Tunable Perpendicular Magnetoresistive Sensor Driven by Shape and Substrate Induced Magnetic Anisotropy

Control of magnetization reversal processes is a key issue for the implementation of magnetic materials in technological applications. The modulation of shape magnetic anisotropy in nanowire structures with a high aspect ratio is an efficient way to tune sharp in‐plane magnetic switching. However, control of fast magnetization reversal processes induced by perpendicular magnetic fields is much more challenging. Here, tunable sharp magnetoresistance changes, triggered by out‐of‐plane magnetic fields, are demonstrated in thin permalloy strips grown on LaAlO3 single crystal substrates. Micromagnetic simulations are used to evaluate the resistance changes of the strips at different applied field values and directions and correlate them with the magnetic domain distribution. The experimentally observed sharp magnetic switching, tailored by the shape anisotropy of the strips, is properly accounted for by numerical simulations when considering a substrate‐induced uniaxial magnetic anisotropy. These results are promising for the design of magnetic sensors and other advanced magnetoresistive devices working with perpendicular magnetic fields by using simple structures.


Introduction
Precise control of magnetic domains and magnetization switching processes in ferromagnetic materials plays an essential role in emerging spintronic technologies. The possibility to induce sharp magnetic reversals at a given switching field has been the target of intense research because of their considerable potential for use in memory and sensing devices. [1,2] Among many DOI: 10.1002/adsr.202200042 different approaches, the anisotropic magnetoresistance (AMR) effect has been widely used to detect the variation of micromagnetic configurations and reversal processes in a large variety of magnetic structures. [3][4][5][6] In particular, magnetic sensing devices based on magnetoresistive effects have attracted large attention in the field of biosensing owing to its design simplicity, easy integration, and relatively large sensitivity as compared with other approaches. [7] Magnetoresistive sensors have generally been manufactured on structures with in-plane magnetic anisotropy. Sensing devices are usually patterned into stripes with high aspect ratio (nanorods or nanowires) to acquire tunable magnetic properties due to their shape anisotropy. [8][9][10] However, the sensitivity of such devices is limited by their reduced effective sensing area, and complex structures involving multi-contact strip arrays, have to be used in order to enhance the sensor surface. [11] The development of perpendicular magnetoresistive devices considered of great technological relevance for sensing and memory applications, is much more challenging. Materials with perpendicular magnetic anisotropy may enable an effective solution although they usually require complicated multilayered stacks [12] or complex structures. [8] In particular, permalloy nanowires and films grown on specially patterned groove-substrates appear as a very powerful technique for single cell detection showing the highest sensitivity for out-of-plane magnetic fields. [13,14] Here, we investigate anisotropic magnetoresistance effects on a series of permalloy strips of different widths and thicknesses for applied magnetic fields perpendicular to the strip plane. Sharp anomalous peaks in the magnetoresistance curves are observed, indicative of an abrupt magnetization reversal mechanism. We show that the switching field where the abrupt magnetization reversal occurs can be tuned by controlling the shape anisotropy created through the width/thickness ratio. Different possible scenarios accounting for the observed effects such as external field misalignment or the existence of magnetic anisotropies are analyzed via micromagnetic simulations. Simulations and experiments indicate that the sharp magnetoresistance changes obtained at certain out-of-plane magnetic fields can be attributed to substrateinduced uniaxial magnetic anisotropy.

Results and Discussion
Permalloy thin films of different thicknesses t = 10 − 300 nm were grown by sputtering on LaAlO 3 single crystal substrates. Strips of different widths w = 1 − 100 μm and lengths L = 100 − 200 μm were fabricated by photolithography and lift-off techniques. Processing details can be found in the Methodology Section. Figure 1a shows a schematic representation of the transport measurement configuration along with a scanning electron microscopy (SEM) image of a Py strip of t = 30 nm and w = 50 μm. Figure 1b shows a schematic representation of Py strip arrays patterned for magnetic measurements and optical microscopy images of two arrays with strips of t = 25 nm w = 10 μm and 100 μm.

Figure 2a
shows the magnetization hysteresis loops for two Py un-patterned films of thickness t = 10 nm and 300 nm with in-plane (IP) and out-of-plane (OOP) applied magnetic field. For both films, the saturation occurs at much higher magnetic field for the OOP configuration (μ 0 H s ≈ 1000 mT) than for the IP configuration, a clear sign of the dominant in-plane anisotropy imposed by the sample's geometry. Insets show magnetic force microscopy (MFM) images obtained for Py films of t = 30 nm and 300 nm. In the thinner film, large in-plane magnetic domains are separated by Néel walls. Increasing the film thickness leads to an out-of-plane component of the mainly in-plane magnetization, thus forming stripe domains separated by a Bloch-type domain wall. [15] Figure 2b,c shows a close look of IP and OOP hysteresis loops at low fields. The IP magnetization of the 10 nm film exhibits a very sharp square loop with a saturation field of 0 H s ≈ 1 mT and a coercive field of 0 H c ≈ 0.5 mT. The 300 nm film shows a nearly reversible linear decrease of the magnetization from its saturated value at 0 H s ≈ 25 mT and a square loop at low fields with 0 H c ≈ 2.5 mT. This magnetic response, typically observed in Py films above a critical thickness, has been ascribed to the presence of a perpendicular anisotropy favoring the formation of a stripe domain structure as revealed by magnetic-force microscopy images (see bottom inset of Figure 2a). For the OOP configuration (Figure 2c), coercive fields of 0 H c ≈ 10 and 1.5 mT are obtained for the 300 and 10 nm films, respectively. It is interesting to note the existence of a small hysteresis loop for the 10 nm-thick sample that could be attributed to either a small in-plane component of the applied field or the presence of an induced out-of-plane uniaxial anisotropy. The influence of the sample's width on the OOP hysteresis loop is analyzed in Figure 2d where we compare the low field hysteresis obtained for arrays of strips with w = 10 μm, w = 100 μm and an unpatterned film of the same thickness. We find that the coercive field of the strips is higher than that of the un-patterned film and increases as w decreases. This trend, which will be further discussed in the following section, can be ascribed to demagnetizing effects.

Anisotropic Magnetoresistance of Permalloy Strips
Magnetoresistance (MR) measurements are used to characterize the magnetic behaviour of patterned Py strips. According to the Anisotropic Magnetoresistance (AMR) effect, the electrical resistance of a monodomain magnetic structure depends on the orientation of the magnetization with respect to the current direction as follows: [16] with 90°− being the angle between the magnetization and the current, while R ⊥ and R ∥ are the resistances when the magnetization is perpendicular ( = 0 o ) and parallel ( = 90 o ) to the current, respectively. Figure 3a shows the variation of the magnetoresistance as a function of the angle , between the out-of-plane z direction and a 100 mT applied magnetic field as indicated in the sketches, obtained for a strip of thickness t = 10 nm and width w = 5 μm. Results for rotation parallel and perpendicular to the applied current direction are plotted. Nearly invariant resistance values are obtained for a wide range of angles, associated to a saturated IP magnetization which is either parallel (R ip ∥ = 543 Ω) or per-pendicular (R ip ⟂ = 531 Ω) to the current. Sharp magnetoresistance peaks/dips appear close to = 0 o and 180 o , i.e., OOP, as a consequence of rapid magnetization rotation inside the sample plane resulting from the shape anisotropy. Figure 3b shows the magnetoresistance curves obtained for the same strip by sweeping the applied magnetic field along the three principal directions defined by the sample geometry. i.e., magnetic field OOP, IP perpendicular to the current and IP parallel to the current (see insets and Figure 1a). The variation of the resistance for the different configurations of applied field can be associated to the AMR effect with a coherent rotation of the magnetization, considering that the mean angle between the current and the magnetization can be determined from the hysteresis loops according to the following equation: [17] where M(H) is the magnetization for a given applied field and M sat is the saturation magnetization. According to the hysteresis loops shown in Figure 2a, the IP magnetoresistance (closed symbols) changes abruptly at the coercive field and corresponds to a maximum disorder of the magnetic domain distribution. [18] For the OOP configuration, a  much smoother magnetoresistance variation is observed which can be associated to the wide hysteresis loop obtained for this configuration (open symbols in Figure 2a). Strikingly, for this particular configuration, in addition to the main magnetoresistance effect associated to a coherent magnetization rotation, two symmetrical abrupt magnetoresistance jumps appear at the switching field 0 H sw ∼ ± 60 mT. Similar jumps in the magnetoresistance have been reported in elongated ferromagnetic nanowires for IP magnetic field applied along its easy axis, [9,19] and attributed to a sharp switching of the magnetic moment due to a curling rotation. [20][21][22][23][24] In order to elucidate the nature of the MR jumps appearing in the Py strips, we have systematically investigated the OOP magnetoresistance curves obtained for strips of different geometries. Figure 4 shows the magnetic field dependence of the OOP magnetoresistance ratio MR(%) = (R(H)-R(0)) ×100/R(0), where R(0) is the resistance at zero field and R(H) the resistance in an external field H, obtained for a series of strips of different widths, w, with thicknesses t = 10 and 300 nm at 100 K. Abrupt MR changes of ≈ 0.2 -1.6 % are identified for all the strips. Similar MR curves are obtained at 200 and 300 K (see Figure S1, Supporting Information) although the MR value changes and, as expected, the value of H sw decreases as the temperature increases. It is worth pointing out that the switching field where the magnetoresistance jumps occur lies in the range 0 H sw ≈ ± 5-200 mT and strongly depends on the strip shape anisotropy. Figure 5a shows the evolution of H sw , with the strip width for samples of different thicknesses. H sw is almost independent of the width for the strips with t = 300 nm whereas changes about one order of magnitude with increasing the strip's width from 1 to 100 μm in the case of thinner strips with t = 10 − 30 nm. We have included in the figure the coercive fields obtained from the hysteresis loops shown in Figure 2d for strips of w = 10 and 100 μm (star symbols) which are in good agreement with the H sw (w)  dependence obtained from MR measurements. In Figure 5b, the switching field H sw is plotted as a function of w/t and shows a collapse of the datapoints onto a single trend indicating that demagnetization effects play an important role in determining the switching field.

Modelling of the Anisotropic Magnetoresistance
To gain a deeper understanding of the experimental results, we performed complementary micromagnetic and electrical transport simulations to evaluate the resistance change of the Py strips at different applied magnetic field values and directions. The modeled system consists of a ferromagnetic strip with saturation magnetization and exchange constant corresponding to conventional Ni 80 Fe 20 alloy, absent of magnetocrystallineanisotropy and without any inhomogeneity or defect. The technical details concerning the micromagnetic simulations can be found in the Ex-perimentalSection. Figure 6a shows the magnetization hysteresis loops along the principal axis defined by the sample geometry (see inset of Figure 1a). Figure 6b  The results of the simulations are in qualitative agreement with the experimental curves shown in Figures 2 and 3. However, for the OOP configuration (see green curves in Figures 3b  and 6b), the numerical findings fail to reproduce the abrupt magnetoresistance jumps observed experimentally. Such sharp resistance changes could be naturally accounted for by a sudden rearrangement of in-plane domains, with a disordered domain distribution at low fields switching to ax-oriented domain distribution at high fields. Indeed, in thin films, the large demagnetization field in theẑ direction confines the magnetization to lie in the plane of the film. This is further confirmed in the inset of Figure 6c where the magnetization angle is plotted as a function of the magnetic field angle for 100 mT. The OOP component of the magnetization remains small (\leq5°) irrespective of the value of , and is not correlated with the angular dependence of the sample's resistance. This reinforces the idea that the resistance changes observed during the OOP-applied field sweeps are likely associated to a change of the IP magnetic domains arrangement.
In order to unveil the origin of this unexpected reversal of magnetization under OOP field, let us focus first on the switching mechanism for IP-applied fields as obtained by the simulations.  to the current direction. It can be observed that the switching mechanism consists of a buckling mode where the domains twist before flipping. At a high negative magnetic field, only one single domain exists and the strip resistance is minimal (maximal) for perpendicular (parallel) configuration. By increasing the field, the initial single domain progressively breaks into several domains with large components perpendicular to the applied field, leading to an increase (decrease) of the resistance. In the perpendicular case (Figure 7a), buckling domains are along the shape anisotropy axis and therefore are much more stable (visible between −5 and 3 mT) than for the parallel case (visible between 1 and 2 mT). A slight increase of magnetic field leads to the reversal of the magnetic domains with an abrupt change (reduction for perpendicular and increase for parallel case) of resistance.
In the following, we discuss two possible mechanisms leading to a fast IP rotation of the magnetization triggered by sweeping the OOP-applied field.
First, the sharp resistance change observed in the OOP magnetoresistance curves may arise from the existence of a small misalignment of the applied field, i.e., ≠ 0°. [25] In this case, the magnetization reversal should occur for a magnetic field H OOP sw ( ) = H IP sw sin −1 ( ), where H IP sw is the in-plane coercive field. In order to explore this possibility, we simulated the MR response for different amplitudes of misalignment by tilting the applied field toward the direction of the current (Figure 8a and perpendicular to it (Figure 8c). Simulations performed with a small inplane component of the magnetic field ( Figure 8a) show a clear jump of MR associated to a fast in-plane reversal of the magnetization, and for both configurations the calculated switching fields follow the expected angular dependence as displayed in the inset of Figure 8a. It is worth noting that the abrupt transition corresponds to an increase of resistance (domains align parallel to the current) in the case of a B x component misalignment while the opposite is observed for a B y component. This is consistent with the buckling mechanism as described for the IP magnetization reversal in Figure 7.
For the sake of comparison, panels b and d of Figure 8 show the experimental MR curves measured under the same conditions. Results show two important differences. First, the predicted sin −1 ( ) dependence is not observed in the experimental results (see inset of Figure 8b). Second, in the case of a B y component (Figure 8d), switching deeps are obtained instead of the peaks predicted by the numerical model in Figure 8c. This discrepancy between simulations and experiments suggests that an unwanted magnetic field misalignment does not provide a satisfactory explanation for the experimental results.
A possible alternative mechanism giving rise to an IP magnetization switching triggered by an OOP external magnetic field could be magnetic anisotropy, so far ignored in our model. While both "bcc" and "fcc" Py structures have negligible magnetocrystalline anisotropy, Py thin films may exhibit an important perpendicular magnetic anisotropy (PMA). This induced magnetic anisotropy can be attributed to the internal stress coupled with non-zero magnetostriction coefficient and/or from columnar grains separated by nonmagnetic intergrain boundaries. [26] For films thicker than a critical thickness (≈200 nm), the stressinduced anisotropy overcomes the shape anisotropy and the PMA becomes visible as Py domains arrange themselves in stripes (as indeed seen in the bottom inset of Figure 2a). For films below the critical thickness, the shape anisotropy masks the effect of the induced uniaxial anisotropy but the latter is expected to be stronger as the stress induced by the substrate tends to relax in thicker films. Indeed, the PMA is expected to evolve as t −2 for thin films. [27] For 50 nm-thick films or thinner, the anisotropy coefficient may be as high as K u1 =100 kJ m −3 without leading to any nucleation of stripes domains because of the strong shape anisotropy. However, we postulate that an induced anisotropy can give rise to an IP magnetization reversal triggered by OOP magnetic field if the direction of the uniaxial anisotropic vector slightly deviates from the normal direction to the film. Such a slight deviation from the perfectly OOP case is possible notably because of misalignment between the sputtering source and the sample [28][29][30][31] or due to the presence of stray field in the vicinity of the sputter head. [32] In addition, surface magnetic anisotropy and/or additional magnetostriction anisotropy may be induced at the interface between the Py film and substrate or a cap layer. [33,34] To qualitatively illustrate how the magnetic anisotropy can account for the OOP AMR response observed experimentally, we will assume a uniaxial anisotropy with an easy-axis u k in the xz plane with an angle from the OOP direction. The intensity of the associated anisotropy field H k can be approximated by with K u1 the anisotropy energy density. The IP component of the anisotropy field depends both on IP and OOP components of the magnetization Therefore, for a positive applied field (and so m z > 0), the IP effective field will favor domains aligned in the direction of u k while the opposite is true for a negative OOP external field, leading to the possibility to induce an IP magnetization switch. In order to favour a magnetic reversal, the x-directed domains have to sustain an anisotropy field oriented in the opposite direction with a large enough intensity (B ≈ 1 mT for the Py bars in this work). Based on Equation (4) and assuming a zero in-plane coercive field, the anisotropy field is opposed to the IP magnetization if m z < 0 and |m z /m x | > tan ( ), which can be approximated by the condition 90°− > with the magnetization angle with respect to the OOP direction.
An example is illustrated in Figure 9a corresponding to the simulated AMR signal of a 10 μm × 1 μm strip with a thickness of 30 nm and uniaxial magnetic anisotropy K u1 = 120 kJ m −3 with an easy-axis forming an angle = 5.7°from the normal direction to the film. The associated in-plane magnetic domain distribution is shown for several selected applied magnetic fields. In this figure, one can observe two sharp MR jumps symmetrically distributed around zero field, as the ones observed in the experiments, triggered by a perfectly aligned OOP magnetic field.
The switching field can be tuned through different properties of the device. In addition to the thickness and width of the strip, it is influenced by the intensity and inclination of the induced uniaxial anisotropy. Figure 9b shows the variation of the switching field for the same device as Figure 9a but with different intensities of induced anisotropy. As expected from Equation (4), H sw decreases linearly with the anisotropy energy constant. Using K u1 ≅125 kJ m −3 , the computed switching field is close to the ex-  perimental value of 100 mT shown in Figure 5 for a magnetic bar of 1 μm wide. It is worth noting that this K u1 remains far from the maximal induced uniaxial anisotropy for a 30 nm-thick sample without stripes domain which is given by K int = 4 2 A∕t 2 FM ≅ 500 kJ m −3 . [27] Interestingly, a reduction of the switching field and an increase of the MR are experimentally observed for thinner samples as shown in Figure 9c, suggesting that the OOP is induced at the substrate interface. Moreover, the experimentally observed MR jumps are almost imperceptible in strips grown on silicon substrates (see Figure S2, Supporting Information) providing further evidence of a substrate-induced magnetic anisotropy. Figure 10a compares the experimental value of the switching field as a function of the misalignment angle (blue dots) with simulated values considering different intensity of uniaxal mag-netic anisotropy. As discussed above, in the absence of any perpendicular magnetic anisotropy (red squares), the switching field at low tilted angles increase as 1/ , leading to a huge discrepancy with experiments. However, when K u1 is around 100-120 kJ m −3 (black and pink triangles), the predicted switching field saturates as tends to zero in agreement with experimental observations. Figure 10b shows the simulated magnetoresistance curves at different values of misalignment obtained for a device with K u1 = 100 kJ m −3 , corresponding to the black triangles of Figure 10a.
The origin of substrate-induced anisotropy may be associated to residual local stresses, [34] dislocations, [35] or associated to dipolar stray fields generated by a periodic modulated substrate. [36,37] Indeed, atomic force microscopy images shown in Figure 11 reveal that Py thin films reproduce the twinned structure of the LAO substrate with an out-of-plane tilting angle of ∼ 0.1-0.5°. These images show large modulations of thickness (≈20 nm) over scales of ≈10 μm coexisting with a smaller scale periodic roughness (≈1 nm) caused by the terraces in the LAO substrate. These features are absent in Si substrates where switching is negligible and therefore the magnetic uniaxial anisotropy could originate from a stress induced at the Py/LAO interface, enhanced by the natural structural modulations of LAO. Interestingly, the intensity of the stress-induced anisotropy can be tuned by adjusting the thickness whereas the angle can be controlled through the inclination of the sample during thin film deposition, forcing an oblique growth of the Py grains.

Conclusions
In summary, we have demonstrated the possibility to induce sharp in-plane magnetization reversals triggered by out-of-plane magnetic fields in permalloy strips on LAO substrates, producing large magnetoresitance changes (1-2 %) at tunable moderate applied fields (5-100 mT). Micromagnetic simulations have been implemented to elucidate the nature of the magnetoresistance jumps observed experimentally and suggest the existence of an important out-of-plane magnetic uniaxial anisotropy. The origin of this effect could be related to the transfer of the structural modulations on the substrate toward the Py film deposited on top. We are able to tailor the magnetic switching field by the shape anisotropy through the strip width-thickness ratio. These results may be relevant in a future generation of magneto-resistive sen-sors and functional devices working under perpendicular applied fields.

Experimental Section
Permalloy, Fe 20 Ni 80 , thin films of different thicknesses were deposited at room temperature by dc magnetron sputtering at a base pressure of 10 −6 mbar and processing Ar pressure of 3.6×10 −3 mbar on 5 mm × 5 mm LaAlO 3 and silicon substrates. A 2 nm capping protective layer of TiO 2 was deposited on the top of the thinner films to avoid oxidation. Strips of different widths were defined by photolithography and lift-off processes. Au contacts for 4-point contact transport measurements were deposited on top of the strips by sputtering. Magnetoresistance measurements were performed using a physical property measurement system (PPMS, Quantum Design) with the sample mounted on a goniometer permitting to change the relative orientation with respect to the applied magnetic field. Magnetization hysteresis loops of permalloy films and strip arrays were measured with a Quantum Design SQUID magnetometer with IP-and OOP-applied magnetic fields.
Micromagnetic simulations were performed using the open-source MuMax3 software for domain distribution calculations, [38] and finiteelement software COMSOL to compute the resistance change of the Py bars at different magnetic field intensities and directions. Due to computational limitations, simulations were performed in structures with reduced dimensions compared to experimental devices. The length L was fixed to 10 μm while the width was optimized (w = 4 μm) in order to have the best compromise between maintaining the aspect ratio and avoiding large shape anisotropy for small w values. The IP micromagnetic cell dimensions were fixed to 10×10 nm 2 and the OOP size was set to 2.5, 5, and 10 nm for thickness of 10, 30 nm and thicker, respectively. Calculations were done using standard parameters for Py thin film M s = 8.6 × 10 5 A m -1 and A ex =13 pJ m -1 . The film was assumed to be free of magneto-crystalline anisotropy and thermal fluctuations were neglected. The four-point resistance was calculated with voltage pads placed at a distance of 5% of the total length from the device edges.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.