The STT is composed of two vector components (Fig. 1a): the in-plane torque (τ) and the perpendicular torque (, also called ‘field-like torque’) normal to τ. Whereas in fully metallic nanopillars is negligible and has been ignored in the analysis of experimental data14, in MgO-based MTJs can be 1030% of τ (refs 8, 9, 10). Previous theoretical12,13 and experimental8,9,10 studies indicate that is a symmetric function of the voltage V at low voltages; where the bias-independent contribution C0 is also known as the interlayer exchange coupling15,16. A more recent theoretical study11 indicates however that the symmetric bias dependence is expected only in symmetric MTJs and that extra antisymmetric components may appear () in asymmetric MTJs where the free and reference layers are made of different materials.

Figure 1: Magnetoresistive properties of asymmetric MgO-based MTJs.
figure 1

a, Schematic of MTJ layer structure (all in nanometres). MF (MP) is the free- (reference)-layer magnetization vector. Positive bias corresponds to electrons flowing from the reference layer to the free layer and thus favours parallel alignment of the two layers. Positive external field favours the antiparallel alignment. The top panel shows the two components τ and of the STT acting on MF. b, Resistance versus bias voltage for MTJ1 and MTJ2 measured at T=4.2 K. c, Room-temperature (dV/dI) versus voltage curves in the P state.

Here, we examined the bias dependence of in asymmetric MTJs. We studied two types of asymmetric MgO-based MTJ of the composition (thickness in nanometres) 15PtMn/2.5Co90Fe10/0.8Ru/2Co40Fe40B20/0.7MgO/Free (Fig. 1a: see the Methods section for sample details) with the free layer in MTJ1 (MTJ2) being 1.8Co20Fe60B20 (2.3Co49Fe21B30). Note that in both MTJs, the free-layer compositions are different from the reference-layer composition. The tunnel magnetoresistance (TMR) of MTJ1 (MTJ2) is 175%/117% (195%/123%) at 4.2 K/300 K (Fig. 1b). Owing to the asymmetry in the MTJs, the current–voltage characteristics are not symmetric even in the parallel magnetic configuration (P state) (Fig. 1c). Note that (d2I/dV2)P at V =0 has opposite sign for the MTJ1 and MTJ2, reflecting the different asymmetries in the two MTJs.

To determine the bias dependence of , we used the thermal activation model17,18,

where the upper (lower) signs apply to the antiparallel-to-parallel (parallel-to-antiparallel) switching, t± is the relaxation time, f0 is the attempt frequency (=109 s−1), kB is the Boltzmann constant, T* is the junction temperature taking into account the bias-induced heating and VC± is the critical voltage for magnetization switching at T*=0 K. Here, the factor arises from the voltage dependence of the energy barrier due to the in-plane torque τ. The junction temperature T* is obtained from commonly used estimation methods (see the Methods section and Supplementary Note S1). Here, EB± reads

where EB0 is the intrinsic energy barrier, Hext is the external magnetic field applied along the easy axis, Hsh is the shift field owing to the orange-peel coupling19 as well as the interlayer exchange coupling C0, HC0 K is the coercivity at T*=0 K and n (=3/2; refs 20, 21) is the exponent characterizing the field-dependence of the energy barrier. Here, we introduce bJ to describe the bias-induced field-like effect, and use the lowest-order expansion bJ=C1V +C2V2 to capture the main effects of its asymmetric and symmetric bias-dependent components. Effects of C1 and C2 on EB± are illustrated in Fig. 2a. At this stage, we do not identify bJ with the bias-dependent part of because such a field-like effect in the thermally activated switching may involve a number of mechanisms: , non-macrospin processes or bias-induced heating. Below, we first evaluate bJ and then discuss its relationship with . From equations (1) and (2), one derives the switching threshold voltage VC (or switching threshold field HC) from exp(−t/t±)=1/2 for the observation time t. The comparison between the calculated switching thresholds and experimentally measured values allows the evaluation of unknown parameters.

Figure 2: Temperature-dependent switching field HC and pulse-width-dependent switching voltage VC (MTJ1).
figure 2

a, Schematic of the effect of bJ on EB± in the two limiting cases; bJ possesses only antisymmetric components (for instance, bJ=C1V; see top panel) and only symmetric components (for instance, bJ=C2V2; see bottom panel). If bJ=C1V, EB+ and EB are expected to be the same, as bJ changes sign when changing the voltage polarity. The sign of C1 determines whether or not EB±>EB0. In contrast, if bJ=C2V2, EB+ is different from EB because bJ keeps its sign regardless of the voltage polarity. The sign of C2 determines whether or not EB+>EB. b, TMR versus the external field measured at T=4.2 and 300 K. Hsh is the shift field originating from the orange-peel coupling and C0. In our samples, the orange-peel coupling seems to be dominant over C0 because C0 generates a negative Hsh for a tunnelling barrier thickness below 1 nm (ref. 16), whereas the observed Hsh is positive. Inset: Temperature-dependent HC. cVC versus log-scaled pulse width at T=300 K. The lines are linear fits for pulse-width>500 ns. In c and the inset of b, VC and HC are averaged values from five measurements.

We first determined EB0 from the temperature-dependent HC at V 0 V (Fig. 2b, inset) and found EB0/(kB(300 K))=61 for MTJ1. Another approach widely used in the literature6,7 consists of estimating EB± from the relationship between the critical voltage VC and the pulse width t of the voltage bias (Fig. 2c). However, this approach should be used cautiously. In the literature6,7, the role of bJ in EB± and the bias-induced heating are commonly ignored. If this common practice were correct, it should yield the same value for EB± as EB0 (=61 for MTJ1). Within these approximations, we found however that the experimental estimations of EB± strongly differ from EB0EB+/(kB(300 K))=37 for V >0 and EB/(kB(300 K))=25 for V <0, indicating that effects of bJ and of heating should be considered as in the following analysis.

To evaluate bJ, we used the switching phase diagrams (SPDs) where HC is measured as a function of V at 4.2 and 300 K. Figure 3a shows the normalized SPDs at 4.2 K for the two MTJs. In the second quadrant (Hext>0 and V <0), both Hext and τ favour the parallel-to-antiparallel switching, whereas in the fourth quadrant (Hext<0 and V >0), both favour the antiparallel-to-parallel switching. Under these bias conditions, bJ has only a minor role and the normalized phase boundaries are almost identical for both MTJs. In contrast, Hext and τ compete with each other in the first and third quadrants. Correlatively, bJ has a strong influence in these quadrants. The difference between MTJ1 and MTJ2 in the first and third quadrants (Fig. 3a) implies different bias dependence of bJ in the two MTJs.

Figure 3: Switching phase diagram of MTJ1 and MTJ2.
figure 3

a, Normalized switching phase diagram of two MTJs measured at T=4.2 K. b, Switching phase diagram of MTJ1 measured at T=4.2 and 300 K. The lines are the best fits using the thermal activation model. The best fit is obtained for experimentally measured parameters (EB0/(kB(300 K))=61, HC4.2 K=218 Oe and Hsh=30 Oe) and fitting parameters (C1=−30 Oe V−1, C2=+130 Oe V−2, VC+=0.44 V, VC=−0.56 V, γAPtoP=3.2×1011 K2 A−2 and γPtoAP=1.3×1011 K2 A−2). c, Switching phase diagram of MTJ2. The best fit is obtained for experimentally measured parameters (EB0/(kB(300 K))=62, HC4.2 K=118 Oe and Hsh=10 Oe) and fitting parameters (C1=+38 Oe V−1, C2=+72 Oe V−2, VC+=0.82 V, VC=−0.93 V, γAPtoP=2.3×1011 K2 A−2 and γPtoAP=0.7×1011 K2 A−2). The dashed lines in c are fits assuming C1=0 (C2=+120 Oe V−2, VC+=0.82 V, VC=−2.70 V, γAPtoP=2.3×1011 K2 A−2 and γPtoAP=0.7×1011 K2 A−2). Note that an unrealistically large VC has to be used for this fit. d, Normalized bJ obtained from the best fit as a function of the voltage.

For the MTJ1 SPD at 4.2 K, the best fitting is obtained with C1=−30 Oe V−1 and C2=+130 Oe V−2 (Fig. 3b). These parameters also fit the SPD at 300 K reasonably well, indicating that the temperature dependence of C1 and C2 is not strong (see Supplementary Note S1). We also measured the MTJ2 SPDs and obtained the best fittings with C1=+38 Oe V−1 and C2=+72 Oe V−2 (Fig. 3c). We point out that if C1 is assumed to be zero, no satisfactory fits of the SPD boundaries in all four quadrants can be obtained (see Fig. 3c and its caption). Thus, considering a non-zero C1 is essential to properly describe the switching boundaries. In Supplementary Note S2, we check the applicability of the fitting parameters to the situation with an in-plane hard-axis field. We also point out that the sign of C1 is different for MTJ1 and MTJ2 (Fig. 3d).

To clarify the relationship between bJ and , we discuss possible mechanisms, other than , that may contribute to bJ. Field-like effects may arise from non-macrospin processes, which can become important when τ acts as an anti-damping term14. However, in the first and third quadrants, τ acts as a damping term and therefore contributes to suppress non-macrospin processes. Thus, the development of magnetic inhomogeneities cannot explain the significant difference between the two MTJs’ SPDs in the first and third quadrants (Fig. 3a).

Inaccuracies in the estimation of the junction temperature T* may lead to a twisted evaluation of Ci values. As T* is also bias dependent, the evaluation of Ci values depends fundamentally on the estimation of T*(V). To gain insight into this issue, we examined several heating estimation methods commonly used for MTJs (refs 18, 22) and found about 10% variation of Ci values (see Supplementary Note S1), which is not a crucial correction. This estimation is also supported by the observation that in the first and third quadrants, which are most influential for the evaluation of Ci values, the effective energy barrier is larger and thus the bias-induced heating is less important than in the second and fourth quadrants.

The reliability of the above estimation depends on how realistic the assumed forms of T*(V) are. Whereas all forms of T*(V) used in our analysis assume a quadratic bias dependence, a linear dependence may arise owing to thermoelectric effects, related to the Peltier effect in metallic spin-valves23 or tunnelling of electrons through normal metal–insulator–superconductor junctions24. However, these mechanisms could be important only when the two electrodes are made of considerably different materials24,25, and thus do not seem relevant to the present situation (that is, the same atomic elements with different compositions). On the basis of this discussion, we conclude that is most likely responsible for the observed bJ. At this point, we also mention that for a more quantitative evaluation of , an accurate experimental estimation of T* is crucial, which is a subject of future studies.

Next we discuss possible origins of the non-zero C1 and its sign change in the context of . Previous studies on symmetric MTJs suggested10,18 that at high bias, the bias dependence of can become asymmetric owing to hot electron-related magnon excitations. However, this mechanism allows only one sign of C1 and thus is inconsistent with our observation of the sign change of C1. A thickness difference between the free and reference layers can also result in non-zero C1 (ref. 26). This mechanism is however suppressed in the presence of thickness fluctuations as small as a single atomic layer13, responsible for the finite orange-peel coupling in our samples. Still another possible mechanism is the asymmetry in the exchange splitting Δ. A recent theoretical study11 demonstrated that the asymmetric bias dependence of can be either positive or negative depending on the relative magnitudes of Δ in the reference and free layers (ΔRef and ΔFree). Note that in MTJ1 (MTJ2), the free layer is Fe-rich (Co-rich), whereas the atomic concentrations of Fe and Co are the same in the reference layer. Therefore, in MTJ1 (MTJ2), ΔFree is expected to be larger (smaller) than ΔRef because Fe has a larger Δ than Co (ref. 27).

To investigate the relationship between the asymmetric Δ and the sign of C1, we carried out a model calculation of the bias-dependent using the free-electron model within the Keldysh formalism26 (see the Methods section for model parameters). We found that C1 is negative (positive) when ΔRef<(>)ΔFree (Fig. 4a). Therefore, the effect of an asymmetric Δ on is qualitatively consistent with the experimental observations. We also tested another possible source of the symmetry breaking, that is, asymmetric barrier height U because the workfunctions of Co, Fe and B are different28. We found however that this effect generates incorrect C1 signs (see Supplementary Note S3).

Figure 4: Sign of C1 and abnormal switching-back phenomenon.
figure 4

a, Theoretical result of bias-dependent for asymmetric Δ (see the Methods section for details of parameters). b, Experimental results of TMR versus voltage measured at pulse width=50 ns, Hext=0 and T=300 K for MTJ2. The switching-back is observed when V >+1.0 V. Inset: Random telegraphic noise measured at V =+1.0 V and Hext=0 Oe. c,d, Zero-field switching probability PSW at various voltages and pulse widths for MTJ2. c is for positive voltages, whereas d is for negative voltages.

The voltage dependence of bJ affects an abnormal switching behaviour at large voltage, which is expected to have significant implications in MTJ-based devices. As indicated by solid up-arrows in Fig. 3d, bJ becomes larger than HC when V increases above a certain threshold. Under these conditions, the influence of bJ and τ starts competing: τ favours the parallel (antiparallel) state for a positive (negative) V, whereas bJ favours the antiparallel state regardless of the voltage polarity. Consequently, when V is positively large, an abnormal switching-back phenomenon is observed, where the parallel-to-antiparallel and antiparallel-to-parallel switchings coexist and thus the random telegraphic noise is observed at Hext=0 (MTJ2: Fig. 4b and inset). The critical voltage for the switching-back is about +1.0 V (+1.4 V) for MTJ2 (MTJ1), corresponding to the voltage at which the phase boundary crosses the zero field axis (indicated by a down-arrow in Fig. 3c). For a better understanding, the switching probability PSW from 100 switching trials was measured at various voltages and pulse widths for MTJ2. For V >+1.0 V, PSW abnormally decreases with increasing V (Fig. 4c), whereas for V <0, PSW shows a normal behaviour (Fig. 4d).

An important aspect of the observed switching-back phenomenon is that it can be controlled by material engineering of ferromagnetic electrodes, thus allowing a tuning of C1. In MTJ2, the positive C1 decreases the switching-back threshold down to +1.0 V, whereas in MTJ1, the negative C1 increases the threshold up to +1.4 V above the breakdown voltage so that no switching-back is observed. Recent experimental studies29,30 reported switching-back phenomena at both voltage polarities. The authors ascribed this observation to a reduced anisotropy field at elevated bias. Note that, in our case, the switching-back is observed at only one polarity, which requires a strong asymmetry in thermally activated switching as discussed above.


Sample preparation.

The resistance–area product for the parallel configuration in our MTJs is about 7–9 Ω μm2. The top CoFeB layer was patterned by photolithography and the reactive-ion etching technique to produce an elliptical cross-section with a nominal size of 180×80 nm2. The etching was stopped at the MgO barrier and thus the bottom layer is unpatterned to minimize the stray field originating from the bottom ferromagnetic electrode. After the patterning process, MTJs were annealed at 300 C for 2 h under an easy-axis magnetic field of 1 T to enhance the TMR and exchange bias. Measurements were carried out on five samples of each type and show similar results. The data presented in this letter are from one sample for each type of MTJ.

Bias-induced heating.

To account for bias-induced heating in the thermal activation model (equations (1) and (2)), we used the following formula for junction temperature: () when the system is initially in the antiparallel (parallel) configuration22. Here, T is the ambient temperature (4.2 or 300 K), I (=V/[R(V,T,P/AP)]) is the current, R(V,T,P/AP) is the experimentally determined junction resistance and γAPtoP and γPtoAP are parameters that depend on the material and geometric heat-transport characteristics. We also tested other heating models18 and found that all of these heating models give similar fitting values of C1 and C2 within 10% difference (see Supplementary Note S1).

Parameters used in the theoretical model for calculating the spin torques.

Details of the model are described in ref. 26. The MTJ consists of two semi-infinite ferromagnets separated by a 0.7-nm-thick insulator with an effective mass me*=0.4me. For the symmetric MTJ, the barrier height U is 3 eV and the exchange splitting Δ is 1 eV. For the asymmetric MTJs, U is kept at a constant of 3 eV, whereas Δ of one ferromagnet is 1.6 eV and Δ of the other ferromagnet is 0.4 eV.