Microscopic Origin of Magnetization Reversal in Nanoscale Exchange-Coupled Ferri/Ferromagnetic Bilayers: Implications for High Energy Density Permanent Magnets and Spintronic Devices

Giant exchange bias shifts of several Tesla have been reported in ferrimagnetic/ferromagnetic bilayer systems, which could be highly beneficial for contemporary high energy density permanent magnets and spintronic devices. However, the lack of microscopic studies of the reversal owing to the difficulty of measuring few nanometer-wide magnetic structures in high fields precludes the assessment of the lateral size of the inhomogeneity in relation to the intended application. In this study, the magnetic reversal process of nanoscale exchange-coupled bilayer systems, consisting of a ferrimagnetic TbFeCo alloy layer and a ferromagnetic [Co/Ni/Pt]N multilayer, was investigated. In particular, minor loop measurements, probing solely on the reversal characteristics of the softer ferromagnetic layer, reveal two distinct reversal mechanisms, which depend critically on the thickness of the ferromagnetic layer. For thick layers, irreversible switching of the macroscopic minor loop is observed. The underlying microscopic origin of this reversal process was studied in detail by high-resolution magnetic force microscopy, showing that the reversal is triggered by in-plane domain walls propagating through the ferromagnetic layer. In contrast, thin ferromagnetic layers show a hysteresis-free reversal, which is nucleation-dominated due to grain-to-grain variations in magnetic anisotropy of the Co/Ni/Pt multilayer and an inhomogeneous exchange coupling with the magnetically hard TbFeCo layer, as confirmed by micromagnetic simulations.


■ INTRODUCTION
The concept of engineering exchange-coupled composites is the most promising approach to meet current challenges in fabricating high energy density permanent magnets. 1−3 Already in 1991, Kneller and Hawig 4 proposed to manufacture magnets with a magnetically hard and soft phase, exchange-coupled at a mutual interface. While the high magnetocrystalline anisotropy of the hard phase provides a high coercive field, the coupled soft phase should contribute to the energy density product by a high saturation magnetization. Due to the soft phase, the demagnetization curve shows a completely reversible part, which led to the term "exchange-spring magnets". Furthermore, exchangecoupled systems employing ferrimagnetic (FI) heavy rare earth (RE)-3d transition metal (TM) alloys provide high tunability, interfacial exchange interaction, and zero magnetic moment at the compensation temperature T comp , 5−17 which is highly beneficial for many applications such as spin valves 18−23 and magnetic tunnel junction devices. 24 Below T comp , the magnetic moment of the RE atoms dominates, which leads to an antiparallel alignment of the net magnetic moments of the FI layer when coupled to a ferromagnetic (FM) layer. As a consequence, a positive horizontal shift of the hysteresis loop of the magnetically softer layer is typically observed after saturation in the positive field direction. In this configuration, a giant exchange bias shift of several Tesla has been reported for various nanoscale FI/FM bilayer systems that can differ in the reversal behavior of the soft layer exhibiting either fully reversible or irreversible switching. 11,25−28 Micromagnetic simulations showed that a partial domain wall is formed at the FI/FM interface layer during the reversal of the FM. 29 The minor loop becomes fully reversible if this domain wall generates a hard-axis field that overcomes the anisotropy field of the FM. It was further reported that the anisotropy and the bulk exchange of both layers as well as the exchange coupling strength and the thickness of the FM play an important role in the reversibility of the FM. The underlying reversal mechanism for reversible switching was studied in detail in a [Co(0.4 nm)/ Pt(0.7 nm)] 5 multilayer exchange-coupled to ferrimagnetic Tb 26.5 Fe 73.5 (20 nm), which acts as a magnetically hard pinning layer. There, a nucleation-dominated magnetization reversal process was revealed, which is caused by grain-to-grain variations in magnetic anisotropy of the Co/Pt multilayer (ML) and an inhomogeneous exchange coupling to the magnetically hard TbFe layer. 30 In a recent study on a nanometer-thick TbFeCo/[Co/Ni/ Pt] N sample series, we have systematically investigated the reversal behavior of the softer FM layer as a function of its thickness, including a detailed theoretical analysis of the full reversibility condition. 29 In the present work, we study in detail two specific FI/FM samples out of this sample series exhibiting two distinct cases of reversible and irreversible switching. The different underlying microscopic reversal processes are investigated using high-resolution magnetic force microscopy and micromagnetic simulations. Having a detailed understanding of such complex magnetization reversals is crucial for future spintronic and high energy density permanent magnet devices.

■ EXPERIMENTAL DETAILS
Film deposition was performed at room temperature by dc magnetron (co-)sputtering from elemental targets on a Si(001) substrate with a 100 nm-thick thermally oxidized SiO x layer. The sputter process was carried out using an Ar working pressure of 5 × 10 −3 mbar in an ultrahigh vacuum chamber (base pressure < 10 −8 mbar). The heterostructures consist of a 20 nm-thick amorphous ferrimagnetic Tb 28 Fe 58 Co 14 layer 17 and a ferromagnetic [Co(0.2 nm)/Ni(0.4 nm)/ Pt(0.6 nm)] N ML on top ( Figure 1). In addition, a 5 nm-thick Pt seed and cover layers were used. The thicknesses of the layers were estimated from the areal densities measured by a quartz balance during deposition, while the elemental composition of the TbFeCo alloy as well as the calibration of the quartz balance was evaluated by Rutherford backscattering spectrometry. Two FI/FM heterostructures with different repetition numbers (N = 5 and 9) of the ferromagnetic multilayer were chosen for this study, exhibiting different reversal mechanisms. 29 Furthermore, reference samples of the individual layers were prepared.
The integral magnetic properties of the FI/FM heterostructures were investigated by superconducting quantum interference device− vibrating sample magnetometry (SQUID-VSM). All M−H minor and full loops were measured at 40 K in the out-of-plane geometry, revealing for both systems strong perpendicular magnetic anisotropy where the ferrimagnetic layer acts as a magnetically hard pinning layer. Furthermore, the ferrimagnet is Tb-dominant over the entire temperature range that we investigated, meaning that the Tb magnetic moment is always larger than the total Co/Ni moment. Consequently, the net moments of the FI/FM heterostructures are antiferromagnetically aligned in the ground state at zero field. The magnetic properties of the full sample series can be found in ref 29. More details on the magnetic properties of Co/Ni/Pt MLs can be found in ref 31. Complementary, the complex reversal behavior was locally imaged at 40 K by an ultrahigh vacuum magnetic force microscope operating in magnetic fields of up to 7 T. 32 Details on the magnetic force microscopy (MFM) data acquisition and data processing can be found in refs 30 and 33.

■ EXPERIMENTAL RESULTS
Macroscopic Minor Loop Studies. The M−H full hysteresis and also minor loops of the exchange-coupled FI/FM systems and of reference samples consisting only of the FI or FM layers recorded at 40 K are shown in Figure 2. Both reference samples show strong perpendicular magnetic anisotropy with coercive fields of about 3 T for the FI layer and 200 mT for the Co/Ni/Pt MLs. For the exchangedcoupled FI/FM heterostructures, starting from saturation, by lowering the magnetic field, the FM layer reverses due to the strong antiferromagnetic coupling. At a high opposite field of about 3 T, eventually, the magnetically hard FI layer switches. It is observed that the field required for reversing the FM layer becomes larger with decreasing number N (thickness), which is expected if the interfacial exchange coupling remains constant. 29,34 The minor loops were captured to analyze the switching process of the softer FM layer and show two distinct switching mechanisms. While the FI/FM heterostructure with the thick FM layer exhibits a hysteretic reversal process (Figure 2a), the thinner FM layer reveals fully reversible switching (Figure 2b).
High-Resolution Magnetic Force Microscopy Studies. Here, we concentrate on studying the thicker FM layers (N = 9) to extract the microscopic mechanisms leading to the transition from a nonhysteretic to hysteretic minor loop magnetization process when increasing the FM layer thickness from N = 5 to 9. For this, the sample was demagnetized to acquire the virgin M−H dependence at 40 K for fields raised from 0   26 The weak granular contrast is caused by variations of the z component of the magnetic moment density arising, for example, from spatial film inhomogeneities (e.g., in the TbFeCo composition 35,36 ). The details of the underlying reversal mechanism of the fully reversible switching case were already reported for a similar TbFe/[Co/ Pt] 5 heterostructure. 30 There, a nucleation-dominated three-stage magnetization reversal process was revealed, which is caused by grainto-grain variations in magnetic anisotropy of the Co/Pt ML and an inhomogeneous exchange coupling to the magnetically hard TbFe layer. The reversal steps are schematically illustrated in Figure 4. They consist of a rotation-dominated part of the FM layer starting at the top surface of individual grains (ii) followed by the full reversal (iii) till saturation (iv). The last reversal step is again characterized by a rotation part of the FI domains till saturation (v).

■ MICROMAGNETIC SIMULATIONS
In this section, finite element simulation results obtained with the finite element package magnum.fe 37 are presented. This is to reproduce the different minor loop behaviors observed for thin and thick FM layers and from that gain a more fundamental understanding of the relevant physics governing the experimental observations.  As shown in Figure 5, we model 100 nm × 100 nm films consisting of a 20 nm-thick FI layer and FM layers of a 6.0 and 10.8 nm thickness, corresponding to the two different repetition numbers of N = 5 and 9, respectively. The structures consist of grains having an average diameter of 10 nm, generated by Voronoi tessellation. Due to the required small discretization length of 2 nm and the resulting large computational effort, the lateral dimensions are kept at 100 nm × 100 nm, which is considerably smaller than the typical domain structures observed by MFM, as displayed in Figure 3b−i. However, given that single grains with a lateral length of 50 nm were well approximated with a spin chain model in a previous work, 30 a homogeneous magnetization within this distance in the in-plane direction can be assumed. Hence, the lateral film dimensions for our simulation work are justified. The grains of our model are fully exchange-coupled in the lateral directions. The uniaxial magnetic anisotropy K u is normally distributed with a mean of 430 kJ/m 3 and a standard deviation of 75 kJ/m 3 (total range of 255−619 kJ/m 3 ), and the ratio J iex /K eff,FM of interface exchange constant between the two layers and the respective effective magnetic anisotropy constant of the FM is kept constant at −0.1 μm (see the color code in Figure 5). All other material parameters are given in Table 1.
The assumptions of a strong variation in the magnetic anisotropy of the FM layer and simultaneously in the interface exchange constant at the FI/FM interface are based on previous results reported in refs 29 and 30. In ref 30, a hysteresis-free minor loop was found for a similar heterostructure with a thin FM layer of 5.5 nm, and in ref 29, the relevant parameters and a condition for hysteresis-free minor loops were derived.
For the modeling, the ground state of the heterostructure with the FI layer magnetization pointing in the +z direction and that of the FM layer pointing in the −z direction is considered. Subsequently, the field magnitude is increased stepwise in 50 mT increments up to 4 T and then decreased back to 0 T. After each field step, the micromagnetic state of the system is relaxed for 1 ns. Note that the variation of the applied field in the simulations is performed much faster than that used during the experiments. However, because of the high damping constant (α = 1.0) used for the simulations, a stationary state is obtained within 1 ns such that the modeled loops are representative of the experimental loops. Figure 6 displays minor loops of heterostructures with a thick (N = 9) and thin (N = 5) FM layer. While the loop for the thick FM layer shows a lower switching field of about 580 mT and a hysteresis width around 300 mT, the switching field for the thin FM layer is higher than 1 T and the hysteresis is absent. This reproduces the experimentally observed switching behavior of the FM layer (see black lines in Figure 2a,b). Note that, for the modeling, the only parameter changed was the thickness of the FM layer.
To gain a more fundamental understanding of the reversal process of the FM layer and to understand the MFM contrast evolution with the field (Figure 3b   20.0 6.0/10.8 a K u is the uniaxial magnetic anisotropy constant, M S is the saturation magnetization, A ex is the exchange coupling in the bulk, J iex is the interface exchange coupling between the antiferromagnetically coupled layers, α is the damping constant, a is the lateral size of the modeled film, and t is the thickness of the layers. The anisotropy axis is tilted by 1°against the z direction in both layers to avoid metastable states. ACS Applied Nano Materials www.acsanm.org Article weak contrast appears, which can be attributed to a difference in the canting of the magnetic moments in the individual grains with different magnetic anisotropy. The moments in grains with small anisotropy show more canting than those in grains with higher anisotropy. The contrast further increases with an increasing external field. Note that the simulation is performed only for the domain with an up magnetization of the FI layer and a down magnetization of the FM layer because the opposite domain with an up FM magnetization would not be affected by an applied field well below the coercivity of the FI layer. The simulation thus reveals a continuous raise of the up magnetization of the FM down domain and hence a decrease of the magnetization difference between the FM down and up domains. Therefore, the field arising from the pattern of domains in the FM that is antiparallel to that of the FI layer is reduced, and consequently, the MFM contrast is increased. This explains the small increase in contrast observed when comparing the MFM images from Figure 3b,c. At a field of about 800 mT, a domain wall forms throughout the whole film, starting from the grain with the lowest anisotropy, as illustrated in Figure 7e−h. The domain wall propagates through the film until all parts have switched parallel to the field (and parallel to the FI net magnetization), which is a fully irreversible process in agreement with the Experimental Results. Note that, since in the relaxed magnetization state, at 800 mT, the domain wall propagation cannot be seen, Figure  7e−h shows the dynamic process at 800 mT, as indicated by the simulation time in the upper right corner. To compare the simulation results with the observed MFM data, some limitations of the simulation work need to be further elaborated. To keep the computational effort at an acceptable level, the simulation considers only a small area within an initially down FM magnetization. Thus, the magnetostatic energy arising from the up/down FM and down/up FI domain pattern and the existence of an initial vertical domain wall inside the FI and FM is not considered. For this reason, the simulation reveals the switching of a low anisotropy grain followed by a rapid expansion of the reversal domain. In contrast, the MFM data recorded in fields from 0.8 to 1.05 T (Figure 3d−g) show steady states of the domain wall propagation that cannot be observed in the model used for simulation. The MFM images reveal that no domain reversal occurs inside the FM down domain but that the reversal starts by the propagation of an already existing wall and that the propagating wall again becomes pinned for fields from 0.8 to 1.05 T. This can be explained by the up field arising from the FI up domains, which is the strongest in the inside of the FM down domain near its wall (Figure 7k). This stray field from the FI layer adds to the applied up external field and thus drives the propagation of the existing wall to a location inside the FI up domain where the up stray field from the FI domain pattern is weaker. Because our simulation considers a FM down domain only, this behavior cannot be modeled. The simulation however reveals that, once a reversal domain exists, a rapid wall propagation follows. This explains why the field interval where a domain wall propagation is observed remains small, i.e., about After the FM has switched, the contrast becomes abruptly weak and decreases with increasing the external field, as displayed in Figure 7i,j. Note that, again, only the FM magnetization inside an initial FM down domain is considered. The simulation shows that the grain-to-grain variation of the up magnetic moment is reduced with increasing the up field, which corresponds to a compression of the in-plane domain wall that has formed at the FI/FM interface. Hence, the up magnetic moment of the FM layer is increased, approaching that of a FM domain with an initial up magnetization. The down/up field from the FM layer that weakened the up/down field of the domains inside the FI layer thus becomes gradually smaller. This explains the small increase of the MFM contrast observed when the field is increased from 1.05 to 2 T (Figure 3g,h).
Note that the magnetization process observed here for the thicker FM layer is fundamentally different from that observed in our previous work 30 for a thinner FM layer. For this reason, the modeling is also performed for the thinner FM layer using the parameters describing the FI/FM heterostructure samples prepared here. The results are displayed in Figure 8. Again, the modeling is performed for a film area with an initial down FM magnetization. As in our previous work, 30 a three-stage magnetization process is observed. Stage 1 (Figure 8a−c) is characterized by a rotation of the initially down magnetic moments near the top of the FM layer toward the up direction of the applied field. In stage 2 (Figure 8d−g), the magnetic moments of isolated grains switch toward the up direction to improve the alignment of the magnetic moments to the applied field. The angle between the magnetic moments and the field is then smaller for the moments near the top of the FM film and larger for those near the FI/FM interface. Because this switching process depends on the properties of individual grains, a large grain-to-grain variation occurs. In stage 3 (Figure 8h−l), all grains have switched to have a predominately up magnetization. The contrast drops as the horizontal domain wall at the FI/FM interface is compressed, and the local variation of the domain wall thickness is decreased. As observed by MFM in our previous work, 30 no lateral propagation of a vertical domain wall inside the FM layer occurs, but a three-stage magnetization process takes place for each individual grain. This reversal process is hysteresis-free (red curve with squares in Figure 6).
The condition for hysteresis-free switching derived in ref 29 can be applied here. Using the parameters listed in Table 1 for the thicker FM layer clearly reveals that 90% of the grains in the heterostructure remain above the threshold for hysteresis-free switching (K uni ≤ 330 kJ/m 3 ), while for the system with the thinner FM, the threshold value is K uni ≤ 418 kJ/m 3 . This means that 40% of the grains are below the threshold and hence show a hysteresis-free process. For the thinner FI/FM heterostructure with N = 5, this means that almost half of the FM grains show a gradual, hysteresis-free rotation of the magnetization. Based on this behavior and the small thickness of the FM, short vertical domain walls can form, as schematically illustrated in Figure 4, and the observed three-stage process with a local rearrangement of domains in the switching process occurs. In contrast, in the thick FM layer with N = 9, almost all grains show an irreversible, hysteretic reversal. An abrupt switch of individual grains would generate several large vertical domain walls, which is energetically unfavourable due to the thickness of the FM. This is the reason why we observe only one domain wall, which is independent from the granular structure, propagating through the FM layer and causing irreversible switching of the macroscopic minor loop.

■ CONCLUSIONS
We reveal two distinct magnetic reversal mechanisms in a nanometer-thick exchange-coupled bilayer system consisting of a ferrimagnetic TbFeCo alloy layer and a ferromagnetic [Co/ Ni/Pt] N multilayer. The reversal characteristics depend critically on the thickness of the FM layer. By minor loop M−H measurements, we observed an irreversible hysteretic switching process of the bilayer with N = 9 and a reversible switching for N = 5. The underlying microscopic origin is revealed by highresolution MFM. For N = 9, the FM switches by in-plane domain wall propagation. In contrast, thinner FM layers exhibit a nucleation-dominated reversal due to grain-to-grain variations in magnetic anisotropy of the Co/Ni/Pt multilayer and an inhomogeneous exchange coupling with the magnetically hard TbFeCo layer. The coupled FM layers of both systems were modeled by finite element simulations with individual grains varying in K u . The simulated macroscopic minor loops agreed very well with the experiments. The simulated MFM contrast of the thicker FM layer revealed a dynamic process of the domain wall motion during switching in contrast to the experimentally observed magnetic relaxed states. This difference could be explained by the additional local field arising from the FI layer, which is absent in the model. With this exception, the simulations replicated the two switching mechanisms of both systems.
High-resolution magnetic force microscopy together with micromagnetic modeling gave detailed insights into which magnetic system parameters are responsible for the complex magnetization reversal process of these ferri-/ferromagnetic exchange-coupled double-layer structures. These insights are crucial for the realization of submicron high energy density permanent magnets and spintronic devices. The implications are not only restricted to antiferromagnetically coupled ferri-/ ferromagnetic bilayers but are also valid for further exchangecoupled composite media. 38,39 We thus conclude that this work will be beneficial for the understanding of the magnetization reversal of exchange-coupled structures that is potentially interesting for various applications.