Abstract
Mnbased alloys exhibit unique properties in the spintronics materials possessing perpendicular magnetic anisotropy (PMA) beyond the Fe and Cobased alloys. It is desired to figure out the quantum physics of PMA inherent to Mnbased alloys, which have never been reported. Here, the origin of PMA in ferrimagnetic Mn_{3− δ} Ga ordered alloys is investigated to resolve antiparallelcoupled Mn sites using xray magnetic circular and linear dichroism (XMCD/XMLD) and a firstprinciples calculation. We found that the contribution of orbital magnetic moments in PMA is small from XMCD and that the finite quadrupolelike orbital distortion through spinflipped electron hopping is dominant from XMLD and theoretical calculations. These findings suggest that the spinflipped orbital quadrupole formations originate from the PMA in Mn_{3− δ} Ga and bring the paradigm shift in the researches of PMA materials using xray magnetic spectroscopies.
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Introduction
Perpendicular magnetic anisotropy (PMA) is desired for the development of highdensity magnetic storage technologies. Thermal stability of ultrahigh density magnetic devices is required to overcome the superparamagnetic limit^{1,2,3}. Recently, research interests using PMA films have focused on not only magnetic tunnel junctions^{4,5,6,7} toward the realization of spintransfer switching magnetoresistive randomaccess memories but also antiferromagnetic or ferrimagnetic devices^{8,9}. To design PMA materials, heavymetal elements that possess large spinorbit coupling are often utilized through the interplay between the spins in 3d transitionmetals (TMs) and 4d or 5d TMs. The design of PMA materials without using the heavymetal elements is an important subject in future spintronics researches. Recent progress has focused on the interfacial PMA in CoFeB/MgO^{10} or Fe/MgO^{11,12}. However, a high PMA of over the order of MJ/m^{3} with a large coercive field is needed to maintain the magnetic directions during device operation^{13}. Therefore, the materials using high PMA constants and without using heavymetal atoms are strongly desired.
MnGa binary alloys are a candidate that could overcome these issues. Mn_{3− δ} Ga alloys satisfy the conditions of high spin polarization, low saturation magnetization, and low magnetic damping constants^{14,15,16,17,18}. Tetragonal Mn_{3− δ} Ga alloys are widely recognized as hard magnets, which exhibit high PMA, ferromagnetic, or ferrimagnetic properties depending on the Mn composition^{15}. Two kinds of Mn sites, which couple antiferromagnetically, consist of Mn_{3− δ} Ga with the D0_{22}type ordering. Meanwhile, the L1_{0}type Mn_{1} Ga ordered alloy possesses a single Mn site. These specific crystalline structures provide the elongated caxis direction, which induces the anisotropic chemical bonding, resulting in the anisotropy of electron occupancies in 3d states and charge distribution. There are many reports investigating the electronic and magnetic structures of Mn_{3− δ} Ga alloys to clarify the origin of large PMA and coercive field^{19,20,21}. To investigate the mechanism of PMA and large coercive fields in Mn_{3− δ} Ga, sitespecific magnetic properties must be investigated explicitly.
Xray magnetic circular/ linear dichroism (XMCD/ XMLD) may be a powerful tool to study the orbital magnetic moments and magnetic dipole moments of higher order term of spin magnetic moments^{22,23}. However, the difficulty in the deconvolution of two kinds of Mn sites prevents siteselected detailed investigations. Within the magnetooptical spin sum rule, using the formulation proposed by C.T. Chen et al.^{24}, the orbital magnetic moments are expressed as proportional to r/q, where q and r represent the integral of the xray absorption spectra (XAS) and XMCD spectra, respectively, for both L_{2} and L_{3} edges. In the cases of two existing components, the orbital moments are not obtained from the whole integrals of spectra; by using each component r_{1}, r_{2}, q_{1}, and q_{2}, the value of \(({r}_{1}/{q}_{1})\) + \(({r}_{2}/{q}_{2})\) should be the average value. The value of (\({r}_{1}+{r}_{2}\))/(\({q}_{1}+{q}_{2}\)) does not make sense as an average in the case of corelevel atomic excitation, leading to the wrong value in the XMCD analysis. As a typical example, for the mixed valence compound CoFe_{2}O_{4}, the Fe^{3+} and Fe ^{2+} sites can be deconvoluted by the ligandfield theory approximation^{25}. However, the deconvolution of featureless line shapes in a metallic Mn_{3− δ} Ga case is difficult by comparison with the theoretical calculations. To detect the sitespecific antiparallelcoupled two Mn sites, systematic investigations using Mn_{3− δ} Ga of δ = 0, 1, and 2 provide the information of sitespecific detections. In previous reports, although Rode et al. performed XMCD measurements of Mn_{3} Ga and Mn_{2} Ga^{19}, the comparison of XMCD line shapes with that of the single Mn sites in Mn_{1} Ga is necessary. Recently, the crystal growth techniques of Mn_{3− δ} Ga were developed using CoGa buffer layers to synthesize compositioncontrolled Mn_{3− δ} Ga thin films^{26}, which enables discussion of the electronic structures of Mn_{3− δ} Ga in δ = 0, 1, and 2. We adopted this growth technique and performed XMCD. By contrast, the XMLD in Mn Ledges enables detection of the element of quadrupole tensor Q_{zz} by adopting the XMLD sum rule^{27}. Although many reports of XMLD for inplane magnetic easy axis cases exist, perpendicularly magnetized cases are attempted firstly in Mn_{3− δ} Ga using perpendicular remnant magnetization states.
The firstprinciples calculations based on the density functional theory (DFT) suggest the unique band structures in the Mn sites of mixed spinup and down bands at the Fermi level (E_{F}), which allow the spin transition between up and down spin states, resulting in the stabilization of the PMA^{28,29,30}. Usually, the PMA originates from the anisotropy of orbital magnetic moments in the large exchangesplit cases, such as Fe and Co, using secondorder perturbation for spinorbit interaction^{31,32}. Meanwhile, for Mn compounds, the contribution from orbital moment anisotropy for PMA is smaller than the spinflipped contribution to PMA^{33,34,35}. However, this picture has not been guaranteed completely from an experimental viewpoint until now.
In this study, we performed the deconvolution of each Mn site using the systematic XMCD and XMLD measurements for different Mn contents in Mn_{3− δ} Ga. We discuss the sitespecific spin and orbital magnetic moments with magnetic dipoleterm, which corresponds to electric quadrupoles. These are deduced from the angulardependent XMCD and XMLD and compared with the DFT calculations to understand the PMA microscopically.
Results
Xray magnetic spectroscopies
The Mn Ledge XAS and XMCD for L1_{0}type Mn_{1} Ga with a single Mn site (MnI), and D0_{22}type Mn_{2} Ga and Mn_{3} Ga with two kinds of Mn sites (MnI and MnII) are shown in Fig. 1. The XAS were normalized to be one at the postedges. With increasing Mn concentrations (decreasing δ), the intensities of XAS increased and the difference between μ^{+} and μ^{−} became small, resulting in the suppression of XMCD intensities because of the increase of antiparallel components. In the case of Mn_{2} Ga and Mn_{3} Ga, the XMCD line shapes in the L_{3} and L_{2} edges, of slightly split and doublet structures, became clear because of the increase of another MnII component with opposite sign. Furthermore, the elementspecific hysteresis curves in XMCD at a fixed photon energy of Mn L_{3}edge exhibit similar features with the results of the magnetooptical Kerr effects. Coercive fields (H_{c}) of 0.5 T were obtained for the Mn_{2} Ga and Mn_{3} Ga cases because the two kinds of Mn sites enhance the antiparallel coupling.
To deconvolute the MnI and MnII sites in the XMCD spectra, we performed the subtraction of XMCD between Mn_{1} Ga and Mn_{3} Ga. Figure 2 displays the XMCD of Mn_{1} Ga and Mn_{3} Ga, and their differences after the normalization considering the Mn compositions. The XMCD signal with opposite sign was clearly detected for MnI and MnII components. As the lattice volume of Mn_{3− δ} Ga on the CoGa buffer layer remained almost unchanged with different δ^{26}, the validity of the subtraction of XMCD is warranted because the density of states (DOS) for MnI is similar in all δ regions as shown in latter (Fig. 4). To apply the magnetooptical sum rule for effective spin magnetic moments (\({m}_{s}^{{\rm{eff}}}\)) including magnetic dipole term (m_{T}) and orbital magnetic moments (m_{orb}), the integrals of the XMCD line shapes are needed^{24}. Further, the integrals of XAS were also estimated for MnI and MnII, divided by the composition ratios. The electron numbers for 3d states of MnI and MnII were estimated from the bandstructure calculations to be 5.795 and 5.833, respectively. Thus, \({m}_{s}^{{\rm{eff}}}\) and m_{orb} for MnI were estimated to be 2.30 and 0.163 μ_{B}, respectively. For MnII, 2.94 μ_{B} (\({m}_{s}^{{\rm{eff}}}\)) and 0.093 μ_{B} (\({m}_{{\rm{orb}}}^{\perp }\)) were obtained for perpendicular components with the error bars of 20% because of the ambiguities estimating spectral background.
Here, we claim the validity of \({m}_{s}^{{\rm{eff}}}\) and m_{orb} in Mn_{3− δ} Ga deduced from XMCD. First, these m_{orb} values are too small to explain stabilizing the PMA because the magnetic crystalline energy \({E}_{{\rm{MCA}}}\propto \frac{1}{4}\alpha {\xi }_{{\rm{Mn}}}\) \(({m}_{{\rm{orb}}}^{\perp }{m}_{{\rm{orb}}}^{})\) within the scheme of the Bruno relation^{32}, assuming the spinorbit coupling constant \({\xi }_{{\rm{Mn}}}\) of 41 meV and the bandstate parameter α = 0.2 for Mn compounds, which is estimated from the DFT calculation. For Mn_{1} Ga, as the saturation magnetic field along hard axis direction was less than 1 T, the projected component \({m}_{{\rm{orb}}}^{}\) could be deduced as \(\Delta {m}_{{\rm{orb}}}(={m}_{{\rm{orb}}}^{\perp }{m}_{{\rm{orb}}}^{})\) of less than 0.01 μ_{B}, resulting in \({E}_{{\rm{MCA}}}\,\mathrm{=\; 1}\times {10}^{5}\) eV/atom, that is, 5.7 × 10^{4} J/m^{3} using the unit cell of MnGa. Therefore, orbital moment anisotropy cannot explain the PMA of the order of 10^{6} J/m^{3} in Mn_{3− δ} Ga^{26}. As the electron configuration is close to the halffilled 3d^{5} case, the quenching of the orbital angular momentum occurs in principle. In Mn_{3− δ} Ga, since the electron filling is not complete halffilled cases, small orbital angular momentum appears. Second, another origin for the large PMA is considered as the spinflipped contribution between the spinup and down states in the vicinity of the E_{F}. The magnetic dipole term (m_{T}) also stabilizes the magnetocrystalline anisotropy energy (E_{MCA}) by the following equation^{33,34}:
where \(\Delta {E}_{{\rm{ex}}}\) denotes the exchange splitting of 3d bands. Positive values of E_{MCA} stabilize the PMA. The second term becomes dominant when proximitydriven exchange split cases, such as the 4d and 5d states, are dominant^{36,37}. In the case of Mn_{3− δ} Ga, the Mn 3d states were delicate regarding the mixing of the spinup and down states at the E_{F}, which corresponds to the quadrupole formation and the band structure α values. The second term is expressed by m_{T} in the XMCD spin sum rule of \({m}_{s}+7{m}_{{{\rm{T}}}_{{\rm{z}}}}\) along the outofplane z direction^{38}. For Mn_{1} Ga, if \({m}_{{T}_{z}}\) is negative, resulting in \({Q}_{zz} > \) 0 in the notation of \({m}_{{\rm{T}}{\rm{z}}}={Q}_{zz}\langle S\rangle \) using expectation value of spin angular momentum, which exhibits the prolate shape of the spin density distribution; the second term favors PMA because of the different sign for the contribution of orbital moment anisotropy in the first term. Since 7 m_{Tz} is estimated to be in the order of 0.1 μ_{B} from angulardependent XMCD between surface normal and magic angle cases, Q_{zz} is less than 0.01, resulting that the orbital polarization of less than 1% contributes to stabilize PMA. In this case, the contribution of the second term in Eq.(1) is one order larger than the orbital term, which is essential for explaining the PMA of Mn_{3− δ} Ga. Third, in a previous study^{19}, quite small \(\Delta {m}_{{\rm{orb}}}\) and negligible \({m}_{{{\rm{T}}}_{{\rm{z}}}}\) were reported for Mn_{2} Ga and Mn_{3} Ga. Their detailed investigation claims that \(\Delta {m}_{{\rm{orb}}}\) of 0.02 μ_{B} in MnI site contributes to PMA and MnII site has the opposite sign. These are qualitatively consistent with our results. The difference might be derived from the sample growth conditions and experimental setup. Fourth, the reason why H_{c} in Mn_{1} Ga is small can be explained by the L1_{0}type structure, due to the stacking of the Mn and Ga layers alternately, which weakened the exchange coupling between the Mn layers. Finally, we comment on the XMCD of the Ga Ledges. This also exhibits the same sign as the MnI component, suggesting that the induced moments in the Ga sites were derived from the MnI component (Fig. S1), which was substituted by the MnII for Mn_{2} Ga and Mn_{3} Ga.
To determine the effect of \({m}_{{{\rm{T}}}_{{\rm{z}}}}\), we performed XMLD measurements. Figure 3 shows the E vector polarization dependent XAS, where the electric field E is perpendicular and horizontal to the magnetization direction. After magnetizing perpendicular to easyaxis direction by the pulse of 1 T, the XMLD was measured at the remnant states. The XMLD between the vertical and horizontal polarized excitations were detected in grazing incident beams, where the sample surface normal is tilted 60° from the incident beam. The differential line shapes were similar to those of other Mn compounds^{39,40}. We estimate that the xray linear dichroism (XLD) components are less than 20% by the measurements at the same geometry without magnetizing. With increasing Mn composition, the XMLD signal intensities were enhanced because XMLD detects the square of magnetization \(\langle {M}^{2}\rangle \) contribution. In Mn_{3} Ga, XMLD includes the summation of both \(\langle {M}_{{\rm{MnI}}}^{2}\rangle +\langle {M}_{{\rm{MnII}}}^{2}\rangle \) contributions. Therefore, the contributions from XLD are not dominant factor in spectral analyses. We note that the integrals of the XMLD line shapes are proportional to Q_{zz} along the sample surface normal direction. We confirmed that the integral converges to a positive value, deducing that the sign of Q_{zz} is positive with the order of 0.01 for both MnI and MnII components by applying the XMLD sum rule in the notation of \({m}_{{\rm{Tz}}}={Q}_{zz}\langle S\rangle \); that is, 3 z^{2}−r^{2} orbitals are strongly coupled with E and are elongated to an easyaxis direction after subtracting the XLD contribution. The detail of estimation of Q_{zz} is explained in the Supplemental Note and ref.^{41}. This value is consistent with that estimated from XMCD spin sum rule. These suggest the orbital polarization of Mn 3d states along zaxis direction forming the cigartype prolate unoccupied orbital orientation. Therefore, combining both XMCD and XMLD, the order of m_{Tz} can be estimated as two order smaller than the spin moments.
DFT calculation
Figure 4 shows the DOS of Mn_{1} Ga and Mn_{3} Ga with site and orbitalresolved contributions by the DFT calculation. The contributions for the E_{MCA} of each atom and spin transition processes through the secondorder perturbation of the spinorbit interaction are also shown for the MnI and MnII sites using a tetragonal unit cell. In the DOS of the MnI and MnII sites, all orbital states were split through exchange interaction. However, exchange splitting was incomplete where complete spin splitting was required, in the Bruno formula^{32}, which enabled the transitions by spin mixing between occupied spinup and unoccupied spindown states. Four types of spin transition processes occurred between the occupied and unoccupied states, as shown in the bottom panel of Fig. 4. The positive values in the presented bar graphs stabilize the PMA. The’updown’ process implies a virtual excitation from an occupied upspin state to an unoccupied downspin state in the secondorder perturbation, which forms the magnetic dipoles. While spin conserved transition terms are slightly positive, spinflipped transition terms show dominant contribution to PMA. The further orbitalresolved anatomy of the spinflipped transition revealed the transition between the yz and 3z^{2} states, which induces the prolatetype spin distribution. The matrix elements of L_{x} between \(m=\pm 1\) and 0 through the transitions of different magnetic quantum numbers m were predominant for the MnI site in Mn_{1} Ga (see Supplemental Materials). As shown in Fig. S2, the matrix elements of L_{x} between yz and 3z^{2} in spinflipped transition (blue bar graph) have large positive values, indicating contribution to the PMA. Meanwhile, for D0_{22}type Mn_{3} Ga, the contributions to MCA energy were different. Although the spinconserved transition terms are enhanced as compared with Mn_{1} Ga, the spinflipped contributions were still dominant, which explains the suppression of the orbital moment anisotropy in Mn_{1} Ga. The MnI 3z^{2} orbitals were located near the E_{F} in Mn_{3} Ga in the spindown states, strongly affecting the appearance of the finite matrix elements. Figure S3 shows the large matrix elements of L_{x} between yz and 3z^{2} in the spinflipped transition of Mn I, which are similar to those of Mn_{1} Ga. The difference in the MnII sites between Mn_{1} Ga and Mn_{3} Ga can be derived from the location of neighboring Mn atoms, which promotes exchange interaction between the MnI and MnII sites.
For Mn_{1} Ga, the orbital moments along the c and aaxis, \({m}_{{\rm{o}}{\rm{r}}{\rm{b}}}^{\perp }\) and \({m}_{{\rm{o}}{\rm{r}}{\rm{b}}}^{}\), were estimated to be 0.022 and 0.0207 \({\mu }_{{\rm{B}}}\), respectively, by the DFT calculation. Using Eq. (1), \(\Delta {m}_{{\rm{orb}}}\) and \({m}_{{{\rm{T}}}_{{\rm{z}}}}\) were estimated to be \(0.0014\) \({\mu }_{{\rm{B}}}\) and \(0.0493\) \({\mu }_{{\rm{B}}}\), respectively. We note that \({Q}_{zz}\) was estimated to be 0.0986 from the DFT calculation, which is similar to the results of the XMLD through the relation of \({m}_{{\rm{T}}{\rm{z}}}={Q}_{zz}\langle S\rangle \). These values provide the anisotropic energies of the first and second terms in Eq. (1) as \(0.014\) meV and 0.37 meV, respectively, by using \(\varDelta {E}_{{\rm{ex}}}\) of 2.3 eV and \({\xi }_{{\rm{Mn}}}\) of 41 meV for Mn atoms. The amplitude of the spinflipped term is larger than the orbital moment anisotropy to stabilize the PMA energetically. These estimations are consistent with the values deduced from the XMCD and XMLD analyses. Equation (1) was modified using the energy difference of each component \(i\): \(\Delta {E}_{i}={{E}_{i}}^{}{{E}_{i}}^{\perp }\) and the relation of: \({E}_{{\rm{MCA}}}=\Delta {E}_{L\uparrow }+\Delta {E}_{L\downarrow }+\Delta {E}_{{\rm{T}}}+\Delta {E}_{{\rm{LS}}}\), where \({E}_{{\rm{MCA}}}\) is expressed by the summation of the orbital parts of spin up and down states (\(\Delta {E}_{L\uparrow }+\Delta {E}_{L\downarrow }\)), the \({m}_{{\rm{T}}}\) term, and the residual of \(\Delta {E}_{{\rm{LS}}}\)^{33}. We confirmed that electron number dependence mainly obeys the \(\Delta {E}_{{\rm{T}}}\) term (Fig. S4). Therefore, the finite value of \({T}_{z}\), which contributes to the second term in Eq. (1), is indispensable for the PMA in MnGa.
Discussion
Considering the results of the XMCD, XMLD, and DFT calculation, we discuss the origin of PMA in Mn_{3− δ} Ga. As the orbital magnetic moments and their anisotropies are small, the contribution of the first term in Eq. (1) is also small, which is a unique property of Mn alloy compounds and contradicts the cases of Fe and Co compounds exhibiting PMA. Beyond Bruno’s formula^{31}, the mixing of majority and minority bands in Mn 3d states enables the spinflipped transition and \({Q}_{zz}\). However, comparing with the CoPd or FePt cases, where the exchange splitting was induced in the 4d or 5d states, a small \({\xi }_{{\rm{Mn}}}\) and large \(\Delta {E}_{{\rm{ex}}}\) in the Mn 3d states suppress the contribution of the second term. Large \({Q}_{zz}\) values were brought by the crystalline distortion accompanied by the anisotropic spin distribution, resulting in the PMA energy of Mn_{3− δ} Ga exhibiting a similar order with those in heavymetal induced magnetic materials. Therefore, the large PMA in Mn_{3− δ} Ga originates from the specific band structure of the Mn 3d states, where the orbital selection rule for the electron hopping through spinflipped \(\langle yz\uparrow {L}_{x}{z}^{2}\downarrow \rangle \) provides the cigartype spin distribution^{28}. As the spinflipped term of \(\Delta {E}_{{\rm{T}}}+\Delta {E}_{{\rm{LS}}}(=\Delta {E}_{{\rm{sf}}})\) for PMA energy, except the orbital contributions, can be written as:
the difference between the \({L}_{x}^{2}\) and \({L}_{z}^{2}\) terms through the spinflipped transitions between the occupied (\(o\)) to unoccupied (\(u\)) states is significant for the gain of the PMA energy. The matrix elements of \(\langle u\uparrow {{L}_{x}}^{2}o\downarrow \rangle \) were enhanced in the spinflipped transition between \(yz\) and \({z}^{2}\), and those of \(\langle u{{L}_{z}}^{2}o\rangle \) were enhanced in the spinconserved case between \(xy\) and \({x}^{2}{y}^{2}\)^{28}. These transitions favor the magnetic dipole moments of prolate shapes for unoccupied states (\(\langle {Q}_{zz}\rangle =\langle 3{L}_{z}^{2}{L}^{2}\rangle > 0\)) described by the Mn 3d each orbital angular momenta and detected by XMLD. We emphasize that the signs of \(\Delta {m}_{{\rm{orb}}}\) and \({Q}_{zz}\) for occupied states are opposite, which is essential to stabilize the PMA by the contribution of the second term in Eq. (1). The PMA energy of FePt exhibits around MJ/m^{3} and the contribution of the second term in Pt is four times larger than the Fe orbital anisotropy energy^{28}. Therefore, MnGa has a specific band structure by crystalline anisotropy elongated to the caxis and intraCoulomb interaction in Mn sites to enhance the PMA without using heavymetal atoms.
In conclusion, we investigated the origin of PMA in Mn_{3− δ} Ga by decomposing into two kinds of Mn sites for XMCD, XMLD, and the DFT calculation. The contribution of the orbital moment anisotropy in Mn_{3} Ga is small and that of the mixing between the Mn 3d up and down states is significant for PMA, resulting in the spinflipped process through the electron hopping between finite unforbidden orbital symmetries in the 3d states through the quadratic contribution. Composition dependence reveals that the orbital magnetic moments of the two antiparallelcoupled components in Mn sites were too small to explain the PMA. These results suggest that the quadrupolelike spinflipped states through the anisotropic \(L{1}_{0}\) and \(D{0}_{22}\) crystalline symmetries are originated to the PMA in Mn_{3− δ} Ga. The present study provides a promising strategy to investigate quadrupoles in antiferro or ferrimagnetic materials with PMA.
Materials and Methods
Sample growth and characterization
The samples were prepared by magnetron sputtering. The 40nmthick Cr buffer layers were deposited on singlecrystal MgO (001) substrates at room temperature (RT), and in situ annealing at 700 °C was performed. Subsequently, a 30nmthick Co_{55} Ga_{45} buffer layer was grown at RT with insitu annealing at 500 °C, then 3nmthick Mn_{3− δ} Ga layers were grown at RT. Here, the composition of Mn_{3− δ} Ga films were controlled by Ar gas pressure during deposition and cosputtering technique with MnGa and Mn target. Finally, a 2nmthick MgO capping layer was deposited. Using the CoGa buffer layer, ultrathin Mn_{3− δ} Ga layer deposition was achieved^{26}. Curie temperatures of samples are higher than RT. Magnetic anisotropy energy of Mn_{1} Ga and Mn_{2} Ga was estimated to be approximately 0.13 and 0.9 MJ/m^{3}, respectively, at RT, by using vibrational sample magnetometer and tunnel magnetoresistance curves shown in ref.^{26}.
XMCD and XMLD measurements
The XMCD and XMLD were performed at BL7A and 16 A in the Photon Factory at the HighEnergy Accelerator Research Organization (KEK). For the XMCD measurements, the photon helicity was fixed, and a magnetic field of ± 1.2 T was applied parallel to the incident polarized soft Xray beam, defined as μ^{+} and μ^{−} spectra. The total electron yield mode was adopted, and all measurements were performed at room temperature. The XAS and XMCD measurement geometries were set to normal incidence, so that both the photon helicity and the magnetic field were parallel and normal to the surface, enabling measurement of the absorption processes involving the normal components of the spin and orbital angular momenta^{36}. In the XMLD measurements, the remnant states magnetized to PMA were adopted. For grazing incident measurements in XMLD and XLD, the angle between incident beam and sample surface normal was kept at 60° tilting as shown in the inset of Fig. 3. The direction of the electric field of the incident synchrotron beam E was tuned horizontally and vertically with respect to the magnetization M. We define the sign of XMLD by the subtraction of the (\(ME\))–(\(M\perp E\)) spectra^{35}.
Firstprinciples calculation
The firstprinciples calculations of MCA energies for Mn_{1} Ga and Mn_{3} Ga were performed using the Vienna ab initio simulation package (VASP). We calculated the secondorder perturbation of the spinorbit interaction to MCA energies for each atomic site using wave functions in the VASP calculations. Details of the perturbation calculation are described in^{42}. In this paper, we estimated the spinorbit coupling constant of Mn and Ga atom as 41 and 35 meV, respectively, by the calculation.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
Wolf, S. A. et al. Spintronics: A SpinBased Electronics Vision for the Future. Science 294, 1488 (2001).
Dieny, B. & Chshiev, M. Perpendicular magnetic anisotropy at transition metal/oxide interfaces and applications. Rev. Mod. Phys. 89, 025008 (2017).
Mangin, S. et al. Currentinduced magnetization reversal in nanopillars with perpendicular anisotropy. Nat. Mater 5, 210 (2006).
Locatelli, N., Cros, V. & Grollier, J. Spintorque building blocks. Nat. Mater. 13, 11 (2014).
Kwak, W.Y., Kwon, J.H., Grünberg, P., Han, S. H. & Cho, B. K. Currentinduced magnetic switching with spinorbit torque in an interlayercoupled junction with a Ta spacer layer. Sci. Rep. 8, 3826 (2018).
Worledge, D. C. et al. Spin torque switching of perpendicular Ta/CoFeB/MgO based magnetic tunnel junctions. Appl. Phys. Lett. 98, 022501 (2011).
Kurebayashi, H. et al. An antidamping spinorbit torque originating from the Berry curvature. Nature Nanotech 9, 211 (2014).
Fukami, S. et al. Magnetization switching by spinorbit torque in an antiferromagnetferromagnet bilayer system. Nat. Mater. 15, 535 (2016).
Marti, X. et al. Roomtemperature antiferromagnetic memory resistor. Nat. mater. 13, 367 (2014).
Ikeda, S. et al. A perpendicularanisotropy CoFeBMgO magnetic tunnel junction. Nat, Mater. 9, 721 (2010).
Koo, J. W. et al. Large perpendicular magnetic anisotropy at Fe/MgO interface. Appl. Phys. Lett. 103, 192401 (2013).
Okabayashi, J. et al. Perpendicular magnetic anisotropy at the interface between ultrathin Fe film and MgO studied by angulardependent xray magnetic circular dichroism. Appl. Phys. Lett. 105, 122408 (2014).
Mizukami, S., Sakuma, A., Sugihara, A., Suzuki, K. Z. & Ranjbar, R. Mnbased hard magnets with small saturation magnetization and low spin relaxation for spintronics. Scripta Materia 118, 70 (2016).
Mizukami, S. et al. LongLived Ultrafast Spin Precession in Manganese Alloys Films with a Large Perpendicular Magnetic Anisotropy. Phys, Rev. Lett. 106, 117201 (2011).
Mizukami, S. et al. Composition dependence of magnetic properties in perpendicularly magnetized epitaxial thin films of MnGa alloys. Phys. Rev. B 85, 014416 (2012).
Wu, F. et al. Epitaxial thin films with giant perpendicular magnetic anisotropy for spintronic devices. Appl. Phys. Lett. 94, 122503 (2009).
Zhu, L. et al. Multifunctional L1_{0}Mn_{1.5} Ga Films with Ultrahigh Coercivity, Giant Perpendicular Magnetocrystalline Anisotropy and Large Magnetic Energy Product. Adv. Mater. 24, 4547 (2012).
Kurt, H., Rode, K., Venkatesan, M., Stamenov, P. & Coey, J. M. D. Mn_{3−x} Ga (0 ≤ x ≤ 1): Multifunctional thin film materials for spintronics and magnetic recording, Phys. Status Solidi B 248, 2338 (2011).
Rode, K. et al. Sitespecific order and magnetism in tetragonal Mn_{3} Ga thin films. Phys. Rev. B 87, 184429 (2013).
Glas, M. et al. Xray absorption spectroscopy and magnetic circular dichroism studies of L1_{0}MnGa thin films. J. Appl. Phys. 114, 183910 (2013).
Oshima, D. et al. Ion IrradiationInduced Magnetic Transition of MnGa Alloy Films Studied by XRay Magnetic Circular Dichroism and LowTemperature Hysteresis Loops. IEEE Trans. Magn. 52, 1 (2016).
Thole, B. T., Carra, P., Sette, F. & van der Laan, G. Xray circular dichroism as a probe of orbital magnetization. Phys. Rev. Lett. 68, 1943 (1992).
Carra, P., Thole, B. T., Altarelli, M. & Wang, X. XRay Circular Dichroism and Local Magnetic Fields. Phys. Rev. Lett. 370, 694 (1993).
Chen, C. T. et al. Experimental confirmation of the Xray magnetic circular dichroism sum rules for iron and cobalt. Phys. Rev. Lett. 75, 152 (1995).
Moyer, J. A. et al. Magnetic structure of Fedoped CoFe_{2}O_{4} probed by xray magnetic spectroscopies. Phys. Rev. B 84, 054447 (2011).
Suzuki, K. Z. et al. Perpendicular magnetic tunnel junction with a strained Mnbased nanolayer. Sci. Rep. 6, 30249 (2016).
Carra, P., König, H., Thole, B. T. & Altarelli, M. Magnetic Xray dichroism General features of dipolar and quadrupolar spectra. Physica B 192, 182 (1993).
Kota, Y. & Sakuma, A. Mechanism of Uniaxial Magnetocrystalline Anisotropy in Transition Metal Alloys. J. Phys. Soc. Jpn. 83, 034715 (2014).
Kim, D., Hong, J. & Vitos, L. Epitaxial strain and compositiondependent magnetic properties of Mn_{x} Ga_{1−x} alloys. Phys. Rev. B 90, 144413 (2014).
Yun, W. S., Cha, G. B., Kim, I. G., Rhim, S. H. & Hong, S. C. Strong perpendicular magnetocrystalline anisotropy of bulk and the (001) surface of D0_{22} Mn_{3} Ga: a density functional study. J. Phys. Condens. Matter. 24, 416003 (2012).
Yoshida, K., Okiji, A. & Chikazumi, S. Magnetic Anisotropy of Localized State in Metals, Prog. Theoretical Phys 33, 559 (1965).
Bruno, P. Tightbinding approach to the orbital magnetic moment and magnetocrystalline anisotropy of transitionmetal monolayers. Phys. Rev. B 39, 865(R) (1989).
van der Laan, G. Microscopic origin of magnetocrystalline anisotropy in transition metal thin films. J. Phys. Condens. Matter. 10, 3239 (1998).
Wang, D. S., Wu, R. & Freeman, A. J. Firstprinciples theory of surface magnetocrystalline anisotropy and the diatomicpair model. Phys. Rev. B 47(14), 932 (1993).
Stöhr, J. & Siegmann, H.C. Springer series in solid state sciences 152, SpringerVerlag Berlin Heidelberg, Magnetism, From Fundamentals to Nanoscale Dynamics (2006).
Ikeda, K. et al. Magnetic anisotropy of L1_{0}ordered FePt thin films studied by Fe and Pt L2,3edges xray magnetic circular dichroism. Appl. Phys. Lett. 111, 142402 (2017).
Okabayashi, J., Miura, Y. & Munekata, H. Anatomy of interfacial spinorbit coupling in Co/Pd multilayers using Xray magnetic circular dichroism and firstprinciples calculations. Sci. Rep. 8, 8303 (2018).
Stöhr, J. & Konig, H. Determination of Spin and OrbitalMoment Anisotropies in Transition Metals by AngleDependent XRay Magnetic Circular Dichroism. Phys. Rev. Lett. 75, 3748 (1995).
Huang, D. J. et al. Orbital Ordering in La_{0.5} Sr_{1.5} MnO_{4} Studied by Soft XRay Linear Dichroism. Phys. Rev. Lett. 92, 087202 (2004).
Aruta, C. et al. Strain induced xray absorption linear dichroism in La_{0.7} Sr_{0.3} MnO_{3} thin films. Phys. Rev. B 73, 235121 (2006).
Okabayashi, J., Iida, Y., Xiang, Q., Sukegawa, H. & Mitani, S. Perpendicular orbital and quadrupole anisotropies at Fe/MgO interfaces detected by xray magnetic circular and linear dichroisms. Appl. Phys. Lett. 115, 252402 (2019).
Miura, Y. et al. The origin of perpendicular magnetocrystalline anisotropy in L1_{0}FeNi under tetragonal distortion. J. Phys. Condens. Matter. 25, 106005 (2013).
Acknowledgements
This work was partially supported by JSPS KAKENHI (Grant No. 16H06332), and Spintronics Research Network of Japan. Part of research was performed under the support from Toyota Physical and Chemical Research Institute. Parts of the synchrotron radiation experiments were performed under the approval of the Photon Factory Program Advisory Committee, KEK (Nos. 2017G060 and 2019G028).
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J.O. and S.M. planned the study. K.Z.S. prepared the samples and characterized the properties. J.O. set up the XMCD and XMLD measurement apparatus at Photon Factory and collected and analyzed the data. Y.M. performed the firstprinciples calculation. Y.K. and A.S. also performed the densityfunctionaltheory calculation. J.O. and Y.M. constructed the scenario of quadrupole physics. All authors discussed the results and wrote the manuscript.
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Okabayashi, J., Miura, Y., Kota, Y. et al. Detecting quadrupole: a hidden source of magnetic anisotropy for Manganese alloys. Sci Rep 10, 9744 (2020). https://doi.org/10.1038/s41598020664329
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DOI: https://doi.org/10.1038/s41598020664329
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