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Gaurav K. Shukla, [Prabhat Kumar](https://orcid.org/0000-0003-3897-193X), [Shinji Isogami](https://orcid.org/0000-0001-7230-6090)

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[Berry curvature induced intrinsic spin Hall effect in the light-element-based CrN system for magnetization switching](https://mdr.nims.go.jp/datasets/fe32a058-061c-4c3a-b9f3-51b2cb257643)

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Spin Berry curvature-induced intrinsic spin Hall effect in light-element-based CrNsystem for magnetization switchingGaurav K. Shukla*,1 Prabhat Kumar,1 and Shinji Isogami†11National Institute for Materials Science (NIMS), Tsukuba 305-0047 JapanThe current-induced spin-orbit torque-based devices for magnetization switching are commonlyrelied on the 4d and 5d heavy metals owing to their strong spin-orbit coupling (SOC) to producelarge spin current via spin Hall effect (SHE). Here we present the sizable SHE in CrN, a light-element-based system and demonstrate the current-induced magnetization switching in the adjacentferromagnetic layer [Co(0.35 nm)/Pt(0.3 nm)]3, which exhibits perpendicular magnetic anisotropy.We found the switching current density of 2.6 MA/cm2. The first principles calculation gives thespin Hall conductivity (SHC) ∼ 120 ( ℏe) S/cm due to intrinsic spin Berry curvature arising fromSOC induced band splitting near Fermi-energy. The theoretically calculated intrinsic SHC is closeto the experimental SHC extracted from second harmonic Hall measurement. We estimated spinHall angle (θSH) ∼ 0.09, demonstrating efficient charge-to-spin conversion in CrN system.I. INTRODUCTIONSpintronics revolutionized the area of data storagetechnology harnessing the electron spin in role insteadof charge current [1, 2]. Spin Hall effect (SHE), wherean unpolarized charge current flowing through high spin-orbit coupled material is converted into transverse spin-polarized current, has attracted significant interest inspintronics as an efficient way to generate spin current[3, 4]. SHE has two kinds of origin, one is intrinsic mech-anism related to the spin Berry curvature associated withBloch bands and extrinsic mechanism related to the scat-tering events [5]. The spin Hall conductivity (SHC) andspin Hall angle (θSH) are two factors that determines theperformance of SHE-based devices [6] (Here, SHE is de-fined as a comprehensive term that includes both SHCand θSH in this study). The SHC is the sum of thespin Berry curvature of the occupied states in the Bril-louin zone, while θSH is the ratio of SHC to the chargeconductivity (θSH = σSHσxx), that describes the charge-to-spin conversion efficiency [3, 7, 8]. Unlike the conven-tional or charge Berry curvature, the spin Berry curva-ture does not vanish in systems with time-reversal sym-metry (TRS) and inversion symmetry (IS) [9–11] as in-clusion of band off-diagonal components of the spin ma-trix in wave packet dynamics inherently breaks the TRS[9, 10]. Integration of spin Berry curvature gives rise tothe conventional SHE, with mutually perpendicular spinpolarization and spin current, as observed in Pt and Au[8–10, 12–14].The spin current generated by the SHE can exerttorque on an adjacent ferromagnetic layer, which isknown as spin-orbit torque (SOT), and the magneti-zation switching by the SOT is a key mechanism fornext-generation magnetoresistive random access memory(MRAM) devices [15–18]. So far, SOT research has pri-marily concentrated on heavy-metal (HM)/ferromagnetic(FM) heterostructures [16, 19–21] due to the large SHE ofHMs such as W, Ta and Pt, arising from high spin-orbitcoupling (SOC) [3, 22]. On the other hand, there hasbeen growing interest on light 3d metals with low SOCsuch as Cr and V, as a candidate for replacing the HMsin terms of their environmental compatibility and cost-effectivity[23–25]. However, the SHE of light 3d metalsis lower than that of HMs in general, which is an issue tobe solved and a challenge for their use in energy-efficientSOT devices [22, 26, 27].In recent years, Nitrogen (N)-based systems widelygarnered attention due to their higher stability, long spindiffusion length, topological band feature and seamlesshybridization with the light 3d metals, enabling the ma-nipulation of their intrinsic properties [28–32]. In ad-dition, it is reported that N also offers a significantimpact on the SHE of antiferromagnets [29]. Thus,the N incorporation is expected to enhance the SHEof light 3d metals even though the SOC is low, whichmay lead to the device applications. Although θSH ofCr, which is one of the light 3d metals, is half size ofPt [22, 24, 27], current-induced magnetization switch-ing (CIMS) has been demonstrated in the Cr-based SOTdevice, Cr/CoFeB/MgO/Cr [24]. In this study, there-fore, we focused on CrN, a light-element-based system,where incorporating N into Cr. The CrN is a stablecompound with a rock salt structure (NaCl-type, spacegroup Fm3̄m) and paramagnetic structure at room tem-perature [33, 34], whose electrical resistivity is reportedto be ranging from 0.75 to 300mΩcm [35]. Below theNéel temperature (272K-280K), transformation to theantiferromagnetic state takes place with an orthorhom-bic crystal structure [34].In this work, we experimentally demonstrated CIMSin a Co/Pt ferromagnetic multilayer due to spin currentfrom CrN, using the CrN-based SOT device. We mea-sured the switching current density to be 2.6 MA/cm2in the device. Theoretical calculation gives the intrin-sic SHC arising from spin Berry curvature-induced bandsplitting near the Fermi energy. The theoretically cal-culated intrinsic SHC is close to the experimental SHCextracted from second harmonic Hall measurement. Weestimated θSH of CrN ∼ 0.09, which surpasses the θSHof Cr (∼ 0.05) [27], demonstrating its efficient charge-to-spin conversion.2II. METHODSCrN(5)/[Co(0.35)/Pt(0.3)]3/MgO(3) (here parenthesisdenotes nominal thickness in nm) multilayer is grown onc-plane oriented Al2O3 substrate using DC and RF mag-netron sputtering technique [36]. The CrN was depositedusing direct current power source at 650 ◦C. The Co,Pt and MgO layers were deposited using radio-frequencypower source at room temperature. The base pressure ofthe chamber was better than 6×10−6 Pa. The thin filmwas patterned into Hall bar device using photolithogra-phy and Argon (Ar) ion etching technique. The gold(Au) was sputtered for electrical contact. X-ray diffrac-tion measurement (λ = 1.54Å) was performed for struc-tural analysis. The magnetization measurement was per-formed using Magnetic Properties Measurement System(MPMS). The anomalous Hall effect and the CIMS mea-surements were done using home-build set-up. For CIMS,initially a pulse current with a width of 10ms was appliedusing a pulse generator. A 0.2mA of sensing current wasapplied from DC power source and the Hall voltage wasread using digital multimeter after each interval of cur-rent pulse for 1 sec. The magnetic field was applied byan electromagnet. The second-harmonic Hall voltage wasmeasured with a lock-in amplifier while varying in-planemagnetic field. A sinusoidal wave with an effective am-plitude of 2.3 mA (current density ∼ 3.3 MA/cm²) and afrequency of 33.123 Hz was generated using a pulse gen-erator. The same device and sample package were uti-lized for both CIMS and second-harmonic Hall measure-ments. All the measurements were conducted at roomtemperature. The electronic structure of CrN was cal-culated employing density functional theory (DFT) us-ing Quantum Espresso package [37]. We employed thePerdew-Burke-Ernzerhof (PBE) type generalized gradi-ent approximation (GGA) for the exchange-correlationfunctional [38]. The kinetic energy cutoff of 80Ry wastaken for the plane-wave basis. A 8 × 8 × 8 k-pointmesh was used for the Brillouin zone (BZ) sampling. Theonsite coulomb interaction (U) of 3.0 eV for Cr atom istaken in the calculation. The spin transport propertieswere calculated employing the maximally localized Wan-nier functions using the Wannier90 code [39]. The Kuboformula implemented in Wannier90 code is used to calcu-late the k-resolved spin Berry curvature, which is givenas [8, 40]Ωn,ij(k) = ℏ2Im∑m̸=n−2 ⟨nk|ĵsi |mk⟩ ⟨mk|ν̂j |nk⟩(ϵnk − ϵmk)2, (1)where ĵsi = 12{σz, vi} represents the spin-current opera-tor.The intrinsic SHC is calculated using followingformulae[41]σkij = −e2ℏ1V N3k∑n∑kΩn,ij(k)fnk, (2)where V is the primitive cell volume and N3k is the num-ber of k -points in the Brillouin zone. fnk is the Fermi-Dirac distribution function.III. RESULTS AND DISCUSSIONA. Structure and magnetizationFigure 1(a1) shows a three-dimensional unit-cell ofCrN. Crystallographic studies suggest that CrN be-longs to face-centered cubic (FCC) lattice (Fm3̄m spacegroup), with Cr (red spheres) and N (light blue spheres)atoms at (0, 0, 0) and (0.5 ,0.5 ,0.5) Wyckoff positions, re-spectively [42]. The (111)-oriented view of CrN is shownin Fig.1(a2). In this orientation, CrN retains a mirrorsymmetry along the [1-10] direction (m1−10), while themirror symmetry along [11-2] (m11−2) is broken. Thegreen shaded region in Figs.1a(1) and a(2) show the (111)plane. Figure 1(b) shows the room-temperature X-raydiffraction patterns of the grown samples, where differentN2 flow rate was introduced for the phase optimization of5 nm thick CrN on c-plane oriented Al2O3 substrate. Atan initial N2 flow rate of 10% (Ar: 90 sccm,N2: 10 sccm),Cr2N is observed as the dominant phase, with a charac-teristic peak at 2θ∼ 40.15 degree. As the N2 flow rateincreases, the Cr2N phase diminishes, and the CrN phasebegins to form. At 30% N2 flow rate, a pure CrN phase isobserved. CrN crystallizes in a (111) oriented FCC cubiclattice on Al2O3 substrate, with a lattice parameter ∼4.18 Å, as determined by XRD data.To determine the transition temperature of CrN,we measured the field cooled (FC) magnetization ofAl2O3/CrN(5) from 150K to 300K at 1000 Oe (Fig.1(c)).The antiferromagnetic-to-paramagnetic transition (TN )is observed at 277K, which is consistent with the litera-ture. Noteworthy, the negative value of magnetization isdue to contribution from Al2O3 substrate [34, 43].Following the confirmation of the optimizationconditions for CrN (111) phase, we synthesizedCrN(5)/[Co(0.35)/Pt(0.3)]3/MgO(3) multilayer de-vice on c-plane oriented Al2O3 substrate. Figure 1(d)presents the magnetic hysteresis loop of the devicemeasured at room temperature, where the magnetic fieldis varied along out-of-plane (black curve) and in-plane(red curve) directions. The out-of-plane magnetizationsaturates at a much lower field compared to the in-planemagnetization, indicating easy-axis along out-of-planedirection. The unidirectional magnetic anisotropy (Ku)was estimated using the in-plane and out-of plane M−Hcurves using following equation [44]Ku = Keffu + 2πM2s (3)Keffu =(µ0∫ Ms0Hdm)hard axis−(µ0∫ Ms0Hdm)easy axis(4)where the second term of Eq.3 represents the demag-netization component. Using saturation magnetization(Ms) of 890 emu/cm3, Ku was found to be ∼ 8.07× 106erg/cm3. This value suggest that device has significant3FIG. 1. (a1) A face-centered cubic unit cell (space group Fm3̄m) of CrN. Red and light blue spheres represent the Cr and Natoms, respectively. (a2) The (111)-oriented view of CrN unit cell. The mirror symmetry is preserved along [1-10] direction,while broken along [11-2] direction (dashed lines). The green shaded region in Figs.(a1) and (a2) shows the (111) plane. (b)X-ray diffraction patterns at different N2 flow rate. (*) denotes the substrate peaks. (c) Field cooled (FC) magnetization curvefor Al2O3/CrN(5) in the temperature range of 150K to 300K at 1000 Oe. (d) Out-of-plane (black curve) and in-plane (redcurve) magnetization of CrN(5)/[Co (0.35)/Pt(0.3)]3/MgO(3) multilayer device.preference of the along out-of-plane direction, which iscrucial for SOT driven magnetization switching.B. Current induced magnetic switchingNow, we investigate the transport properties of the fab-ricated multilayer device. For the magnetization switch-ing it is crucial that ferromagnetic layer on top of spin-current source should show the perpendicular magneticanisotropy (PMA). To measure this, we fabricated theHall bar device with current channel along [1-10] direc-tion (along the mirror symmetry line shown in Fig.1(a2))and voltage channel along [11-2] direction. The length(L) and width (w) of the current channel are 25 µm and10 µm, respectively. An optical microscope image of theHall bar device is shown in the inset of Fig.2(a). Thisgeometry allows to detect the magnetization state viaanomalous Hall effect (AHE). AHE is a phenomenon,where the electric current through the ferromagnetic ma-terial generates the transverse voltage due to its magne-tization [45, 46]. The anomalous Hall resistance (Rxy)of device as a function of out-of-plane external magneticfield (H//[111] and I//[1-10]) is shown in Fig.2(a). Asquare-shape hysteresis loop as well as sharp transition ofRxy shows the easy-axis along [111] direction. The coer-civity, which is measure of resistance to change the mag-netization state is measured to be 247Oe. Figure 2(b)shows the Rxy as a function of in-plane magnetic field(H and I//[1-10]). The Rxy saturates at 15 kOe suggest-ing the [1-10] direction is hard axis of magnetization.After confirming the PMA in the device, we esti-mated the resistivity of each conducting layer to mea-sure the actual current passing through CrN layer. Forthis, we fabricated a multilayer device with CrN thick-ness varying from 0 to 5 nm i.e. Al2O3/CrN(0-5)/[Co(0.35)/Pt(0.3)]3/MgO(3) and measured the thickness de-pendent longitudinal resistance (Rxx). The Rxx wasmeasured in four-point probe geometry. The inverse ofthe sheet resistance i.e. L/(Rxxw) of the multilayer de-vice as a function of CrN thickness (tCrN ) is shown inFig.2(c). The linear fitting of this data using equation4FIG. 2. (a) Anomalous Hall resistance (Rxy) as a function of out-of-plane magnetic field (H//[111]). Inset shows an opticalmicroscope image of the actual device. (b) Anomalous Hall resistance (Rxy) as a function of in-plane magnetic field (H//[1-10]).(c) The inverse of sheet resistance L/(Rxxw) versus CrN layer thickness tCrN plot (black balls). Red line represents the fitteddata to extract resistivity of each layer. Current-induced magnetization switching (CIMS) curves as function of current densitythrough CrN layer at (d) positive and (e) negative in-plane external magnetic fields. (f) Variation of switching current densityJc for different in-plane magnetic fields values.LRxxw= tCrNρCrN+tCo/PtρCo/Pt(red line) gives ρCrN and ρCo/Ptof 1.09mΩcm and 57 µΩcm, respectively. The valueof the ρCrN is consistent with the reported in literature[34, 35].We employ the CIMS measurement in the presenceof in-plane external magnetic field (H//[1-10]). Fig-ure2(d) shows the current-induced magnetization switch-ing curves as a function of the current-density (J)through CrN layer under different in-plane positive mag-netic fields. At 100Oe of magnetic field, no obviousswitching was observed. Further increasing magneticfield to 200Oe and onward, the magnetization of top fer-romagnetic layer switches at J ∼ 2.6MA/cm2. For neg-ative magnetic fields (Fig.2(e)), a sign reversal of switch-ing curve, indicates the magnetization switching is due tothe SOT. Notably, the measured switching current den-sity in our device is lower or comparable to the severalHM/FM hetero-structure such as Ta/CoFeB/MgO [47],Ta/CoFeB/MgO/Ta [48], Pt/Co/AlOx [49], Pt/Co bi-layer [50], Ta/CoFeB/TaOx [51], and Hf/CoFeB/MgO[52]. Figure 2(f) illustrates the plot of the switchingcurrent density (Jc) at which magnetization switches,against the in-plane magnetic fields. The Jc lowers withincreasing the magnetic field, which is a characteristicsof SOT switching [53, 54]. Since the current channel ofthe device is along [1-10] direction, therefore charge cur-rent flowing in [1-10] direction produces the spin currentflowing in [111] direction with spin-polarization along[11-2] direction. This spin-polarization exert a damping-like field on the magnetization of top ferromagnetic layeralong [1-10] direction. When an external magnetic fieldis applied in [1-10] direction, the deterministic switchingtake place due to interfacial symmetry-breaking. It isimportant to note that our studied device contains Pt,which may facilitate magnetization switching within theferromagnetic layer, a phenomenon known as self-inducedSOT switching. A detailed discussion on self-inducedSOT within the multilayer structure is provided in theAppendix of the manuscript.5FIG. 3. (a) First-harmonic AHE loop (Rxy1ω) for the out-of-plane magnetic field (H z). (b) Dependence of Rxy1ω onthe in-plane angle of magnetic field (ϕ) with respect to thecurrent flow direction. (c) Rxy1ω for the in-plane magneticfield (H x). (d) Second-harmonic AHE loop (Rxy2ω) for theH x. The red curves in Figs.3(b) and 3(d) correspond to thefitting results by Eq.5 and Eq.6, respectively.C. Second harmonic Hall measurementIn order to extract the damping-like SOT field andexperimental SHC, we performed the second-harmonicHall measurement [55], in which we applied AC currentof 2.3 mA (3.3 MA/cm2) to measure the first- (Rxy1ω)and second-harmonic Hall resistances (Rxy2ω) [23]. Fig-ure3(a) shows the Rxy1ω as a function of magnetic fieldin the out-of-plane direction (H z), suggesting the mag-netic easy-axis points in the out-of-plane direction. Theamplitude RAHE was measured to be 10Ω. Figure 3(b)shows the Rxy1ω as a function of in-plane field angles (ϕ)with respect to the AC current direction. The planarHall resistance (Rxy1ω)-ϕ can be expressed as [56, 57]R1ωxy = RPHEsin2ϕ. (5)The RPHE is found 0.55Ω by the fitting with Eq.5 (redcurve in Fig.3(b)), which is 20 times smaller than theRAHE of 10Ω (Fig.3(a)). Figure 3(c) shows the Rxy1ω asa function of in-plane field (H x). TheHeffk was measuredto be 7 kOe, which is consistent with that obtained inFig.1(d). Figure 3(d) shows the Hx-dependent R2ωxy up tofield of 20 kOe. To extract the damping like-torque field,the Rxy2ω data was fitted using equation [58]R2ωxy =RAHE2HDL|Hx| −Hkeff+RPHEHFL+Oe|Hx|+RTH , (6)for the high field (shown in the red curve in Figure 3(d)).RTH and HFL+Oe are the resistance originating from themagneto-thermoelectric effect and the HFL that is con-taminated by Oersted field, respectively. The RTH com-prises of contribution in the Rxy due to ordinary Nernsteffect (ONE), anomalous Nernst effect (ANE) and spinSeebeck effect (SSE). Using RAHE(PHE) ∼ 10Ω (0.55Ω) and Heffk ∼ 7 kOe, we found HDL= 135A/m andHFL+Oe = 5490 A/m, where the latter includes the Oer-sted field as well. Notably, the damping-like torque, givenby m×(m×σ), acts along the spin polarization directionand hence plays a decisive role in driving magnetizationswitching. The RTH corresponds to the offset with re-spect to R2ωxy ∼ 0 at high field (∼2T) [Fig.3(d)] is 5 mΩfrom fitting, suggesting that the magneto-thermoelectriceffect is minor. It is important to note that Eq.6 is ap-plicable for fitting the high-field regime of R2ωxy , specif-ically for field range well above the Heffk , so that themagnetization is fully aligned in the in-plane direction.The Eq.6 is undefined for Hx =Heffk , where R2ωxy divergesand becomes unphysical. The equation is also not valid,when Hx < Heffk , as R2ωxy becomes negative (positive) forpositive (negative) magnetic fields. Since Heffk for thedevice was found to be 7 kOe, we performed the fittingin the field range from 20 kOe down to 10 kOe, which iswell above the Heffk to ensure that the magnetization re-mains fully in-plane. When the field range was extendeddown to 7 kOe or below, Eq. 6 failed to fit the data, asHx ≤ Heffk . Using the obtained HDL from fitting, we cal-culated the effective spin Hall angle (θeffSH ) using equation[23]θeffSH =2eℏµ0MstHDLJCrN, (7)where e, ℏ, Ms, t and J represent the electronic charge,reduced plank constant, saturation magnetization of topferromagnetic layer, and current density through theCrN layer, respectively. From above equation usingHDL = 135A/m, t = 1.95 nm , Ms = 8.9 × 105 A/mand JCrN = 0.5 × 1010 A/m2, we estimated θeffSH to be0.18. The value of θeffSH is used to calculate SHC usingℏ2eθeffSHρ , where ρ is the resistivity of the CrN layer[59].We found SHC (σyzx) to be 83 (ℏe ) S/cm. Here x [1-10],y [11-2] and z [111] represent the direction of charge cur-rent, spin-polarization and spin-current, respectively. Wecalculated the θSH using the formula θSH = eℏσyzxσxx. Us-ing σxx = 917 S/cm from experiment, we calculated θSH∼ 0.09, highlighting efficient charge-to-spin conversion inCrN. We also fabricated a device with the current chan-nel along the [11-2] direction, which is the direction ofbroken mirror symmetry. We found similar magnetiza-tion switching behavior as that with current along [1-10];that is, an in-plane magnetic field was still required, andno signature of unconventional SHE enabling field-freeswitching was observed due to broken mirror symmetry.6FIG. 4. (a) Band structure of CrN in presence of SOC. (b)Berry-curvature distribution along the same high-symmetryk-path. Inset shows a Brillouin zone of FCC lattice.D. First principles calculationSince the spin-current from CrN switches the magne-tization of the top ferromagnetic layer, it is essential andintriguing to investigate the origin of SHE in CrN us-ing first-principles calculations. The first-principles cal-culation was performed keeping z-axis of the CrN unitcell in calculation along [111] direction and hence corre-sponding orthogonal x and y axis along [1-10] and [11-2] directions, respectively, to match with experimentalsituations (as CrN grow in (111) orientation on Al2O3substrate). The Atomsk software was used for rotatingthe unit cell [60]. Figure 4(a) shows the band structureof CrN with SOC along the high-symmetry k-path inthe FCC Brillouin zone. A FCC Brillouin zone is shownin the inset of Fig.4(b). Around the Γ high-symmetryk-point (near the Fermi energy), the bands shows de-generacy commonly refers to band splitting [61] due toSOC. Since the transport properties mainly influence bythe state close the Fermi energy, this band splitting couldgive the spin Berry curvature in the momentum space.It is noteworthy that the spin Berry curvature (non-Abelian Berry curvature), exhibits fundamentally dif-ferent behavior from the conventional Berry curvature(Abelian/charge Berry curvature) [9–11]. In systemswith both TRS and IS, the conventional Berry curvaturevanishes, prohibiting the AHE [46]. This is only true forspinless systems, where band off-diagonal terms of spinmatrix are neglected in wave packet dynamics [9]. How-ever, when spin current operator is explicitly included,the spin Berry curvature remains finite even under TRSand IS [9–11] since in fully relativistic systems, TRS andIS enforce Kramers degeneracy, leading to non-AbelianBerry curvature and finite SHC [12]. For example, Pt[8] and Au [13], though centrosymmetric and nonmag-netic, exhibit significant SHC due to spin Berry curva-ture. Since the SHE is described by a third-rank tensorσkji (i,j and k denote charge current quantity, spin cur-rent, and spin polarization directions, respectively), thecomponent of SHC is strictly follows the constraint im-posed by crystal symmetry. In TRS and IS preservingsystems, spin current and spin polarization are orthogo-nal to each other and SHE is termed as conventional SHE[14, 62]. However, breaking IS, TRS, or certain mirrorsymmetries can allow collinear configurations, where thespin current and spin polarization are in same direction, leading to unconventional SHE [14, 62], which has re-cently gained attention for field free switching [63, 64].We computed k-resolved spin Berry curvature asshown in Fig.4(b) using Eq.1. The Berry-curvature isnegligible along the high symmetry k-path except aroundΓ point, where it shows spike like behavior due to SOC in-duced band splitting. When the SOC-induced gap arisesin the band structure, the denominator of Eq.1 becomessmall, leading to the emergence of spin Berry curvature inthe material, which is inversely proportional to the mag-nitude of the SOC-induced gap. The band gap is minimalto the left of the Γ point (∼ 1.5 meV), resulting in a largespin Berry curvature contribution in that region, whereasthe gap increases toward the right of Γ (about 50meV),leading to a small spin Berry curvature. It is worthwhileto mention here that distribution of spin Berry curvaturedoes not solely depend on location of the minimum en-ergy gap but also the point, where SOC promotes stronginterband hybridization. Since the device has a currentchannel along the mirror symmetry line (i.e., the x[1-10]direction), the charge current in the [1-10] direction gen-erates a spin current flowing through the z[111] direc-tion with spin polarization along the y[11-2] direction.Therefore our interest of calculation is y-component ofSHC (σyzx). Integration of spin Berry curvature in wholeBrillouin zone using Eq.2 gives σyzx ∼ 120 ℏe S/cm atthe Fermi energy. This SHC value is close to the ob-tained from second harmonic Hall measurement, whichis responsible for magnetization switching in the device.IV. DiscussionIn discussion, we focused on N incorporation in Cr toform stoichiometric CrN to investigate SHE and magne-tization switching using experiment and theoretical cal-culations. Since the spin Berry curvature itself is not aphysical observable quantity, a direct comparison of spinBerry curvature between Cr and CrN is not straight-forward. However, its effects can be inferred throughSHE and SOT characterization. We achieved the θeffSHof 0.18 for the CrN-based SOT device, surpassing the7θeffSH of 0.088 reported for the Cr-based SOT device (Cr/-CoFeB/MgO/Cr) [24]. Our findings reveal that the in-crease in θeffSH originates from the intrinsic enhancementof SHE, rather than extrinsic mechanism. The spin-current originating from CrN switches the magnetiza-tion of adjacent ferromagnet at a switching current den-sity of 2.6 MA/cm2, which is comparable to the existingHMs/FM systems. The agreement between experimen-tal and theoretical SHC confirms its intrinsic origin fromspin Berry curvature in CrN and indicates only a mi-nor contribution from extrinsic mechanisms.. In addi-tion to the intrinsic mechanism for the impact from N,some reports suggest the extrinsic contribution. Xu et al.studied the impact of N incorporation in Pt, and foundthe increased θeffSH from 0.12 to 0.16 by the N ratio of8%. Spin-dependent scattering at the interface is consid-ered to be one of the causes, where N incorporation im-proves interfacial spin transparency and reduces effectivemagnetic damping [65]. Shashank et al. suggested thatincreasing dose of N into Pt enhances the damping-likeefficiency due to the extrinsic side jump mechanism [66].As mentioned above, it is revealed that N incorporationinto metals can provide a significant impact on their SHEowing to both intrinsic and extrinsic contributions. Ourresults open an alternative approach to enhance the SHEeven when the value of pristine metals is not sufficient,as in the case of light 3d metals.V. CONCLUSIONWe experimentally demonstrated CIMS in theAl2O3/CrN(5)/[Co(0.35)/Pt(0.3)]3/MgO(3) multilayerdevice at a switching current density ∼ 2.6 MA/cm2, inthe presence of an in-plane external magnetic field. Theo-retical calculations give the SHC (σyzx) ∼ 120 ℏe S/cm dueto spin Berry curvature originating from SOC-inducedband splitting, which is close to the experimental SHC.We found θSH to be 0.09, demonstrating efficient charge-to-spin conversion in CrN. Our work shows that light-element-based systems could be promising for energy-efficient and cost-effective SOT devices, even though theypossess low SOC.ACKNOWLEDGMENTThis work was supported by KAKENHI Grants-in-AidNo. 23K22803 from the Japan Society for the Promotionof Science (JSPS). Part of this work was carried out underthe Cooperative Research Project Program of the RIEC,Tohoku University.These corresponding authors equally contributed tothis work* shukla.gauravkumar@nims.go.jp†isogami.shinji@nims.go.jpAppendixThe SHE arises due to SOC of the material and be-comes more pronounced for HMs such as Pt, Ta, and W.Since top ferromagnetic layer [Co(0.35)/Pt(0.3)]3 of thestudied device consist of Pt, therefore the spin-currentfrom the Pt may induced SOT and facilitates magnetiza-tion switching in the ferromagnetic layer, a phenomenonalternatively called self-induced SOT switching. How-ever, the studied multilayer is vertically symmetric i.e.there is no vertical composition gradient in top ferro-magnetic layer, therefore the torque induced by top Ptlayer on Co will be be canceled out by bottom Pt layer.Thus, the chance of the self-induced SOT is minimal inthe device. Nevertheless, to further confirm whether self-induced SOT is present or not in the device, we syn-thesized [Co(0.35)/Pt(0.3)]6 multilayer on c-plane ori-ented Al2O3 substrate without CrN layer. We fabri-cated Hall bar device and successfully achieved PMAin the device as shown in Rxy versus out-of-plane mag-netic field curve (Fig.A.1(a)). Next we measured theCIMS in the presence of in-plane magnetic field of 100Oe, 500 Oe and 800 Oe. The CIMS curve versus cur-rent density through the ferromagnetic layer is presentedin Fig.A.1(b). From the switching curve we found thatvery small switching happens with in the ferromagneticlayer [Co(0.35)/Pt(0.3)]6. 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