Giant nonvolatile manipulation of magnetoresistance in magnetic tunnel junctions by electric fields via magnetoelectric coupling

Electrically switchable magnetization is considered a milestone in the development of ultralow power spintronic devices, and it has been a long sought-after goal for electric-field control of magnetoresistance in magnetic tunnel junctions with ultralow power consumption. Here, through integrating spintronics and multiferroics, we investigate MgO-based magnetic tunnel junctions on ferroelectric substrate with a high tunnel magnetoresistance ratio of 235%. A giant, reversible and nonvolatile electric-field manipulation of magnetoresistance to about 55% is realized at room temperature without the assistance of a magnetic field. Through strain-mediated magnetoelectric coupling, the electric field modifies the magnetic anisotropy of the free layer leading to its magnetization rotation so that the relative magnetization configuration of the magnetic tunnel junction can be efficiently modulated. Our findings offer significant fundamental insight into information storage using electric writing and magnetic reading and represent a crucial step towards low-power spintronic devices.

It is obvious that surface roughness of PMN-PT is larger than that of silicon wafer. The scale bar is 1 μm. c,d, Typical TMR curves of MTJs on PMN-PT and Si, whose TMR ratios are nearly 240% and 300%, respectively. The TMR ratio is defined as   -800  According to Julliere's model 2 , the dependence of resistance R of a MTJ unit on the rotation angle φ can be written as 3 : where c R is a coefficient, and S1 and S2 are the tunneling spin polarizations at Fermi level EF of the two magnetic layers. For magnetization configurations of parallel and antiparallel, the corresponding rotation angles φ are 0° and 180°, respectively. So the resistances R  and R  can be expressed as follows: The values of R  and R  can be gotten from Supplementary Fig. 3a, so c R and S1S2 also can be calculated using Supplementary Equation (2). Then using Supplementary Equation (1), the rotation angle can be obtained at certain () R  and it can be written as: Using Supplementary Equation (3), the rotation angles of the free layer around zero magnetic field for E = ±0 kV cm -1 in Supplementary Fig. 3b were deduced from corresponding resistances in Supplementary Fig. 3a. Supplementary Table 1  Additionally, the TMR curve at E = +0 kV cm -1 (Fig. 1c) is not square and sharp suggesting the existence of multidomain in the micrometer-sized circular-shaped MTJ. This also can lead to the rotation angle of the free layer smaller than 90°.

Supplementary Note 2│Electric-field modification of magnetic anisotropy for CoFeB film on PMN-PT.
To study the effect of this nonvolatile strain on magnetic anisotropy of the CoFeB film, Owing to this giant electric-field-tuned magnetic anisotropy, the electric field can significantly tune the magnetization state of the FM thin film. Supplementary Fig. 8a shows the M-H loops measured along the [100] direction at E = 0 kV cm -1 , respectively, which have a remarkable change. Supplementary Fig. 8b presents magnetization versus electric field curve measured at H = 0 Oe. Importantly, this nonvolatile electric-field-controlled magnetism has two distinct magnetization states after removing the asymmetric electric fields at E = 0 kV cm -1 and these two magnetization states are very stable as shown in Supplementary Fig. 8c.
This nonvolatile electrical control of magnetism in CoFeB is certainly the cornerstone of reversible and reliable nonvolatile electrical manipulation of magnetoresistance of the MTJs in Fig. 1f.
These results can be understood by the anisotropic strain of the PMN-PT (011) in Supplementary Fig. 6c as follows. In Supplementary Fig. 6c, the anisotropic strain at E = 0 kV cm -1 after applying kV cm -1 is negative, which is compressive strain along y axis, so the magnetic easy axis is along the [100] direction considering the positive magnetostriction coefficient of CoFeB film 9,10 . In contrast, the anisotropic strain at E = 0 kV cm -1 after applying 1.6 kV cm -1 is positive, which is tensile strain along y axis, so the strain-induced magnetic anisotropy is along the [011 __ ] direction leading to the rotation of magnetic easy axis.
Thus through strain-mediated magnetoelectric coupling, the magnetic easy axis of CoFeB film can be reversibly switched by applying asymmetric electric fields, which can modify the magnetization.

Supplementary Note 3│Estimation of the width of electric-field pulse.
The width of electric-field pulse depends on the time that is required to switch the magnetization of the free layer. This time mainly includes three parts: the average magnetization switching time tFM of the free layer in MTJ, the ferroelectric polarization switching time tFE to produce nonvolatile strain, and the time tstrain for strain transfer from the ferroelectric layer to the free layer. The LLG is expressed as follows 8,12,13 : Where γ is the gyromagnetic ratio, α is the damping constant and m is a cosine vector of magnetization m = (mx, my, mz Here, H0 (about 90 Oe) is the magnetic anisotropy field resulting from the initial randomness of ferroelectric domains in PMN-PT (ref. 9 ). Heff,S is the strain-induced effective anisotropy field, the out-of-plane effective anisotropy field H ⊥ is about 1 T as shown by our previous electron spin resonance results 15 . The dipole field from the pinned layer is neglected assuming that this dipole field can be cancelled out by synthetic ferromagnetic reference layer 16 .
Supplementary Fig. 9 presents the simulation results of magnetization rotation under electric fields. The0 kV cm -1 state is obtained by applying an electric field of 1.6 kV cm -1 .
It includes two steps, i.e., applying 1.6 kV cm -1 and removing it. It can be seen from Supplementary Fig. 9 that the magnetization takes about 5 ns to rotate to the y direction and stabilizes at the y direction after removing 1.6 kV cm -1 . The total time is less than 10 ns.
Similarly, the 0 kV cm -1 state is obtained by applying and then removing an electric field of 8 kV cm -1 . From 0 kV cm -1 to 8 kV cm -1 , because the magnetic easy axes of both of them are along the y direction and the magnetization almost does not change, the time for magnetization rotation is neglected as shown in Supplementary Fig. 9 and the width of voltage pulse is determined by the time for ferroelectric domain switching from the in-plane to the out-of-plane. When removing electric field to 0 kV cm -1 , the magnetization takes less than 10 ns to rotate back to the x direction. Thus the time for magnetization rotation is less than 10 ns for both 0 kV cm -1 state and 0 kV cm -1 .

2),
The tFE is usually below 10 ns and the polarization normally switches much faster than the magnetization 17,18 .

3),
The tstrain can be estimated by 19 Where d is the distance between ferroelectric and the free layer, and v is the velocity of sound in the buffer layer. It is well known that the speed of sound varies from substance to substance, but generally it travels very fast in solids. We assume v = 3000 m s -1 (ref. 17 ). So tstrain ≈ 0.009 ns for d = 27 nm.
In summary, the width of voltage pulse is less than 20 ns for our devices. In addition, the theoretical work on multiferroics heterostructures using ferroelectric films reported that the strain-induced switching of multiferroic nanomagnets can be less than 10 ns (refs. 17,20 ) and even less than 1 ns (ref. 21 ).

Supplementary Note 4 │ Calculation of the power consumption for electrical manipulation of MR in MTJs.
In our devices, the power consumption per unit area can be estimated by CV 2 /A (ref. 20,21,22 ), where C, V and A denote the capacitance of the piezoelectric layer, the applied voltage and the area of the device, respectively. The capacitance can be written as C = εrε0A/d (ref. 22 ), assuming a parallel plate capacitor (A is the area of the electrode, d is the thickness of the piezoelectric layer, εr is the relative dielectric constant of the piezoelectric and ε0 is the vacuum dielectric constant). Thus the power consumption per unit area can be expressed as εrε0V 2 /d. In our devices, the operation electric fields for 0 kV cm -1 states in Fig. 1 are 8 kV cm -1 and -1.6 kV cm -1 , so the operation voltages are 400 V and -80 V, respectively, considering the 500 μm thickness of PMN-PT substrate. The relative dielectric constant εr of PMN-PT is about 3000 (ref. 23 ). So the power consumptions per unit area are about 0.85 mJ cm -2 and 0.034 mJ cm -2 for 0 kV cm -1 states, respectively.
The state-of-the-art spin-transfer-torque magnetic tunnel junctions require about a 0.7 V voltage pulse of 500 ps (ref. 24 ) or 120 ps (ref. 25 ) in duration through a 60-70 nm×180 nm device, producing an energy dissipation per unit area of 3-4 mJ cm -2 . So the power consumption per unit area in our devices is remarkably smaller than that of the state-of-the-art spin-transfer-torque devices. Additionally, there are also some theoretical work reporting that ultralow power dissipation can be achieved in multiferroics heterostructures using ferroelectric films 17,20,26 . For example, energy dissipation per unit area can be reduced to 4 μJ cm -2 with high-speed operation below 10 ns (ref. 17 ). High quality PMN-PT epitaxial thin films on Si wafers with giant piezoelectricity have been reported 27 , which makes our work more attractive for future applications. Our present work shows that integrating spintronics and