Perpendicular Magnetic Insulator Films for Spintronics

2.1 Atomic structure of BaM thin films

BaM is a hexagonal ferrite, which consists of close-packed layers of oxygen ions. Figure 1 shows a unit cell of BaM. The Ba²⁺ ion is large, as is the O²⁻ ion, and the barium always replaces oxygen somewhere in the oxygen lattice. The close-packed layers form six fundamental blocks, namely, S, S^*, R, R^*, T, and T^* [5, 6, 7]. The S block consists of close-packed oxygen layers stacking in an ABCABC… sequence. It has a cubic spinel arrangement with the <1 1 1 > axis along the vertical direction. There are two units of Fe₃O₄ without any barium ions in each S block. The R block comprises close-packed oxygen layers stacking in an ABAB… sequence. It has a hexagonal closest packed structure along the vertical axis. Each R block has a unit formula of BaFe₆O₁₁. The T block is made of four oxygen layers, with a barium ion replacing an oxygen ion in the middle two layers, which gives a unit formula of Ba₂Fe₈O₁₄. The S^*, R^*, and T^* blocks are 180° rotations around the c-axis from the S, R, and T blocks. BaM is built from the stacking of S, R, S^*, and R^* blocks.

Trivalent Fe³⁺ ions occupy tetrahedral and octahedral sites as well as one trigonal bipyramidal site. Different sites account for different spin orientations and Bohr magnetons (μ_B). For example, a tetrahedral site contributes 2μ_B, while an octahedral site contributes 4μ_Bwith opposite spin orientations in the S block. In the end, S, S^*, R, and R^* blocks contribute 2μ_Beach, leading to a moment of 40μ_Bfor each unit cell. This gives a saturation magnetization of ∼4700 G in bulk BaM. BaM has a strong anisotropy field of 17 kOe, which is along the caxis. This comes from the trigonal bipyramidal site Fe³⁺ ions, as well as breaking crystal symmetry in the R/R^* blocks. This is the most distinguished property of BaM, because the perpendicular anisotropy field originates from bulk intrinsic anisotropy. BaM has a large cconstant of 23.2 Å and an aconstant of 5.89 Å. The x-ray density is about 5.29 g/cm³. The Curie temperature of bulk BaM is 725 K, which is much higher than the room temperature. The exchange constant is 6.4 × 10⁻⁷ erg/cm [7].

2.2 Growth techniques

A variety of techniques are used to grow BaM thin films, including pulsed laser deposition (PLD) [8, 9, 10], alternating target laser ablation deposition (ARLAD) [11, 12], molecular beam epitaxy (MBE) [13], liquid phase epitaxy (LPE) [14, 15], magnetron sputtering [16, 17], and so on. Guo et al. at Boston Applied Technologies proposed a chemical solution deposition process to deposit BaM. Song and his colleagues succeeded in the PLD growth of BaM thin films that showed an FMR linewidth as narrow as single-crystal BaM bulks. However, these films showed a remanent magnetization much smaller than the saturation magnetization [9]. This problem was improved in the later experiments when tuning the deposition conditions [18]. Figure 2 shows the PLD parameters which decide the thin film quality. Figure 2b shows that c-axis out-of-plane BaM grains can be grown on (0001) Al₂O₃ substrates; c-axis in-plane BaM grains can be grown on (11 −20) Al₂O₃ substrates. A typical procedure is as follows: the oxygen pressure is set at 300 mTorr, and the substrate is heated to 800°C. The substrate-to-target separation is fixed at 4 cm, and the energy fluence of the laser beam is set to 0.7 J/cm². The laser pulse repetition rate is increased from 1 to 5 pulse(s) per second in five equal steps over the first 5 min and is then set to 10 pulses/s for the remaining deposition. After the deposition, the substrate is cooled down at a rate of 2°C/min in 400 Torr oxygen. The sample is then annealed at 850°C for 4 h in a standalone tube furnace, with a heating rate of 10°C/min and a cooling rate of 2°C/min.

2.3 BaM thin film grown on (0001) c-plane Al₂O₃ substrate

In microwave device applications, BaM films usually have a thickness of several microns. For spintronic devices, the thickness is reduced to tens of nanometers. Figure 3 shows the structure and magnetic properties of nanometer-thick BaM thin films grown on a c-axis Al₂O₃ substrate. The atomic force microscopy (AFM) image in Figure 3a shows a uniform and smooth surface, and the analysis of the AFM data yielded an RMS surface roughness of 0.19 ± 0.03 nm. These results, together with other AFM data not shown, indicate that the BaM film has a reasonably good surface, which is critical for the realization of high-quality BaM thin films. The roughness value here is an average over the measurements of nine different 1 × 1 μm areas, and the uncertainty is the corresponding standard deviation.

Figure 3b shows a 2θ/ω x-ray diffraction (XRD) scan, with the XRD intensity on a log scale. The x-ray θrotation gave a scattered beam that matched the specular reflection from the surface. The detected (001) diffraction peaks all come from c-plane scattering of the BaM film. The (006) sapphire substrate peak was also detected. The hysteresis loops in Figure 3c were measured by a vibrating sample magnetometer with different field orientations, as indicated. The loops clearly show that the BaM film has perpendicular anisotropy, which confirms the c-axis orientation of the film. Analysis of the hysteresis data yielded an effective perpendicular anisotropy field around H_ani = 20 kOe, which is larger than the bulk value (17 kOe). The normalized saturation magnetization 4πM_s = 4.16 kG, which is lower than the bulk value of BaM (4.70 kG). Figure 3d presents a ferromagnetic resonance (FMR) curve obtained with a 20-nm-thick BaM film at ω = 66 GHz. Because of the strong perpendicular anistropy field, the ferromagnetic resonance of BaM film appears between 50 GHz and 75 GHz. In the graph, the blue circles show an FMR profile measured at 66 GHz. The Lorentzian function (red curve) fits the data points better than the Gaussian fit shown as the olive curve, indicating that the film has a uniform quality. The fitting yielded a peak-to-peak linewidth ΔH = 26.59 ± 0.60 Oe and an FMR resonance field H_res = 10.24 kOe. Similar measurements can be carried out to FMR profiles at a variety of frequencies, and a Kittel equation can fit the curve with a magnetic field applied out-of-plane:

Such fitting yielded a gyromagnetic ratio γ = 2.80 ± 0.01 MHz/Oe and H_ani = 19.12 ± 0.04 kOe. The linewidth ΔHvs. frequency ωdata can be fitted with the following equation:

where αis the damping constant and H₀ is the inhomogeneity line broadening, which is a parameter associated with αdescribing the damping of the material. The FMR measurements yielded a damping constant α= (9.7 ± 1.1)×10⁻⁴.

2.4 BaM thin film grown on (1 1 −2 0) a-plane Al₂O₃ substrate

Figure 4 shows the structural and magnetic properties of a representative BaM film that is grown on an (1 1 −2 0) a-plane Al₂O₃ substrate. The film has a thickness of 1.2 μm. Thus, the AFM data show a relatively rough surface with an RMS surface roughness of 14.3 ± 1.6 nm. Figure 4b presents an XRD spectrum. The spectrum consists of a strong peak from the sapphire substrate and the two other peaks for the m-planes of the BaM film, indicating the in-plane orientation of the c-axis. Figure 4c presents the two hysteresis loops of the film measured by a vibrating sample magnetometer. One of the loops was measured with the magnetic field applied along the c-axis, while the other was measured with the field also in the film plane but perpendicular to the c-axis. The dashed lines indicate the extrapolations used to determine the effective anisotropy field H_ani. The dotted line indicates the determination of the saturation induction 4πM_s. These data show that the film has a well-defined in-plane uniaxial anisotropy with the easy axis along the c-axis. From the hysteresis loops, it can be concluded that H_ani = 16.5 kOe and 4πM_s = 3.87 kG. Moreover, the film has a large remanent magnetization-to-saturation magnetization ratio of about 0.89 along the c-axis. This large ratio results from the strong in-plane uniaxial anisotropy. This means that the film is self-biased to a large degree at zero fields, which allows for the use of BaM in self-bias spintronic experiments. Figure 4d shows the FMR spectrum of the c-axis in-plane BaM film shown by the blue, open circles measured at 64 GHz. The curve is fitted to the derivatives of a trial Lorentzian function and a Gaussian function. Similar to the FMR curve in Section 2.3, it fits better with the Lorentzian function, indicating a uniform film. The Lorentzian fitting yields H_res = 4.55 kOe and ΔH = 318 Oe. The dependence of H_ani and the microwave frequency fcan be fitted by a Kittel equation for field applied in-plane:

3.1 Introduction to spintronics

In the following sections, we introduce recent spintronic experiments using MIs with strong anisotropy fields. Devices that incorporate the unique properties of MIs are an excellent potential solution for the power consumption and heat dissipation problems of conventional electronics, as they would consume much less energy and generate significantly less heat. We introduce the use of different techniques in generating pure spin currents, using bilayer heterostructures of a normal metal (NM)/ferromagnetic material. There are a variety of normal metal choices such as platinum (Pt) and Gold (Au). Both have been explored and tested in spintronics related studies and experiments [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33].

In the first two sections, we will explore the generation of pure spin currents using the spin Seebeck effect (SSE) and the photo-spin-voltaic effect (PSVE). Both techniques take advantage of a NM coupled with a MI. In SSE, a temperature gradient in the MI is the main factor that induces the MI to inject pure spin currents into the NM layer. In PSVE however, the light of certain wavelengths reaching the atomic layers of the NM, exciting the NM electrons near the NM/MI interface, is what generates the pure spin currents. SSE and PSVE Experimentation results will also be explored and discussed. Then, in the last two sections, we will demonstrate how pure spin currents can be used practically to enhance magnetic switching in MIs in a significant and meaningful way. NM/MI bilayers will not be the only type of heterostructure discussed here, we will also explore topological insulator/MI structures and demonstrate the significance of topological insulators in spintronics.

3.2 Generation of pure spin currents through SSE using NM/BaM structures and photo-spin-voltaic effect in Pt/BaM structure

3.2.1 The spin Seebeck effect

The traditional Seebeck effect, first discovered by Thomas Seebeck in 1821 [34], refers to the generation of electric potential in a conductor when a temperature gradient is applied to it. The electric potential is caused by charge carriers within the conductor moving from the hot region to the cold region. A thermocouple consists of two dissimilar conductors that are joined to form a junction; when a heat gradient is applied across the thermocouple (see Figure 5a), a voltage difference can be observed across them. The sign of the voltage flips when the direction of the temperature gradient is flipped. The traditional Seebeck effect is the basic principle behind most thermoelectric generators.

The spintronic equivalent of the traditional Seebeck effect, called the spin Seebeck effect, was first discovered in 2008 [19, 28]. SSE is a phenomenon that can be observed in ferromagnetic and ferrimagnetic materials when a heat gradient is applied to them [19, 28, 35]. The heat gradient induces a spin voltage in the ferromagnet that can be used to inject pure spin currents into a conductor attached to the ferromagnet. Here, spin voltage is a potential for the spin of electrons, rather than their charge, to drive spin current [19, 36, 37, 38]. Previously mentioned bilayer heterostructures of normal metal/magnetic material have been used to study the SSE in two different configurations: transverse and longitudinal [19, 39]. In the transverse configuration, the generated spin current is perpendicular to the temperature gradient [28]. The generated spin current in the longitudinal configuration is parallel to the temperature gradient [19] (see Figure 5b). The longitudinal configuration has been the dominant choice for SSE research, owing to its simplicity [19]. Magnetic insulators (such as YIG, BaM, etc.) offer an ideal platform for observing the longitudinal spin Seebeck effect (LSSE) [19, 40]. In a conductive ferromagnet, the longitudinal configuration can give rise to a large anomalous Nernst effect (ANE)-induced voltage, which makes it difficult to distinguish between ANE and SSE [19, 33, 41, 42].

If SSE generates pure spin currents, then an important question would be how do we measure them? The absence of charge flow makes it impossible to use conventional methods to measure the spin currents. One way to measure LSSE-generated spin current is to first convert it into a charge current that can then be measured by conventional means. In this context, the choice of the normal metal in the bilayer heterostructure becomes very important. Heavy metals, such as Pt and Au, have strong spin-orbit coupling [43, 44], offering an effective mechanism to convert a transverse spin current into a longitudinal charge current through inverse spin Hall effect (ISHE) [43, 45, 46, 47]. The ISHE charge current across the heavy metal surface creates an electric field E_ISHE that can be measured with a voltmeter. The magnitude and sign of E_ISHE depend on internal and external factors. In Figure 5b, an external magnetic field His applied in the xdirection. The magnetization Mof the MI layer is aligned to the xdirection as well. The temperature gradient is applied across the zdirection, generating a spin voltage in the MI layer, injecting spin current across the interface and into the normal metal layer parallel to the temperature gradient. The polarity of electron spins in the normal metal layer is influenced by Mfrom the MI layer. The ISHE field, E_ISHE, is measured across the ydirection. E_ISHE is proportional to the cross product of the spatial direction of the generated spin current J_sand the polarity vector of electron spins in the normal metal layer. The following equation explains the relationship between E_ISHE, J_s, and σ[19]:

EISHE∝Js×σE4

In summary, the voltage measured across the normal metal surface is strongest when Mis perpendicular to both the heat gradient and E_ISHE; the voltage will flip its sign if Mis flipped by flipping the external magnetic field H; the voltage measured will be zero when Mis parallel to E_ISHE.

This discussion sheds light on the importance of the existence of an external magnetic field Hto enable E_ISHE when using soft magnetic insulators such as spinels and garnets. A strong enough His necessary to saturate the magnetization of such insulators, as well as to control the direction of the magnetization. Indeed, SSE cannot be observed in samples incorporating spinels or garnets with a temperature gradient alone. Due to their low remnant magnetization, an appropriate external magnetic field is required to saturate them.

An exception to the external magnetic field requirement is made when using BaM thin films due to their strong uniaxial anisotropy [18]. In the absence of an external magnetic field, the magnetization of BaM films, caused by the spins of unpaired electrons, tend to favor one axis, called the easy axis, over any other axis. Thus, most electron spins within the BaM film tend to align themselves with the easy axis, randomly up or down, in the absence of an external magnetic field. Therefore, BaM films have uniaxial anisotropy. The uniaxial field of BaM was found to be around 16.5 kOe [9, 18]. Applying a magnetic field of this value or higher along the easy axis of the film causes all the electron spins to align themselves in the direction of the magnetic field, removing the magnetic field then will leave a large remnant magnetization within the BaM film owing to its uniaxial anisotropy. Namely, the film becomes self-biased and does not require an external field to magnetize it.

An LSSE experiment and its results using a Pt/BaM heterostructure [18] will be discussed next. In this experiment the sample consisted of a micron-thick BaM layer, topped with a 2.5-nm-thick Pt layer. The BaM layer was grown on a 0.5 mm sapphire substrate. The easy axis of the BaM film was in the plane of the film.

Figure 6 shows the experiment setup and results. Figure 6a shows a schematic diagram of the experimental setup that was used to test LSSE within the sample. The sample was put on an aluminum plate to act as a heat sink. An incandescent light bulb was placed directly on top of the sample, acting as the heat source. The easy axis of the BaM layer was along the y-axis, and the voltage was measured along the x-axis. All measurements were performed without an external magnetic field. However, a magnetic field of 10 kOe was used prior to the experiment to set the magnetization Mof the BaM film in the positive (or negative) ydirection.

The heat from the light bulb, along with the aluminum plate acting as a heat sink, created the temperature gradient across the BaM film thickness; the difference in temperature between the bottom surface and top surface of BaM, ΔT, was measured using two thermocouples connected to them. When the light is turned on, SSE occurs, the heat gradient induces a spin voltage in the BaM film that injects spin currents across the interface and into the Pt layer. Due to ISHE, the spin current is converted to a charge current across the Pt surface creating a voltage. The voltage was measured by connecting a nanovoltmeter to the opposite ends of the Pt surface across the x-axis.

Figures 6b and c demonstrate the relationship between the difference in temperatures ΔTand the generated voltage, with time, for M∥yand M∥−y, respectively. ΔTwas changed by changing the height of the light bulb. These results show that the SSE-generated spin current, and therefore the observed voltage, changes in exactly the same manner that ΔTchanges with. This result is expected as the difference in temperature is what causes the spin voltage in the BaM film, which ultimately gives us the voltage reading across the Pt layer.

Figure 6d shows an important property of SSE, namely, the sign of the generated voltage flips when the direction of the BaM magnetization is flipped. The graph shows the relationship between ΔTand measured voltage for M∥y(red) and M∥−y(blue). The result again proves that the voltage change with respect to ΔTis identical (mirrored when M∥−ydue to the sign flip), in both cases.

Control measurements were performed and are shown in Figure 7. Changing the lateral position of the light bulb did not have any noticeable effect on the measured voltage. This is to be expected, as the temperature gradient depends on the height of the light bulb, rather than its lateral position. This is demonstrated in Figure 7a, where the light position was changed to six different lateral positions. The figure shows that, other than jumps from electrical disturbance caused by the position change, the measured voltage remained largely unchanged.

Using a Peltier cooler as an added source for the temperature gradient in addition to the light bulb also did not have a noticeable change in the relationship between the measured voltage and ΔT. This is shown in Figure 7b, where a light source was used to create ΔT, and a Peltier cooler was turned on under the sample midway through. Figure 7c shows the voltage change with time for a similar sample with a BaM layer thickness of 0.4 μm, and only a Peltier cooler was used to create the temperature gradient. Both Figure 7b and c show the same result: the measured voltage is directly related to ΔT, regardless of the method used to achieve ΔT.

The importance of using a metal with strong spin-orbit coupling is demonstrated through Figure 7d, where Cu, which has very weak spin-orbit coupling, and therefore very weak ISHE, was used in a Cu (9 nm)/BaM (1.2 μm)/sapphire (0.5 mm) sample. The figure shows a behavior that is different from the Pt/BaM samples, indicating the absence of SSE in this sample. A likely source for the signal shown in Figure 7d is the conventional Seebeck effect, caused by a temperature gradient across the sample’s length. (All figures, experimentation setup and results were taken from [18] with appropriate permissions).

3.2.2 Photo-spin-voltaic effect

A closely related but fundamentally different effect to SSE is the photo-spin-voltaic effect (PSVE). PSVE happens in NM/MI heterostructures; it generates pure spin currents across the NM thickness that can be measured through ISHE. Light can generate spin voltage and drive spin currents through PSVE. While the spin voltage is generated in the MI layer in the SSE case, the spin voltage in PSVE is generated in the atomic layers of the NM that are close to the interface due to magnetic proximity effect [48]. When light of a certain wavelength hits the sample, photons excite electrons in the Pt layer, causing them to move to higher energy bands. The efficiency of this photon-driven excitation varies because of the spin orientation. The difference in efficiency, along with different diffusion rates of excited electrons and holes, generates the spin voltage through PSVE [48].

Figure 8 shows PSVE in a Pt/MI structure. An important question arises due to the extremely similar setup of both LSSE and PSVE: how can we determine the source of the ISHE generated voltage? It could be due to LSSE, or PSVE, or both. Fortunately, research in this area determined several distinguishable factors that make it possible to disentangle LSSE from PSVE. The most important factor is the wavelength of the light used to excite the sample. Experimental results determined that PSVE can only be observed when the wavelength of the light used falls in the range 1600–2000 nm [48]. Using a light source with a wavelength outside that range or a heat source other than light, such as a Peltier cooler, will only give us LSSE in our sample and no PSVE [49]. Other factors include the type of materials and device geometries used in the studies. For example, different MI types and thicknesses give widely different signals in LSSE. A recent work showed that the main contribution in the voltage comes from LSSE rather than PSVE [50]. However, experiments have shown that using a light source with the appropriate wavelength gives extremely similar results in Pt that is coupled with MI of varying types and thicknesses [48].

Figure 9 shows the results of PSVE in three different samples: Pt (2.5 nm)/YIG (78 μm), Pt (2.5 nm)/YIG (21 nm), and Pt (2.5 nm)/BaM (1.2 μm). For each sample, three different experimental setup configurations were tested: illuminating from the sample’s top, illuminating from the sample’s bottom, and illuminating from both the top and bottom of the sample. The phenomena of PSVE in all cases were similar, with a difference that is no bigger than an order of magnitude. This confirms that the voltage is induced by PSVE instead of SEE. Only the sign of the voltage, but not its magnitude, flipped with the flipping of the magnetization of the MI film; this confirms the spin origin of the measured voltage. (All the PSVE information and experimental setup and discussion were taken from [48] with appropriate permissions).

3.3 Spin-orbit torque-assisted switching in magnetic insulators

The uniaxial anisotropy and the nonvolatile nature of easy axis-aligned magnetization within the BaM film can be used to design memory and logic-based systems. If the magnetization is up, it will keep its direction until a magnetic field flips it toward the opposite direction. If an efficient way can be found to switch the magnetization states of the magnetic insulator thin films, then they can be used in magnetic memory systems commercially [51].

In a NM/MI structure, such as Pt/BaM, SHE can be used to convert a charge current across the Pt surface into a spin current that flows across the thickness of Pt through spin-orbit coupling; this process will accumulate spins at the Pt/BaM interface. The spin accumulation generates spin-orbit torques (SOTs) that can be used to switch the BaM magnetization. Each electron provided by the charge current can undergo several spin-flip scatterings at the interface, breaking the conventional spin-torque switching limit and increasing the switching efficiency considerably [51].

We discuss the SOT experimental details of a Pt(5 nm)/BaM(3 nm) sample. The easy axis of the BaM film was perpendicular to the surface of the film. Figure 10b shows the hysteresis loop of the film, measured by a vibrating sample magnetometer, when an out-of-plane external magnetic field was applied (red curve). The olive curve shows the hysteresis loop along the hard axis when the external magnetic field is applied in the plane of the film. This figure confirms the perpendicular uniaxial anisotropy of the film, with a perpendicular anisotropy field of 17.6 kOe. A Hall bar structure was fabricated out of the Pt/BaM bilayer and is shown in Figure 10a. Figure 10c shows a hysteresis loop on the Hall resistance, revealing an anomalous Hall effect (AHE)-like behavior. It is unclear whether the AHE-like behavior is from magnetic proximity effect or spin Hall magnetoresistance. However, R_AHE behaves in a very similar manner to the perpendicular magnetization component of the BaM film M⊥(compare Figure 10b to Figure 10c). This allows for the gauging of M⊥in the BaM film by simply measuring R_AHE.

The first experiment demonstrated was the out-of-plane switching; the external magnetic field is fixed out of the film’s plane and 20° off the easy axis. The purpose of this tilt was to break the magnetization symmetry due to the external field, allowing for the observation of the SOT effect. One would expect that if the SOT field is along the -zdirection, it would act against the external field, thereby increasing the total field required to saturate the magnetization within the BaM film, while a SOT field along the zdirection will aid the external field, resulting in a smaller field required to saturate the magnetization of the BaM film.

Indeed, experimental results, shown in Figure 11, confirm exactly that. Namely, when charge currents of varying intensities are applied to the Pt film along the −ydirection, the SOT direction is opposite to that of H(as shown in Figure 11a), and the resultant hysteresis loops, gauged by R_AHE, become wider as the current intensity increases. This is shown in Figure 11c, where the gray loop is for I = 0; blue, I = −2 mA; olive, I = −4 mA; and red, I = −6 mA. This confirms the existence and the direction of pure spin current-generated SOTs near the interface, the magnitude of which is proportional to the intensity of the supplied current. Flipping the direction of the supplied charge currents flips the direction of the SOT as shown in Figure 11b. The resultant hysteresis loops, shown in Figure 11d, become narrower as the supplied charge current increases, indicating that SOT, in the direction of H, assisted in the magnetization flipping, reducing the overall total external field needed to flip M⊥in the BaM film.

Further experiments were performed to confirm the existence of spin current-generated SOT near the Pt/BaM interface. This time, the external field Hwas within the film plane. This means that applying a saturation field in the film plane will align the electron spins along the hard axis of the BaM film. When His removed, the spins will return to their easy axis, randomly up or down, resulting in a net M⊥of zero. However, when a charge current is supplied to the Pt surface, SOT near the interface will influence the direction of the spins of electrons when His reduced and they start to align to their easy axis. This results in remnant magnetization that is represented by a hysteresis loop. If the direction of the supplied charge current is flipped, the resultant hysteresis loop will be the opposite of the first hysteresis loop. This is shown in Figure 12. This confirms that the direction of the SOT can be controlled by changing the sign of the supplied charge current.

These results confirm that SOT due to pure spin currents, generated by SHE in Pt/BaM structures, can be used to assist the magnetization switching in BaM films. It should be noted however, that SHE generates two different torques: a damping-like torque (DLT) and a field-like torque (FLT). The effective fields for DLT and FLT are H_DLT and H_FLT, respectively. Thus, the total field affecting M⊥of the BaM film can be written as follows [51]:

where His the external field as indicated in Figure 11, H_a is the anisotropy field of the BaM film, and xis the unit vector along the +xdirection. Two different simulation models were carried out to determine the SOT field strength: macrospin model simulation and microspin model simulation.

Carrying out both simulations involved three main steps: first, H_c was calculated when J_c is set to zero. H_DLT and H_FLT were both set to zero as well. H_a was set such that when His equal to the experimentally measured H_c and pointing in the direction opposite to its initial direction, mflips. The second step considers the case when J_c≠0 and H_FLT = 0. Simulations are then performed at given H_DLT values to find the corresponding H_c values. This is because a flip in the direction of H_DLT breaks the symmetry, thereby affecting H_c. A flip in the direction of H_FLT on the other hand does not affect H_c as H_FLT is orthogonal to H_a, H, and m. The third step considers non-zero values of H_DLT and repeats the simulations to find H_c for given combinations of H_DLT and H_FLT values.

The results from running the two different models of simulations were very close and are shown in Figure 13. The blue dots show the linear nature of the relationship between H_c and H_DLT, when H_FLT = 0. This is similar to the experimental H_c vs. J_c data. The simulation showed that when H_DLT is -400 Oe, H_c increases to about 2.0 kOe, and when H_DLT is 400 Oe, H_c decreases to about 0.95 kOe. This same change was experimentally observed when J_c changed between -10⁷ A cm⁻² and 10⁷ A cm⁻². Thus, we can conclude that H_DLT in the Pt/BaM is about 400 Oe at J_c = 10⁷ A cm⁻². The red and olive dots in Figure 13a and b show the same relationship when H_FLT = H_DLT/2 and H_FLT = H_DLT, respectively. The red dots show that the effect of H_FLT is negligible when H_FLT = H_DLT/2, while the olive dots show a deviation for strong negative charge currents that was not observed experimentally. The red and olive portions of both figures prove that the majority of the SHE generated torque is due to DLT, with FLT having a relatively small effect in comparison. The experimental results, along with the simulation data, show that SOT in Pt/BaM films can reduce the required switching field by as much as 500 Oe.

Further improvements and enhancements in the switching efficiency can be achieved by using materials with higher spin-orbit coupling, resulting in stronger SOT. Topological insulators exhibit such requirements and will be the topic of the next section. (All figures, experimentation setup, and results were taken from [51] with appropriate permissions).

3.4 Magnetization switching with topological insulators

Topological insulators (TI) are of great interest in spintronic-related studies. A TI is a material with nontrivial symmetry-protected topological order that behaves as an insulator in its interior but whose surface contains conducting states. What differentiates a TI from other materials with conducting surfaces is that its surface states are time-reversal symmetry-protected. Due to the very strong spin-orbit coupling of TIs [10, 52], if a charge current is supplied to their surface, the surface states induce spin polarity and therefore generate a spin current, owing to the SHE. The SHE in TIs is several times stronger than in heavy metals such as Pt, and it can become hundreds of times stronger at very lower temperatures [10].

Theoretically, the very strong SHE in a TI can generate SOT that is much stronger than its counterpart in heavy metals. This strong SOT can then be exploited for magnetization switching by pairing it with a ferromagnet, similar to what was discussed in the previous section. Using a conductive ferromagnet, however, can completely suppress the surface states of a TI [49, 50, 51, 52, 53, 54, 55, 56], preventing the generation of spin currents, therefore making it impossible for SOT magnetization switching to happen in TI/conductive ferromagnet structures.

Here, the usefulness and importance of magnetic insulators are again emphasized. Pairing a TI with MI keeps the integrity of the surface states. Various materials can be used to create a TI, such as (Bi_xSb_1-x)₂ Te₃. The choice of xcan ensure protection from time-reversal symmetry. Figure 14a and b show the sheet resistance measurements of a (Bi_xSb_1-x)₂Te₃ film that was grown on a MI (Tm₃Fe₅O₁₂, TIG) for x= 0.2 and x= 0.3, respectively. The lower inset of both figures show the broken symmetry of the topological surface states of both configurations. The sheet resistance in both figures shows a linear portion, attributed to the normal Hall effect, and a hysteresis loop portion. The different slopes indicate opposite carriers in each sample. The hysteresis portion indicates strong magnetic uniaxial anisotropy in the TI owing to highly spin-polarized electrons on the TI’s surface. This uniaxial anisotropy is maintained at room temperature and up to T = 400 K [57].

In another experiment, the authors used a Bi₂Se₃/BaM heterostructure to explore the effect of topological surface state in switching the magnetization of a magnetic insulator [10]. The BaM layer used had similar characteristics to the BaM layer used in the Pt/BaM experiment. The BaM film was 5-nm-thick and had a uniaxial anisotropy axis perpendicular to the surface, as shown by the two hysteresis loops in Figure 15a. The blue hysteresis loop was measured when the external field was applied perpendicular to the BaM film’s surface. The red loop was measured when an external field was applied along the BaM film plane. The two loops together confirm the perpendicular orientation of the anisotropy axis of the BaM film.

A Hall bar was fabricated on the Bi₂Se₃/BaM bilayer film. Figure 15c shows that, similar to the Hall bar setup of the Pt/BaM experiment discussed in the previous section, the AHE contribution to the Hall bar resistance, R_AHE, scales with the perpendicular magnetization M⊥of the BaM film and therefore can be used as an easy way to probe M⊥of the BaM film during experimentation. While Figure 15c shows the R_AHE response in room temperature settings, Figure 15d shows R_AHE when T = 3 K. The figure shows a hysteresis loop that is very close to the one in Figure 15c. The hysteresis loop widths are very similar, indicating that the same field strength His required to saturate the magnetization of the BaM film when T = 3 K and when T = 300 K. The value of R_AHE is slightly higher when T = 3 K than when T = 300 K, indicating that the saturation of the BaM film increases slightly as T decreases. The effect of the temperature change on the values of the saturation magnetization of the BaM film and the coercive field required to saturate it are both shown in Figure 15b.

Figure 16a shows the SOT switching experiment configuration. An external field Hwas applied along the xdirection to aid in the SOT switching of M⊥in the BaM film. M⊥was initially along the positive zdirection. Figure 16b shows the experimentation results when T = 200 K and H= -15 kOe. The blue data points show the effect of sweeping a DC charge current I_dc from positive to negative. When the supplied current was positive, the SOT direction was also in the positive zdirection, so we see no change in R_AHE. When I_dc is <0, however, the SOT direction flips to the negative zdirection. When the torque generated by the polarized spin accumulation at the Bi₂Se₃/BaM becomes strong enough, the magnetization within the BaM film switches to the negative zdirection, as indicated by the change in R_AHE value from positive to negative. Sweeping I_dc from negative to positive generates SOT in the +z direction when I_dc > 0; when the SOT is strong enough, it flips the magnetization of the BaM film again, indicated by the red points in the figure. The result from both cases is a hysteresis loop in R_AHE that can be seen in the figure.

Figure 16c,d, and e shows the results of the same experiment performed at decreasing temperatures. The figures clearly indicate that the current required for magnetization switching becomes smaller as temperature decreases. This is due to the enhancement of the topological surface states in Bi₂Se₃ as T decreases.

Figure 17 further demonstrates the effect of SOT on the magnetization switching of the BaM film. The experiment was performed at T = 3 K; the external field was applied at 45 degrees angle out of the plane of the film as shown in the inset of the figure. The blue hysteresis loop is the result of applying a negative charge current that generated a SOT acting against H. The result is a wider hysteresis loop when compared with the normal hysteresis loop of the BaM film shown in Figure 15. This is due to the SOT acting against H, therefore hindering the magnetization switching and requiring a stronger external field to switch the magnetization of the BaM film. The red hysteresis loop shows the result of applying a positive charge current, which caused SOT that was in the direction of the external magnetic field, significantly decreasing the switching field required as shown by the much narrower hysteresis loop. This confirms the strength and significance of SOT in TIs and how it can be used to assist in magnetization switching.

The efficiency of SOT switching can be calculated using the following expression [58]:

where H_SW is the switching field, w is the Hall bar width, and t is Bi₂Se₃ or Pt thickness. The increase of SOT efficiency as the temperature decreases is demonstrated in Figure 18. The blue data points show ηof Bi₂Se₃/BaM as a function of temperature. Note that the Debye temperature of Bi₂Se₃ is about 180 K [59]. When T is >>Debye, the efficiency is proportional to T⁻¹, but when the temperature is <<Debye (at T = 100 K), the efficiency is proportional to T⁻⁵. Pt/BaM SOT efficiency is also shown as a function of temperature on the same plot (red points). The data show that decreasing the temperature has a negligible effect on the efficiency in Pt/BaM bilayers. The exponential improvement in SOT efficiency of Bi₂Se₃/BaM is caused by the fact that the surface conductance in TIs increases with decreasing temperatures, while the bulk conductance decreases. This means that the decrease in T enhances the TSS in TIs, resulting in a higher charge current to spin current conversion efficiency, increasing the spin polarity in TIs and therefore generating higher SOT. (All figures, experimentation setup and results were taken from [10] with appropriate permissions).

3.5 Summary and outlook

Magnetic insulators with perpendicular anisotropy have become an important class of materials in the development of spintronic devices. For magnetic domain devices, the low-damping and large anisotropy features can enable high-speed domain-wall motion with a small current threshold, fueling the development of domain-wall memory and logic devices. Moreover, low-damping is significant for SOT oscillator applications, where the current threshold for self-oscillations decreases with damping. Recent experiments show that spin waves can be used to control magnetic domains through spin-orbit torques [60, 61]; this effect can be amplified and become more efficient in magnetic insulators. The strong magnetic anisotropy also allows the engineering of spin-wave dispersion relation without the need for large bias magnetic fields [62]. This will expand the horizon for magnonic and spin-wave devices, allowing the development of new magnon-photon coupling devices for quantum transduction and microwave photonic systems [63, 64].