Magnetization process

The relevant quasi-static magnetization curves and corresponding anisotropic magnetoresistance (AMR) responses from non-irradiated and irradiated full films with the exchange bias direction oriented at ±π/4 to the applied magnetic field are shown in Fig. 2. The exchange bias fields for the as-deposited and the fully irradiated samples are H eb,dep = 2.04 kA/m and H eb,irr = 1.7 kA/m, respectively. The maximum AMR ratio AMR max for the as-deposited sample is AMR max,dep = 0.023. AMR max,irr = 0.022 for the irradiated sample is of equivalent value. No noticeable difference in saturation magnetization was detected. In accordance with the imprinted direction of exchange bias, the net magnetization in remanence is M r /M s,±π/4 ≈ 0.7 (Fig. 2(a–d)) for the non-irradiated as for the irradiated sample. The amplitude of the AMR response at the coercive fields indicates a perpendicular alignment of magnetization relative to the applied magnetic field direction during switching. A relative remanent AMR response AMR r /AMR max of AMR r,±π/4 /AMR max ≈ 0.5 is obtained. The AMR amplitude peaks at the coercive field H c with AMR/AMR max close to unity. The findings indicate reversal by coherent magnetization rotation. The coherent rotation of magnetization is affirmed by high resolution magneto-optical Kerr microscopy domain imaging23, where no magnetic domain activity was observed. Analyzing the magnetization response together with the AMR response provides a complete picture of angular magnetization behavior. An ion irradiation induced rearrangement of the equilibrium state of magnetization from −π/4 to −3π/4 with similar magnetic film properties is achieved.

Figure 2 Magnetization curves M(H)/M s = cos (θ) and corresponding magnetoresistance (AMR) AMR(H)/AMR max = sin2(θ) response of an as-prepared full film with the magnetic field H ext aligned under an angle of (a) θ dep = π/4 and (b) θ dep = −π/4 with respect to the initial direction of exchange bias. Corresponding data for an ion irradiated full film with (c) θ irr = −π/4 and (d) θ irr = −3π/4 relative to the rearranged unidirectional anisotropy (π/4 and −π/4 to the original direction of exchange bias). The data for applying a field along the direction of exchange bias is indicated in (a). Corresponding M(H) and AMR curves for structures with a stripe width of (e,f,i,j) 6 μm and (g,h,k,l) 1 μm and with (e–h) head-to-tail-to-head-to-tail (〈+ − + −〉) and (i–l) head-to-head-to-tail-to-tail (〈+ + − −〉) unidirectional anisotropy configurations with the magnetic field H ext aligned perpendicular [(e,g,j,l)] and parallel [(f,h,i,k)] to the stripe axis. The magnetic field direction, stripe orientation and direction of net exchange bias EB net are sketched. The angles of EB dep and EB irr relative to the direction of H ext are indicated (see also Fig. 1). Full size image

Exemplary magnetization and AMR response curves of the patterned thin film with the head-to-tail-to-head-to-tail (〈+ − + −〉, Fig. 1(b)) and head-to-head-to-tail-to-tail (〈+ + − −〉, Fig. 1(c)) alignments of exchange bias for an external magnetic field H ext perpendicular and parallel to the long axis of the stripes are shown in Fig. 2(e–h,i–l), respectively. For the 〈+ − + −〉 structures and applying the external magnetic field perpendicular to the stripe orientation, the bi-modal magnetic structure with the largest stripe width of 6 μm switches at H c ≈ 1.5 kA/m (Fig. 2(e)). The remanent magnetization increases as compared to the single phase material, thus the net magnetization pointing along the median direction of magnetization increases. This indicates an increased tilting of magnetization in the direction perpendicular to the stripe axis. The magnetization loop of the 1 μm stripe width displays similar behavior (Fig. 2(g)). Yet the remanent magnetization increases further, pointing to a further increase of alignment of magnetization perpendicular to the grating’s long axis and the magnetic phase borders. Applying the field parallel to the grating results in a pronounced two-staged magnetization curve for both stripe widths. The two-step magnetic hysteresis loop displays an intermediate magnetization plateau at low external fields (Fig. 2(f)) and the plateau width decreases with decreasing stripe width (Fig. 2(h)) (see also Supplementary Fig. S1). Probing the transversal magnetization component by AMR clarifies the overall magnetization behavior. Setting the external magnetic field perpendicular to the stripes’ long axis leads to an AMR response with a well-defined maximum at the switching field. The decrease of AMR r /AMR max,π/4 for 6 μm and 1 μm stripe widths as compared to the AMR r /AMR max,π/4 values shown in Fig. 2(a–d) confirms the transversal alignment of magnetization relative to the orientation of the grating. For narrower stripes, the remanent and switching ratio AMR r /AMR max,π/4 further decreases. The magnetization straightens perpendicular to the stripes’ long axis. Analyzing the AMR response shows that the net magnetization is tilted away from the originally imprinted ±45° to on average ±38° for a stripe width of 6 μm and down to ±24° for the 1 μm grating. Thus, for the 〈+ − + −〉 configuration the net magnetization and effective exchange bias increases perpendicular to the induced magnetic phase boundaries with smaller feature size.

Different modifications of magnetization reversal behavior are obtained for the highly magnetically charged 〈+ + − −〉 configurations as shown in Fig. 2(i–l). Application of the external magnetic field parallel to the stripes’ long axis leads to an almost instantaneous switching of magnetization for the large stripe width (6 μm, Fig. 2(i)). Notably, a slightly increased effective exchange bias is obtained for 1 μm stripes (Fig. 2(k)). The reversal process displays almost no change in AMR signal at the switching field in accordance with the easy axis loop obtained under a different field angle (+0π in Fig. 2(a)). For the 〈+ + − −〉 configuration, the net magnetization and effective exchange bias increase parallel to the induced magnetic phase boundaries with smaller feature size. With perpendicular field alignment, non-hysteretic hard axis loops without the development of plateaus around zero field are obtained for both stripe widths (Fig. 2(j,l)). The corresponding AMR signals show a clear maximum at zero field close to unity of AMR(H)/AMR max , implying an alignment of magnetization along the magnetic grating at zero magnetic field for the 〈+ + − −〉 configuration. Yet the AMR value is slightly higher and the magnetization is aligned nearly to the stripe axis for the 1 μm stripes. From the AMR response, the tilting of magnetization away from the imprinted ±45° is estimated to be on average ±33° for a stripe width of 6 μm and down to at least ±40° for the 1 μm grating, but the opposite for the 〈+ − + −〉 case.

Magnetization structure

Micromagnetic simulations of the ground-state of the magnetization configurations merely based on the full film magnetic properties are used to quantify the states of magnetization. A summary of the results is displayed in Fig. 3. The profiles of magnetization components across the stripes for the 〈+ − + −〉 configurations show all the characteristics of overlapping Néel wall structures (Fig. 3(a)). With decreasing stripe width, the alteration of m y across the domain wall and the stripe border reduces. Correspondingly, the m x -component of magnetization (Fig. 3(c)) increases. In agreement with the experimental results, the magnetization aligns more perpendicular to the magnetic phase boundaries with decreasing stripe width. For the 〈+ + − −〉 configurations, m y is close to unity even for the greatest stripe width (Fig. 3(b)). This is a direct consequence of the charged 〈+ + − −〉 magnetization structure, leading to long tail Néel wall structures. The magnetization aligns along the stripe axis. The magnetization component m x perpendicular to the stripe axis varies only slightly (Fig. 3(d)). The offset of m x from zero is attributed to the differences in exchange bias amplitude of the non-irradiated and the irradiated phase. In accordance with the zero field data displayed in Fig. 2(i,k), m y is close to unity for the 〈+ + − −〉 configuration (Fig. 3(e)). Comparing the experimentally (see Fig. 2(e,g)) obtained integral values of m x with the results of the micromagnetic simulations for the 〈+ − + −〉 configuration from various stripe widths, nearly perfect agreement is obtained (Fig. 3(f)). This proves the accuracy and the validity of the micromagnetic simulation data in order to describe the magnetization behavior. The lateral directions of exchange bias together with the calculated alignment of magnetization for the 〈+ − + −〉 and 〈+ + − −〉 structures are shown in (Fig. 3(g)). The special micromagnetic structures also modify the magnetization processes in a unique way.

Figure 3 Calculated magnetization components (a,b) m y and (c,d) m x for the (a,c) 〈+ − + −〉 and the (b,d) 〈+ + − −〉 stripe configuration, varying across the stripes. The individual stripe widths are indicated. Corresponding average magnetization components m y and m x for the 〈+ + − −〉 and 〈+ − + −〉 configurations are given in (e,f), respectively. (g) Exemplary data of the calculated magnetization configuration across the magnetic phase boundaries for a stripe width of 1 μm for the 〈+ − + −〉 and 〈+ + − −〉 configuration. The orientation of stripes and EB net is sketched (H ext = 0). Full size image

Magnetic domain behavior

The variable magnetic reversal behavior of the magnetic domain wall loaded parts is demonstrated by high resolution magneto-optical Kerr effect microscopy in the longitudinal mode23. The reversal modes perpendicular and along the stripe axis for a stripe width of 1 μm are shown in Fig. 4 (for a stripe width of 6 μm see Supplementary Fig. S2).

Figure 4 Magnetic domain behavior for the (a–i) 〈+ − + −〉 and the (j–r) 〈+ + − −〉 configuration with magnetic field orientation parallel to the stripe axis. The stripe width is 1 μm. The external magnetic field axis (H ext ) and the magneto-optical sensitivity axis (||) are indicated. Net directions of magnetization for the whole structure are exemplarily sketched as hollow arrows. The orientation of stripes and EB net is sketched in (b,k). The direction and amplitudes of H ext are indicated. Full size image

With small stripe width and high density of imprinted domain walls, the interaction between the magnetic phases leads to fundamental changes in the magnetization reversal behavior as compared to a single phase magnetic thin film. For the 〈+ − + −〉 configuration with the magnetic field parallel to the grating (compare to Fig. 2(h)), the magnetization distribution unfolds by the movement of a superdomain wall (SDW) across the stripes below a threshold field (Fig. 4(c)). The magnetic charge stabilized structure is then stable over a wide magnetic field range (Fig. 4(c–g)). Generation and annihilation of the magnetically modulated structure takes place by magnetization rotation in the irradiated and the non-irradiated stripes. Nonetheless, limited low angle domain wall motion across the stripe borders occurs in the intermediate low field regime (Fig. 4(d–f)). The charge stabilized magnetization regime coincides with the low permeability central regime displayed in Fig. 2(h).

For the 〈+ + − −〉 configuration with the alignment of net magnetization along the grating, a very different reversal behavior is observed (Fig. 4(j–r)). With the magnetic field aligned along the grating of exchange bias (see Fig. 2(k)), the magnetization first rotates and then forms a modulated magnetization structure. The magnetization unfolds to the modulated structure close to the magnetic switching field (Fig. 4(m,n)). Yet reversal takes place by switching of the magnetization in individual stripes (Fig. 4(o,p)). The unfolding occurs through individual stripe reversal (Fig. 4(m–o)) in a non-collective way. No low angle domain wall motion across the stripes takes place in the intermediate low field regime.

Domain wall dynamics

The dense magnetic domain configurations also alter the dynamics of magnetic properties significantly. For dense domain wall gratings the overall dynamics are dominated by the domain walls and not the matrix phase. The dynamic permeability spectra of the samples were obtained by pulsed inductive microwave magnetometry (Fig. 5). For the data shown the films are oriented with the dynamic pulse field perpendicular to the net magnetization, aligned parallel for 〈+ − + −〉 to the stripe long axis, respectively perpendicular for 〈+ + − −〉. For the 〈+ − + −〉 structure, two distinct regions occur (Fig. 5(a,c)). Above a negative and positive threshold field, the precessional frequency displays a regular Kittel mode with a collective single precessional frequency f res,k . The Kittel region reflects the single domain status of the sample (Figs 2(h) and 4(a–c,g–i)). Yet the central region, where the grated multi-domain wall state is in place (plateau region in Figs 2(h) and 4(c–g)), displays a unique and strongly modified dynamic magnetization behavior. Two distinct precessional frequency peaks f res,w and f res,b are seen in Fig. 5(a). Both precessional frequencies exhibit a maximum at zero magnetic field. The slight asymmetry of the precessional frequency dependence in the bi-modal region and the frequency minima reflect the asymmetric effective exchange bias fields of the individual stripe fractions. This also shows in the slight shift of extrapolated Kittel modes from both high field branches.

Figure 5 Dynamic permeability spectra maps μ(| f |, H ext ) of films with (a) 〈+ − + −〉 and (b) 〈+ + − −〉 exchange bias modulation at a stripe width of 1 μm. (c,d) Dominant precessional frequencies derived from the data in (a,b). The dynamic Kittel behavior is fitted. H ext is applied parallel to the stripe axis. The direction of the pulsed magnetic field H p is indicated. (The two other corresponding configurations are shown in Supplementary Fig. S3). Full size image

For the 〈+ + − −〉 structure with nearly homogeneous magnetization (Fig. 3), only a single Kittel mode is seen for the complete magnetic bias field range (Fig. 5(b,d)). In agreement with the effective net exchange bias along the stripe axis in the stripe 〈+ + − −〉 structures (Fig. 2(h)), the curve is shifted to negative field values.

Clarity on the bi-modal dynamic behavior is obtained from direct comparison of dynamic inductive and modeling data. Agreement of simulation and experiments over the whole frequency range is demonstrated in Fig. 6. The data is normalized to the permeability amplitude of the higher frequency mode at f res,b . A bi-modal dynamic response is observed for all stripe widths (Fig. 6(a)). Both modes shift to higher frequencies for smaller stripe widths and increasing domain wall density and magnetic charge density. With the increase of the domain wall density, the amplitude of the lower frequency modes at f res,w relative to f res,b increases strongly, indicating a spatial localization of the low frequency mode at the imprinted domain walls of the grated film structure. This assumption is proven by analyzing the calculated spatial distribution of the dynamic magnetization modes for a stripe width of 1 μm, as shown in Fig. 6(b) (for corresponding time domain data of m(t) see Supplementary Fig. S5). A spatial localization of the low frequency mode f res,w in the core of the domain walls at the stripe borders becomes obvious. The mode localization results from the formation of a potential well for the dynamic modes in the inhomogeneous internal magnetic field of the domain wall, similar to the edge regions of nearly saturated magnetic stripes24. The overall amplitude of the high frequency mode f res,b , clearly located in the domain wall tail region in the center of the individual stripes, is significantly lower. An analysis similar to Fig. 6(a) but now for the domain wall core and center of the stripes is shown in Fig. 6(c). The overall excitation inside the domain walls is much higher than in the stripes. Only a weak crosstalk from the stripe into the domain wall region (and vice versa) is seen from the data. A channel with reduced dynamic activity bordering the domain walls can be identified in Fig. 6(b). Yet the total contribution of the stripe bulk mode f res,b to the overall dynamic behavior Fig. 6(b) is still comparable to the domain wall mode contribution at f res,w due to the limited volume of the constricted domain walls. Thus, in agreement with the experiments, the contributions from the domain walls increase and dominate for high domain wall densities. A conclusive comparison of the exhibited frequencies of the modes is displayed in Fig. 6(d), confirming the consistency of the experimental and modeling results.