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thanks: Corresponding author: zhdchi93@gmail.com; Present affiliation: Mitsubishi Electric Corporation.thanks: Present address: Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

On the relationship between orbital moment anisotropy, magnetocrystalline anisotropy, and Dzyaloshinskii-Moriya interaction in W/Co/Pt trilayers

Zhendong Chi Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan    Yong-Chang Lau Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan    Vanessa Li Zhang School of Physics and Technology, Wuhan University, Wuhan 430072, China    Goro Shibata Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan Materials Sciences Research Center, Japan Atomic Energy Agency, Sayo, Hyogo 679-5148, Japan    Shoya Sakamoto Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan    Yosuke Nonaka Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan    Keisuke Ikeda Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan    Yuxuan Wan Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan    Masahiro Suzuki Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan    Masashi Kawaguchi Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan    Masako Suzuki-Sakamaki Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan Graduate School of Science and Technology, Gunma University, Kiryu, Gunma 376-8515, Japan    Kenta Amemiya Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan    Naomi Kawamura Japan Synchrotron Radiation Research Institute (JASRI), Sayo 679-5198, Japan    Masaichiro Mizumaki Japan Synchrotron Radiation Research Institute (JASRI), Sayo 679-5198, Japan    Motohiro Suzuki Japan Synchrotron Radiation Research Institute (JASRI), Sayo 679-5198, Japan    Hyunsoo Yang Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Singapore    Masamitsu Hayashi Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan    Atsushi Fujimori Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan Department of Physics and Center for Quantum Science and Technology, National Tsing Hua University, Hsinchu 30013, Taiwan
Abstract

We have studied the Co layer thickness dependences of magnetocrystalline anisotropy (MCA), Dzyaloshinskii-Moriya interaction (DMI), and orbital moment anisotropy (OMA) in W/Co/Pt trilayers, in order to clarify their correlations with each other. We find that the MCA favors magnetization along the film normal and monotonically increases with decreasing effective magnetic layer thickness (tefft_{\mathrm{eff}}). The magnitude of the Dzyaloshinskii-Moriya exchange constant (|D||D|) increases with decreasing tefft_{\mathrm{eff}} until tefft_{\mathrm{eff}}\sim1 nm, below which |D||D| decreases. The MCA and |D||D| scale with 1/teff1/t_{\mathrm{eff}} for tefft_{\mathrm{eff}} larger than \sim1 nm, indicating an interfacial origin. The increase of MCA with decreasing tefft_{\mathrm{eff}} continues below tefft_{\mathrm{eff}} \sim 1 nm, but with a slower rate. To clarify the cause of the tefft_{\mathrm{eff}} dependences of MCA and DMI, the OMA of Co in W/Co/Pt trilayers is studied using x-ray magnetic circular dichroism (XMCD). We find non-zero OMA when tefft_{\mathrm{eff}} is smaller than \sim0.8 nm. The OMA increases with decreasing tefft_{\mathrm{eff}} more rapidly than what is expected from the MCA, indicating that factors other than OMA contribute to the MCA at small tefft_{\mathrm{eff}}. The tefft_{\mathrm{eff}} dependence of the OMA also suggests that |D||D| at tefft_{\mathrm{eff}} smaller than \sim1 nm is not related to the OMA at the interface. We propose that the growth of Co on W results in a strain and/or texture that reduces the interfacial DMI, and, to some extent, MCA at small tefft_{\mathrm{eff}}.

I Introduction

Ultrathin film heterostructures that consist of ferromagnetic metal (FM) layers and non-magnetic heavy metal (HM) layers are attracting great interest as various novel phenomena that originate from the strong spin-orbit coupling in bulk and at interfaces have been discovered. For example, efficient current-induced magnetization reversal Miron et al. (2011a) and fast motion of magnetic domain walls Miron et al. (2011b) have been demonstrated in heterostructures with perpendicular magnetic anisotropy (PMA), which are essential in ultra-high-density magnetic memories. These phenomena are attributed to spin-orbit coupling-induced effects such as spin Hall effect Dyakonov and Perel (1971); Hirsch (1999); Sinova et al. (2015); Liu et al. (2011), Rashba-Edelstein effect Bychkov and Rashba (1984); Edelstein (1990), and Dzyaloshinskii-Moriya interaction (DMI) Dzyaloshinskii (1957); Moriya (1960). Among these effects, strong DMI is especially necessary for racetrack memories because it stabilizes chiral Ne´\rm{\acute{e}}el domain walls and skyrmions Bode et al. (2007); Parkin et al. (2008); Hayashi et al. (2008); Heide et al. (2008); S. Mu¨\rm{\ddot{u}}hlbauer et al. (2009); Yu et al. (2010); Thiaville et al. (2012); Emori et al. (2013); Fert et al. (2013); Tacchi et al. (2017); Ma et al. (2017). Therefore, solid understanding of these interfacial phenomena is essential to develop spintronic devices with significant PMA and DMI.

Recently, the microscopic origins of PMA and interfacial DMI have been discussed in relation to the orbital moment anisotropy (OMA) Bruno (1989); Yamamoto et al. (2017) and the magnetic dipole moment in the FM layer van der Lann (1998); Kim et al. (2018). As OMA should exist both in the FM and HM elements Solovyev et al. (1995), it is of high importance to identify what role the OMA (of FM and HM elements) plays in PMA and DMI in FM/HM heterostructures.

Here, we study correlation between the magnetocrystalline anisotropy (MCA), DMI and OMA in W/Co/Pt trilayers. The Co layer thickness dependences of MCA and DMI in W/Co/Pt trilayers are studied using vibrating sample magnetometer (VSM) and Brillouin light scattering spectroscopy (BLS), respectively. As for the OMA, we study the Co layer thickness dependences of the spin and orbital magnetic moments of Co in W/Co/Pt trilayers, where W works as a seed layer, and the proximity-induced magnetization in W and Pt in W/Co and Pt/Co bilayers using x-ray magnetic circular dichroism (XMCD). We find that the MCA, DMI, and OMA of Co show different Co layer thickness dependences in the W/Co/Pt trilayers. The origin of these observations will be discussed.

II Experiment

Co thin films sandwiched by W and Pt, i.e. Sub./3 W/tCot_{\mathrm{Co}} Co/1 Pt/1 Ru (the numbers denote the nominal thicknesses in nm) were grown on 10×\times10 mm2 thermally oxidized Si substrates by magnetron sputtering at room temperature in a base pressure better than 5×\times10-7 Pa. The top Ru layer is used to protect the trilayers from oxidation. The Ar pressure and RF power were kept constant (0.5 Pa and 50 W) for the sputtering of all the metallic materials. The Co layer thickness (tCot_{\mathrm{Co}}) was varied from 0.6 to 1.7 nm (0.6, 0.7, 0.8, 1.0, 1.1, 1.2, 1.3, 1.4, and 1.7 nm) in different samples. The thicknesses were determined by a constant deposition rate, which has been calibrated by x-ray reflectivity and tunneling electron microscopy Liu et al. (2015). The magnetic hysteresis loops (in-plane and out-of-plane) of the samples were measured using a VSM at room temperature. The magnetic field was applied up to 1.6 T during the measurement.

The magnitude of DM exchange constant (|D||D|) was investigated by BLS, with the same measurement setup in our previous studies Zhang et al. (2015); Di et al. (2015). The BLS measurements were carried out in the 180 back-scattering geometry, using the 514.5 nm radiation of an argon-ion laser and a six-pass tandem Fabry-Perot interferometer. An in-plane saturation magnetic field H0H_{0} was applied perpendicular to the incident plane of light, corresponding to the Damon-Eschbach geometry, to obtain the spin-wave dispersion relation. The schematic of the measurement geometry is shown in Fig. 4(a). The angle between the incident light and the film normal is defined as θ\theta, resulting in the wave vector k=4πsinθ/514.5k=4\pi\sin\theta/514.5.

X-ray absorption spectroscopy (XAS) and XMCD measurements at the Co L3,2L_{3,2} edges were performed using soft x rays at the helical undulator beamline BL-16A1 of Photon Factory, High Energy Accelerator Research Organization (KEK-PF). The spectra were measured in the total electron yield (TEY) mode. The measurements were performed at room temperature in a vacuum better than 5×1075\times\rm{10^{-7}} Pa. The magnitude of the magnetic field was set at 5 T and the field was applied parallel to the incident x rays in all measurements. The XAS and XMCD measurements using hard x rays were conducted at BL39XU of SPring-8. The partial fluorescence yield (PFY) and x-ray polarization switching modes were used. The measurements were performed at atmospheric pressure and at room temperature. A magnetic field of up to 2 T was applied during the measurements. In order to obtain the out-of-plane and in-plane components of the magnetic moments, the magnetic field was applied to the sample along the film normal and 3030^{\circ} with respect to the sample surface, referred to as out-of-plane and “in-plane” magnetic fields hereafter. Note that the position of the Pt L3L_{3} edge (11.563 keV) is excessively close to that of the W L2L_{2} edge (11.544 keV): these two peaks will overlap with each other in the W/Co/Pt trilayer and complicate the data analysis. Thus, two W/Co and Pt/Co bilayers were prepared by magnetron sputtering for measuring the W and Pt L3,2L_{3,2}-edge XAS and XMCD spectra. The bilayer, i.e. Sub./0.6 W/0.8 Co/1 Ru and Sub./0.6 Pt/0.8 Co/1 Ru, were also grown on 10×\times10 mm2 thermally oxidized Si substrates by magnetron sputtering at room temperature and the 1-nm-thick Ru served as the capping to avoid the bilayer from surface oxidation.

III Results and Discussion

Selected magnetic hysteresis loops of the trilayers with different Co thicknesses measured by using the VSM are shown in Fig 1. The easy axis of the trilayers are confirmed to lie in the film plane. The magnetic moment increases with Co thickness. The magnetic properties of the trilayers determined by the magnetic hysteresis loops are shown in Fig. 2. The tCot_{\mathrm{Co}} dependence of the magnetic moment is shown in Fig. 2(a). A linear function is fitted to the data with larger weight for films with larger tCot_{\mathrm{Co}}. The slope of the linear function is proportional to the saturation magnetization (per unit volume) MsM_{\mathrm{s}} and the horizontal axis intercept represents the magnetic dead layer thickness tDt_{\mathrm{D}}. By taking into account the area of the samples, we find Ms1350±50M_{\mathrm{s}}\sim 1350\pm 50 emu\cdotcm-3 and tD0.14±0.05t_{\mathrm{D}}\sim 0.14\pm 0.05 nm. The value of MsM_{\mathrm{s}} is close to that of bulk Co Coey (2010). tDt_{\mathrm{D}} is typically negative when Co faces a Pt layer due to proximity-induced magnetization Ueno et al. (2015); Lau et al. (2019), we infer that a magnetic dead layer at the W/Co interface exists and compensates the negative tDt_{\mathrm{D}} at Co/Pt interface. Based on the reported values of proximity-induced moment at Co/Pt interface (tDt_{\mathrm{D}} 0.06\sim-0.06 nm) Ueno et al. (2015), the tDt_{\mathrm{D}} at W/Co interface is estimated as 0.20±0.05\sim 0.20\pm 0.05 nm.

Refer to caption
Figure 1: Magnetic hysteresis loops of W/Co/Pt trilayers measured by a VSM. The magnetic field is applied perpendicular (blue) and parallel (red) to the film plane. The thickness of the Co layer is (a) 0.6, (b) 0.8, (c) 1.0, (d) 1.2, (e) 1.3, (f) 1.7, respectively.
Refer to caption
Figure 2: (a) Magnetic moment of W/Co/Pt trilayers as a function of Co layer thickness, tCot_{\mathrm{Co}}. The solid line is a linear fit to the data for tCo>1t_{\mathrm{Co}}>1 nm. (b) Product of the effective magnetic anisotropy energy, KeffK_{\mathrm{eff}}, and effective magnetic layer thickness, tefft_{\mathrm{eff}}, plotted as a function of tefft_{\mathrm{eff}}. The solid line is a linear fit to the data for teff>1t_{\mathrm{eff}}>1 nm.

The effective magnetic anisotropy energy density, KeffK_{\mathrm{eff}}, is obtained by taking the difference between the integrated areas of the easy-axis and hard-axis magnetization hysteresis loops. With the effective magnetic layer thickness defined by tefftCotDt_{\mathrm{eff}}\equiv t_{\mathrm{Co}}-t_{\mathrm{D}}, the product of KeffK_{\mathrm{eff}} and tefft_{\mathrm{eff}}, KeffteffK_{\mathrm{eff}}t_{\mathrm{eff}}, is given by the following equation Sinha et al. (2013); Lau et al. (2019):

Keffteff=KI+(KB2πMs2)teff,\centering K_{\mathrm{eff}}t_{\mathrm{eff}}=K_{\mathrm{I}}+(K_{\mathrm{B}}-2\pi M_{\mathrm{s}}^{2})t_{\mathrm{eff}},\@add@centering (1)

where KBK_{\mathrm{B}} and KIK_{\mathrm{I}} represent the bulk and interfacial contributions to KeffK_{\mathrm{eff}}. The 2πMs22\pi M_{\mathrm{s}}^{2} term represents the shape anisotropy energy density. KeffteffK_{\mathrm{eff}}t_{\mathrm{eff}} is plotted against tefft_{\mathrm{eff}} in Fig. 2(b). Negative KeffteffK_{\mathrm{eff}}t_{\mathrm{eff}} corresponds to the magnetization easy axis lying along the film plane. A linear function is fitted to the data with larger weight on films with larger tefft_{\mathrm{eff}}. The slope and the yy-axis intercept of the linear function represent KB2πMs2K_{\mathrm{B}}-2\pi M_{\mathrm{s}}^{2} and KIK_{\mathrm{I}}, respectively. From the linear fit, we obtain KB(0.8±0.7)×106K_{\mathrm{B}}\sim(0.8\pm 0.7)\times 10^{6} erg\cdotcm-3 and KI0.6±0.1K_{\mathrm{I}}\sim 0.6\pm 0.1 erg\cdotcm-2. KIK_{\mathrm{I}} is smaller than that the values typically reported for structures which include Co/Pt interfaces Ueno et al. (2015); Lau et al. (2019). Note that the data show small but systemic deviation from the linear fitting when tefft_{\mathrm{eff}} is smaller than \sim 1.0 nm.

Refer to caption
Figure 3: (a) tefft_{\mathrm{eff}} and (b) 1/teff1/t_{\mathrm{eff}} dependence of magnetocrystalline anisotropoy (MCA) in W/Co/Pt trilayers. The solid curves in panels (a) and (b) are calculated using Eq. (2) and the values of KIK_{\mathrm{I}} and KBK_{\mathrm{B}} obtained from the fitting shown in Fig. 2(b).

The MCA of the trilayers is given by excluding the shape anisotropy from KeffK_{\mathrm{eff}}:

MCAKeff+2πMs2=KIteff+KB.\centering\mathrm{MCA}\equiv K_{\mathrm{eff}}+2\pi M_{\mathrm{s}}^{2}=\frac{K_{\mathrm{I}}}{t_{\mathrm{eff}}}+K_{\mathrm{B}}.\@add@centering (2)

We plot the tefft_{\mathrm{eff}} and 1/teff1/t_{\mathrm{eff}} dependences of the MCA in Figs. 3(a) and (b), respectively. MCA increases monotonically with decreasing tefft_{\mathrm{eff}}. The calculated MCA using the parameters obtained from the fitting in Fig. 2(b) is shown by red solid lines in Fig. 3. Although the MCA is proportional to 1/teff1/t_{\mathrm{eff}} for teff>t_{\mathrm{eff}}> 1 nm, it clearly deviates from the scaling for teff1t_{\mathrm{eff}}\lesssim 1 nm.

The properties of DMI in W/Co/Pt trilayers was investigated by BLS measurements. Figure 4(b) exhibits the BLS spectra for a 3 W/1.2 Co/1 Pt trilayer sample measured with different wavefactor kk. Due to the lifted chiral degeneracy arising from DMI, the dispersion curves are asymmetrical with respect to k=0k=0, where kk is the frequency shift. Fitting the measured dispersion data to the equation derived from the Landau-Lifshitz-Gilbert equation Di et al. (2015):

ω=ω0+ωDM=μ0γ[H0+Jk2+ξ(kteff)Ms][H0HU+Jk2+Msξ(kteff)Ms]2γMsDk,\omega=\omega_{0}+\omega_{\mathrm{DM}}=\mu_{0}\gamma\sqrt{\left[H_{0}+Jk^{2}+\xi\left(kt_{\mathrm{eff}}\right)M_{\mathrm{s}}\right]\left[H_{0}-H_{\mathrm{U}}+Jk^{2}+M_{\mathrm{s}}-\xi\left({kt_{\mathrm{eff}}}\right)M_{\mathrm{s}}\right]}-\frac{2\gamma}{M_{\mathrm{s}}}Dk, (3)

where ω0\omega_{0} represents the angular frequency in the absence of DMI, and ωDM\omega_{\mathrm{DM}} is the frequency shift induced by DMI. μ0\mu_{0} is the vacuum permeability, and γ\gamma is the gyromagnetic ratio set to 194±2194\pm 2 GHz/T (corresponding to a gg factor of \approx 2.2). J=2A/(μ0Ms)J=2A/({\mu_{0}}{M_{\mathrm{s}}}), where AA is the exchange stiffness constant, and ξ(x)=1(1e|x|)/|x|\xi\left(x\right)=1-\left(1-e^{-|x|}\right)/\left|x\right|. HU=2MCA/(μ0Ms)H_{\mathrm{U}}=2\mathrm{MCA}/\left({\mu_{0}}{M_{\mathrm{s}}}\right) is the uniaxial anisotropic field, with the strength input from the measured MCA values in Fig. 3. The fitting of the spectra measured with different kk (i.e., different θ\theta) yields the magnitude of the Dzyaloshinskii-Moriya exchange constant (|D||D|) based on this equation.

The tefft_{\mathrm{eff}} and 1/teff1/t_{\mathrm{eff}} dependences of |D||D| are plotted in Figs. 4(c) and (d), respectively. |D||D| increases with decreasing tefft_{\mathrm{eff}} until teff1t_{\mathrm{eff}}\sim 1 nm, below which it drops. A similar tendency has been observed in other HM/FM systems Cho et al. (2015); Belmeguenai et al. (2018), which is not in accordance with the simple picture of interface-driven DMI. The 1/teff1/t_{\mathrm{eff}} dependence of |D||D| in Fig. 4(d) is fitted using a linear function with a larger weight on thicker tefft_{\mathrm{eff}}, as shown by a red solid line. The parameters obtained by the linear fitting are used to calculate the tefft_{\mathrm{eff}} dependence of |D||D| in Fig. 4(c), as shown by a red solid line. Figures 4(c) and (d) display that the experimental data deviates from the linear fitting for teff<1t_{\mathrm{eff}}<1 nm. We note that |D||D| of W/Co/Pt trilayer grown by molecular beam epitaxy (MBE) has also investigated in a recent study Jenaa et al. (2021). The value of |D||D| in a trilayer with 0.7-nm-thick Co layer, >> 2 erg/cm2\mathrm{erg/cm^{2}}, is much larger than our samples grown by magnetron sputtering. We suggest the difference can be attributed to the different growth techniques.

Refer to caption
Figure 4: (a) The schematic image of the BLS measurement geometry. The scattering angle is 180. (b) BLS spectra of a 3 W/1.2 Co/1 Pt trilayer measured under different incident light angle θ\theta. (c) tefft_{\mathrm{eff}} and (d) 1/teff1/t_{\mathrm{eff}} dependence of the magnitude of the Dzyaloshinskii-Moriya exchange constant (|D||D|) in W/Co/Pt trilayers deduced by Brillouin light scattering spectroscopy (BLS) measurements. The solid lines in (a) and (b) show fit to the data from teff>1t_{\mathrm{eff}}>1 nm.
Refer to caption
Figure 5: XAS, and XMCD spectra of Co in W/Co/Pt trilayers. Spectra after background subtraction are shown. (a) XAS,XMCD and (b) the integrated XMCD spectra at the Co L3,2L_{3,2} edges for samples with different Co thicknesses. The spectra obtained under the out-of-plane and “in-plane” magnetic fields are plotted by solid and dashed curves, respectively.

To identify the origin of the tefft_{\mathrm{eff}} dependences of MCA and DMI in the W/Co/Pt trilayers, the XAS and XMCD spectra of Co are studied. The setup of the measurements is schematically illustrated in the inset of Fig. 6(a). Figure 5(a) shows the XAS and XMCD spectra at the Co L3,2L_{3,2} edges of the W/Co/Pt trilayers measured under a magnetic field of 5 T. The intensity is normalized to the L3L_{3} peak after removing a background consisting of two step functions. No obvious peak shift or spectral line-shape change is found in both the XAS and XMCD spectra between different tefft_{\mathrm{eff}}, suggesting that there is no significant changes in the chemical state of Co, i.e., the oxidation of Co is negligibly small. The solid and dashed curves in Fig. 5(a) represent the spectra measured with out-of-plane and “in-plane” magnetic fields, respectively. The integrated XMCD spectra, as displayed by the corresponding curves in Fig. 5(b), show clear differences between measurements under out-of-plane and “in-plane” magnetic field directions. These results indicate that the magnetic moment of Co is anisotropic.

Refer to caption
Figure 6: tefft_{\mathrm{eff}} dependence of (a) the spin moment (mspinm_{\mathrm{spin}}) and (b) the out-of-plane component of magnetic dipole (mT0m_{\mathrm{T}_{0}}). tefft_{\mathrm{eff}} dependence of the orbital magnetic moment (morbm_{\mathrm{orb}}) and normalized orbital magnetic moment (morb/mspinm_{\mathrm{orb}}/m_{\mathrm{spin}}), for different magnetization directions, are shown in (c) and (d), respectively. The spin, orbital and normalized orbital moment values of bulk hcp Co Coey (2010) are shown using dashed horizontal lines. The schematic images of the XAS and XMCD measurements setup are shown as the inset in panel (a).

The effective spin magnetic moment (meffm_{\mathrm{eff}}) of Co atom is estimated using the XMCD sum rule Thole et al. (1992); Carra et al. (1993):

meff\displaystyle m_{\mathrm{eff}} =mspin+72mT\displaystyle=m_{\mathrm{spin}}+\dfrac{7}{2}m_{\mathrm{T}} (4)
=2L3Δμ𝑑ν4L2Δμ𝑑νL3,2μ𝑑νnh,\displaystyle=-\dfrac{2\int_{L_{3}}\Delta\mu d\nu-4\int_{L_{2}}\Delta\mu d\nu}{\int_{L_{3,2}}\mu d\nu}n_{h},

where Δμ\Delta\mu and μ\mu are the difference and sum of the XAS spectra obtained using right- and left-handed circularly polarized light, mspinm_{\mathrm{spin}} is the spin magnetic moment of the Co atom, mTm_{\mathrm{T}} is the magnetic dipole, nhn_{h} is the number of holes in the 3dd band of the Co atom. Here, we present magnetic moments in units of Bohr magneton per Co atom using nh=2.45n_{\textrm{h}}=2.45 Nakajima et al. (1998). The out-of-plane and in-plane components of the magnetic moments are obtained from the integrated XAS/XMCD spectra measured under the out-of-plane and “in-plane” magnetic fields, respectively. mspinm_{\mathrm{spin}} is considered to be isotropic, but mTm_{\mathrm{T}} possesses an angular dependence mT=12mT0(13sin2θ)m_{\mathrm{T}}=-\dfrac{1}{2}m_{\mathrm{T}_{0}}\left(1-3\sin^{2}\theta\right) Wu and Freeman (1994); Sto¨\rm{\ddot{o}}hr (1999). Here, mT0m_{\mathrm{T}_{0}} represents the out-of-plane component of mTm_{\mathrm{T}} and θ\theta is the angle between the magentization and the film plane.

The estimated values of mspinm_{\mathrm{spin}} and mT0m_{\mathrm{T}_{0}} are shown in Figs. 6(a) and 6(b) as a function of tefft_{\mathrm{eff}}, respectively. mspinm_{\mathrm{spin}} deviates from its bulk value, shown by a horizontal dashed line Coey (2010), and tends to decrease with decreasing tefft_{\mathrm{eff}}. Such variation of mspinm_{\mathrm{spin}} with film layer thickness has also been observed in similar systems Ueno et al. (2015). mspinm_{\textrm{spin}} can be fitted against tCot_{\textrm{Co}} using the relation mspin=(1tD/tCo)mspin,activem_{\textrm{spin}}=\left(1-t_{\textrm{D}}/t_{\textrm{Co}}\right)m_{\textrm{spin,active}}, where mspin,activem_{\textrm{spin,active}} is the active spin magnetic moment, to estimate the tDt_{\textrm{D}} in the Co layer. From the fitting, we obtain tD0.20±0.03t_{\mathrm{D}}\sim 0.20\pm 0.03 nm, which is consistent with the dead layer thickness determined from the VSM measurements. mT0m_{\mathrm{T}_{0}}, which is considerably smaller than mspinm_{\mathrm{spin}}, represents the anisotropic spin-density distribution, and its strength characterizes the anisotropy of the spin-density distribution of the dd orbitals. Although it has been reported that mT0m_{\mathrm{T}_{0}} is related to the emergence of PMA van der Lann (1998) and DMI Kim et al. (2018), here its magnitude is considerably smaller than the previous reports Kim et al. (2018).

The orbital magnetic moment (morbm_{\mathrm{orb}}) of Co atom is estimated using the XMCD sum rule Thole et al. (1992); Carra et al. (1993):

morb=43L3,2Δμ𝑑νL3,2μ𝑑νnh.\centering m_{\mathrm{orb}}=-\dfrac{4}{3}\dfrac{\int_{L_{3,2}}\Delta\mu d\nu}{\int_{L_{3,2}}\mu d\nu}n_{h}.\@add@centering (5)

The out-of-plane component of morbm_{\mathrm{orb}}, morbm_{\mathrm{orb}}^{\perp}, is estimated from the XAS and XMCD spectra measured under the out-of-plane magnetic field. The in-plane component, morbm_{\mathrm{orb}}^{\parallel}, is obtained using the spectra measured under the out-of-plane and “in-plane” fields according to the relationship,

morb(θ)=morbsin2θ+morbcos2θ,\centering m_{\mathrm{orb}}(\theta)=m_{\mathrm{orb}}^{\perp}\sin^{2}\theta+m_{\mathrm{orb}}^{\parallel}\cos^{2}\theta,\@add@centering (6)

with θ=30\theta=30^{\circ}. The tefft_{\mathrm{eff}} dependence of morbm_{\mathrm{orb}} is plotted in Fig. 6(c). Both morbm_{\mathrm{orb}}^{\perp} and morbm_{\mathrm{orb}}^{\parallel} decrease with decreasing tefft_{\mathrm{eff}} from their bulk value. We find the decrease of morbm_{\mathrm{orb}}^{\parallel} with tefft_{\mathrm{eff}} is stronger than that of morbm_{\mathrm{orb}}^{\perp}. This difference leads to the OMA of Co which is illustrated by black squares in Fig. 6(c), showing an increasing trend with decreasing tefft_{\mathrm{eff}}. The normalized orbital magnetic moment morb/mspinm_{\mathrm{orb}}/m_{\mathrm{spin}} is plotted against tefft_{\mathrm{eff}} in Fig. 6(d). The out-of-plane component, morb/mspinm_{\mathrm{orb}}^{\perp}/m_{\mathrm{spin}}, increases with decreasing tefft_{\mathrm{eff}} whereas the in-plane component, morb/mspinm_{\mathrm{orb}}^{\parallel}/m_{\mathrm{spin}}, decreases. The normalized OMA of Co, illustrated by black diamonds in Fig. 6(d), increases with decreasing tefft_{\mathrm{eff}}, especially for tefft_{\mathrm{eff}}\lesssim 0.8 nm. These results indicate that the charge redistribution at the HM/Co interfaces takes place and induces OMA. Considering the density of Co crystal as 8.9 g\cdotcm-3, we estimate the total magnetization of the W/Co/Pt trilayer with tefft_{\textrm{eff}}=0.9 nm as 1300 emu\cdotcm-3. This value is in good agreement with that determined by using the VSM.

Refer to caption
Figure 7: XAS and XMCD spectra at the W (a) and Pt (b) L3,2L_{3,2} edges in W/Co and Pt/Co bilayers. The intensity of the XMCD spectra of W (Pt) is enlarged by a factor of 25 (10).

We have also performed W and Pt L3,2L_{3,2}-edge XMCD measurements on W/Co and Pt/Co bilayers to study the proximity-induced magnetization. The XAS and XMCD spectra are shown in Fig. 7. XMCD signals are found only in the Pt/Co bilayer. These results indicate that proximity-induced magnetization exists at the Pt/Co interface but does not exist at the W/Co interface.

Now, we discuss the relationship between the MCA, DMI and OMA of Co in W/Co/Pt trilayers. According to Figs. 3 and  4, MCA and |D||D| scale with 1/teff1/t_{\mathrm{eff}} for teff1t_{\mathrm{eff}}\gtrsim 1 nm, indicating the interfacial origin of the two properties. Bruno has proposed that the MCA and OMA are proportional to each other in FM monolayers Bruno (1989). Both MCA and the OMA of Co indeed increase with decreasing tefft_{\mathrm{eff}} smaller than 0.8\sim 0.8 nm. However, the OMA tends to increase more rapidly with decreasing tefft_{\mathrm{eff}} than what the Bruno’s law predicts from the values of MCA. These results suggest additional contributions to MCA, such as strain or magnetic dipole mTm_{\mathrm{T}}. Previous studies have indicated that strain in the film texture can weaken the MCA when the magnetic layer thickness is reduced to a few atomic layers Johnson et al. (1996); Lau et al. (2017). The tefft_{\mathrm{eff}} dependences of MCA and KeffteffK_{\mathrm{eff}}t_{\mathrm{eff}} are in accordance with such studies. In a very recent study, MCA has been found directly determined by the strain while OMA doesn’t follows the prediction by Bruno’s rule in a Heusler alloy Kubota et al. (2022). These results also suggest that the strain can play a significant role on MCA besides OMA. van der Laan has also shown that mTm_{\mathrm{T}} affects MCA in strongly spin-orbit coupled systems, which has been associated with spin-flip virtual excitation van der Lann (1998). Such relationship has been confirmed in recent experiments Miwa et al. (2017); Ikeda et al. (2017); Shibata et al. (2018). Unfortunately, the XMCD spectra of our W/Co/Pt trilayers does not have sufficient resolution to derive mTm_{\mathrm{T}} accurately.

The DMI, on the other hand, approaches near zero as tefft_{\mathrm{eff}} is reduced below \sim1 nm. Due to the strong spin-orbit coupling and broken inversion symmetry, the electronic structures in system exhibiting strong DMI are significantly altered by interfacial conditions Yang et al. (2015); Ham et al. (2023). Recent studies have shown that DMI is related with mTm_{\mathrm{T}} at the HM/FM interfaces Kim et al. (2018) and the OMA of the FM atoms Yamamoto et al. (2017). Comparing the results presented in Figs. 4(c) and 6(c), we consider that such relations do not hold in the current system because the tefft_{\mathrm{eff}} dependences of OMA and DMI are opposite to what one expects from the scaling reported in Ref. Yamamoto et al. (2017). The magnitude of mTm_{\mathrm{T}} found in this system is considerably smaller than that reported in Ref.Kim et al. (2018) and, therefore, its contribution to DMI, if any, is also likely small. Furthermore, DMI in our sputtered samples is much smaller than that in MBE-grown W/Co/Pt trilayer Jenaa et al. (2021). Thin films grown by MBE usually show better interfacial roughness and crystal texture compared to films grown by magnetron sputtering. We thus speculate that the DMI is more sensitive to strain effect or the (111) texture of Co. Theoretical studies Yang et al. (2015); Hrabec et al. (2014) have indicated that the crystal structure at the HM/FM interface influences the strength of DMI dramatically. In the present case, strain and texture of the Co layer near the W/Co interface may significantly degrade |D||D| for teff1t_{\mathrm{eff}}\lesssim 1 nm. With further increasing Co thickness, such effects are then mitigated by the Co/Pt interface that favors the (111) texture, resulting in the following decrease of |D||D|. This hypothesis is further supported by another study which also suggests that strain at the Co/Pt interface can significantly modify DMI through charge redistribution within the in-plane dd-orbitals Deger (2020). We note that the same work also points out that the strain-induced tailoring of DMI is related to the charge redistribution within in-plane dd-orbitals. This mechanism differs from MCA adjustments, which involve altering electron occupation between in-plane and out-of-plane orbitals Shibata et al. (2018), indicating the complicated relationship between MCA, DMI, and orbital properties in FM/HM heterostructures.

IV Summary

We have studied the effective magnetic layer thickness (tefft_{\mathrm{eff}}) dependences of magnetocrystalline anisotropy (MCA), Dzyaloshinskii-Moriya interaction (DMI), and orbital moment anisotropy (OMA) in W/Co/Pt trilayers. For tefft_{\mathrm{eff}} larger than \sim1 nm, MCA and DMI scale with 1/teff1/t_{\mathrm{eff}}, indicating an interfacial origin. However, whereas MCA continues to increase with decreasing tefft_{\mathrm{eff}}, DMI tends to decrease when tefft_{\mathrm{eff}} is reduced below \sim1 nm. The OMA of Co deduced from x-ray magnetic circular dichroism (XMCD) measurements is almost zero (below the detection limit) when tefft_{\mathrm{eff}} is larger than \sim0.8 nm, below which the OMA of Co increases with decreasing tefft_{\mathrm{eff}}. The rate at which the OMA of Co increases with decreasing tefft_{\mathrm{eff}} is larger than what is predicted from the MCA using Bruno’s formula. The reduction of DMI with decreasing tefft_{\mathrm{eff}} for films with teff1t_{\mathrm{eff}}\lesssim 1 nm, despite the presence of OMA, suggests that other factors contribute to the DMI in this thickness range. We infer that the strain/texture in the Co layer induced by the W underlayer significantly weakens the DMI and, to a lesser extent, the MCA. Further studies are necessary to clarify the latter points. Our results provide a microscopic understanding for designing viable FM/HM-interface-based multifunctional spintronic devices.

Acknowledgements.
We thank H. Shimazu for samples preparation. This work was supported by Grants-in-Aid for Scientific Research from JSPS (Grant Nos. 15H02109, 15H05702, 16H03853, 20K14416, and 22K03535) and by the National Science and Technology Council of Taiwan under a Grant No. 113-2112-M-007-033. The XMCD experiment was performed at BL-16A of KEK-PF with the approval of the Photon Factory Program Advisory Committee (proposal Nos. 2016S2-005 and 2016G066) and at BL39XU of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (proposal Nos. 2017A1048 and 2018A1058). M.H. and A.F. are adjunct members of Center for Spintronics Research Network (CSRN), the University of Tokyo, under Spintronics Research Network of Japan (Spin-RNJ). Z.C. is supported by Materials Education program for the future leaders in Research, Industry, and Technology (MERIT) and JSR Fellowship, The University of Tokyo. Y.-C.L. is supported by JSPS International Fellowship for Research in Japan (Grant No. JP17F17064). S.S. and Y.-X.W. acknowledges financial support from Advanced Leading Graduate Course for Photon Science (ALPS). S.S. acknowledges financial support from the JSPS Research Fellowship for Young Scientists. A.F. acknowledges the support from the Yushan Fellow Program under the Ministry of Education of Taiwan.

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