Ferromagnetic Resonance Field Research Articles

Nanostructured Coatings of 3d-Metals Produced by Green Chemistry Methods: Analysis of Inhomogeneities by Static and Dynamic Magnetic Methods

The study investigates carbon-containing coatings of 3d-metals (Ni, Co, Fe) produced by chemical deposition method using arabinogalactan. The coatings were analyzed using X-ray diffraction, FMR, and M(H) magnetometry. Measurement of M(H) in plane and perpendicular to the plane of the magnetic coatings allowed determining the distribution of demagnetizing factor in the studied coatings. The obtained distributions of the demagnetizing factor were used to analyze the angular dependences of the ferromagnetic resonance field. The values of magnetization and perpendicular anisotropy field were estimated. The paper illustrates the effect of texture on the magnetic parameters.

Effects of Magnetostatic Interactions in FeNi-Based Multilayered Magnetoimpedance Elements.

Multilayered [Cu(3 nm)/FeNi(100 nm)]5/Cu(150 nm)/FeNi(10 nm)/Cu(150 nm)/FeNi(10 nm)/Cu(150 nm)/[Cu(3 nm)/FeNi(100 nm)]5 structures were obtained by using the magnetron sputtering technique in the external in-plane magnetic field. From these, multilayer magnetoimpedance elements were fabricated in the shape of elongated stripes using the lift-off lithographic process. In order to obtain maximum magnetoimpedance (MI) sensitivity with respect to the external magnetic field, the short side of the rectangular element was oriented along the direction of the technological magnetic field applied during the multilayered structure deposition. MI sensitivity was defined as the change of the total impedance or its real part per unit of the magnetic field. The design of the elements (multilayered structure, shape of the element, etc.) contributed to the dynamic and static magnetic properties. The magnetostatic properties of the MI elements, including analysis of the magnetic domain structure, indicated the crucial importance of magnetostatic interactions between FeNi magnetic layers in the analyzed [Cu(3 nm)/FeNi(100 nm)]5 multilayers. In addition, the uniformity of the magnetic parameters was defined by the advanced technique of the local measurements of the ferromagnetic resonance field. Dynamic methods allowed investigation of the elements at different thicknesses by varying the frequency of the electromagnetic excitation. The maximum sensitivity of 40%/Oe with respect to the applied field in the range of the fields of 3 Oe to 5 Oe is promising for different applications.

Signatures of magnetism control by flow of angular momentum

Exploring new strategies to manipulate the order parameter of magnetic materials by electrical means is of great importance not only for advancing our understanding of fundamental magnetism but also for unlocking potential applications. A well-established concept uses gate voltages to control magnetic properties by modulating the carrier population in a capacitor structure1–5. Here we show that, in Pt/Al/Fe/GaAs(001) multilayers, the application of an in-plane charge current in Pt leads to a shift in the ferromagnetic resonance field depending on the microwave frequency when the Fe film is sufficiently thin. The experimental observation is interpreted as a current-induced modification of the magnetocrystalline anisotropy ΔHA of Fe. We show that (1) ΔHA decreases with increasing Fe film thickness and is connected to the damping-like torque; and (2) ΔHA depends not only on the polarity of charge current but also on the magnetization direction, that is, ΔHA has an opposite sign when the magnetization direction is reversed. The symmetry of the modification is consistent with a current-induced spin6–8 and/or orbit9–13 accumulation, which, respectively, act on the spin and/or orbit component of the magnetization. In this study, as Pt is regarded as a typical spin current source6,14, the spin current can play a dominant part. The control of magnetism by a spin current results from the modified exchange splitting of the majority and minority spin bands, providing functionality that was previously unknown and could be useful in advanced spintronic devices.

Greatly Improved the Tunable Amplitude of Ferromagnetism Based on Interface Effect of Flexible Pt/YIG Heterojunctions.

Flexible quantum spin electronic devices based on ferromagnetic insulators have attracted wide attention due to their outstanding advantages of low-power dissipation and noncontact sensing. However, ferromagnetic insulators, such as monocrystalline yttrium iron garnet (Y3Fe5O12, YIG), hve weak stress effects with a small magnetostrictive coefficient (λ110, 10 ppm), making it difficult to achieve a large magnetic tunable amplitude. In this paper, large-scale (with a diameter of 40 mm), flexible Pt/YIG heterojunctions were obtained by double-cavity magnetron sputtering technology, indicating typical soft magnetism and good bending fatigue characteristics. Here, the 3 nm thickness of the Pt layer triggers an obvious magnetic proximity effect, in which the in-plane ferromagnetic resonance field is decreased by 70 Oe compared to flexible Cu/YIG heterojunctions. Meanwhile, it shows a wide tunable amplitude of 110 Oe under the flexible bending stresses, which is induced by the sensitive interface effect of Pt (3 nm)/YIG heterojunctions. The saturation magnetization of Pt/YIG heterojunctions is negatively correlated with Pt thickness rather than the relative stability of Cu/YIG heterojunctions, depending on the magnetic proximity effect. It brings greater application possibilities for flexible stress-sensitive magnetic oxides in spin logic electronic devices.

Electrostatic Gating of Spin Dynamics of a Quasi-2D Kagome Magnet.

Electrostatic gating has emerged as a powerful technique for tailoring the magnetic properties of two-dimensional (2D) magnets, offering exciting prospects including enhancement of magnetic anisotropy, boosting Curie temperature, and strengthening exchange coupling effects. Here, we focus on electrical control of the ferromagnetic resonance of the quasi-2D Kagome magnet Cu(1,3-bdc). By harnessing an electrostatic field through ionic liquid gating, significant shifts are observed in the ferromagnetic resonance field in both out-of-plane and in-plane measurements. Moreover, the effective magnetization and gyromagnetic ratios display voltage-dependent variations. A closer examination reveals that the voltage-induced changes can modulate magnetocrystalline anisotropy by several hundred gauss, while the impact on orbital magnetization remains relatively subtle. Density functional theory (DFT) calculations reveal varying d-orbital hybridizations at different voltages. This research unveils intricate physics within the Kagome lattice magnet and further underscores the potential of electrostatic manipulation in steering magnetism with promising implications for the development of spintronic devices.

Characterization of In‐Plane Piezoelectric Strain of Ferroelectric Thin Films by the Magnetoelectric Coupling Effect

Piezoelectric response of the ferroelectric/piezoelectric thin films is crucial for actuation of micro‐electromechanical systems (MEMS) devices as well as strain‐mediated electronic devices. Among many piezoelectric modes, longitudinal and transverse piezostrain is the most widely used. Various methods have been well established for quantitative characterization of the longitudinal piezostrain, such as laser interferometer and piezoelectric force microscopy. However, it is still a great challenge to characterize transverse piezostrain. Herein, a new method is established to characterize the transverse (in‐plane) piezostrain of ferroelectric/piezoelectric thin films by the inverse magnetoelectric (ME) coupling effect. A ferromagnetic thin film is patterned onto the ferroelectric thin film to form an artificial multiferroic heterostructure. The transverse piezostrain can transfer from the ferroelectric layer to the ferromagnetic layer and shift its ferromagnetic resonance field through the ME coupling effect. By comparing with a control sample of “bulk piezoceramic/ferromagnetic thin film” whose in‐plane piezostrain can be easily measured, the in‐plane piezostrain and piezoelectric coefficient of the ferroelectric thin films are then estimated. The in‐plane piezoelectric coefficient d31 and piezoelectric strain S31 of Pb(Zr,Ti)O3 (PZT) thin films are measured by this method. This new method will promote to fully understand the piezoelectric properties of the ferroelectric/piezoelectric thin films.

Twisted Integration of Complex Oxide Magnetoelectric Heterostructures via Water-Etching and Transfer Process

HighlightsThe (001)-oriented ferromagnetic La0.67Sr0.33MnO3 films are stuck onto the (011)-oriented ferroelectric single-crystal 0.7Pb(Mg1/3Nb2/3)O3–0.3PbTiO3 substrate with 0° and 45° twist angle.By applying a 7.2 kV cm−1 electric field, the coexistence of uniaxial and fourfold in-plane magnetic anisotropy is observed in 45° Sample, while a typical uniaxial anisotropy is found in 0° Sample.Manipulating strain mode and degree that can be applied to epitaxial complex oxide thin films have been a cornerstone of strain engineering. In recent years, lift-off and transfer technology of the epitaxial oxide thin films have been developed that enabled the integration of heterostructures without the limitation of material types and crystal orientations. Moreover, twisted integration would provide a more interesting strategy in artificial magnetoelectric heterostructures. A specific twist angle between the ferroelectric and ferromagnetic oxide layers corresponds to the distinct strain regulation modes in the magnetoelectric coupling process, which could provide some insight in to the physical phenomena. In this work, the La0.67Sr0.33MnO3 (001)/0.7Pb(Mg1/3Nb2/3)O3–0.3PbTiO3 (011) (LSMO/PMN-PT) heterostructures with 45º and 0º twist angles were assembled via water-etching and transfer process. The transferred LSMO films exhibit a fourfold magnetic anisotropy with easy axis along LSMO < 110 >. A coexistence of uniaxial and fourfold magnetic anisotropy with LSMO [110] easy axis is observed for the 45° Sample by applying a 7.2 kV cm−1 electrical field, significantly different from a uniaxial anisotropy with LSMO [100] easy axis for the 0° Sample. The fitting of the ferromagnetic resonance field reveals that the strain coupling generated by the 45° twist angle causes different lattice distortion of LSMO, thereby enhancing both the fourfold and uniaxial anisotropy. This work confirms the twisting degrees of freedom for magnetoelectric coupling and opens opportunities for fabricating artificial magnetoelectric heterostructures.

Flexible, Bending Stable, and Biocompatible Silk Fibroin/NiFe Films for Bio‐Integrated Microwave Applications

AbstractIntegration of magnetic materials into bio‐integrated flexible electronics will bring multi‐functionality, such as magnetoception and wireless communication. In practical application, the performance of magnetic materials and devices should remain stable during cyclic bending–unbending and they can be degradable within a designated lifetime. However, direct integration of magnetic materials with flexible and biocompatible materials and maintaining mechanically stable microwave performance have not been achieved yet. Here, ultrathin (5–50 nm) permalloy (NiFe) films deposited on biocompatible silk fibroin (SF) films are shown to be bending stable, and dissolvable. The ferromagnetic properties of NiFe films deposited on SF, Kapton, and silicon are studied and compared by ferromagnetic resonance. Benefiting from the low surface roughness of fibroin, which is only ≈0.8 nm, SF/NiFe films exhibit comparable ferromagnetic properties to Si/NiFe, better than that of Kapton/NiFe films. Moreover, the ferromagnetic resonance field of SF/NiFe films remains highly stable during cyclic bending that is exposed to both compressive and tensile strain/stress, and its temperature stability is very close to that of Si/NiFe. Finally, the whole SF/NiFe films are demonstrated to be dissolvable and biocompatible. Therefore, SF/NiFe films can be a useful and stable platform for flexible and biocompatible microwave applications.

Electric field control of the ferromagnetic resonance linewidth in synthetic antiferromagnetic heterostructure

In this study, we present a novel approach to control the microwave properties of a Co/Ru/FeNi film, characterized by strong antiferromagnetic coupling and in plane uniaxial anisotropy. The film is fabricated on a Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) ferroelectric substrate using the magnetron oblique sputtering. Our experimental results demonstrate a remarkable non-volatile mediation of the ferromagnetic resonance (FMR) field and linewidth by applying the perpendicular-bias electric field. The observed asymmetric butterfly curve indicates the existence of electric mediation dominated by strain effect. Moreover, we investigate the angular dependence of FMR under different electric field, which reveals changes in magnetic anisotropy including FMR field. Notably, the FMR linewidth exhibits a distinctive four-fold anisotropy. Through microstructure analysis of the film surface, we identify that the origin of this FMR linewidth anisotropy is attributed to the two-magnon scattering induced by the oblique sputtering.

Manipulations of Spin Wave by Photoelectrons in Ferromagnetic/Non-Ferromagnetic Alloyed Film.

Spin wave is considered an alternative carrier with great promise for information sensing. The feasible excitation and low-power manipulation of spin waves still remain a challenge. In this regard, natural light enables spin wave tunability is profoundly investigated in Co60 Al40 alloyed film. A reversible manner with 2° of the critical angle of the body spin wave is achieved successfully. Meanwhile, an eye-catching shift (817Oe) of the ferromagnetic resonance (FMR) field is obtained optically, leading to changes in magnetic anisotropy. Based on the modified Puszkarski's surface inhomogeneity model, the sunlight control of spin-wave resonance (SWR) can be comprehended by a photoelectron-doping-induced effective surface magnetic anisotropy change. Furthermore, the body spin wave is modulated stably with natural light illumination, confirming a non-volatile, reversible switching behavior. This work has both practical and theoretical importance for developing future sunlight-tunable magnonics/spintronics devices. This article is protected by copyright. All rights reserved.

Spin mixing conductance and spin magnetoresistance of the iridate/manganite interface

We present results on experimental studies of spin current, measured under spin pumping at ferromag-netic resonance in wide frequency band 2-20 GHz for SrIrO3/La0.7Sr0.3MnO3 heterostructures fabricated by RF magnetron sputtering at high temperature. The epitaxial growth of the thin film in heterostructure by a cube-on-cube mechanism was confirmed by XRD and TEM analysis. Taking into account the con-tribution of anisotropic magnetoresistance the spin current was estimated as 1/3 of the total response. We show that both real and imaginary parts of spin mixing conductance are valuable for heterostructures with strong spin-orbit interaction in SrIrO3. Imaginary part of spin mixing conductance was estimated by means of shift of ferromagnetic resonance field of La0.7Sr0.3MnO3 layer in heterostructure. The spin mag-netoresistance was evaluated from angular dependencies of magnetoresistance measured in planar Hall configuration. In order to extract the influence of anisotropic magnetoresistance a La0.7Sr0.3MnO3 film was measured as well. The spin Hall angle for heterostructure was found higher than for interface Pt/ La0.7Sr0.3MnO3.

Electric field tuning of ferromagnetic resonance field and linewidth in epitaxial LiFe5O8/PMN-PT (0 1 1) heterostructure

Here a typical ME heterostructure is prepared by growing epitaxial LiFe5O8 (LFO) thin films on Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) (011) substrates by pulse laser deposition (PLD). Ferromagnetic resonance (FMR) test results at in situ voltage show that the tunability of FMR field (Hr) and linewidth (ΔH) have strong angular dependences with external magnetic field. It is inferred that the change of the orientation of equilibrium magnetization contributes to the abnormal enhancement of ME coupling at certain angles. The theoretical fitting reveals that the Gilbert damping (ΔHGilb), two-magnon scattering (ΔHTMS) and inhomogeneous broadening (ΔHinhom) play the different roles for the increase of linewidth of LFO film at various magnetic field directions. Additionally, the ME coupling in LFO/PMN-PT (011) heterostructure shows well temperature stability at range of 100–300 K. Those discoveries enrich the understanding of the ME phenomenon and provide guidance to the development of novel multiferroic materials and devices.

Magneto-mechanical Effect of NiFe Thin Films Depending on the Intrinsic Magnetic Anisotropy

Verifying magnetic anisotropy is essential for developing flexible magnetic devices. The magneto-mechanical effect is a unique phenomenon in magnetic materials for bending geometries and produces the stress magnetic anisotropy depending on the stress direction and its magneto-striction coefficient. In addition, the fabrication process for the flexible magnetic devices, such as deposition, annealing, and patterning, significantly causes the intrinsic magnetic anisotropy to change the reversal behaviors in the devices. This study investigated the variation of the stress magnetic anisotropy in the flexible NiFe (permalloy) thin films as a function of the bending repetition and its direction when the thin films had a different easy axis caused by the sputtering process. The variation of the stress magnetic anisotropy was observed by the magnetization reversal behaviors and the typical ferromagnetic resonance field detection before and after the application of the tensile stress. The stress effect was exponentially accumulated with increasing bending repetition on the thin film in both samples. However, when the repeated stress was applied in alternating x- and y-directions, minor resonance field fluctuation was observed in the film, which had the tilted intrinsic magnetic anisotropy. This result indicated that intrinsic magnetic anisotropy during the fabrication process played an essential role in determining the amount of effective field for designing flexible magnetic devices.

Bending Switch of Gigahertz La0.67Sr0.33MnO3 Thin Film Under Spin Wave Excitation

Spin waves, used for information processing and transmission, promise huge potential in the applications of the spintronic devices with low loss, minimal sizes, and high frequency. More attentions have been focused on all-magnon data processing utilizing traveling spin waves and moving domain walls. Bending control of spin wave is an effective modulation method for magnetic properties, and easily attuned to the trends of flexible magnon spintronics in future. In this work, we demonstrate the excitation of spin waves in the flexible La0.67Sr0.33MnO3 thin film by mechanical bending, which can be taken as the states for On and Off in microwave single-pole single-throw switches. Besides, the microwave magnetisms of the unbent and bending La0.67Sr0.33MnO3 thin films have been studied. The bending of La0.67Sr0.33MnO3 thin films does not change the microwave ferromagnetic resonance field. Our results demonstrate that the controllable spin wave state by mechanical bending has enormous potential for future flexible magnon spintronics.

Anomalous temperature dependence of phonon pumping by ferromagnetic resonance in Co/Pd multilayers with perpendicular anisotropy

We demonstrate the pumping of phonons by ferromagnetic resonance in a series of [Co(0.8 nm)/Pd(1.5 nm)]$_n$ multilayers ($n =$ 6, 11, 15, and 20) with large magnetostriction and perpendicular magnetic anisotropy. The effect is shown using broadband ferromagnetic resonance over a range of temperatures (10 to 300 K), where a resonant damping enhancement is observed at frequencies corresponding to standing wave phonons across the multilayer. The strength of this effect is enhanced by approximately a factor of 4 at 10 K compared to room temperature, which is anomalous in the sense that the temperature dependence of the magnetostriction predicts an enhancement that is less than a factor of 2. Lastly, we demonstrate that the damping enhancement is correlated with a shift in the ferromagnetic resonance field as predicted quantitatively from linear response theory.

Strain Modulation of Perpendicular Magnetic Anisotropy in Wrinkle-Patterned (Co/Pt)5/BaTiO3 Magnetoelectric Heterostructures.

The rapid development of spintronics requires the devices to be flexible, to be used in wearable electronics, and controllable, to be used with magnetoelectric (ME) structures. However, the clamping effect inevitably leads to a decreased ME effect on the rigid substrate, and it remains challenging to directly prepare high-quality ferroelectric (FE) membranes on the widely used flexible substrate such as MICA or polyimide (PI). Here, periodic wrinkle-patterned flexible (Co/Pt)5/BaTiO3 (BTO) perpendicular magnetic anisotropy (PMA) heterostructures were prepared using the water-soluble method. The high-quality single-crystal BTO membrane ensures that intricate wrinkles do not fracture and a high ME coefficient is achievable. The transferred sample that is released from the clamping effect shows an enhanced ME effect in both in-plane and out-of-plane directions, with the ME coefficient reaching up to 68 Oe °C-1. The ferromagnetic resonance (FMR) field of the flexible sample can be tuned by tensile strain up to 272 Oe. The finely controlled wrinkle shows periodic strain variations at peak and valley regions that switch the PMA magnetic domain motion as an effective control method. The proposed ultraflexible wrinkle sample shows great potential for combining multiple magnetization tuning approaches, allowing it to potentially serve as a tunable high-density 3D storage prototype.

Photoelectron-induced quantitative regulation of ferromagnetism in Permalloy at room temperature for photovoltaic flexible spintronics

Flexible spintronics has recently sparked an upsurge due to the growing demand for miniaturization, high-speed, integration and energy-saving in portable and wearable devices. However, the stress/strain during the substrate deformation process is inevitable for flexible spintronic devices and may be available to assist the switching of the magnetization, accordingly. Therefore, combined with the previously discovered high energy efficient sunlight controlled magnetization switching, we propose a bending-insensitive photovoltaic flexible spintronic device constructed by PET/Ta/Permalloy/(PC71BM: PTB7-Th)/Pt heterostructure. The bent device achieved a 281 Oe of maximal ferromagnetic resonance (FMR) field shift by photoelectrons in a reversible manner under the sunlight soaking at room temperature. And the magnetic change as a function of the external light radiation was precisely determined. These findings provide a feasible way to combine the flexible substrate and photoelectrons for energy-saving and precise manipulation of magnetism in bendable spintronic devices.

Linearly shifting ferromagnetic resonance response of La0.7Sr0.3MnO3 thin film for body temperature sensors.

Human body temperature not only reflects vital signs, but also affects the state of various organs through blood circulation, and even affects lifespan. Here a wireless body temperature detection scheme was presented that the temperature was extracted by investigating the out-of-plane (OP) ferromagnetic resonance (FMR) field of 10.2 nm thick La0.7Sr0.3MnO3 (LSMO) film using electron paramagnetic resonance (EPR) technique. Within the range of 34–42 °C, the OP FMR field changes linearly with the increasing or decreasing temperature, and this variation comes from the linear responses of magnetization to the fluctuant temperature. Using this method, a tiny temperature change (< 0.1 °C) of organisms can be detected accurately and sensitively, which shows great potential in body temperature monitoring for humans and mammals.

Twofold and fourfold anisotropies in zinc ferrite thin films investigated by ferromagnetic resonance

By means of the ferromagnetic resonance (FMR) technique (at the $X$ band) we investigated the magnetic properties of ${\mathrm{ZnFe}}_{2}{\mathrm{O}}_{4}$ (ZFO) films grown on different substrates. Angular dependence of the FMR field showed the existence of twofold and fourfold anisotropies for the same material, grown on Si(111), MgO(100), and STO(100), respectively. By using a model that takes into consideration the relevant contributions to the energy, we were able to extract the following parameters: effective magnetization ${M}_{\mathrm{eff}}$, cubic magnetocrystalline anisotropy field, in-plane and out of plane uniaxial anisotropy fields, and the $g$ factor. The samples deposited on Si showed a twofold in-plane anisotropy while a fourfold magnetic anisotropy was observed for the ZFO/MgO and ZFO/${\mathrm{SrTiO}}_{3}$ samples. All samples showed a strong perpendicular uniaxial anisotropy above 1 kOe and low in-plane uniaxial and cubic anisotropy field, on the order of tens of oersteds. The FMR linewidth ($\mathrm{\ensuremath{\Delta}}H$) fitted from FMR data shows $\mathrm{\ensuremath{\Delta}}H$ values above 190 Oe for all samples, indicating high damping of this material to be $\ensuremath{\sim}{10}^{\ensuremath{-}2}$ for the ZFO/MgO. The present analysis compared the FMR data obtained for the in-plane and out of plane measurements. Likewise, the effective magnetization and perpendicular uniaxial anisotropy field by FMR were compared with the magnetic response obtained by a vibrating sample magnetometer.

Magnetic anisotropy and reversal in epitaxial FeGa/IrMn bilayers with different orientations of exchange bias

Epitaxial FeGa/IrMn bilayers with exchange biases along the FeGa[100] and [110] directions are prepared on MgO(001) single crystal substrates by magnetron sputtering through controlling the orientation of the external field &lt;i&gt;in situ&lt;/i&gt; applied during growth. The effect of the exchange bias orientation on the magnetic switching process and the magnetic switching field are studied. The X-ray &lt;i&gt;φ&lt;/i&gt;-scan indicates that the FeGa layer is epitaxially grown with a 45° in-plane rotation on the MgO(001) substrate along the FeGa(001)[110] direction and the MgO(001)[100] direction. The measurements of the angular dependence of the ferromagnetic resonance field and the corresponding fitting to the Kittel equation show that the samples have a superposition of fourfold symmetric magnetocrystalline anisotropy &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$ {K}_{1} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M4.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M4.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;, unidirectional magnetic exchange bias anisotropy &lt;inline-formula&gt;&lt;tex-math id="M5"&gt;\begin{document}$ {K}_{\mathrm{e}\mathrm{b}} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M5.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M5.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;, and uniaxial magnetic anisotropy &lt;inline-formula&gt;&lt;tex-math id="M6"&gt;\begin{document}$ {K}_{\mathrm{u}} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M6.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M6.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; with configuration of &lt;inline-formula&gt;&lt;tex-math id="M7"&gt;\begin{document}$ {K}_{\mathrm{e}\mathrm{b}}//\left[100\right] $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M7.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M7.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; or &lt;inline-formula&gt;&lt;tex-math id="M8"&gt;\begin{document}$ {K}_{\mathrm{e}\mathrm{b}}//\left[110\right] $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M8.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M8.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;. The combined longitudinal and transverse magneto-optical Kerr effect measurements show that sample with &lt;inline-formula&gt;&lt;tex-math id="M9"&gt;\begin{document}$ {K}_{\mathrm{e}\mathrm{b}}//\left[100\right] $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M9.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M9.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; exhibits square loops, asymmetrically shaped loops, and one-sided two-step loops in different external magnetic field directions. In contrast, the sample with &lt;inline-formula&gt;&lt;tex-math id="M10"&gt;\begin{document}$ {K}_{\mathrm{e}\mathrm{b}}//\left[110\right] $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M10.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M10.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; exhibits one-sided two-step and two-sided two-step loops as the magnetic field orientation changes. Because the &lt;inline-formula&gt;&lt;tex-math id="M11"&gt;\begin{document}$ {K}_{1} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M11.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M11.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; is superimposed by &lt;inline-formula&gt;&lt;tex-math id="M12"&gt;\begin{document}$ {K}_{\mathrm{u}} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M12.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M12.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; and &lt;inline-formula&gt;&lt;tex-math id="M13"&gt;\begin{document}$ {K}_{\mathrm{e}\mathrm{b}} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M13.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M13.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;, the in-plane fourfold symmetry of the magnetic anisotropy energy is broken. The local minima are no longer strictly along the in-plane &lt;inline-formula&gt;&lt;tex-math id="M14"&gt;\begin{document}$ \left\langle{100}\right\rangle $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M14.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M14.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; directions, but make a deviation angle which depends on the relative orientation and strength of magnetic anisotropy. A model based on the domain wall nucleation and propagation is proposed with considering the different orientations of &lt;inline-formula&gt;&lt;tex-math id="M15"&gt;\begin{document}$ {K}_{\mathrm{e}\mathrm{b}} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M15.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M15.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;, which can nicely explain the change of the magnetic switching route with the magnetic field orientation and fit the angular dependence of the magnetic switching fields, indicating a significant change of domain wall nucleation energy as the orientation of &lt;inline-formula&gt;&lt;tex-math id="M16"&gt;\begin{document}$ {K}_{\mathrm{e}\mathrm{b}} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M16.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M16.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; changes.