Strain-Induced Reversible Manipulation of Orbital Magnetic Moments in Ni/Cu Multilayers on Ferroelectric BaTiO3

Controlling magnetic anisotropy by orbital magnetic moments related to interfacial strains has considerable potential for the development of future devices using spins and orbitals. For the fundamental physics, the relationship between strain and orbital magnetic moment is still unknown, because there are few tools to probe changes of orbital magnetic moment. In this study, we developed an electric-field- (E)-induced X-ray magnetic circular dichroism (EXMCD) technique to apply E to a ferroelectric BaTiO3 substrate. We reversibly tuned the interfacial lattice constants of Ni/Cu multilayers on BaTiO3 using this technique. As the domain structures in BaTiO3 are modulated by E, EXMCD measurements reveal that the changes in the magnetic anisotropy of Ni/Cu films are induced through the modulation of orbital magnetic moments in Ni with magneto-elastic contributions. The strained Ni layer that induces the perpendicular magnetic anisotropy without E is released at E = 8 kV/cm, and in-plane magnetization also occurs. We observed that EXMCD measurements clarified the origin of the reversible changes in perpendicular magnetic anisotropy and established the relationship between macroscopic inverse magnetostriction effects and microscopic orbital moment anisotropy.


Introduction
The coupling between ferromagnetic and ferroelectric properties has recently attracted considerable attention toward the creation of novel devices using multiferroic controlling of their properties [1][2][3][4][5][6][7] . In particular, the hetero-interfaces in thin films comprising both ferromagnets and electrically polarized materials produce a rich variety of possibilities for creating multifunctional properties [8][9][10][11][12][13][14][15][16][17][18] . Modulation of interfacial lattice constants by an electric field (E) induces interfacial changes in magnetism. The interfacial lattice distortion produces variations in magnetic properties, which are recognized as inverse magnetostriction effects [19][20][21][22][23] . Moreover, magnetic anisotropy is tuned by lattice distortions. Recently, the magnetic anisotropy controlled by E has become an important subject in spintronics, which is the study aiming at the realization of devices operating with low energy consumption [24][25][26][27][28] . Recent attempts have been focused on the modulation of the number of charge carriers at the interface between an ultrathin ferromagnetic layer and an oxidebarrier insulator in magnetic tunnel junctions. Other approaches, which are our focus in this study, are based on the interfacial mechanical-strain coupling between ferromagnetic and ferroelectric layers using multiferroic hybrid structures. As one of the candidate approaches, applying E to BaTiO3 provides the possibility to tune the lattice constants by modulating the domain structures along the a-and c-axes directions by 3.992 Å and 4.036 Å, respectively, at room temperature 29,30 .
There exist some reports related to depositing magnetic thin-film layers onto BaTiO3 for Einduced magnetism with abrupt interfaces between BaTiO3 and Fe or Co 12,[14][15][16]21,22,24 . In other cases, thin Ni layers sandwiched by Cu layers exhibit perpendicular magnetic anisotropy (PMA) because of the interfacial tensile strain in the Ni layers 31 . Recently, E-control of the magnetic properties of Ni/Cu multilayers on BaTiO3 was achieved; the magnetization was switched from the perpendicular axis to the in-plane easy axis by tuning the lattice distortion through the application of E 32 . These effects may be explained phenomenologically by inverse magnetostriction effects. Although anisotropic energies depend on orbital magnetic moments, the microscopic origin of the control of the anisotropic energy dependent on strain is still not known explicitly. Theoretical approaches that consider spin-orbit interactions, as well as crystalline potentials, as perturbative treatments have been developed 33 . Moreover, strain-induced orbital magnetic moments have been discussed alongside calculations on the strained Ni layers 34 , but the relationship between strain and orbital moments is still unknown.
Element-specific magnetic properties and their origins should be investigated by applying E explicitly to clarify the relationship between lattice distortion and magnetic properties. In particular, magnetic anisotropy is related to the anisotropy of orbital magnetic moments 35 . A unique tool to deduce spin moments as well as orbital moments is X-ray magnetic circular dichroism (XMCD) with magneto-optical sum rules 36,37 . Recent developments of XMCD by applying E have focused on charge accumulation at the interface of FePt/MgO 38 , interfacial oxidation reaction of Co/Gd2O3 39 , and other cases [40][41][42] . In the case of FePt/MgO, the difference in the Fe XMCD by applying E is negligibly small because of the quite small amounts of charge accumulation at the interfaces. In the case of Co/Gd2O3, the chemical reaction at the oxide interfaces becomes dominant. Investigating the orbital moment anisotropy (OMA) by applying E is a challenging approach to initiate novel research into the physics of the relationship between lattice distortion and orbital magnetic moments, which is a fundamental and unsolved problem in the scientific research field. Considering the relationships between spin magnetic moments (ms), orbital magnetic moments (morb), and strain (ε), the spin-orbit interaction links ms and morb, and the magnetostriction links ms and ε . However, the relationship between morb and distortion is still unexplored. To understand this relationship and the elastic phenomena from the view point of morb, we developed a technique by applying an electric field in XMCD measurements (EXMCD) to clarify the mechanism of the electric-field-induced changes in the magnetic anisotropy of Ni/Cu multilayers on BaTiO3 hetero-structures through lattice distortions. In this study, we aim to clarify the relationship between strain and orbital magnetic moments using the EXMCD method; we also present first-principles calculation of the changes in magnetic anisotropy.

Strain introduced into the samples
First, we mention the values of the strain introduced into the samples, as illustrated in Fig. 1a.
Without applying E, the Ni layer possesses a tensile strain of 2% through the sandwiched-Cu layers, and the Ni layer exhibits PMA as shown in Fig. 1b. When E is zero, the a-and c-domain structures are mixed in BaTiO3. By applying E, the c-domain structures become dominant, from which it may be inferred that the application of the electric field, E, compresses the lattice constant of BaTiO3 and releases the strain in the Ni layer, thereby resulting in the magnetization in the in-plane easy axis in the Ni layers. Therefore, in the a-and c-domain structures of BaTiO3, the Ni layer exhibit PMA and in-plane anisotropy, respectively 32 . Figure 1c displays the differential interference microscopy images of the a-and c-domains before and during the application of E. The bright area indicates the a-domain structure. Both a-and c-domain structures without E are clearly observed, and they align to the c-domain structure by applying ±5 kV/cm, which is consistent with the magnetization. The area of a-domain structure is estimated from the images in Fig. 1c as approximately 50 % without E. We emphasize that the strain propagation proceeds into all multilayers by the modulation of lattice constants of BaTiO3 substrates due to the high strain-transfer parameter value. 32,43 In the case of 20-nm-thick Fe film on BaTiO3, strain propagation into the surfaces is also detected. 44 Further, we confirmed that this process is reversible by removing E.

XAS and XMCD
Results from X-ray absorption spectroscopy (XAS) and XMCD in the total-electron-yield   Table I. The modulation of the orbital magnetic moments by 0.01 µB upon applying E is related to the induced lattice distortion of 2% from the BaTiO3 substrates. Moreover, after releasing E to zero, spectral line shapes also revert to the pristine state. For grazing incident (GI) case, XAS and XMCD spectra with and without E are displayed in Figs. 3c and 3d. The values of ms and morb are also listed in Table I. Effects of electric field in GI are smaller than those in NI because oblique configuration of 60° from sample surface normal detects the half of in-plane components (cos60°=1/2). Angular dependence depicts the changes of ms eff which includes ms+7mT and the magnetic dipole term of mT cancels in the magic angle 53.7° of near GI set up. Details are explained in supplemental material. Thus, the value of mT is estimated less than 0.001 µB. Therefore, these results originate from the modulation of not spin moments but orbital moments, suggesting that the inverse magneto-striction effects are derived from the changes of orbital moments.
The element-specific magnetization curves (M-H curves) at the L3-edge of Ni during the application of E in the normal incidence setup are shown in Fig. 4. As the normal of the sample surface is parallel to both incident beam and magnetic field, the contribution from the easy axis in PMA is observed. By applying an electric field, E, of ±8 kV/cm, the M-H curves change to those of the in-plane easy-axis behavior, which is related to the changes in the orbital magnetic moments in Ni. After switching off E, the M-H curves exhibit the PMA characteristics again, as shown in Fig.   4b. Moreover, the reversible changes observed by applying E in XMCD are confirmed by the changes in the XMCD line shapes. The amounts of the changes in the M-H curves at the Ni L3-edge XMCD are a little similar to those measured by the magneto-optical Kerr effect 32 . This phenomenon suggests that the domain structures in the observed area in the EXMCD measurements can be changed from the a-domain to the c-domain by applying E.

First-principles density-functional-theory calculation
We performed first-principles calculations of magneto-crystalline anisotropy (MCA) energies for fcc Ni as a function of the in-plane lattice constant (a||). Assuming the motion of free electrons as a ground state, spin-orbit interaction is adopted as a perturbation term for the estimation of MCA energy. The MCA energy is defined as the difference between the sums of the energy eigenvalues for magnetizations oriented along the in-plane [100] and out-of-plane  46 . First, the spin-conservation term ΔE↓↓ increases with increasing a|| of fcc Ni and qualitatively reproduces the a|| dependence of the MCA energies and Δmorb. Second, the spin-flip term ΔE↑↓ decreases with increasing a||, indicating that the origin of the change of the MCA energies of fcc Ni by the tetragonal distortion can be attributed to the ΔE↓↓. We confirmed the strain dependence of spin magnetic moments is ten times smaller than Δmorb. Therefore, this means that the MCA of fcc Ni can be described mainly by Bruno's relation through the orbital moment anisotropy 35 . Since ΔE↓↓ and ΔE↑↓ can be described as the energy differences between the z and x directions, (1) The matrix elements of Lx and Lz, depending on in-plane strain, provide the orbital-resolved contributions; o(u) represents occupied (unoccupied) states. 48 We adopted spin-orbit coupling

Discussion
Considering the above results, we discuss the relationship between the OMA and the magnetoelastic energy. In particular, we analyze the magnetic anisotropy energies in the strained Ni layers depending on the magnetization and the lattice distortion. Microscopically, the OMA can be described by Bruno's relation 35 through the second-order perturbation of the spin-orbit interaction.
Moreover, the OMA produces the crystalline anisotropy ∆Κ = αξ∆morb, where ∆morb is the difference between the orbital moment of the component perpendicular to the film and that of inplane component, with the coefficient of the spin-orbit coupling constant ξ and the band-structure parameter α=1/4 for a more-than-half-filled 3d transition metal Ni. The XMCD shown in Fig. 3 clearly exhibits OMA that depends on the applied electric fields. The value of ∆morb is estimated to be 0.01 µB for a strain modulation of 2%, which results in the anisotropy energy of 6.8×10 5 J/m 3 by assuming fcc-Ni lattice constants of 3.524 Å. As the hysteresis curves in Fig. 1  (2) As the interfacial strain modulates the orbital magnetic moment, the strength of the distortion , quantified as a ratio of the length difference, is scaled to ∆morb, which is deduced from the band-structure calculation. In general, eq. (2) consists of two terms of ∆morb and mT. However, the contribution of mT is much smaller than ∆morb in 3d TMs. Then, we focus on only the first term. Figure 5a confirms the linear relationship between ε and ∆morb. The slope in Fig. 5a quantitatively describes the dependence of ∆morb on ε in Eq. (2). By applying E to BaTiO3, the released lattices shorten the in-plane lattice distances, thereby resulting in the decrease of perpendicular orbital moments. Quantitatively, the 2% modulation of the lattice generates the OMA of 0.01 µB, which is of the same order as that deduced from the first-principles calculations.
Next, we discuss the discrepancy between XMCD and first-principles calculation. The discrepancy might be understood as the underestimating of morb in the calculation because of the lack of considering Hund's second rule in the electron correlation 49 . By considering orbital polarization, ∆morb estimated from the first-principles calculation becomes similar to that deduced from XMCD. Other reasons for the discrepancy might originate in the spin-flipped contribution through ΔE↓↑. On the other hand, EXMCD measurements also deduced the magnetic dipole term in Ni, the order of which is smaller than ∆morb. However, this term proposed by van der Laan 50 which is deduced from Δ ↑↓ in eq. (1) is smaller than OMA. Therefore, the modulation of the magnetic anisotropy introduced by the macroscopic strain in the Ni layers is connected mainly with the OMA as a microscopic origin. Further, EXMCD and first-principles calculation explain qualitatively that the ms values are less sensitive to the strain and orbital hybridization, resulting in the changes of morb.
In conclusion, by using the novel EXMCD technique, we clarified that the reversible PMA changes in the Ni/Cu film on BaTiO3 are induced by the modulation of orbital magnetic moments in Ni. The strained Ni layer that induces the PMA without E is released upon the application of an E-field and is modulated to produce in-plane magnetization. Moreover, the magnetization curves in the Ni L3-edge EXMCD measurements are modulated between out-of-plane and in-plane magnetization. We revealed that the changes of magnetic anisotropy by E, which were explained by the phenomenological magneto-elastic description, may be understood microscopically by OMA.
These results introduce the concept of orbital-striction or orbital-elastic effects at the heterointerfaces beyond established magnetostriction effects.     Normal incidence set up was adopted. (a) Increasing the electric field from 0 kV/cm up to 8 kV/cm, and (b) decreasing the electric field from 8 kV/cm to 0 kV/cm.