Fourfold magnetic anisotropy induced in CoFeB/IrMn bilayers by interfacial exchange coupling

Exchange bias (EB) occurring in ferromagnetic (FM)/antiferromagnetic (AFM) bilayers conventionally can lead to a unidirectional magnetic anisotropy ( Keb ) as well as an accompanied uniaxial magnetic anisotropy ( Ku ). We observed an additional fourfold magnetic anisotropy ( K4 ) induced by interfacial exchange coupling in amorphous CoFeB/epitaxial IrMn bilayers with an EB. Because of the combined effect of the three kinds of magnetic anisotropies, one- and two-step magnetic switching processes were observed at different magnetic field orientations, which usually appear in single-crystal FM layer with an intrinsic magnetocrystalline anisotropy but not in amorphous FM layer. The angular dependent magnetic switching fields can be nicely fitted by a phenomenological model based on domain wall nucleation and propagation with the in-plane K4 along <100>. The ferromagnetic resonance measurements indicate that the specific strength of K4 for EB along [100] is larger than that for EB along [110]. The induced K4 can be understood by considering two types of AFM domains caused by both monatomic steps and defects and their induced net uncompensated spins along the in-plane <100> axes. The different dependence of K4 on the EB direction are because of the different effects of growth magnetic field on the presence of AFM domains.


Introduction
Phenomena of exchange bias (EB) with a hysteresis loop shift and a coercivity enhancement occur when a ferromagnetic (FM) layer is exchange coupled to an antiferromagnetic (AFM) layer across the interface [1][2][3]. Unidirectional and uniaxial magnetic anisotropies induced by EB in FM/AFM bilayers are technically important for applications in information storage devices, such as pinning the magnetization of reference magnetic layer in magnetic tunnel junctions or stabilizing magnetic moments in nanoparticles against thermal excitation [4][5][6][7].
Most of previously studied FM/AFM EB systems existed in polycrystalline form, whose magnetic switching processes can be described by the Stoner-Wohlfarth (SW) model considering both unidirectional and uniaxial magnetic anisotropies [8,9]. Epitaxial EB systems are considered as ideal systems for fundamental physics studies because of the sharp interface and the well-ordered arrangement of atoms and magnetic moments, thus having been highly regarded in recent years. In addition to the unidirectional and uniaxial magnetic anisotropies, a single crystal FM layer may display an intrinsic magnetocrystalline anisotropy, e.g. an in-plane fourfold magnetic anisotropy for Fe with body-centered-cubic (BCC) crystal structure [10][11][12]. The three kinds of magnetic anisotropies jointly determine the magnetic switching processes, rendering multi-step loops observed in epitaxial EB bilayers, which can be explained by a phenomenological model based on domain wall (DW) nucleation and propagation [13,14].
Epitaxial AFM layers also have an important impact on the interfacial exchange coupling and the resulting magnetic anisotropies in the adjacent FM layers. Previous studies have shown that an uncompensated AFM surface can collinearly exchange couple to an FM layer [15,16], leading to an additional uniaxial anisotropy parallel to the unidirectional anisotropy, while a compensated AFM surface can result in an additional uniaxial anisotropy perpendicular to the unidirectional anisotropy in the FM layer exchange coupled due to the spin-flop coupling [17][18][19]. We have recently demonstrated that the magnetocrystalline anisotropy of epitaxial FeRh layer in both AFM and FM states can be imprinted to an amorphous CoFeB layer due to the interfacial exchange coupling [20,21]. Chen et al, have in situ studied ultrathin Co/FeMn bilayers and found that when the epitaxial FeMn layer starts to establish an AFM order, a fourfold magnetic anisotropy can be induced in the single-crystal Co layer because of the interfacial spin frustration [22,23]. However, such a high-symmetric magnetic anisotropy caused by the interfacial exchange coupling has not yet been observed in conventional FM/AFM bilayers with an obvious EB and the dependence on EB is still not known well.
In this paper, we selected typical EB bilayers comprising amorphous CoFeB and epitaxial IrMn layers grown on MgO(001) substrates. The renewed interest in IrMn comes from the application of EB system in spintronic devices, they are widely used as alternative AFM layers to pinning the magnetic moment of adjacent FM layers [19,24]. CoFeB exhibits excellent soft magnetic behaviors because of the absence of magnetocrystalline anisotropy caused by the lack of long-range atomic order. The additional behavior of high spin polarization makes CoFeB extensively used in spintronic devices [25][26][27]. In such EB bilayers, in addition to an obvious EB and an accompanied uniaxial anisotropy, an induced fourfold magnetic anisotropy was observed in CoFeB layer along IrMn <100> regardless of the orientation of EB. The induced fourfold magnetic anisotropy for EB along [100] is much stronger than that for EB along [110]. Combined with the 3Q spin structure of IrMn, two types of AFM domains respectively caused by monatomic steps and defects were proposed to explain this phenomenon.

Experimental details
CoFeB(10 nm)/IrMn(30 nm) bilayers were deposited on commercial (001)-oriented MgO single-crystal substrates (see figure 1(a)) in a magnetron sputtering system with a base pressure below 1.0 × 10 −8 Torr. Before deposition, MgO substrates were annealed at 500 • C for 1 h in the vacuum chamber. IrMn layers were grown by sputtering an Ir 20 Mn 80 target at 400 • C or 500 • C and annealed at the growth temperature for 1 h. After cooling to room temperature, a CoFeB layer was deposited on top of the IrMn layer by sputtering a Co 40 Fe 40 B 20 target. To avoid an oblique-growth-induced anisotropy, all samples were deposited while rotating the MgO substrates. A magnetic field H growth of 500 Oe provided by a permanent magnet was applied during growth to induce an EB along the MgO[100] or [110] axes. Before removed from the vacuum chamber, the samples were capped by a 3 nm Ta layer to avoid oxidation. A reference CoFeB single layer with 10 nm in thickness was fabricated as well by using the same parameters. The film thicknesses were controlled by the deposition time, which have been calibrated by x-ray reflectivity. The crystal structure and the epitaxial nature of IrMn films were analyzed by x-ray diffraction (XRD) θ-2θ and in-plane Φ scans. The magnetic switching processes were measured by using a combined longitudinal (||) and transverse (⊥) magneto-optical Kerr effect (MOKE) setup. The magnetic anisotropy was quantitatively measured by a ferromagnetic resonance (FMR) spectroscopy at a radio frequency of 9.31 GHz. Figure 1(b) shows the XRD θ-2θ patterns of the CoFeB/IrMn bilayers grown at 400 • C and 500 • C. The observation of γ-IrMn 3 (002) peak indicates an (001) growth orientation on the MgO(001) substrates. The γ-IrMn 3 (001) peak becomes visible at the growth temperature of 500 • C, implying a slight atomic order. No CoFeB peak is detected due to the amorphous structure. The x-ray in-plane Φ scan with a fixed 2θ at the (022) reflection reveals the cube-on-cube epitaxial growth of IrMn layer at 500 • C with a relationship of IrMn(001)[100]||MgO(001)[100], as shown in figure 1(c). MgO substrate shows a NaCl-type structure with a lattice constant of 0.4212 nm while the lattice parameter of γ-IrMn 3 is 0.3808 nm [28]. Although the lattice mismatch between MgO(001) and γ-IrMn 3 (001) is as large as 9.6%, the epitaxial growth can be successfully obtained by carefully controlling the growth parameters [24,28]. In contrast, IrMn grown at 400 • C is considered to be polycrystalline, since no Φ scan peak can be detected. Similar to disordered FeMn alloy, γ-IrMn 3 has a 3Q spin density wave structure with 109.5 • between spins proposed by the first-principles calculations from theoretical point of view [29,30]. Figure 1(d) presents a schematic diagram of the 3Q spin structure of γ-IrMn 3 with face-centered-cubic crystal structure [31,32]. Ir and Mn atoms have no specific lattice site preference [24]. A unit cell consists of four sublattices with the spins pointing to four different <111> directions. The adjacent layers ideally have an in-plane component of spins perpendicular to each other, giving rise to a magnetic compensated (001) surface.

Results and discussion
Both longitudinal (||) and transverse (⊥) MOKE loops were measured with an in-plane magnetic field H parallel and perpendicular to the plane of laser incidence, respectively. The in-plane magnetization components m x parallel H and m y perpendicular H can be obtained, thus the exact path of magnetization reversal occurring at different orientation φ of H with respect to MgO[100], i.e. IrMn[100] can be known well [13,14]. The sample with polycrystalline IrMn layer grown at 400 • C, named as S-poly, shows a square hysteresis loop at φ = 0 • with a small EB field H eb = −20 Oe and a small coercivity H c = 17 Oe, as shown in figure 2(a) [12]. This is because the EB direction is more energetically favorable than the opposite direction. For samples with an epitaxial IrMn layer grown at 500 • C, the one with EB set parallel to IrMn[100] is named as S-100, another one with EB along IrMn[110] is S-110. In comparison with S-poly, both samples exhibit enhanced H eb and H c along the EB direction, indicating a strong exchange coupling between CoFeB and epitaxial IrMn layer. For S-100, a square loop with H eb = −104 Oe and H c = 98 Oe is obtained at the EB direction of φ = 0 • , indicating an easily magnetized behavior, as shown in figure 2(b). The transverse MOKE signal is weak, which implies the magnetization reversal mechanism of DW nucleation and propagation. At φ = 90 • , the EB vanishes and the loop exhibits a two-step process. The transverse MOKE signal shows that the magnetic switching routes between IrMn[0-10] and [010] for both descending and ascending branches are mediated via an intermediated state along the EB direction of IrMn[100] [13,14,20], which is similar to the case of S-poly. For S-110, a round loop with H eb = −124 Oe and H c = 43 Oe is observed at the EB direction are mediated via the same intermediated state along IrMn[100] although it is no longer the EB direction. The multi-step magnetic switching processes have been often observed in epitaxial FM layers due to the intrinsic magnetocrystalline anisotropy [10][11][12]. The magnetization can be switched between the in-plane fourfold easy axes, thus displaying one-, two-, and even three-step processes [13,14]. However, the reference CoFeB single layer only displays a weak uniaxial magnetic anisotropy because of the amorphous structure. We tentatively suppose that a fourfold magnetic anisotropy along IrMn <100> is extrinsically induced in the amorphous CoFeB layer by the epitaxial IrMn layer through the interfacial exchange coupling. In order to facilitate the discussion on the magnetization reversal mechanism of the samples with an epitaxial IrMn layer, the magnetic switching fields are defined as H c1 to H c4 in the clockwise direction and H c1 ′ to H c4 ′ in the counterclockwise direction according to the initial and final easy axes of the fourfold anisotropy involved in a switching process, as illustrated in figure 3(a). Taking the descending branch of S-100 measured at φ = 90 • as an example, the critical field for the switching from [010] to [100] is H c4 , and the one for the following switching from [100] to [0-10] is H c1 , as remarked in figure 2(b).  polycrystalline FM/AFM EB system [33], the angular dependent behaviors can be described by the SW model [8]. Considering a unidirectional anisotropy K eb collinear to a uniaxial anisotropy K u [9], the energy per unit volume of the system is given as E = −K u cos 2 θ − K eb cos θ − M s H cos (φ − θ), where M s is the saturation magnetization, which is 1400 emu cc −1 for CoFeB films, and θ is the orientation of M s with respect to MgO[100]. The theoretical curve with parameters of K eb = 2.8 × 10 4 erg/cc and K u = 0.8 × 10 4 erg/cc can nicely reproduce the experimentally obtained H eb , but the values of H c are obviously higher than the theoretical ones. This discrepancy is because both K eb and K u for the polycrystalline grains in S-poly do not strictly orient along an identical direction but are distributed around the average direction [34,35]. S-100 shows one-step and two-step loops when H is near and perpendicular to the EB direction, respectively. Therefore, H c and H eb can no longer be given by conventional methods similar to S-poly. The angular dependence of magnetic switching field is symmetric about the EB direction, as shown in figure 3(c). The angular dependent behaviors can be fitted by the DW nucleation and propagation model, which has been demonstrated in the epitaxial systems of FeGa/IrMn [13] and Fe/MnPd [14]. Considering an induced fourfold anisotropy K 4 along IrMn <100> and both K eb and K u along IrMn[100], the total energy for the FM layer can be written as E = K4 4 sin 2 2θ − K u cos 2 θ − K eb cos θ − M s H cos (φ − θ). The theoretical switching fields for 90 • magnetic transitions can be derived from the energy gain between the local minima at the initial and final easy axes involved. They are written as H c1−4,c1 ′ −4 ′ = ε 90 • ±(K eb ±Ku) ±Ms(sinφ±cosφ) , where ε 90 • is the 90 • DW nucleation energy and the sign of each term depends on the range of φ as described elsewhere [13,14]. The experimental data can be nicely fitted by the theoretical equations with parameters of K eb = 1.5 × 10 5 erg/cc, K u = 1.5 × 10 4 erg/cc, and ε 90 • = 8.4 × 10 4 erg/cc, which suggests the reversal mechanism of DW nucleation. As shown in figure 3(d)  K u = 0.3 × 10 4 erg/cc, and ε 90 • = 8.7 × 10 4 erg/cc. The angular dependent behaviors of the EB bilayers with an epitaxial IrMn layer can be well described by the model of DW nucleation based on the combined K 4 , K eb , and K u , which implies that an in-plane fourfold magnetic anisotropy is extrinsically induced in the amorphous CoFeB layer. In contrast to the fourfold magnetocrystalline anisotropy in epitaxial FM layers, this fourfold magnetic anisotropy in CoFeB layer is caused by the interfacial exchange coupling of IrMn layer, whose direction may intimately depend on the spin structure of IrMn.
Although the MOKE measurements can indicate the emergency of an extrinsic fourfold anisotropy K 4 in amorphous CoFeB, its strength could not be quantified. Thus, the FMR derivative absorption spectra for these samples are detected at various φ at room temperature and the resonance fields H r are obtained by fitting to a sum of symmetric and antisymmetric Lorentzian functions [36][37][38][39]. For the reference CoFeB single layer, the H r achieves two equal local minima at φ = 0 • and 180 • , indicating a K u along MgO[100], as shown in figure 4(a). For S-poly, the angular dependent H r exhibits a uniaxial symmetry, but the local minimum at φ = 0 • is lower than that at 180 • due to the unidirectional symmetry of K eb , as shown in figure 4(b). The K u induced by EB is collinear with the K eb as often observed in previously studied EB bilayers. The magnetic anisotropies can be quantitatively obtained by fitting to a simplified equation derived from the Landau-Lifshitz equation [40]:  As a result, K 4 = 1.4 × 10 5 erg/cc, K eb = 1.5 × 10 5 erg/cc, and K u = 1.5 × 10 4 erg/cc are obtained for S-100. K 4 = 6.4 × 10 4 erg/cc, K eb = 1.7 × 10 5 erg/cc, and K u = 0.3 × 10 4 erg/cc are obtained for S-110. It should be noted that the measured FMR signal and the derived magnetic anisotropies are of the CoFeB layer but not the IrMn layer because the resonance frequency of an AFM layer is enhanced by the exchange coupling of sublattices and is usually in the terahertz range [41,42]. Our results indicate that the interfacial exchange coupling to an epitaxial AFM layer can give rise to not only a well-known K eb and an accompanied K u , but also a K 4 in the amorphous CoFeB layer. The induced K 4 in S-100 is obviously larger than that in S-110, although both of them possess the identical layered structure. In contrast, the induced K eb are comparable. The K u of S-100 is slightly larger than that of S-110. This is because although the K u caused by the EB is reoriented with the K eb , another contribution of K u originating from the presence of atomic steps due to the miscut of MgO substrates always points to the [100] direction [10].
The magnetic anisotropies induced in the amorphous CoFeB layer can be interpreted by considering the noncollinear 3Q spin structure of γ-IrMn 3 which originates from the stable establishment of the AFM order, since the layer thickness is far larger than the AFM ordering thickness of 5 nm [43]. The in-plane projections of the AFM spins on the (001) surface are aligned along <110>, exhibiting a well-defined compensated AFM surface. The interface roughness may lead to monatomic steps at the AFM surface [23,44], so that the AFM surface shows two kinds of spin configurations with orthogonal orientations on two adjacent atomic terraces. These AFM domains caused by the intrinsic 3Q spin structure of IrMn cannot be eliminated by a cooling magnetic field or a growth magnetic field usually used to induce an EB. Near the DWs of these intrinsic AFM domains, net uncompensated spins can be induced along the monatomic steps along the in-plane four <100> axes, which may exchange couple to the covered CoFeB spins and therefore produce an in-plane K 4 along <100>. In contrast, the monatomic steps along the in-plane four <110> axes cannot engender net uncompensated spins, and therefore not contribute to K 4 [23]. In addition, it is well known that AFM domains can also be extrinsically formed due to the present of defects [45,46]. Even on the same atomic terrace, the AFM domains can orientate orthogonally, which can in the same way contribute to the net uncompensated spins and the induced K 4 along <100>. Different from the AFM domains caused by the monatomic steps, the ones due to the defects can be possibly eliminated by a cooling or growth magnetic field and then display the same spin configuration. In case of H growth applied along [100], as shown in figure 5(a), the AFM spins along [110] and [−110] are energetically equivalent, so the extrinsic AFM domains with orthogonal orientations can exist on one terrace. For H growth along [110], the AFM spins prefer to be aligned perpendicular to the H growth , so the formation of extrinsic AFM domains can be greatly suppressed, as shown in figure 5(b). As a consequence, the net uncompensated spins along the DWs and the induced K 4 in the exchange coupled FM layer remarkably decrease, which can account for the reduced K 4 experimentally observed in S-110. In addition, H growth may break the random distribution of net uncompensated AFM spins along the in-plane four <100> axes by adjusting the ratio of two kinds of AFM domains with different orientations. Consequently, the net uncompensated spins become dominant along [100] for S-100 and along both [100] and [010] for S-110, which therefore results in an EB collinear with the applied H growth .

Conclusions
In summary, we fabricated amorphous CoFeB/epitaxial IrMn bilayers on MgO(001) substrates and a growth magnetic field was applied in the directions of MgO[100] or [110] axes to induce an EB. The MOKE measurements indicate that a larger EB effect is obtained in S-100 and S-110, in comparison with S-poly. The angular dependence of magnetic switching fields for S-100 and S-110 can be fitted by the DW nucleation and propagation model, indicating the presence of an extrinsic fourfold anisotropy K 4 . The FMR measurements show that the specific strength of K 4 in S-100 is larger than that in S-110. Considering the 3Q spin structure of IrMn and two types of AFM domains induced by both monatomic steps and defects, net uncompensated spins are induced along the in-plane four <100> axes, which lead to a K 4 along <100> when exchange coupling to CoFeB layer. Due to the different responses of AFM domains to H growth along [110], the disappearance of the extrinsic AFM domains caused by defects account for the reduced K 4 in S-110.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).