Dual-axis control of magnetic anisotropy in a single crystal Co2MnSi thin film through piezo-voltage-induced strain

Voltage controlled magnetic anisotropy (VCMA) has been considered as an effective method in traditional magnetic devices with lower power consumption. In this article, we have investigated the dual-axis control of magnetic anisotropy in Co2MnSi/GaAs/PZT hybrid heterostructures through piezo-voltage-induced strain using longitudinal magneto-optical Kerr effect (LMOKE) microscopy. The major modification of in-plane magnetic anisotropy of the Co2MnSi thin film is controlled obviously by the piezo-voltages of the lead zirconate titanate (PZT) piezotransducer, accompanied by the coercivity field and magnetocrystalline anisotropy significantly manipulated. Because in-plane cubic magnetic anisotropy and uniaxial magnetic anisotropy coexist in the Co2MnSi thin film, the initial double easy axes of cubic split to an easiest axis (square loop) and an easier axis (two-step loop). While the stress direction is parallel to the [1−10] easiest axis (sample I), the square loop of the [1−10] direction could transform to a two-step loop under the negative piezo-voltages (compressed state). At the same time, the initial two-step loop of the [110] axis simultaneously changes to a square loop (the easiest axis). Otherwise, we designed and fabricated the sample II in which the PZT stress is parallel to the [110] two-step axis. The phenomenon of VCMA was also obtained along the [110] and [1−10] directions. However, the manipulated results of sample II were in contrast to those of the sample I under the piezo-voltages. Thus, an effective dual-axis regulation of the in-plane magnetization rotation was demonstrated in this work. Such a finding proposes a more optimized method for the magnetic logic gates and memories based on voltage-controlled magnetic anisotropy in the future.


Introduction
Pure electrical manipulation of magnetization rotation in magnetic devices is a desirable way for spintronic applications, which is suitable for the scaling of devices in the integrated circuit. To date, there have been multiple types of electrical manipulation ways of the magnetization rotation or magnetic anisotropy variation, such as spin-orbit torque (SOT), 1-7 spin transfer torque (STT), [8][9][10][11] magneto-electrical coupling (MEC) effect, [12][13][14][15][16][17] and strain. [18][19][20][21][22][23][24][25] The piezo-voltage-induced strain, as a way of voltage-controlled magnetic anisotropy (VCMA), has attracted the attention of many researchers due to the performance of low-power consumption. 22,25 The main studies of strain controlled magnetization are related to the inverse piezoelectric effect of piezoelectric materials in the ferromagnetic/piezoelectric heterostructure. The magnetocrystalline anisotropy is controlled by voltage through the piezo-voltage-induced strain transformed to the magnetic thin lm. Usually, the change of magnetocrystalline anisotropies is related to the strain-manipulated variations of the lattice constant. 23 However, the previous relative studies of straincontrolled magnetization rotation were mainly demonstrated in a uniaxial regulation manner. [22][23][24]26 The stress regulation characteristic disappears or weakens when the specic crystal orientation of magnetic thin lms rotates relative to the stress axis. This problem would be effectively avoided by realizing dual-axis or multi-axis stress-regulated magnetization rotation. However, the related research is still relatively lacking.
In recent years, the Co-based full-Heusler alloys have attracted considerable interest due to the high spin polarization and Curie temperature, 27 which are promising candidates for the next generation information processing and storage in spintronic devices. The coexistence of the in-plane cubic and uniaxial magnetic anisotropies was observed when Heusler alloys are deposited on the GaAs (001) substrate. [28][29][30] The initial in-plane easiest axis (square loop) and easier axis (two-step loop) have been measured along two axes of minimum value of the cubic anisotropy, which is caused by the superposition of the uniaxial anisotropy. It is well known that a uniaxial stress could induce an extra uniaxial anisotropy in magnetic lms. Thus, using the competition of uniaxial anisotropy induced by interface and stress in magnetic lms can realize the regulation of magnetic anisotropy energy and magnetization rotation.
In this work, we have studied the dual-axis control of magnetic anisotropy in the Co 2 MnSi/GaAs/PZT heterostructures through piezo-voltage-induced strain. By studying the variation of the magnetic coercivity (H c ) and remnant magnetization (M r ) in Co 2 MnSi magnetic thin lm, the strong voltage-controlled magnetic anisotropy was veried. Furthermore, we measured the periodic-strain controlled magnetization by applying pulsed piezo-voltages. Two stable states have been achieved with the periodic measurement in two samples. The dual-axis control of the magnetic anisotropy in this work proposes a method of voltage-controlled magnetic logic devices, which will simplify the growth process of magnetic materials and reduce energy consumption.

Methods
The 10 nm Co 2 MnSi thin lm was grown at 250 C on a GaAs (001) substrate using molecular-beam epitaxy (MBE). 28,29 Its Curie temperature is 985 K. 27 Following the growth of 10 nmthick single crystal Co 2 MnSi, a 3 nm thick platinum (Pt) layer was deposited to avoid the oxidation (as shown in Fig. 1a). In order to guarantee that the strain induced by the lead zirconate titanate (PZT) piezotransducer can be effectively transferred to the Co 2 MnSi lm, we thinned the GaAs substrate of the sample to 100 mm before it was bonded to PZT by two-component epoxy. To study the dual-axis control of magnetic anisotropy, the [1À10] and [110] directions of Co 2 MnSi samples are parallel to the z-axis of PZT, respectively. The Co 2 MnSi/GaAs/PZT heterostructure was in a compressed state when the piezo-voltage was negative, and in a stretched state when the piezo-voltage was positive (as shown in Fig. 1a). The magnitude of the additional uniaxial strain for a piezo-voltage of 80 V is approximately 5.2 Â 10 À4 . 30 The magnetization vectors of the Co 2 MnSi samples (S ¼ 3 Â 4 mm 2 ) were measured by longitudinal magneto-optical Kerr microscopy (Nano MOKE3) and a superconducting quantum interference device (SQUID) magnetometer. The piezo-voltages were applied with an Agilent B1500A with the leading and trailing time being both 100 ns. All the measurements were carried out at room temperature. To further study the dual-axis control of magnetic anisotropy in Co 2 MnSi/GaAs/PZT heterostructures, we measured the magnetic hysteresis loops of two samples along the [1À10], [110] and [100] directions under positive and negative piezovoltages. Fig. 2 shows the piezo-voltage controlled magnetic hysteresis loops in sample I. With the piezo-voltages increasing from À10 to 40 V, the loops of the [1À10] direction kept stabilized (as shown in Fig. 2a). At the same time, we also measured the loops of the [110] direction and the loops changed to a twostep loop, accompanied by increasing the saturation eld from 6.1 to 13.1 Oe (as shown in Fig. 2c). From there, the stretched strain could effectively manipulate the in-plane magnetocrystalline anisotropy. In contrast, we also measured the loops compression state under negative piezo-voltages. The magnetic hysteresis loops of the [1À10] easy axis showed obvious regulatory phenomena (as shown in Fig. 2b). With the piezo-voltages changing from À30 to À60 V, the saturation eld of the two-step loop increased from 7.2 to 16.5 Oe. However, the loop of the [110] axis changed to a square curve and kept stabilized (as shown in Fig. 2d). Through the regulation of piezo-voltages, we can obtain two completely opposite and stable phenomena under AE40 V (as shown in Fig. 3a and b), which would be able to meet the needs of two states and facilitate the design of magnetic storage and logic devices. In order to clarify the discipline of VCMA in sample I, the dependence of the saturation eld with piezo-voltages along the [110] and [1À10] directions is summarized in Fig. 3c. Obviously, the saturation eld changes gradually with the piezo-voltage and the variation trend of the saturation eld is exactly opposite in the [110] and [1À10] directions. It indicates that the in-plane magnetocrystalline anisotropy of the Co 2 MnSi lm is obviously controlled under the regulation of piezo-voltages. In addition, we also measured the magnetic hysteresis loops along the [100] crystal direction (as shown in Fig. 3d). The loops of the [100] direction keep a hard axis loop with a slight change of coercive eld under positive or negative piezo-voltages. Through the study of piezovoltage controlled in-plane crystalline anisotropy in sample I, the VCMA is well demonstrated in the Co 2 MnSi/GaAs/PZT heterostructures.

Results and discussion
In order to verify the dual-axis control of magnetic anisotropy in the Co 2 MnSi thin lm, we also studied the VCMA in sample II. direction changes to a square curve from a two-step loop, which indicates that [110] has been converted to an easy magnetized axis. However, the [110] direction keeps a two-step loop under the negative piezo-voltages (compressed state) (as shown in Fig. 4b).
The saturation eld increased with the piezo-voltages changing from À20 to À50 V. In order to analyze the variation of magnetocrystalline anisotropy, we measured the magnetic hysteresis loop of the [1À10] direction under positive and negative piezovoltages. In contrast to sample I, the magnetic hysteresis loops of the [1À10] varied from a square curve to a two-step loop with the piezo-voltage increasing from À10 to 60 V (as shown in Fig. 4c). Under the negative piezo-voltages, the loops of the [1À10] direction keep the square curve stabilized (as shown in Fig. 4d). We also measured the magnetic hysteresis loops of the [100] hard magnetic axis and the loops maintained the hard magnetic properties with the positive or negative piezo-voltages (only a part of the loops shown in Fig. 5b). Through the magnetic measurement along different directions, we summarized the variation of the saturated eld with the piezo-voltage in     Through the demonstration of dual-axis control of magnetic anisotropy in epitaxial Co 2 MnSi thin lms through piezovoltage-induced strain, we could achieve a purely electrical controlled magnetization rotation. The magnetization rotation could attribute to an extra in-plane uniaxial anisotropy induced by the piezo-voltage in the Co 2 MnSi thin lms. In order to quantify the magnetocrystalline anisotropy of Co 2 MnSi thin lms with the piezo-voltages, the magnetic anisotropy energy E can be described as 31 where K U and K C are the effective uniaxial and cubic anisotropy constants respectively, H is the applied external magnetic eld, M S is the saturation magnetization, q is the angle between the magnetization and the easiest axis [1À10], and a is the angle between the external magnetic eld and the easiest axis [1À10] (see the inset of Fig. 5b). With the saturation eld and slope of the two-step loops, the K U and K C can be calculated as where H Sp is the so-called split eld and s is the constant slope between H Sp and ÀH Sp . 31 In this work, we calculated the values of K U and K C under AE40 V piezo-voltages in sample I. The K U and  ), which also induced the transformation of the easiest magnetization axis and magnetization 90 rotation. Based on the demonstration of dual-axis control of magnetization rotation in Co 2 MnSi/GaAs/PZT heterostructures, it will be promising to be applied in the design of magnetic functional devices, such as magnetic tunneling junction (MTJ) and planar Hall devices. To further study the response performance of the Co 2 MnSi/GaAs/PZT device, we measured the magnetization during the periodic change of piezo-voltage between À40 and 40 V in sample I without the external magnetic eld. The magnetization periodically switched from 7.5 to 2.3 mdeg, which correspond to the '1' and '0' states of the logic device (as shown in Fig. 6). The time response of the piezo-voltage controlled device has been investigated, where the rising and falling time are 361.7 ms and 376.2 ms, respectively. Therefore, we could utilize voltage control of magnetization rotation to design and fabricate the magnetic logical arrays to realize the information processing in Heusler alloys. Our study identied that the dual-axis control of magnetization rotation through strain engineering could have a great prospect for spintronic applications.

Conclusions
In summary, we have demonstrated the dual-axis (the [1À10] and [110] directions) control of magnetic anisotropy in epitaxial Co 2 MnSi thin lms through piezo-voltage induced strain. Furthermore, we demonstrated the periodically voltagecontrolled magnetization rotation in the Co 2 MnSi/GaAs/PZT heterostructure. Under applied piezo-voltages, the in-plane magnetization rotation could be implemented without extra  magnetic eld. The piezo-voltage-induced strain is the primary mechanism in the Co 2 MnSi/GaAs/PZT heterostructure, which induces an extra uniaxial anisotropy along the in-plane crystalline orientation of the Co 2 MnSi lm and manipulates the direction of the minimal anisotropy energy. Compared with the uniaxial control effect of many magnetic materials, the dual-axis control of Co 2 MnSi could be manipulated effectively through the strain and is more suitable for the magnetic logic devices. This result will pave the way to the design and fabrication of dual-axis control of spintronic devices based on the voltagecontrolled magnetic anisotropy.

Conflicts of interest
There are no conicts to declare.