Domain wall asymmetries in Ni81Fe19/NiO: proof of variable anisotropies in exchange bias systems

Multiple changes in the internal structure of magnetic domain walls due to alterations of the interfacial coupling across the ferromagnetic/antiferromagnetic interface are reported for Ni81Fe19/NiO exchange coupled films. Depending on the antiferromagnetically induced anisotropy, three different types of domain walls are observed. Cross-tie domain wall structures of decreased vortex to anti-vortex spacing develop with the addition of a thin antiferromagnetic layer. For exchange biased samples strong asymmetries in domain wall structure occur for the ascending and descending branch of the magnetization loop. For the descending branch a symmetric 180° Néel wall develops, whereas a folded cross-tie domain wall structure forms during magnetization reversal along the ascending loop branch. The novel type of ‘zig-zagged’ cross-tie wall is characterized by cross-ties reaching differently into the surrounding domain areas. The wall alterations indicate the existence of bi-modal coupling strengths in exchange coupled systems, which is in accordance with models of exchange bias that assume pinned and unpinned spins at the ferromagnetic/antiferromagnetic interface.


Introduction
Exchange biased magnetic multilayers are one of the key components in current high-sensitivity magneto-resitive devices [1]. The exchange bias effect is associated with a magnetic loop shift [2] that occurs in coupled ferromagnetic/antiferromagnetic (F/AF) thin films. Despite the technological relevance of exchange biased systems in spintronic applications, and extensive experimental as well as theoretical investigations, the nature of exchange coupling between the spins of an F layer and an adjacent antiferromagnetic AF layer is still under discussion. An exchange bias field H eb [3]- [5] is found, the value of which can be predicted by different theories [6]- [12]. Recent experimental evidence [13,14] indicates that for many material systems only a small fraction of uncompensated pinned spins at the interface between the F and AF contributes to the exchange bias effect. In addition, a larger remaining fraction of coupled but rotatable spins exists, which does not contribute to the magnetic loop shift. Hence, for an alignment of the F layer magnetization along the exchange bias direction, the pinned and unpinned interfacial moments are aligned in parallel. For the state of antiparallel alignment of F layer magnetization and unidirectional anisotropy, the pinned and unpinned moments are oriented antiparallel. As a consequence, the effective coupling or AF-induced anisotropy acting on the F layer should change with reversal and alignment of the F layer relative to the direction of exchange bias.
One indication of such an interaction in exchange biased samples is derived from magnetometry and magnetoresistance measurements [15]- [18] as well as magnetic domain observations [19]- [25], which reveal asymmetric remagnetization processes. Nevertheless, no direct observation of the magnetic domain wall structure itself has been made so far.
For single-layer F films, it is known that the domain wall structure depends on the F layer thickness t F and magnetic anisotropy [26]. Essentially, three different types of 180 • domain walls are observed in magnetic films: symmetric Néel walls, cross-tie walls and asymmetric Bloch walls. Cross-tie walls are characterized by an alteration of Bloch-like vortex and antivortex transitions along the domain wall segmented by 90 • Néel walls of opposite chirality (figure 1). As the specific energy of a 90 • Néel wall is significantly lower than that of a 180 • Néel wall, the complicated 90 • domain wall network of the cross-tie wall saves energy compared with a regular 180 • domain wall. In the cross-tie arrangement the magnetic flux of the long-range magnetic tails is partially closed in the vicinity of the walls. The occurrence of cross-tie walls in low anisotropy Ni 81 Fe 19 films is limited to a narrow t F range. Below t F ≈ 10 nm 180 • Néel walls and above t F ≈ 100 nm asymmetric Bloch walls form. In the intermediate F layer thickness of cross-tie wall stability, the cross-tie spacing λ ct scales reversely with the magnetic anisotropy energy constant K u,eff or anisotropy field H k,F . This behavior is found experimentally [27]- [29] and only basic features can be modeled theoretically [27,28]. For a given film thickness, the experimentally found dependency of λ ct with anisotropy of a single F layer is where the exponent n depends on the F layer thickness [28]. This relation provides merely a rough guidance for the change of λ ct with anisotropy and is only valid for small values of anisotropy. Nevertheless, λ ct serves as a sensitive measure of changes in the effective anisotropy in ferromagnetic thin films. Above a certain value of anisotropy the cross-tie wall transforms into a symmetric 180 • Néel wall [29]. This is due to an increased energy contribution from the Bloch lines inside the domain wall with smaller cross-tie spacing, i.e. increased Bloch line density.
In this paper, we directly analyze the magnetization structure of cross-tie domain walls with constant F layer thickness, but varying NiO layer thickness t NiO . The measured cross-tie spacing is used as an indicator for the effective AF induced anisotropy acting on the F layer. As demonstrated, the observation of the domain wall structure opens the unique opportunity to probe changes in the effective magnetic anisotropies during reversal, simultaneously for the switched and non-switched regions. From the alterations in domain wall structure and the reversal asymmetry we are able to derive conclusions on the effective anisotropy contributions arising from the AF layer. The cross-tie domain wall structure acts as a micromagnetic sensing tool for variable anisotropy states in exchange coupled systems.

Experimental details
Si/SiO 2 /Ta(4 nm)/Ni 81 Fe 19 (30 nm)/NiO(0-50 nm) F/AF structures were prepared by magnetron sputtering in a high vacuum sputter system with a base pressure below 2 × 10 −7 mbar at an Ar pressure of 8 × 10 −4 mbar. The Ta seed layer ensures a 111 -textured growth of the polycrystalline films. The deposition rate for the NiO layer was 1.7 nm min −1 . The F uniaxial anisotropy axis and the exchange bias direction were set in an applied magnetic in-plane field of H dep = 20 kA m −1 during film deposition. No post-annealing was performed. Inductive magnetometry at 10 Hz was used to characterize the magnetic properties of the films. The formation of ferromagnetic domains was imaged by real-time magneto-optical Kerr microscopy [26] in the longitudinal mode through the covering NiO AF layer. All experiments were carried out at room temperature.

Magnetometry
Hysteresis loops for the pure F film and double layers with two different NiO thicknesses are displayed in figure 2. For the thinnest NiO layer (t NiO = 5.0 nm, figure 2(b)) an increase in coercivity H c,EA along the easy axis (EA) is seen. This change is accompanied by the formation of a double-stage magnetization curve visible in the hard axis (HA) loop. A similar two-step magnetization reversal was also reported in [30]. This S-shaped HA loop was interpreted as an AF induced uniaxial anisotropy field H k,AF , only existing at low fields and 'unsnapping' at higher magnetic fields [30,31]. With increasing AF layer thickness, t NiO = 30 nm is shown in figure 2(c), a magnetic loop shift is observed along the EA. The coercivity has again decreased relative to the sample with t NiO = 5 nm. From the HA loop the effective field consisting of anisotropy field H k,F and exchange bias field H eb acting on the F layer could in principle be derived. However, comparing the effective field to the value of H eb,EA , as derived from the EA loop shift, a discrepancy becomes obvious, which we treat as an AF induced uniaxial anisotropy field H k,AF . From this we extract the effective anisotropy fields H k,eff acting on the F layer by taking the following contributions into account [31]: The dependences of H eb,EA , H k,eff and the coercivity values H c,EA with t NiO are summarized in figure 2(d). The coercivity peaks at the onset of exchange bias at an AF thickness of t NiO = 10 nm and then decreases with the occurrence of exchange bias. This dependency can be interpreted as a transformation of a 'mobile' AF spin structure into an AF 'static' domain structure with stabilization of the AF magnetization [10,32] with increasing AF thickness. Correlated to the coercivity is the dependency of H k,eff , which peaks with H c,EA and decreases with the onset of H eb,EA . Even for a stable exchange bias, a uniaxial-like anisotropy contributes to the magnetization reversal. A detailed discussion of the different anisotropy contributions in NiFe/NiO layers can be found in [31].

Domain wall observation
Additional evidence for the existence of an AF induced uniaxial-like anisotropy contribution to the reversal process is derived from the magnetic domain wall structure in the bilayer films. Domain images of a single Ni 81 Fe 19 layer and a Ni 81 Fe 19 /NiO (5 nm) structure are shown in figures 3(a) and (b), respectively. Adding the thin NiO layer, a drastic decrease in cross-tie spacing of the F layer from λ ct,F = 11.5 µm down to λ ct,F−AF = 2.6 µm for the exchange coupled but zero loop shift sample is found. The reduction in λ ct,F is due to an increase of effective anisotropy H k,eff with the addition of the NiO layer and confirms the additional anisotropy contribution to the F layer that arises from the AF layer. The narrow Bloch line spacing in the cross-tie wall is already close to the stability limit of cross-tie wall formation. This is evident in figure 3(b), where a segment of the domain wall film has already transformed into a regular symmetric 180 • Néel wall. A similar lower limit of cross-tie spacing (λ ct,min ≈ 3 µm) was found for amorphous FeCoBSi single-layer films with variable uniaxial anisotropy [29]. This lower limit can be undercut for confined structures [33], in which the spreading of the Néel wall tails is limited.
Additional transformations in the domain wall structure are observed with further increasing NiO thickness. For the two magnetization reversal paths along EA an asymmetry in domain wall type is found. In figures 4(a) and (b), the domain wall structures in a Ni 81 Fe 19 /NiO (30 nm) bilayer during the magnetic switching events at H c1 and H c2 (see EA loop in figure 2(c)) are shown. During reversal, neither signs of coherent or incoherent rotation of magnetization, nor signs of loop asymmetry are found. However, for the descending loop branch (figure 4(a)) no cross-tie domain wall structure is visible. Due to a high effective anisotropy acting on the F layer, a symmetric 180 • Néel wall instead of a cross-tie wall develops. This observation is consistent with an increase in effective anisotropy beyond the case shown in figure 3(b). For the ascending loop branch, however, the reversal process takes place by the movement of an almost regular cross-tie wall. The cross-tie period of λ ct,F−AF = 7.5 µm lies between the low and high anisotropy cases shown in figures 3(a) and (b), respectively. This clearly indicates that the average effective anisotropy, which acts on the F layer along the ascending loop, branch is lower as for the descending loop branch. Nevertheless it is still higher than for the single F layer case with narrow cross-tie spacing. The alteration in domain wall structure in dependence of the magnetic history verifies the existence of asymmetric AF anisotropy contributions that change with the reversal of the ferromagnetic layer and which lead to the observed asymmetric domain wall behavior.
In addition, the cross-tie wall structure is further modified as compared with the regular wall presented in figure 1. Notably, the cross-ties extend further into the surrounding domain of the non-switched portion of the film (bottom domain in figure 5(a)), indicating different effective anisotropies at both sides of the domain wall. A detailed sketch of the asymmetrically shaped cross-tie wall similar to figure 1 is given in figure 5(b). The asymmetrically shaped domain wall proves that with the switching of the F layer the effective coupling field also changes. The asymmetric magnetization and effective anisotropy distribution in the distorted cross-tie structure is also evident from the 'zig-zagging' of the domain wall. The wall is folded by an angle ≈ ±10 • relative to the net direction of the wall. The asymmetry in the domain wall structure is qualitatively illustrated by differently tilted magnetization vectors on both sides of the wall in figure 5(b). The values of the effective anisotropy before and after switching, respectively on both sides of the domain walls, cannot be determined directly from the images. However, from simple micromagnetic arguments, by minimizing the magnetic charges across the domain wall segments and assuming a symmetric anisotropy energy contribution from both sides of the domain wall, the effective magnetic anisotropy ratio in the domains can be derived. It is expressed by where K u,eff1 , K u,eff2 , and H k,eff1 , H k,eff2 are the effective anisotropy energy constants, respectively magnetic anisotropy fields, of the regions surrounding the domain wall. 1 and 2 are the corresponding angles of magnetization of the cross-ties as labeled in figure 5. With a folding angle = 10 • , i.e. a change in magnetization angle of ± relative to the regular cross-tie wall configuration ( 1 = 2 = π/4), a change of anisotropy during switching by a factor of 2 is derived. Hence, the novel type of folded cross-tie wall directly evidences the modification of the effective anisotropy and the simultaneous occurrence of bi-modal anisotropy states during the switching of magnetization in the exchange biased ferromagnet.

Summary
In conclusion, we identified drastic changes of the internal domain wall structure in exchange coupled thin films. The observed changes in the internal ferromagnetic domain wall structure are concurrent with varying anisotropy contributions from the AF layer in Ni 81 Fe 19 /NiO films. Different types of characteristic wall structures form during magnetization reversal along the forward and recoil branches of the hysteresis loop for films exhibiting exchange bias. Asymmetric anisotropy fields acting on the F layer during reversal induce an asymmetrically jagged type of cross-tie domain wall structure. This wall folding indicates the existence of unstable AF magnetization contributions, resulting in changes in the effective anisotropy. 8 This is the first direct observation of domain wall transformations during magnetization reversal due to antiferromagnetic exchange coupling. The domain walls act as an indicator for variable anisotropy changes in F/AF thin film systems.