) GaFeN zz and in-plane (cid:15) GaFeN xx strain and σ GaFeN xx stressin the Ga δ FeN thin layer. The Fe y N nanocrystal phases identified by HRXRD and HRTEM arealso listed. x Al R % (cid:15) GaFeN xx (cid:15) GaFeN zz σ GaFeN xx Fe y N NCs Phases(%) (%) (%) (%) (GPa) − − γ ’-Ga y Fe − y N5 0 − − ε -Fe N/ γ ’-Ga y Fe − y N10 13 − − ε -Fe N/ γ ’-Ga y Fe − y N22 67 − − ε -Fe N/ γ ’-Ga y Fe − y N41 85 − − ε -Fe N/ γ ’-Ga y Fe − y N lie in the range of the reported literature values for both phases: the hexagonal ε -Fe N with a = 0.469 nm and c = 0.437 nm [28], and the fcc γ ’-Ga y Fe − y N with a = 0.379 nm [15]. For thereference sample, only the γ ’-Ga y Fe − y N phase is observed.A close-up of the region around the (0002) diffraction peak of the Ga δ FeN overlayer andof the Al x Ga − x N buffer is presented in Figure 2b, showing the shift of the buffer peak tohigher diffraction angles with increasing Al concentration, pointing at a reduction in the c -lattice parameter. The position of the diffraction peak related to the Ga δ FeN thin layerremains unchanged for the buffers with x Al ≤
10% and shifts to lower angles for increasingAl concentrations, i.e., larger c -lattice parameter. This suggests that the Ga δ FeN layer iscompressively strained on the Al x Ga − x N buffers.To analyze the strain state and to obtain the in-plane a -lattice parameter, reciprocalspace maps at the (10¯15) diffraction plane are acquired. The RSM for the samples withbuffers containing 5% and 41% of Al are shown in Figure 2c and (d), demonstrating thatwhile the Ga δ FeN layer grows fully strained on the Al . Ga . N buffer, it is partially relaxedon the Al . Ga . N one. The in-plane percentage of relaxation R % of the Ga δ FeN thin layerwith respect to the buffer is obtained directly from the respective in-plane d -lattice spacingsas [29]: 7 % = d GaFeN(m) (cid:107) − d AlGaN(m) (cid:107) d GaN(0) (cid:107) − d AlGaN(0) (cid:107) × , (1)where d (cid:107) refers to the in-plane lattice spacings d . The values in the numerator are the mea-sured ones and those in the denominator are the values for free-standing GaN and Al x Ga − x Naccording to the Vegards law. The calculated R % values for the samples considered here,are reported in Table I, showing that for x Al < δ FeN layers grow fully strainedon the buffers and the onset of relaxation occurs at x Al ≥ x Al , where the lattice parameter a for the Ga δ FeN layer is found to deviate from the one of the Al x Ga − x N buffer with x Al > c -lattice parameter for the Ga δ FeN layer is not significantly affected by increasing theAl concentration, a matches the one of the buffer until x Al ≈
10% and then deviates signif-icantly, confirming the relaxation of the Ga δ FeN thin layer. Considering that the Ga δ FeNthin layer has only biaxial in-plane strain, the strain (cid:15)
GaFeN xx and stress σ GaFeN xx tensors arecalculated employing a linear interpolation between the value of the Young modulus E andthe stiffness constants C ij of GaN ( E = 450 GPa, 2 C /C = 0.509) and AlN ( E = 470GPa, 2 C / C = 0.579) [30]. The values reported in Table I show that independent of theAl concentration, the Ga δ FeN layers are all under a comparable compressive strain.The (0002) diffraction peak of the Al x Ga − x N buffers presented in Figure 2b broadenswith increasing Al concentration, pointing at an increment of defects and dislocation den-sity in the buffer layers. In [0001]-oriented III-nitride films, three main types of threadingdislocations are commonly observed: edge-, mixed- and screw-type. The analysis of theintegral breadth of the diffraction peaks originating from the (000 l ) planes allows estimatingthe density of screw dislocations, while the one in the (20¯24) plane provides informationon the density of edge and mixed type dislocations [22]. According to Dunn and Koch, thedensity of dislocations D B is given by [31]: D B = β . b , (2)where β is the integral breadth and b is the Burgers vector. This equation was previouslyemployed to estimate the dislocation density in GaN thin films [32]. The dislocation densities8 a)(b) a lattice parameter Al x Ga x N Ga d FeN l a tt i c epa r a m e t e r( n m ) a GaN Al x Ga x N Ga d FeN c GaN c lattice parameter (c) D edge/mixed D TEM D screw D B ( d i s l o c ./ c m - ) x Al (%) FIG. 3. ( a , b ): Lattice parameters a and c of the Al x Ga − x N buffer (full squares) and the Ga δ FeNlayers (empty circles) vs. x Al . The dashed line corresponds to the Vegards law and the dashed-dotted line indicates the literature values of the lattice parameters a and c for GaN [30]. ( c )Dislocation densities—edge-mixed (full circles) and screw (empty stars) in the Al x Ga − x N bufferlayers estimated from XRD and TEM (half-filled squares) as a function of x Al . obtained from HRXRD analysis for all buffer layers as a function of x Al are reported inFigure 3c, where a linear increase is observed reaching values up to four times larger thanthose of the GaN buffer for both edge-mixed and screw dislocations in the buffer withthe highest Al concentration. These results are consistent with the observations from thecross-section and plan-view TEM images shown in Figure 1. The dislocation density isalso estimated from TEM micrographs, yielding larger values for the Al x Ga − x N buffersthan those obtained from the XRD analysis, but following the same trend: the greater the9 (nm) (a) C ( n m ) x Al = 0% x Al = 5% x Al = 10% (b) (c) A (nm) x Al = 41% (e)
20 51015 C ( n m ) A (nm) x Al = 22% (d)(f) x yz [ ] A C A
FIG. 4. Size distribution of 200 NCs measured in cross-section HRTEM for x Al in the buffers equalto: ( a ) 0%, ( b ) 5%, ( c ) 10%, ( d ) 22%, and ( e ) 41%. The dimensions A and C correspond to theschematic representation depicted in ( f ) and correspond to half the size perpendicular and parallelto the [0001] growth direction, respectively. concentration of Al in the buffer, the higher the dislocation density.The increased dislocation density in the Al x Ga − x N buffers with x Al >
10% leads to therelaxation of the Ga δ FeN thin layers. As observed in Figure 1f, a fraction of the dislocationsfrom the Al . Ga . N buffer runs throughout the entire Ga δ FeN layer, promoting the ag-gregation of Fe along the defects and, therefore, the preferential formation of nanocrystals.Interestingly, the nanocrystals stabilized at the dislocations are predominantly elongatedalong the [0001] growth direction.A more detailed analysis of the NCs sizes is performed on cross-section and plan-viewTEM images. The size of the NCs is determined with an accuracy of ± A ) and parallel ( C ) to the [0001]growth direction for the different x Al in the buffers. The solid line marks the aspect ratio(AR) equal to 1, i.e., A = C . From the size distributions presented in Figure 4, it is seen10 (b) DMP (c) SMP
10 nm [ ][ ] (d) M P t y pe ( % ) x Al (%) DMP SMP [ ] (a)50 nm A l G a N . . G a d F e N FIG. 5. ( a ) Cross-section HRTEM image showing the distribution in pairs of prolate NCs alongdislocations in the Ga δ FeN/Al . Ga . N sample. ( b , c ) HRTEM images of nanocrystals with doubleand single Moir´e-patterns, respectively. ( d ) Fraction of NCs displaying SMP and DMP as a functionof x Al . that the size of the NCs in the reference sample has a broader distribution and particularlya larger in-plane A than in the samples grown on the Al x Ga − x N buffers. Although thesize of the NCs in the reference sample tends to lie on or below the solid line, indicatingan AR ≤ y -axis elongated in the plane of thelayer—the size of the NCs in the layers grown on the Al x Ga − x N buffers lies above the solidline, i.e., with an AR¿1, pointing at prolate NCs elongated along the [0001] growth direction.From the measured dimensions of the NCs, the average sizes parallel and perpendicular tothe growth direction [0001] are estimated, confirming the decrease in the size perpendicularto the growth direction for the nanocrystals embedded in the Ga δ FeN layers grown on theAl x Ga − x N buffers.Furthermore, it is found that in all samples the nanocrystals located at dislocation sitesare predominantly prolate. This suggests that the increase in dislocation density for thelayers grown on the Al x Ga − x N buffers promotes the formation of prolate NCs, which aremostly arranged in pairs aligned along dislocations, as shown in Figure 5a. In contrast, theoblate NCs are all located at the same depth in the layers.In addition to providing the size and phase, the characterization of the Moir´e patterns11MPs) observed in the HRTEM micrographs yields further relevant information about theembedded NCs. The origin of MPs in general is the result of the overlap of two lattices withequal spacings that are rotated with respect to each other, or of the superposition of latticeswith slightly different spacings. This leads to a pattern with Moir´e fringe spacings witheither single periodicity (line pattern) or double periodicity (grid-like pattern). ExemplaryNCs showing a double and a single MP are presented in Figure 5b,c, respectively. TheMoir´e fringe spacings depend on the two underlying crystal structures, on their orientationrelationship, and on the lattice strain. The fraction of nanocrystals displaying single MP(SMP) and double MPs (DMP) is shown in Figure 5d. Up to 78% of the NCs exhibit singleMPs and 22% produce double MPs in the reference Ga δ FeN grown on GaN buffer, while forthe films grown on the Al x Ga − x N buffers this tendency is inverted. The double MP patternis an indication of an in-plane misorientation of the NCs, which is related to the enhanceddislocation density in the underlying buffer layers and to the formation of the NCs alongthe dislocations, leading to slight distortions and strain within the GaN matrix.The Fe y N phases identified in the HRXRD spectra depicted in Figure 2a are confirmedby HRTEM analysis. In HRTEM micrographs showing NCs, the regions of interests areFourier transformed by Fast Fourier Transformation (FFT) using the Gatan Digital Micro-graph (Gatan Inc.) software. Micrographs of two NCs are shown in Figure 6a,d along withthe corresponding FFTs in Figure 6b,e. The FFT images are used to determine the latticeparameters by measuring the spacings in the two directions of the diffraction pattern. Toidentify the NCs orientation with respect to the GaN matrix, a comparison with the diffrac-tion patterns simulated by the JEMS software is performed [34]. Employing this procedure,the investigated NC in Figure 6a is identified as ε -Fe N oriented along the zone axis (ZA)[110] NC , which is parallel to the ZA [210] GaN , and therefore corresponds to an epitaxial re-lation [11¯20] NC (cid:107) [10¯10] GaN . A schematic representation of the epitaxial relation is sketchedin Figure 6c, showing that the NC is 30 ◦ rotated with respect to the crystallographic axis ofGaN, but parallel to the one of the sapphire substrate, similarly to the fcc NCs studied inGa δ FeN/GaN layers [13]. The above procedure is applied to the NCs found in the referencesample and reproduced in Figure 6d, revealing the epitaxial relation [110] NC (cid:107) [11¯20] GaN pre-sented in Figure 6f and previously reported for γ ’-Ga y Fe − y N NCs in Ga δ FeN layers grownon GaN [13]. The majority of the NCs found in the Ga δ FeN layers grown on the Al x Ga − x Nbuffers are identified as the hexagonal ε -Fe N phase, while those in the reference sample are12
ZA[001] ,[0001]
Fe4N GaN
GaNFe N (a) (e) GaNFe N [ ] [ ] [1120] ll[1010] Fe3N GaN (c)(d)
20 nm20 nm
ZA[001] ,[0001]
Fe3N GaN
GaNFe N (b) GaNFe N [ ] [110] [ ] [110] ll[1120] Fe4N GaN (f)
FIG. 6. Plan-view HRTEM images of exemplary Fe y N nanocrystals embedded in a Ga δ FeN layergrown on ( a ) an Al . Ga . N buffer, and ( d ) GaN. ( b , e ) FFT of the images presented in ( a , d ),respectively, showing the epitaxial orientation of the NCs with respect to the GaN matrix. TheFFT in ( c ) corresponds to the NCs marked by the square in ( a ). ( c , f ): Schematic representationof the epitaxial relation in ( b , e ). associated with the cubic γ ’-Ga y Fe − y N phase oriented preferentially as [001] NC (cid:107) [0001] GaN ,in agreement with the results from the XRD spectra presented in Figure 2a. From elementalcomposition analysis via
EDX line-scans, the presence of Al in the Ga δ FeN layers is ruledout as shown in Fig. S1 of the Suplemental Material.
B. Magnetic properties
In the previous section it has been demonstrated that the basic structural characteristicsof the NCs change considerably with the incorporation of Al into the buffer layer. To shedlight onto how the magnetic characteristics of the layers are modified by these structuralchanges, a comparative analysis of the magnetic properties of the reference Ga δ FeN/GaNand the Ga δ FeN/Al . Ga . N samples is performed. As indicated in Table I and depictedin Figure 2, the former contains mostly γ ’-Ga y Fe − y N NCs, which are characterized by a13alanced distribution of prolate and oblate shapes, whereas in the latter, prolate ε -Fe NNCs prevail over the γ ’-Ga y Fe − y N ones.The formation of the Fe-rich NCs in GaN is the direct consequence of the solubility limitof Fe in GaN being (1 . × ) cm − or 0.4% at the growth conditions considered here [35–37].Therefore, when the doping level exceeds this concentration, the Fe ions are found both in Gasubstitutional sites as Fe and in the phase-separated NCs. The Fe-rich NCs form disperseensembles of large ferromagnetic macrospins with specific size and shape distributions. Inthe absence of mobile carriers, the randomly distributed Fe ions, despite their high spinstate ( L = 0 , S = 5 / δ -doped layer [38]. This substantially increases the total amount of the diluteFe , making the intensity of the paramagnetic signal at low temperatures comparable tothe one of the ferromagnetic NCs. Therefore, a dedicated experimental approach is requiredto distinguish between the two contributions.The isothermal magnetization curves with the magnetic moment as a function of theapplied magnetic field m ( H ) for the reference sample ( x Al = 0%) are plotted for selectedtemperatures (solid symbols) in Figure 7. As mentioned, the bare magnetic signal consistsof two distinct contributions. At temperatures above 50 K, the fast saturating responseresembling a Langevin’s L ( H ) function at weak fields is attributed to the ferromagneticNCs. However, the lack of a systematic T -dependency satisfying the H/T scaling [39] andthe presence of a weak magnetic hysteresis indicate that the majority of the NCs is notin thermal equilibrium and their magnetic response is affected by the presence of energybarriers and governed by their distribution. At temperatures below 50 K, the m ( H ) gainsin strength and a slowly saturating contribution originating from the non-interacting Fe ions retaining their own magnetic moment dominates [36, 37, 40, 41].The paramagnetism of the Fe ions is described by the Brillouin function B S for S = J =5 / m ( H ) between m ( H ) at, e.g.,2 K and 5 K permits the quantification of the ions’ contribution by fitting ∆ B S ( H, ∆ T ) = B S ( H, − B S ( H, m ( H ) with the procedure described in detail in Ref. [37].The open circles in Figure 7 represent the experimental difference ∆ m ( H ) between m ( H )at 2 K and 5 K, whereas the dotted line follows the magnitude of the expected change14
20 40 60 80-50050100150200 /400300100502052
X19Z002K_RCqm X19Z005K_RCqm L19Z020K_CLm X19Z050K_CLm X19Z300K_CLm A19Z100K_CLm Y19Z395K_CLm X19Z002K_Bqm B52FigM1_A X19Z002K_PM A19Z100K_B X19Z300K_A Y19Z395K_A X19Z002K_RPM m ( H ) ( - e m u / c m ) H ( kOe ) T/K Ga FeN / GaN PM N P M ( c m - ) m NC ( - e m u / c m D ( 10 cm -2 ) (a) (b) (c) GaN (Al,Ga)N-buffer S a t x Al (%) 5 FIG. 7. ( a ) (Solid symbols) Isothermal magnetization curves of the reference Ga δ FeN/GaN struc-ture at selected temperatures. The open circles denote the difference ∆ m ( H ), whereas the dashedline corresponds to the calculated difference of the respective Brillouin functions calculated forthe paramagnetic Fe ions with N PM = (1 . × ) cm − . The solid lines mark the resultingmagnitudes of m NC ( H ) of the NCs, after subtracting the paramagnetic component. The soliddown–arrow indicates the degree of the reduction of m ( H ) due to the subtraction of the paramag-netic contribution. ( b , c ) N PM and m sat NC plotted as a function of total dislocation density D . Thesquares represent the reference Ga δ FeN/GaN structure, the circles mark data for the layers grownon the Al x Ga − x N buffers. The corresponding concentration of Al in the Al x Ga − x N buffers isindicated in panel ( b ). Dashed lines in panels ( b , c ) are guide to the eye. ∆ B / ( H, ∆ T ) corresponding to several ions N PM = (1 . × ) cm − . The dashed lineindicates the magnitude of the paramagnetic contribution corresponding to N PM at 2 K.Having established N PM in each of the investigated structures, the paramagnetic contribu-tion m PM ( H ) = gµ B SN PM B / ( H, T )—where g is the g-factor and µ B the Bohr magneton—is calculated and subtracted from the experimental data to obtain the magnitude m NC ( H, T )of the magnetization corresponding to the NCs. The results are indicated by solid lines inFigure 7. It is worth noting that m NC ( H, T ) saturates at all investigated temperatures for H ≥
10 kOe, confirming the ferromagnetic order within the NCs. The evolution of N PM and m NC as a function of the dislocation density is presented in Figure 7b,c, respectively.The former decreases, whereas the latter increases with the dislocation density, suggesting15
100 200 300 4004050607080 m NC ( - e m u / c m ) Temperature ( K ) '-Ga y Fe N M ( e m u / c m ) Temperature ( K ) -Fe N (a) (b) S a t S a t T C ’- T C - F e N Ga y Fe N Ga FeN / GaN ( ’-Ga y Fe N) Ga FeN / Al Ga N ( -Fe N + ’-Ga y Fe N) FIG. 8. ( a ) Comparison of the temperature dependence of m satNC ( T ) in the studied Ga δ FeN layersgrown on a GaN buffer (squares) and grown on a Al . Ga . N buffer (circles). Solid symbols: m satNC inferred from the m NC ( H ) isotherms. Open symbols: direct continuous sweeping of T at H = 20 kOe. ( b ) Temperature dependence of the saturation magnetization M Sat of the two Fe y Ncompounds formed due to the epitaxy of the Ga δ FeN layers. The solid lines mark two classicalLangevin functions L ( T ) rescaled to follow the corresponding experimental result for 2 K < T <
400 K. The dashed lines are Brillouin functions B / ( T ) rescaled to reproduce the correspondingmagnitudes of m satNC (0) and T C . that the dislocations originating at the sapphire/Al x Ga − x N interface serve as preferentialsites for the aggregation of the Fe ions. This is substantiated by the fact that the magnitudeof N PM in the reference structure and related solely to the layer nominally containing Fe,i.e., (60–100) nm, corresponds to (4 × ) cm − or (cid:39)
1% of Fe ions, largely exceeding theFe solubility limit in GaN. Thus, the Fe ions are distributed across the entire depth inthe structure of the reference sample, whereas in the layers grown on the Al x Ga − x N buffersa significant fraction of the Fe ions migrates to the dislocations, where they aggregate intothe hexagonal ε -Fe N NCs. Since the dislocation density is found to correlate with the Alcontent in the buffer, as presented in Figure 3c, the Al content in the Al x Ga − x N buffer isinstrumental to control both the substitutional Fe atoms concentration and the strength ofthe ferromagnetic signatures related to the NCs.The temperature dependence of the saturation magnetization m satNC ( T ) of the ferromag-netic signal specific to the NCs for the layer grown on the Al . Ga . N buffer (circles) and for16he reference one (squares) is reproduced in Figure 8. These dependencies are establishedupon performing a m ( H ) analysis similar to the one exemplified in Figure 7 (solid symbols),as well as from direct continuous sweeping of T at H = 20 kOe (open symbols). This al-lows quantifying the temperature dependence of the saturation magnetization M sat of the γ ’-Ga y Fe − y N and ε -Fe N present in the structures.To quantify the magnetization of the NCs, their average volume is estimated from the sizedistribution shown in Figure 4 and the average densities established from TEM by taking intoaccount that (50-70)% of the prolate NCs in the Ga δ FeN/Al x Ga − x N structures grow in pairsalong the dislocations, as shown in Figure 5a. The estimated values of the NCs magnetizationare (1700 ± for the NCs in the reference sample containing γ ’-Ga y Fe − y N NCs,and (1400 ± for the NCs present in the Ga δ FeN/Al . Ga . N structure, whereabout 80% of the NCs are ε -Fe N and 20% are γ ’-Ga y Fe − y N. These values are consistentwith those estimated from ferromagnetic resonance measurements [17], shown in Fig. S2 ofthe Suplemental Material, and in good agreement with the respective ranges of M sat reportedin the literature for these compounds. For γ ’-Fe N, the M sat ranges between 1500 emu/cm and 2000 emu/cm [2, 44–46], so that the values obtained for the γ ’-Ga y Fe − y N NCs con-sidered here point at high crystallinity and low dilution by Ga, i.e., ( y (cid:28) . Ga . N buffer the M sat established, taking into account a 20% contribu-tion of γ ’-Ga y Fe − y N NCs, yields a corrected value of M sat = (1300 ± for the ε -Fe N NCs, consistent with previous studies [2, 5, 47–53].The resulting magnitudes of M Sat ( T ) for both compounds are represented as solid symbolsin Figure 8b. The experimental trends of M Sat ( T ) for both Fe y N compounds are comparedwith the spontaneous magnetization calculated as a function of T based on the molecularfield theory in the classical limit and with the Langevin function L ( T ), i.e., correspondingto a large magnetic moment of the NCs J = S → ∞ (solid lines). It is observed that thelow- T fast drop of m FM ( T ) starting at T ≈
50 K, is indeed well captured by L ( T ), and couldnot be reproduced by a Brillouin function. For comparison, the B / ( T ) functions are addedto Figure 8b as dashed lines. The L ( T ) is then extrapolated to assess the T C of the NCs ineach sample.In the reference sample containing mostly γ ’-Ga y Fe − y N NCs a T C = ( 630 ±
30) K isfound, i.e., about 100 K lower than the values reported for Ga-free γ ’-Fe N of T C = 716 K [46]and 767 K [6]. This is attributed to a partial replacement of the Fe ions by Ga, which17 IG. 9. ( a , b ) ZFC, FC and the calculated temperature derivative of the thermoremanence mag-netization (TRM): − d ( M FC − M ZFC ) dT in the studied Ga δ FeN structures grown either on GaN oron the Al . Ga . N buffer. ( c ) Superparamagnetic limit distribution in the Ga δ FeN/GaN structurecalculated based on the size and shape distributions of the NCs taken from Figure 4a. ( d ) Directmeasurement of TRM in Ga δ FeN/Al . Ga . N after cooling down in a saturating H = 10 kOe and( e ) its T –derivative. The dashed lines in ( d ) point to the superparamagnetic limit of about 500 K. leads to a magnetic dilution and randomization of spins breaking down the ferromagneticorder [15, 54]. However, the Ga incorporation is minimal, since the ternary GaFe N is weaklyantiferromagnetic [15]. The same extrapolation method yields T C = (670 ±
30) K for thelayer grown on the Al . Ga . N buffer, which contains predominantly ε -Fe N NCs and alimited amount of γ ’-Ga y Fe − y N. No quantitative conclusion about the T C of ε -Fe N NCscan be made, nevertheless it can be stated that its value is significantly greater than thepreviously reported 575 K [5] and (500–525) K [52, 55]. This result is relevant, since despitethe high potential of ε -Fe N for spintronics [5], the technological development of this materialhas been limited by its high chemical reactivity and by challenges in obtaining the requiredstoichiometry [56]. The magnitude reported here for ε -Fe N NCs points, on the other hand,to the possibility of stabilizing, in a controlled fashion, relevant Fe y N nanostructures in aGaN matrix.The magnetothermal behavior of these ensembles of NCs traced for two orientations of H , i.e., H (cid:107) parallel (full symbols) and H ⊥ perpendicular (open symbols) to the film planeis shown in Figure 9a and follows a trend specific to ferromagnetic nanoparticle ensemblespreviously reported for Fe-rich NCs stabilized in GaN [18, 36, 37]. These features indicate18hat independently of the orientation, a specific distribution of energy barriers E B = K eff V NC for the ferromagnetic moment reversal determines the response in the whole temperaturerange. Here K eff is the effective magnetic anisotropy energy density specific to a given NCwith volume V NC . The effect is particularly significant in the Ga δ FeN/Al . Ga . N layer for H ⊥ . This finding demonstrates that the predominantly prolate character of the ε -Fe N NCsin the layers grown on the Al x Ga − x N buffers dramatically affects the magnetic anisotropy(MA), which will be treated in detail later.For an ensemble of non-interacting magnetic NCs the temperature derivative of the ther-moremanence magnetization (TRM) provides qualitative information on the E B distributionin the ensemble [57]. From M TRM = M FC − M ZFC , the − d ( M FC − M ZFC ) dT is calculated anddisplayed in Figure 9b, with non-zero values in the whole T -range and exhibiting a peak ataround 50 K. From this, the magnitude of the superparamagnetic limit T SP in the layers isquantified. Here, T SP is the temperature above which a given magnetic NC or an ensembleof NCs is in thermal equilibrium and is defined by E B = 25 k B T SP [58], where k B is theBoltzmann constant and the numerical factor 25 corresponds to the typical magnetometryprobing time of 100 s.Due to the fact that all considered layers contain γ ’-Ga y Fe − y N NCs, their size dis-tribution is taken into account. For each NC, the individual K eff = K mcr + K sh , where K mcr = (3 × ) erg/cm is the magnitude of the cubic magnetocrystalline anisotropy pa-rameter of γ ’-Fe N [59], is calculated. The positive sign indicates that the magnetic easyaxes are directed along the [100] direction, which is parallel to the c -axis of GaN. The shapecontribution to the MA for each NC: K sh = ( N A − N C ) M / , (3)is determined by the difference N A − N C of the demagnetizing coefficients N of the consid-ered nanocrystals according to the ellipsoid with semi-axes A and C [60]. The experimentalmagnitude of M sat = 1700 emu/cm established here is employed, considering that the maincrystallographic axes of the NCs and their axes of revolution are aligned with those of thehost lattice. The magnitudes of K mcr and K sh can be added with the caveat that all NCswith negative values of K eff are discarded. This is because for K eff < M rotates smoothly by 180 o to facilitate the reversal and the NCs are atthermal equilibrium at any T , thus not contributing to TRM. Based on the data presented19n Figure 4a, as much as 50% of the NCs belong to this category, a decisive factor for un-derstanding the magnetic softness of the ensembles of NCs [18, 19, 24, 36, 37]. The largenumber of NCs in equilibrium explains also the low magnitude of M FC (and M TRM ), i.e.,less than 20% of the total saturation value. Finally, for nearly spherical NCs (
C/A (cid:39) K mcr prevails, E B = K eff V NC / (cid:104) (cid:105) family of directions ( K cubicmcr >
0) [61].The calculated T SP distribution as a function of the K eff V NC / (25 k B ) is depicted in Figure 9cand is in agreement with the experimental data in Figure 9b. The calculated distributionpeaks around 40 K, decreases at higher temperatures, and remains non-zero up to 400 K, asfound experimentally.The non-conventional behavior of M ZFC and M FC of the Ga δ FeN/Al . Ga . N structureprobed for H ⊥ indicates that even at T = 400 K the field of 100 Oe is too weak to overcomethe energy barriers. Therefore, direct TRM measurements to establish the actual magnitudeof the low– T M
TRM are performed. To this end, the sample is cooled down at a saturatingfield of 10 kOe to T = 2 K, then the field is quenched and at H (cid:39) H (cid:107) . Theresults and their T -derivatives are presented in Figure 9d,e, respectively. The magnitudeof the irreversible response increases for the perpendicular orientation (empty symbols) toabout 80% of the total magnetic saturation. Taking into account the significant MA ofhexagonal ε -Fe N and the much weaker one of cubic γ ’-Ga y Fe − y N, the 80% level is takenas a coarse estimate of the relative content of the ε -Fe N NCs in the layer grown on theAl . Ga . N buffer.Both TRMs remain non-zero even at 400 K. By extrapolating the curves to zero, withthe maximum value of T SP located at 500 K. This procedure is valid because the derivatives dM TRM /dT increase as T →
400 K. Interestingly, the T -derivative of M TRM for the in-planeconfiguration is featureless and larger than the one established at low fields in the ZFC andFC measurements, suggesting that in these two measurements two different subsets of NCsdetermine the response.The normalized magnetization
M/M sat of the layers as a function of the magnetic field ispresented in Figure 10a,b, where both M ( H ⊥ ) and M ( H (cid:107) ) show the sensitivity of the magne-tization to the orientation of H for the reference structure and for the Ga δ FeN/Al . Ga . Nlayer, respectively. The measured M ( H ) saturates beyond ±
10 kOe and does not signifi-20
IG. 10. Normalized magnetization
M/M sat acquired at 2 K for the two magnetic field configura-tions H ⊥ (circles) and H (cid:107) (diamonds) for ( a ) the reference sample, and ( b ) Ga δ FeN/Al . Ga . N.The
M/M sat at 300 K as a function of the magnetic field is depicted in the insets. The verticalarrows mark an inflection point H on M ( H ⊥ ) separating two different contributions to M duringits reversal. The empty arrow marks the coercive field of the whole ensemble, whereas the lengthsof the two full arrows indicate the average coercive field (cid:104) H C (cid:105) of the prolate part of the distribution.( c ) Magnetic anisotropy M ( H ⊥ ) − M ( H (cid:107) ) obtained for the Ga δ FeN/Al . Ga . N sample acquiredat selected temperatures. ( d ) Magnitudes of K eff established from the area under the curves in ( c )plotted as the function of M (diamonds) and of K mcr of ε -Fe N (bullets). Solid lines mark theproportionality of both K eff and K mcr to M . ( e ) Temperature dependence of K mcr of ε -Fe N. cantly depend on H in the whole studied T -range, as demonstrated earlier in Figure 7a forthe reference sample and in previous studies [19, 24]. A similar behavior is observed for allthe layers deposited on the Al x Ga − x N buffers.21t is worth underlining that the main symmetry axes of the ε -Fe N NCs are fixed in thedirection of the c -axis of GaN, i.e., perpendicular to the sample plane, which is essential formodelling the results. The uniaxial magnetocrystalline anisotropy (UMA) of the hexagonal ε -Fe N NCs was found to be between (0.5–1 × ) emu/cm [53] with the easy axis alongthe [0001]-direction. Due to preferential nucleation along the dislocations, the distributionof shapes of the ε -Fe N NCs is highly asymmetric, adding a sizeable shape contribution tothe native crystalline UMA of ε -Fe N. The data presented in Figure 4c yield the averageelongation (cid:104)
C/A (cid:105) = 1 .
34 for the prolate part of the distribution, what, according to Eq. 3and M sat = 1300 emu/cm , points to (cid:104) K sh (cid:105) = (1 . × ) erg/cm , which represents themost relevant contribution to the overall MA of this ensemble.The large UMA along the growth direction is the origin of the pronounced squarenessand the resemblance of the experimental m ( H ⊥ ) to the perpendicular magnetic anisotropy ofbulk ferromagnets and layered structures. This is further demonstrated by the hard-axis-likeshape of m ( H (cid:107) ). The magnitude of the UMA exerted by the considered ensemble of NCsis calculated by taking the experimental difference ∆ M ( H ) = M ( H ⊥ ) − M ( H (cid:107) ), plottedfor selected temperatures in Figure 10c. By definition, the area under the ∆ m ( H ) yieldsthe magnitude of K eff . The established magnitudes are plotted against the correspondingmagnitudes of M in Figure 10d (diamonds). The nearly linear relationship K eff ∝ M confirms the significant UMA in this ensemble, allowing the direct determination from Eq. 3of K mcr of ε -Fe N from the T –dependence of m satNC ( T ) (Figure 8). The resulting magnitudesof K mcr = K eff − K sh established at all the measured temperatures, are shown in Figure 10e(bullets). This is the first direct determination of the absolute magnitudes of K mcr of ε -Fe Nin such a broad and technologically relevant temperature range up to 400 K.On the other hand, as indicated in Figure 10b, the magnetization process in the Ga δ FeN/Al x Ga − x Nstructures is based on two rather independent switching processes. This is seen at the twotemperatures exemplified in Figure 10b. The T = 2 K case, where the thermal activationcontribution to m ( H ) can be neglected, is considered in detail. Here, about a third of thetotal magnetization of the NCs switches at very weak fields. This process completes at weaknegative fields, where a kink is seen in m ( H ⊥ ) at about ± H . Up to H about 30% of the total M has switched or rotated to the new direction of H .This is the result of a narrow band of weak switching fields brought about by the minorityof the oblate NCs (which nominally reverse M at H = 0) and of several cubic γ ’-Ga y Fe − y N22Cs, which reverse M at weak fields, as demonstrated in Figure 10a. For the remaining70% NCs, the switching process begins after H ⊥ passes H and these are the prolate ε -Fe NNCs, which, due to their generally high K eff require larger magnitudes of H to overcome theindividual anisotropy fields H A = 2 K eff /M sat . Since the majority of the NCs is in the singledomain state, the different magnitudes of H A contribute to a broad distribution of switching(coercive) fields H C , resulting in the wide m ( H ⊥ ) for | H | > | H | . From the magnitude of (cid:104) K eff (cid:105) , (cid:104) H C (cid:105) = 3 kOe at low temperatures is obtained and it is also extrapolated directlyfrom the m ( H ) curve in Figure 10b. Since the reversal process of M of the prolate fractionof the NCs ensemble in the Ga δ FeN/Al x Ga − x N structures starts after the magneticallysoft part of the ensemble has reversed, the H C cannot be determined at M = 0. The m ( H )after H is assigned to the prolate ε -Fe N, marked by the arrows in Figure 10b, from wherethe corresponding (cid:104) H C (cid:105) can be obtained. It is worth noting that the difference in (cid:104) H C (cid:105) between the two branches of m ( H ⊥ ) corresponds to the magnitude of the soft part of M which switches within | H | < | H | , i.e. the magnetically hard part of m ( H ⊥ ) correspondingto the prolate NCs is broken up by the magnetically soft component of the distribution. IV. CONCLUSIONS
Strained and partially relaxed Ga δ FeN thin layers grown on Al x Ga − x N buffers byMOVPE reveal the formation of hexagonal ε -Fe N and fcc γ ’-Ga y Fe − y N nanocrystalsepitaxially embedded in the GaN matrix. The Ga δ FeN layers are strained for an Al concen-tration in the buffer up to 10% and then relax up to 85% for an Al concentration of 41%.With increasing Al content, an increase in the dislocation density in the buffer layers isobserved, together with a preferential aggregation of nanocrystals along the dislocations inthe Ga δ FeN layers. The NCs have either oblate or prolate shape, with the majority of theNCs being prolate. Both nanocrystal phases are coherently embedded into the surroundingGaN matrix with an epitaxial relation: [0001] NC (cid:107) [0001] GaN and (cid:104) (cid:105) NC (cid:107) (cid:104) (cid:105) GaN forthe ε -Fe N NCs, and [001] NC (cid:107) [0001] GaN and (cid:104) (cid:105) NC (cid:107) (cid:104) (cid:105) GaN for the γ ’-Ga y Fe − y NNCs.The magnetic response of the layers is consistent with the one previously found forphase-separated (Ga,Fe)N consisting of two components: a dominant paramagnetic low- T contribution from Fe ions dilute in the GaN matrix and in the buffer volume, and a23erromagnetic one dominant above 50 K originating from the γ ’-Ga y Fe − y N and the ε -Fe Nembedded NCs [36, 37]. The low– T contribution of the Fe ions to the total magnetiza-tion reaches magnitudes comparable to those of the NCs. The T C of the reference layercontaining solely γ ’-Ga y Fe − y N is found to be (630 ±
30) K, pointing at the inclusion ofGa into the NCs and therefore lowering the T C with respect to one of γ ’-Fe N [6]. Due tothe formation of additional ε -Fe N in the Ga δ FeN/Al x Ga − x N layers, T C is increased to(670 ±
30) K, indicating a high crystalline and chemical quality of the NCs. Moreover, thecalculated magnetization of the NCs is consistent with literature values. The magnetizationprocess in the Ga δ FeN/Al x Ga − x N structures is based on two substantially independentswitching processes: a relatively fast switching of the oblate and γ ’-Ga y Fe − y N NCs at lowfields, followed by the switching of the ε -Fe N NCs, which require larger magnitudes of H to overcome the individual anisotropy fields. All Ga δ FeN layers grown on the Al x Ga − x Nbuffers exhibit a sizeable uniaxial magnetic anisotropy with the easy axis matching the c -axisof the hexagonal ε -Fe N NCs and the [0001] growth direction of the layers. This suggeststhat the formation of ordered elongated hexagonal ε -Fe N NCs along the dislocations in theAl x Ga − x N buffers is responsible for the observed out-of-plane magnetic anisotropy. Thefinding is substantiated by the value of H C obtained directly from the normalized magneti-zation for H ⊥ that is well reproduced by the calculated value obtained considering the K eff of the prolate ε -Fe N NCs. Significantly, this is the first direct determination of the absolutemagnitudes of K mcr of ε -Fe N in a broad and technologically relevant temperature range upto 400 K.According to these findings, Ga δ FeN/Al x Ga − x N heterostructures provide a control-lable housing for stabilizing ordered arrays of ferromagnetic Fe y N compounds, opening wideperspectives for spin injection in these phase-separated material systems and for the electric-field manipulation of the magnetization [62].
ACKNOWLEDGMENTS
The work has been funded by the Austrian Science Fund FWF Projects No. V478-N36, P26830 and P31423, and the Austrian Exchange Service ( ¨OAD) Project No. PL-01/2017 (DWM.WKE.183.72.2017). The financial support by the Austrian Federal Ministry24or Digital and Economic Affairs, the National Foundation for Research, Technology andDevelopment and the Christian Doppler Research Association is gratefully acknowledged.The authors greatly acknowledge Werner Ginzinger for his extensive work in the samplepreparation and on TEM measurements. [1] Jack, K.H. The Iron-Nitrogen System: The Crystal Structures of ε -Phase Iron Nitrides. ActaCryst. , , 404.[2] Eck, B.; Dronskowski, R.; Takahashi, M.; Kikkawa, S. Theoretical calculations on the struc-tures, electronic and magnetic properties of binary 3d transition metal nitrides. J. Mater.Chem. , , 1527–1537.[3] G¨olden, D.; Hildebrandt, E.; Alff, L. The film phase diagram of iron nitrides grown bymolecular beam epitaxy. J. Magn. Mag. Mater. , , 407–411.[4] Coey, J.; Smith, P. Magnetic nitrides. J. Magn. Magn. Mater. , , 405–424.[5] Leineweber, A.; Jacobs, H.; H¨uning, F.; Lueken, H.; Schilder, H.; Kockelmann, W. (cid:15) -Fe3N:magnetic structure, magnetization and temperature dependent disorder of nitrogen. J. Alloy.Comp. , , 79–87.[6] Shirane, G.; Takei, W.J.; Ruby, S.L. M¨ossbauer Study of Hyperfine Fields and Isomer Shiftsin Fe N and (Fe,Ni) N. Phys. Rev. , , 49–52.[7] Kokado, S.; Fujima, N.; Harigaya, K.; Shimizu, H.; Sakuma, A. Theoretical analysis of highlyspin-polarized transport in the iron nitride Fe N. Phys. Rev. B , , 172410.[8] Shirane, G.; Takei, W.J.; Ruby, S.L. Spin polarization of Fe N thin films determined bypoint-contact Andreev reflection.
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