Research Update: Electrical manipulation of magnetism through strain-mediated magnetoelectric coupling in multiferroic heterostructures A T Chen and Y G Zhao Citation: APL Materials 4, 032303 (2016); doi: 10.1063/1.4943990 View online: http://dx.doi.org/10.1063/1.4943990 View Table of Contents: http://aip.scitation.org/toc/apm/4/3 Published by the American Institute of Physics Articles you may be interested in Giant electric field control of magnetism and narrow ferromagnetic resonance linewidth in FeCoSiB/Si/SiO2/ PMN-PT multiferroic heterostructures APL Materials 108, 232903232903 (2016); 10.1063/1.4953456 Thermal generation of spin current in a multiferroic helimagnet APL Materials 4, 032502032502 (2016); 10.1063/1.4943011 Magnetic microscopy and simulation of strain-mediated control of magnetization in PMN-PT/Ni nanostructures APL Materials 109, 162404162404 (2016); 10.1063/1.4965028 Electric-field-controlled nonvolatile magnetic switching and resistive change in La0.6Sr0.4MnO3/0.7Pb(Mg1/3Nb2/3)O3-0.3PbTiO3 (011) heterostructure at room temperature APL Materials 109, 263502263502 (2016); 10.1063/1.4973355 APL MATERIALS 4, 032303 (2016) Research Update: Electrical manipulation of magnetism through strain-mediated magnetoelectric coupling in multiferroic heterostructures A T Chen and Y G Zhaoa Department of Physics and State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China and Collaborative Innovation Center of Quantum Matter, Beijing 100084, China (Received January 2016; accepted March 2016; published online 16 March 2016) Electrical manipulation of magnetism has been a long sought-after goal to realize energy-efficient spintronics During the past decade, multiferroic materials combining (anti)ferromagnetic and ferroelectric properties are now drawing much attention and many reports have focused on magnetoelectric coupling effect through strain, charge, or exchange bias This paper gives an overview of recent progress on electrical manipulation of magnetism through strain-mediated magnetoelectric coupling in multiferroic heterostructures C 2016 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) [http://dx.doi.org/10.1063/1.4943990] Magnetization control using an electric field1–11 is now drawing much attention due to its expected ultralow power consumption Much progress has been made in a number of different material systems, such as magnetic semiconductor,2,3 ferromagnetic (FM) metal,4–6 and multiferroic material.7–11 Among them, much of the effort has been focused on multiferroics combining FM with ferroelectric (FE) properties,12,13 aiming at electric-field control of magnetism.14–23 The magnetoelectric coupling is relatively small for single phase multiferroic materials,24,25 which usually work at low temperatures, while multiferroic magnetoelectric composites especially multiferroic heterostructures9–11,26,27 have sufficient choices to obtain large magnetoelectric coefficient at room temperature and are more promising to realize practical applications Generally, three mechanisms have been proposed for multiferroic heterostructures to achieve electric-field control of magnetism The first one is the exchange-mediated magnetoelectric coupling in FM/single phase multiferroics which has antiferromagnetic (AFM) order such as YMnO3 28 and BiFeO3.29,30 The second one is the charge-mediated magnetoelectric coupling through electric-field induced depletion or accumulation of interface charge to modulate interfacial magnetization.31 The last one is the strain-mediated magnetoelectric coupling16–18,21,23,32 integrating FE and magnetic materials When applying an electric field, the FE materials will generate a piezostrain ε because of the converse piezoelectric effect Then the piezostrain transfers to the FM materials resulting in a magnetic anisotropy E = 32 λY ε owing to the converse magnetostrictive effect, where λ and Y are the magnetostriction coefficient and Young’s modulus of FM materials, respectively Therefore, the magnetic properties of the FM materials can be modified and magnetization is controlled by electric fields through the strain-mediated magnetoelectric coupling, which has been widely studied considering the tremendous amount of available FE and FM materials Among the large amount of subsistent FE materials, relaxor ferroelectrics Pb(Mg1/3Nb2/3)0.7 Ti0.3O3 (PMN-PT) has been widely used in the strain-mediated magnetoelectric coupling of multiferroic heterostructures16–18,21,23 due to its excellent and ultrahigh strain and piezoelectric behavior.33 Normally, the in-plane piezostrain of PMN-PT with the (001) orientation shows symmetric and volatile butterflylike behavior lacking of remanent strain (Fig 1(a)), i.e., the strain state in an electric field a Electronic address: ygzhao@tsinghua.edu.cn 2166-532X/2016/4(3)/032303/9 4, 032303-1 © Author(s) 2016 032303-2 A T Chen and Y G Zhao APL Mater 4, 032303 (2016) FIG (a) Normal symmetric butterflylike in-plane piezostrain curve without remanent strain of PMN-PT with the (001) orientation Reproduced with permission from Yang et al., Sci Rep 4, 4591 (2014) Copyright 2014 Nature Publishing Group (b) Corresponding behavior of electric-field dependence of magnetization Adapted with permission from Appl Phys Lett 94, 212504 (2009) Copyright 2009 AIP Publishing LLC cannot retain after removing it When FM film is grown on PMN-PT, the magnetization response to electric field will follow the paradigm of piezostrain, resulting in the volatile electrical modulation of magnetization16,17 with only one magnetization state in zero applied electric field no matter polarized by a positive/negative voltage as shown in Fig 1(b) However, this does not meet present development of information storage which requests nonvolatility.34 Recently, Zhang et al.21 have demonstrated a nonvolatile electrical manipulation of magnetism in CoFeB/(001) PMN-PT (Fig 2(a)) that differs from the previous work Figure 2(b) presents the dependences of magnetization and the corresponding polarization current on electric field measured along the [110] direction A looplike behavior can be seen clearly with different magnetization states after polarized by ±8 kV/cm, respectively, and the relative change of magnetization is about 25% Interestingly, the variation of magnetization versus electric-field is accompanied by the polarization current peak, suggesting its close correlation with the FE domain switching in PMN-PT Note that this nonvolatile magnetoelectric effect could not mainly originate from the charge effect,35,36 whose effective depth (a few nanometers) is much smaller than the thickness of CoFeB film (20 nm) PMN-PT with the rhombohedral phase has eight equivalent polarization directions along the ⟨111⟩ directions as shown in Fig 3(a).33 There exist three types of domain switching, i.e., 71◦, 180◦, and 109◦ The 71◦ switching represents polarization switching between r1 and r3 or r2 and r4 and the 180◦ switching occurs in the polarizations with same rhombohedral axis (e.g., r1+ and r1−), while polarization switching between r1/r3 and r2/r4 results in the 109◦ switching The piezoresponse force microscopy (PFM) measurements were also performed to investigate the FE FIG (a) Illustration of the sample and the experimental configuration (b) The looplike electrical modulation of magnetization and the corresponding polarization current recorded synchronously Reproduced with permission from Zhang et al., Phys Rev Lett 108, 137203 (2012) Copyright 2012 American Physical Society 032303-3 A T Chen and Y G Zhao APL Mater 4, 032303 (2016) FIG (a) Schematic of the polarization orientations for (001) PMN-PT (b) Correlation between domain switching and distortion ((c)-(f)) The reflections of RSM around the (113) peak for various electric fields, respectively Reproduced with permission from Zhang et al., Phys Rev Lett 108, 137203 (2012) Copyright 2012 American Physical Society domain structures, revealing the existence of these domain switchings.21 It should be mentioned that the in-plane lattice parameters of r1/r3 and r2/r4 are different along the [110] direction so that different domain switching will induce various interesting strain states as illustrated in Fig 3(b) Obviously, the polarizations experiencing 71◦/180◦ switching not change their in-plane projections while rotating by 90◦ for the 109◦ switching suggesting the strain states have a change for the 109◦ switching and stay the same for the 71◦/180◦ switching Thus the strain states after positive and negative voltages will be different for these three types of domain switching and the 109◦ switching is crucial for the nonvolatile electric-field controlled magnetism It is also noted that if the probabilities of the 109◦ switching along the [110] and [1-10] directions are equal, it could cancel out the nonvolatility of strain, which appears only when they are incoordinate So the net 109◦ switching is the key to realize the nonvolatile electric-field controlled magnetism To obtain the value of the net 109◦ switching in this special type of PMN-PT (100) substrate, reciprocal space mapping (RSM) was carried out to study the distribution of FE domains under various electric fields due to their different lattice parameters (Fig 3(b)) Figures 3(c)-3(f) present RSMs of the (113) peak for different electric fields Comparing Fig 3(c) with Fig 3(d), a noteworthy feature is that the spots mainly remain the same after removing the electric field and so is it for Figs 3(e) and 3(f) However, there is a remarkable difference between Figs 3(d) and 3(f), implying their different FE domain structures and nonvolatility after removal of electric fields Quantitative analysis37 of relationship between the rhombohedral distortions has been performed to figure out the ratios of various FE domains for different electric fields It was found that the percentage of r2/r4 for the negatively polarized case changes from about 4% to 30% for the positively polarized case, and the percentage of r1/r3 has a corresponding reduction to convert to r2/r4 through 109◦ domain switching So the probabilities of the 109◦ switching along the [110] and [1-10] directions are not equal This reveals about 26% net 109◦ domain switching, which is quantitatively comparable to the 25% relative change of magnetization (Fig 2(b)), suggesting that the nonvolatile electrical manipulation of magnetism depends strongly on the 109◦ domain switching of PMN-PT For comparison with this special type of substrates, the normal substrate with the symmetric butterflylike strain (Fig 1(a)) was also measured using RSM with in situ electric fields to investigate its domain structure.38 Indeed, analysis of these results show that the ratios of various FE domains for positive and negative electric fields are almost the same, suggesting absence of net 109◦ domain switching and remanent strain 032303-4 A T Chen and Y G Zhao APL Mater 4, 032303 (2016) FIG (a) Schematic of the sample and the experimental configuration for strain measurements (b) and (c) illustrate the continuous and pulsed methods of strain measurement, and (d) and (e) present the relevant results, respectively (f) The curve is deduced from (d) and (e) by subtracting Reproduced with permission from Yang et al., Sci Rep 4, 4591 (2014) Copyright 2014 Nature Publishing Group Since variation of FE domain can be reflected in piezostrain, a strain gauge was used to measure the electric field dependence of piezostrain (Fig 4(a)).38 Generally speaking, the strain versus electric field curve is measured using the continuous method as shown in Fig 4(b) When applying a voltage, the strain measurement is carried out after a short time of delay and interval, and the voltage does not change until the next cycle Figure 4(d) shows the results measured by the continuous method Though it also looks like a butterfly behavior, it is asymmetric at kV/cm with two remanent strain states This is different from that of Fig 1(a), which is volatile without remanent strain A new approach, pulsed measurement method as schematically shown in Fig 4(c), has been proposed to separate the contribution of the nonvolatile part in the asymmetric butterflylike curve (Fig 4(d)).38 The main difference of continuous and pulsed method is whether the voltage holds on during the interval All the measurements were performed after removing the electric field in the pulsed method, so it can directly reflect the remanent strain As expected, Fig 4(e) shows a looplike piezostrain curve measured by the pulsed method Notably, the strain switches around the coercive electric field (Ec) of PMN-PT (about kV/cm), suggesting its correlation with FE domain switching The remanent strain states due to the net 109◦ domain switching are quite steady no matter polarized by the positive or negative electric fields Interestingly, through subtracting the values of strain in Figs 4(d) and 4(e), a symmetric butterflylike curve similar to Fig 1(a) was achieved from the looplike (Fig 4(e)) and the asymmetric butterflylike (Fig 4(d)) behaviors as shown in Fig 4(f) Accordingly, in this special PMN-PT single crystal, the looplike strain behavior coexists with the symmetric butterflylike strain behavior and the hybrid of them results in the asymmetric butterflylike curve (Fig 4(d)) So the looplike dependence of magnetization on electric field in Fig 2(b) does not copy the looplike strain in Fig 4(e) exactly and instead has a decreasing behavior when the electric field exceeds Ec Using PFM, RSM, strain, and magnetic measurements, two different types of PMN-PT substrates with (001) orientation have been demonstrated and the net 109◦ domain switching plays a pivotal role for the nonvolatile electric-field-controlled magnetism Therefore, the special PMN-PT single crystal with large net 109◦ domain switching is beneficial to achieve the giant nonvolatile electrical control of magnetization which is an urgent requirement for applications However, the origin of the net 109◦ domain switching, which may be closely related to some defects introduced during crystal growth,38 still remains elusive and desperately needs more investigation Another approach to realize nonvolatile electric-field control of magnetism employs unipolar poling electric field in PMN-PT with the (011) orientation.18,39 Figure 5(a) illustrates the crystal structure of (011) PMN-PT with eight possible ⟨111⟩ spontaneous polarization directions For (011) 032303-5 A T Chen and Y G Zhao APL Mater 4, 032303 (2016) FIG (a) Configurations of the polarization orientations for (011) PMN-PT (b) Electric-field dependence of out-of-plane electric displacement (c) In-plane piezostrains along the x and y directions Reproduced with permission from Appl Phys Lett 98, 012504 (2011) Copyright 2011 AIP Publishing LLC PMN-PT, four possible polarization directions lie in the (011) plane while other four point outof-plane When applying bipolar electric fields within ±6 kV/cm, the polarization versus electricfield curve shows a standard hysteresis behavior with a coercive electric field about kV/cm (Fig 5(b)) and the corresponding bipolar strain curve has two peaks around the coercive electric field (Fig 5(c)) without remanent strain The peaks originate from the out-of-plane FE domain switching to in-plane, which is a metastable state And the strain dramatically descends after the applied electric field exceeds Ec The polarization points out-of-plane when positive electric fields are applied and switches back to in-plane with a small electric displacement in negative electric fields which is a little bit smaller than Ec (Fig 5(b)) If decreasing the negative electric field instead of increasing to pass Ec, interestingly, the polarization will stay in-plane until the electric field is changed to positive and strong enough to drive it to the out-of-plane again as shown in Fig 5(b) This evolution of FE domains was also confirmed by PFM.40,41 Therefore, the electric field dependence of polarization, as well as the strain, shows a hysteresis for the unipolar case Figure 5(c) presents the strain measured along the x and y directions (defined in Fig 5(a)), respectively, via unipolar poling electric field with a compressive strain ε x and a tensile strain ε y FM film deposited on PMN-PT will feel an effective anisotropic strain ε y − ε x under an electric field42 which is a nonvolatile strain It is worth noting that for (011) PMN-PT, both 71◦ and 109◦ FE domain switching can make polarizations switch to in-plane leading to a large homogeneous in-plane anisotropic lattice strain, unlike (001) PMN-PT21,38 whose nonvolatile strain only results from the 109◦ switching Further, analysis of RSM for (011) PMN-PT showed that up to 90% of the FE domain in the poled region contributed to this nonvolatile strain.41 Taking advantage of this large anisotropic piezostrain of PMN-PT with (011) orientation, a giant electric-field-tuned magnetization has been demonstrated in CoFeB/PMN-PT multiferroic heterostructures and the maximum relative change of magnetization can be up to 83%.23 Figure 6(a) presents the magnetic hysteresis (M-H) curves versus electric field measured along the [100] direction It can be seen that electric field makes the magnetic switching gradual suggesting the magnetic easy axis has a rotation because of electric-field-induced strain To shed light on this giant FIG (a) M-H curves versus electric-field measured for the [100] direction (b) Polar diagram of the uniaxial anisotropy energy for kV/cm and 17.5 kV/cm measured by Rot-MOKE, respectively (c) Dependences of magnetic anisotropy and the magnetic easy axis orientation on electric field Reproduced with permission from Zhang et al., Sci Rep 4, 3727 (2014) Copyright 2014 Nature Publishing Group 032303-6 A T Chen and Y G Zhao APL Mater 4, 032303 (2016) electric-field-tuned magnetization, the modifications of magnetic anisotropy by electric fields were investigated by Rot-MOKE (magnetic-optical Kerr effect using a rotating field).43 Figure 6(b) shows the angular dependences of the uniaxial anisotropy energy for kV/cm and 17.5 kV/cm with a remarkable change, suggesting that the magnetic easy axis rotates from the [100] direction to the [01-1] direction under electric fields It can be well understood considering the converse piezoelectric effect and converse magnetostrictive effect The transfer of anisotropic strain ε y − ε x induced by an electric field leads to an effective anisotropy field for FM layer, i.e., Heff = 3λY ε y − ε x /MS, where λ, Y , and MS are the magnetostriction coefficient, Young’s modulus, and saturation magnetization of CoFeB, respectively.42 Since λ is positive for CoFeB, the piezostrain induced magnetic anisotropy is along the [01-1] direction which is perpendicular to that of the kV/cm case Thus the orthogonality of magnetic anisotropy with and without electric field results in the rotation of the magnetic easy axis In addition, Fig 6(c) presents the values of magnetic anisotropy and the orientations of easy axis under varying electric fields through detailed Rot-MOKE measurements Obviously, the dependence of magnetic anisotropy on electric field is almost linear and the threshold electric field for the magnetic easy axis switching is about kV/cm Utilizing this electric-field induced 90◦ switching of magnetic easy axis, magnetoelectric random access memories (MeRAM) has been predicted by theory.44–46 The memory cell of MeRAM includes a magnetic tunnel junction (MTJ) deposited on a FE material to rotate magnetization of the free layer by 90◦ via strain-mediated magnetoelectric coupling23 resulting in electrical manipulation of tunneling magnetoresistance (TMR) Current methods of room-temperature electric-fieldcontrolled TMR utilize the electric-field-induced change of coercivity47 or magnetization precession;48 however, a bias magnetic field is necessary and the voltage adding on the junction directly almost reaches the breakdown voltage MeRAM, which can avoid these problems, is now drawing much attention because of its high density, high speed, and low power.46 This three-terminal MeRAM memory element, with terminals on both electrodes of the MTJs and a terminal on bottom of FE material to apply a voltage, complicates the fabrication process and the experiment work is lacking.27 Recently, Li et al.49 demonstrated electrical tune of TMR at zero magnetic field in a MTJ using CoFeB film as the free layer Figure 7(a) illustrates the sample structure with AlOx as the tunneling barrier, which was deposited on (011) PMN-PT, and the pinning direction was set to the [100] orientation for achieving giant electric-field control of TMR Figure 7(b) presents the TMR curves for kV/cm and kV/cm with the ratio of TMR up to 45%, which is comparable to that grown on silicon substrate.50 The TMR has a remarkable change originating from the electric-field induced magnetization rotation of a FM layer in MTJ while the other is fixed, which is confirmed by magnetic measurements To describe the electric-field-controlled TMR better, the value of electrical tune of TMR, ER, is defined as the difference of TMRs with kV/cm on and off, respectively, i.e., ER = TMR(E) − TMR(0) The corresponding ER curve in Fig 7(c) is deduced from Fig 7(b) It is noteworthy that a giant ER is obtained when a bias magnetic field is in the shadow regions marked by blue and green where the magnetic moment switches Specifically for zero magnetic field in the blue region, the remarkable ER reveals that TMR can be tuned via electric-field induced strain FIG (a) Illustration of the MTJ structure on FE single crystal (b) TMR curves for kV/cm and kV/cm, respectively (c) Dependence of ER on magnetic field Reproduced with permission from Li et al., Adv Mater 26, 4320 (2014) Copyright 2014 Wiley-VCH 032303-7 A T Chen and Y G Zhao APL Mater 4, 032303 (2016) FIG (a) Schematic of the sample combining FM/AFM exchanged-biased system with FE material (b) Angular dependences of with kV/cm on and off (c) M-H loops measured along θ = 45◦ Reproduced with permission from Chen et al., Adv Mater 28, 363 (2016) Copyright 2016 Wiley-VCH at zero oersted and the modulation is up to 15% Thus for the first time, electrical manipulation of TMR at zero magnetic field is realized at room temperature and it should be significant for the electric-field-tuned spintronics with ultralow energy consumption In addition, if MTJ with a large TMR using a MgO barrier51–53 is combined with FE materials, considerable electrical modulation of TMR should also be expected Compared with 90◦ magnetization switching, electric-field-reversed magnetization is more popular for practical applications14 such as full electrical control of TMR Purely strain-mediated magnetoelectric coupling, however, is limited to 90◦ switching since electric field cannot break time-reversal symmetry12,13 unless other effects are introduced Alternatively, FM/AFM exchangebiased heterostructure has been grown on FE materials to study electrical manipulation of magnetism.54,55 Recently, by depositing FeMn/Ni80Fe20 exchange-biased system on PZN-PT (lead zinc niobate-lead titanate), an almost 180◦ magnetization switching has been achieved at room temperature via electrical control of exchange bias.55 Whereas this switching of magnetization by electric field is irreversible, i.e., once the magnetization switches and it cannot switch back to the original orientation only by varying electric field Very recently Chen et al.56 demonstrated reversible electrical magnetization reversal at room temperature in CoFeB/IrMn/PMN-PT multiferroic heterostructures, which integrates exchange-biased structures and FE materials Figure 8(a) shows the sample structure with the pinning direction along the [100] direction The exchange-biased system consists of nm thick IrMn and 55 nm thick CoFeB whose thicknesses were meticulously chosen to achieve a suitable unidirectional magnetic anisotropy, comparable to the uniaxial magnetic anisotropy induced by electric field Electric-field could tune the ratio between the uniaxial anisotropy of CoFeB film and the unidirectional anisotropy deriving from FM-AFM interaction, resulting in different angular dependences of exchange bias HEB behaviors under an electric field on and off because of the competing anisotropies57,58 as presented in Fig 8(b) At θ = 45◦ (θ = 0◦ is along the pinning direction), for instance, the variation of HEB with electric field is up to 30 Oe Due to this giant electrical modification of exchange bias, electric fields part the hysteresis regions of M-H curves due to the rather small coercive field as shown in Fig 8(c) so that the magnetization could be reversed with a bias magnetic field as indicated by blue arrow Furthermore, the anisotropy configuration was optimized by deviating the pinning direction from x axis, such as 25◦ shown in Fig 9(a), leading to realization of repeatable electrical magnetization reversal at zero oersted.56 For zero magnetic field, the angular dependences of magnetization at various electric fields with standard trigonometric function behaviors are presented in Fig 9(b), suggesting the agreements between experiment results and simulations Note that there are positive and negative magnetizations in the pink region, so electric fields can switch magnetization at zero magnetic field if the measured direction ( β) belongs to this area For β = 37◦, as an example, Fig 9(c) shows the separated M-H loops with varying electric fields which is analogous to that shown in Fig 8(c) Therefore, with a bias magnetic field in the region surrounded by the two hysteresis regions, including zero magnetic field denoted by the blue arrow in Fig 9(c), repeatable electrical-tuned magnetization reversal can be realized 032303-8 A T Chen and Y G Zhao APL Mater 4, 032303 (2016) FIG (a) Illustration of magnetization orientations at zero magnetic field under electric fields for optimized anisotropy configuration (b) Angular dependences of magnetization for kV/cm on and off at H = Oe (c) M-H curves versus electric field at β = 37◦ Reproduced with permission from Chen et al., Adv Mater 28, 363 (2016) Copyright 2016 Wiley-VCH Additionally, there have been several theoretical schemes to realize electric-field-tuned 180◦ magnetization switching.59,60 In the proposition, a flower-shaped59 or square-shaped60 nanomagnet with a fourfold symmetric shape anisotropy was deposited on FE materials Significantly, there is a small angle mismatch between the anisotropic strain and the easy axis of the shape anisotropy resulting in a small energy barrier so that the magnetization can overcome this barrier with the assistance of an electric field Therefore, a reversible 180◦ magnetization switching can be achieved through a series of continuous 90◦ switching Note that the scale of magnetic island is down to 100 nm, which makes both the fabrication and characterization difficult Moreover, the evolution of magnetization under electric fields for nanomagnet depends strongly on the FE domain state below it32,61 and is different from that of the continuous FM film.21,23,56 Despite all this, experimental realization of this proposition will be an important progress for the purely electrical modulation of magnetism and for new generation of spintronic devices In summary, much progress has been made in electrical manipulation of magnetism in multiferroic heterostructures through strain-mediated magnetoelectric coupling and some prototype devices have also been demonstrated both theoretically and experimentally Present work of magnetoelectric coupling, principally employs macroscale FM/FE heterostructures, is important for revealing electric-field control of magnetism Further, the prospective in-depth research on microscale FM/FE heterostructures, such as how FE and FM couple each other or local nonvolatile electric-field-tuned magnetism and so on, will be significant for realizing electric-field-controlled spintronic devices with ultrahigh density and ultralow power The authors are supported by the 973 project of the Ministry of Science and Technology of China (Grant No 2015CB921402), National Science Foundation of China (Grant No 51572150), and Special Fund of Tsinghua for basic research (Grant No 201110810625) F Matsukura, Y Tokura, and H Ohno, Nat Nanotechnol 10, 209 (2015) H Ohno, D Chiba, F Matsukura, T Omiya, E Abe, T Dietl, Y Ohno, and K Ohtani, Nature 408, 944 (2000) H Ohno, Nat Mater 9, 952 (2010) T Maruyama, Y Shiota, T Nozaki, K Ohta, N Toda, M Mizuguchi, A A Tulapurkar, T Shinjo, M Shiraishi, S Mizukami, Y Ando, and Y Suzuki, Nat Nanotech 4, 158 (2009) C Bi, Y Liu, T Newhouse-Illige, M Xu, M Rosales, J W Freeland, O Mryasov, S Zhang, S G E Te Velthuis, and W Wang, Phys Rev Lett 113, 267202 (2014) U Bauer, L Yao, A J Tan, P Agrawal, S Emori, H L Tuller, S van Dijken, and G S D Beach, Nat Mater 14, 174 (2015) R Ramesh and N A Spaldin, Nat Mater 6, 21 (2007) Y Tokura and J Magn, Magn Mater 310, 1145 (2007) C Nan, M I Bichurin, S Dong, D Viehland, and G Srinivasan, J Appl Phys 103, 031101 (2008) 10 J Ma, J Hu, Z Li, and C Nan, Adv Mater 23, 1062 (2011) 11 C A F Vaz, J Phys.: Condens Matter 24, 333201 (2012) 12 W Eerenstein, N D Mathur, and J F Scott, Nature 442, 759 (2006) 13 N A Spaldin and M Fiebig, Science 309, 391 (2005) 14 J T Heron, J L Bosse, Q He, Y Gao, M Trassin, L Ye, J D Clarkson, C Wang, J Liu, S Salahuddin, D C Ralph, D G Schlom, J Iniguez, B D Huey, and R Ramesh, Nature 516, 370 (2014) 15 J T Heron, M Trassin, K Ashraf, M Gajek, Q He, S Y Yang, D E Nikonov, Y Chu, S Salahuddin, and R Ramesh, Phys Rev Lett 107, 217202 (2011) 16 C Thiele, K Doerr, O Bilani, J Roedel, and L Schultz, Phys Rev B 75, 054408 (2007) 032303-9 17 A T Chen and Y G Zhao APL Mater 4, 032303 (2016) J Yang, Y Zhao, H Tian, L Luo, H Zhang, Y He, and H Luo, Appl Phys Lett 94, 212504 (2009) T Wu, A Bur, P Zhao, K P Mohanchandra, K Wong, K L Wang, C S Lynch, and G P Carman, Appl Phys Lett 98, 012504 (2011) 19 Q Chen, J Yang, Y Zhao, S Zhang, J Wang, M Zhu, Y Yu, X Zhang, Z Wang, B Yang, D Xie, and T Ren, Appl Phys Lett 98, 172507 (2011) 20 T Qu, Y Zhao, P Yu, H Zhao, S Zhang, and L Yang, Appl Phys Lett 100, 242410 (2012) 21 S Zhang, Y Zhao, P Li, J Yang, S Rizwan, J Zhang, J Seidel, T Qu, Y Yang, Z Luo, Q He, T Zou, Q Chen, J Wang, L Yang, Y Sun, Y Wu, X Xiao, X Jin, J Huang, C Gao, X Han, and R Ramesh, Phys Rev Lett 108, 137203 (2012) 22 J Wang, Y Zhao, C Fan, X Sun, S Rizwan, S Zhang, P Li, Z Lin, Y Yang, W Yan, Z Luo, L Zou, H Liu, Q Chen, X Zhang, M Zhu, H Zhang, J Cai, X Han, Z Cheng, C Gao, D Xie, and T Ren, Appl Phys Lett 102, 102906 (2013) 23 S Zhang, Y Zhao, X Xiao, Y Wu, S Rizwan, L Yang, P Li, J Wang, M Zhu, H Zhang, X Jin, and X Han, Sci Rep 4, 3727 (2014) 24 Y S Chai, S Kwon, S H Chun, I Kim, B Jeon, K H Kim, and S Lee, Nat Commun 5, 4208 (2014) 25 Y Tokunaga, Y Taguchi, T Arima, and Y Tokura, Nat Phys 8, 838 (2012) 26 N X Sun and G Srinivasan, SPIN 2, 1240004 (2012) 27 S Fusil, V Garcia, A Barthélémy, and M Bibes, Annu Rev Mater Res 44, 91 (2014) 28 V Laukhin, V Skumryev, X Marti, D Hrabovsky, F Sanchez, M V Garcia-Cuenca, C Ferrater, M Varela, U Lueders, J F Bobo, and J Fontcuberta, Phys Rev Lett 97, 227201 (2006) 29 S M Wu, S A Cybart, P Yu, M D Rossell, J X Zhang, R Ramesh, and R C Dynes, Nat Mater 9, 756 (2010) 30 S M Wu, S A Cybart, D Yi, J M Parker, R Ramesh, and R C Dynes, Phys Rev Lett 110, 067202 (2013) 31 H J A Molegraaf, J Hoffman, C A F Vaz, S Gariglio, D van der Marel, C H Ahn, and J Triscone, Adv Mater 21, 3470 (2009) 32 T H E Lahtinen, K J A Franke, and S van Dijken, Sci Rep 2, 258 (2012) 33 S E Park and T R Shrout, J Appl Phys 82, 1804 (1997) 34 R L Stamps, S Breitkreutz, J Akerman, A V Chumak, Y Otani, G E W Bauer, J Thiele, M Bowen, S A Majetich, M Klaeui, I L Prejbeanu, B Dieny, N M Dempsey, and B Hillebrands, J Phys D: Appl Phys 47, 333001 (2014) 35 W Tsai, S Liao, K Huang, D Wang, and C Lai, Appl Phys Lett 103, 252405 (2013) 36 T Nan, Z Zhou, M Liu, X Yang, Y Gao, B A Assaf, H Lin, S Velu, X Wang, H Luo, J Chen, S Akhtar, E Hu, R Rajiv, K Krishnan, S Sreedhar, D Heiman, B M Howe, G J Brown, and N X Sun, Sci Rep 4, 3688 (2014) 37 S H Baek, H W Jang, C M Folkman, Y L Li, B Winchester, J X Zhang, Q He, Y H Chu, C T Nelson, M S Rzchowski, X Q Pan, R Ramesh, L Q Chen, and C B Eom, Nat Mater 9, 309 (2010) 38 L Yang, Y Zhao, S Zhang, P Li, Y Gao, Y Yang, H Huang, P Miao, Y Liu, A Chen, C W Nan, and C Gao, Sci Rep 4, 4591 (2014) 39 T Wu, A Bur, K Wong, P Zhao, C S Lynch, P K Amiri, K L Wang, and G P Carman, Appl Phys Lett 98, 262504 (2011) 40 M Liu, J Hoffman, J Wang, J Zhang, B Nelson-Cheeseman, and A Bhattacharya, Sci Rep 3, 1876 (2013) 41 M Liu, B M Howe, L Grazulis, K Mahalingam, T Nan, N X Sun, and G J Brown, Adv Mater 25, 4886 (2013) 42 M Liu, O Obi, Z Cai, J Lou, G Yang, K S Ziemer, and N X Sun, J Appl Phys 107, 073916 (2010) 43 R Mattheis and G Quednau, J Magn Magn Mater 205, 143 (1999) 44 N A Pertsev and H Kohlstedt, Appl Phys Lett 95, 163503 (2009) 45 J Hu, Z Li, J Wang, and C Nan, J Appl Phys 107, 093912 (2010) 46 J Hu, Z Li, L Chen, and C Nan, Nat Commun 2, 553 (2011) 47 W Wang, M Li, S Hageman, and C L Chien, Nat Mater 11, 64 (2012) 48 Y Shiota, T Nozaki, F Bonell, S Murakami, T Shinjo, and Y Suzuki, Nat Mater 11, 39 (2012) 49 P Li, A Chen, D Li, Y Zhao, S Zhang, L Yang, Y Liu, M Zhu, H Zhang, and X Han, Adv Mater 26, 4320 (2014) 50 X Han, X Zhang, Z Zeng, F Li, L Jiang, R Sharif, and Y Yao, J Magn Magn Mater 304, 83 (2006) 51 S Parkin, C Kaiser, A Panchula, P M Rice, B Hughes, M Samant, and S H Yang, Nat Mater 3, 862 (2004) 52 S Yuasa, T Nagahama, A Fukushima, Y Suzuki, and K Ando, Nat Mater 3, 868 (2004) 53 S Ikeda, J Hayakawa, Y Ashizawa, Y M Lee, K Miura, H Hasegawa, M Tsunoda, F Matsukura, and H Ohno, Appl Phys Lett 93, 082508 (2008) 54 G A Lebedev, B Viala, T Lafont, D I Zakharov, O Cugat, and J Delamare, Appl Phys Lett 99, 232502 (2011) 55 M Liu, J Lou, S Li, and N X Sun, Adv Funct Mater 21, 2593 (2011) 56 A Chen, Y Zhao, P Li, X Zhang, R Peng, H Huang, L Zou, X Zheng, S Zhang, P Miao, Y Lu, J Cai, and C Nan, Adv Mater 28, 363 (2016) 57 J Camarero, J Sort, A Hoffmann, J M Garcia-Martin, B Dieny, R Miranda, and J Nogues, Phys Rev Lett 95, 057204 (2005) 58 S H Chung, A Hoffmann, and M Grimsditch, Phys Rev B 71, 214430 (2005) 59 J Wang, J Hu, J Ma, J Zhang, L Chen, and C Nan, Sci Rep 4, 7507 (2014) 60 R Peng, J Wang, J Hu, L Chen, and C Nan, Appl Phys Lett 106, 142901 (2015) 61 M Buzzi, R V Chopdekar, J L Hockel, A Bur, T Wu, N Pilet, P Warnicke, G P Carman, L J Heyderman, and F Nolting, Phys Rev Lett 111, 027204 (2013) 18