Evaluation of edge domains in giant magnetoresistive junctions

Spintronics has been attracting intensive studies over the last few decades¹ for efficient computing and sensing. In spintronics, the generation and manipulation of spin-polarized electrons and current control the efficiency. One method is to use the thermal gradient.² Spin-caloritronic devices represent an excellent avenue to improve device performance, efficiency, and running cost by exploiting the waste heat produced in all current-driven devices.³ The thermal effects caused by Joule heating are ubiquitous in device operation and act as an unavoidable source of wasted power, as well as affecting device performance due to thermal effects. However, the generated thermal gradient in a current-driven device can be exploited by the spin-Seebeck,⁴ Peltier,⁵ and Nernst⁶ effects, depending upon which device geometry is needed.

Ferromagnetic insulators (FMIs) such as Fe₂O₃ or yttrium iron garnet (YIG) are extremely sensitive to these thermal gradients to exhibit strong spin-caloritronic effects when exposed to them.^7–10 A spin wave can be generated via the spin-Seebeck effect when a current is applied to a device containing an FMI due to the Joule heating mentioned above. Therefore, by including an FMI in a current-driven device, the thermal gradients can begin to be used as a source of spin-current.

If this spin current can be introduced to the ferromagnetic layers of a magnetoresistive device, then the switching behavior can be manipulated. The generated spin wave should act as a secondary source of torque as current flows through the device. In turn, this should lower the required current density for magnetization switching as the required torque remains unchanged. As such, the efficiency of the device can be improved by harnessing the wasted energy that is usually detrimental to device performance.

In this study, a standard current-perpendicular-to-plane (CPP) giant magnetoresistance (GMR) device based on Heusler alloys has been modified to exhibit these effects. Heusler alloys have been used as they represent a family of materials with excellent potential for device application due to high values of saturation magnetization and Curie temperature (⁠$MS$ > 1000 emu/cm³ and $TC$ > 900 K for Co₂FeSi) and the potential for 100% spin polarization at the Fermi level. The standard insulator around the GMR pillars was replaced with Fe₂O₃ to act as a spin-wave source. This spin-wave generation controls the current density for switching and introduces a strong asymmetry due to the coercivity differences between the Heusler alloy layers and the FMI, allowing us to estimate the volume of the edge domains in a pillar.

An unconventional GMR pillar was fabricated, as shown in Fig. 1. A typical Heusler-based GMR multilayer consisting of Co₂Fe_0.4Mn_0.6Si (CFMS) (5)/Ag_0.78Mg_0.22 (5)/CFMS (5) was grown on a Cr (20)/Ag (40) seed layer on an MgO(001) substrate under ultrahigh vacuum via magnetron sputtering, where all thicknesses are given in nanometers. The Cr/Ag seed layer was used to remove island growth and to promote strong texture in the CFMS layer¹¹ and acted as the bottom electrode of a CPP-GMR junction. A capping layer of Ag (2 nm)/Au (5 nm) was added. The seed and Heusler alloy layers were annealed at $650$ °C and $500$ °C, respectively, to improve the interfacial smoothness and to promote crystallization and ordering of the CFMS and the Ag_0.78Mg_0.22 layers.¹² 

Photo- and electron-beam lithography and Ar-ion milling were used to fabricate a series of elongated pillars with long axes from 100 nm to 800 nm; however, as shown in Fig. 1, the milling stopped 1 nm into the lower FM layer. Fe₂O₃ was then deposited around the pillar in place of the usual AlO insulator. For adhesion, it was necessary to add a secondary seed layer consisting of Cr (1 nm)/AlO (2 nm). Due to the lack of adhesion, it was not possible to stably anneal Fe₂O₃. Therefore, the crystallinity of the FMI channels is limited.

Device properties were measured using an HiSOL HMP400-SMS probe station with a Keithley 2400 sourcemeter and a Keithley 2182A nanovoltmeter, giving high resolution. Magnetization reversal was induced using both field- and current-induced methods to analyze the effects of the FMI channels.

The fabricated GMR pillars were first evaluated in a standard manner using an applied external field. Figure 2(a) shows the magnetoresistance trace for a pillar with Fe₂O₃ present, which was initially saturated by the negative field, fixing the Fe₂O₃ moment as shown in Fig. 2(a). It is immediately obvious that there is a significant asymmetry in the signals between a positive-to-negative and a negative-to-positive field sweep, with the difference in MR between the parallel and antiparallel state (ΔMR) values of $(32.8±0.1)$% and $(10.2±0.1)$%, respectively. Furthermore, there is a large difference between the field values of the peak GMR value, decreasing from $(70±2)$ Oe to $(−18±2)$ Oe when the ΔMR increases. The switching field for nucleated reversal after magnetization rotation, i.e., the sharp change following the sloped parts, changes similarly from $(126±2)$ Oe to $(−54±2)$ Oe. These differences are reproducible and independent of the order of the sweep directions.

The decrease in the switching field can be attributed to the formation of edge domains (partially antiparallel state), whose magnetizations are coupled to the magnetic moments in the Fe₂O₃ surrounding layer. These edge domains can be easily rotated by a small change in the applied field, making the antiparallel state unstable as seen in the figure. Since the coercivity of Fe₂O₃ is greater than the coercivity of the GMR pillars, the edge domains can only be fully aligned in one direction of the magnetization during the reversal as schematically shown in Fig. 2(a).

The reduction in the value of the magnetoresistance is also due to the direct coupling between the layers in the stack and the edge of the pillar coupled with Fe₂O₃, where edge domains form. Since there is no reversal in the magnetization of Fe₂O₃ within the fields applied to achieve the magnetization reversal in the CFMS layers, there has to be a region of transient magnetization at the interface between the Heusler-alloy layers and Fe₂O₃ where the ferromagnetic exchange coupling must be accounted for. The two magnetizations cannot be in direct opposition when in direct contact. This creates regions of spin that are not collinear with the device orientation and as such do not contribute to the GMR signal. They also aid the reversal of the free layer, and such a reduced coercivity is observed.

Additionally, this coupling is responsible for the shape of the positive-to-negative sweep, where a kink is observed in the blue curve at 50 Oe in Fig. 2(a). This is at the same positive field value as the coercivity in the negative-to-positive direction, implying that a magnetization change is occurring not due to the external field but due to the coupling. This is why there is a dramatic change in the shape around this point where the magnetization reversal changes from being dominated by the coupling to controlled by the external field.

Figure 2(b) is measured in the same manner as Fig. 2(a) but for a reference device without Fe₂O₃, insulated by pure AlO. The trace is far more symmetric than for Fig. 2(a), with no field direction dependence on the signal. The coercivity values for the antiparallel-to-parallel switch are $(96±2)$ Oe and $(−92±2)$ Oe in the negative-to-positive and positive-to-negative field directions, respectively. The peak GMR values are $(21.7±0.2)$% and $(22.7±0.3)$% at field values of $(74±2)$ Oe and $(−65±2)$ Oe, comparable to the positive-to-negative field sweep in Fig. 2(a). This is consistent with a lack of exchange coupling from Fe₂O₃.

Figure 3 shows the current-driven reproducible switching behavior for the same device as shown in Fig. 2(a). Figure 3(a) shows the switching behavior starting from the fully antiparallel state as achieved at −10 Oe in Fig. 2(a) in the positive-to-negative field sweep as you approach the peak of the switching at $(−18±2)$ Oe. A negative current (applied top to bottom) reverses the magnetization of the free layer by spin-transfer torque (STT), resulting in a gradual reduction in resistance. The switching current density, $jsw$⁠, is estimated to be $(8.0±0.7)×107$ A/cm². The value is the threshold for a final transition after significant rotation of the magnetization, shown via the extensive curvature in the GMR curves in both field- and current-driven switching systems. Here, we consider three contributions for the magnetization switching, (i) conventional STT by the pinned layer, (ii) the influence of the edge domains exchange-coupled with a spin wave generated in Fe₂O₃, and (iii) Joule heating.

As observed without Fe₂O₃, a negligible asymmetry is measured in the GMR curves from negative to positive saturation and vice versa. However, with Fe₂O₃, a prominent asymmetry is measured as seen in Fig. 2(a), which contains the above explained edge magnetic domains coupled to the spin wave (ii) generated in Fe₂O₃ by the thermal gradient almost perpendicular to the plane. Therefore, the current-driven switching must be affected by Fe₂O₃ around the edge of the free layer, which is aligned parallel to the pinned layer by the initial application of the negative field as described above and, therefore, will produce two contributions (i) and (ii) as schematically shown in the figure. The STT (i) switches a central region of the magnetization of the free layer, while those in the edge domain are maintained by (ii), forming the partially antiparallel state. It is, therefore, possible for the magnetization to be reversed using a negative current from antiparallel to parallel states. Removal of the applied current does not reorient the free layer, but the minor increase in the resistance suggests the decrease in the volume of the edge domains (ii) in addition to the Joule heating by the current (iii). It should be noted that the magnetization switching from the parallel to antiparallel state cannot be achieved by a current up to 40 mA, which indicates that STT (i) may not be strong enough for switching although some minor increase and instability in resistance can be seen in the positive current in the figure.

Figure 3(b) shows the same process in the opposite field orientation starting from the partially antiparallel state as achieved at 75 Oe in Fig. 2(a). Here, $jsw$ has a value of $(7.0±0.5)×107$ A/cm² controlled by the competition between the three contributions (i)–(iii). First, a reduction in the resistance at very low currents is observed, which can be associated with gradual magnetization rotation in the minor domains formed between the central region and the edge domains in the free layer as shown in gray in Fig. 3(b). This may possibly due to STT through the central domain to instabilize the minor domains (i) and the exchange coupling induced by the outer edge domains. A metastable state is then reached as the edge domains (ii) and Joule heating (iii) are not strong to reverse the magnetization in the central region of the free layer up to $jsw$ as the partial antiparallel configuration is stable from the viewpoint of the STT (i). Above $jsw$⁠, spin-torque oscillation may start to occur as reported in a similar system,¹³ which makes the magnetization of the central region unstable and assists the magnetization reversal by processes (ii) and (iii). This may lead to the significant instability of the device resistance at high currents. It is also possible that the instability is due to the lack of total crystallinity in Fe₂O₃ without annealing and local spin waves may be generated, which, in turn, perturb the magnetization in the edge domains of the free layer, causing variations in the resistance. Additional imperfections from diffusion or intermixing in Fe₂O₃ may create pinholes in Fe₂O₃, which further change local spin-wave environments.

Figure 4 shows the current switching data by the conventional STT (i) in a similar device without Fe₂O₃ as shown in Fig. 2(b). It is clear that the antiparallel state is more uniform in this device with two distinct plateaus separated by sharp switching. The switching current densities are lower than for the above case with values of $jsw$ of $(1.1±0.1)×107$ A/cm² and $(2.2±0.2)×107$ A/cm² for the negative and positive currents, respectively. The increased stability is due to the removal of the influence of Fe₂O₃ no longer forming the edge/minor domains. The reversal is simply controlled by a nucleation event, most likely at an edge where damage from milling has occurred as similarly observed in our earlier studies without Fe₂O_3.^12,14 The difference in $jsw$ confirms the magnetic stability of the edge domains induced by Fe₂O₃ in Fig. 3, which may not be ideal for fast and coherent magnetization reversal for device applications. It is, therefore, important to estimate the volume of the edge domains.

These results indicate that the presence of the spin wave in Fe₂O₃ can assist the magnetization reversal only when the spin wave generated in Fe₂O₃ is parallel to the magnetization of the free layer as discussed above; however, the edge/minor domains magnetically coupled to Fe₂O₃ are found to further increase $jsw$⁠. The presence of Fe₂O₃, which has non-ideal crystallinity, may induce strong pinning sites at the interface with the Heusler alloy layer inducing a significant rotational component to the magnetization reversal. Since the rotational components account for 10%–15% of the total resistance change, the edge domain volume can be estimated as this proportion of the free layer as compared with the central region consisting of approximately a half of the volume switched at $jsw$ in Fig. 3, leaving the remaining almost 1/3 of the volume to from minor domains between them. Such estimation can be complementary to the conventional activation volume analysis for the magnetization reversal¹⁵ and suggests that the elimination of such minor domains can reduce $jsw$⁠.

Furthermore, the presence of any disorders or dislocations will reduce the spin polarization of the Heusler alloy layer. If the spin polarization of the pinned layer is reduced, the associated STT is reduced and $jsw$ is increased. Therefore, improvements are needed for the fabrication of the pillars with Fe₂O₃, especially the improvement of the crystallinity of Fe₂O₃, in order to realize the potential to effectively take advantage of thermally induced spin waves.

In summary, we have shown that an FMI in contact with the edge of a GMR device can heavily influence its behavior. Significant asymmetry is induced in the current-induced magnetization switching depending upon the relative magnetization of the FMI and the free layer due to the thermal gradients from Joule heating, which, in turn, creates spin waves in the device coupling with the edge domains in the free layer. This may also create different field-dependent behavior. This is useful for determination of the volume of edge domains and for the evaluation of the nature of coupling between FMI and GMR structures. Control of GMR devices for niche application or asymmetric reversal may be possible using FMI edge channels.

This work was partially supported by the EPSRC-JSPS Core-to-Core Programme (No. EP/M02458X/1), JST CREST (No. JPMJCR17J5), the Global Institute for Materials Research Tohoku (GIMRT), the Institute of AI and Beyond of the University of Tokyo, the JST ERATO “Spin Quantum Rectification Project” (No. JPMJER1402), and the JSPS Grant-in-Aid for Scientific Research (S) (No. JP19H05600) and (C) (Nos. JP20K05297 and JP20K05296). R.R. acknowledges support from the European Commission (Nos. 734187-SPICOLOST and H2020-MSCA-RISE-2016), Marie Sklodowska-Curie Action SPEC (No. 894006), and the Spanish Ministry of Science.