Field-free magnetization reversal by spin-Hall effect and exchange bias

As the first magnetic random access memories are finding their way onto the market, an important issue remains to be solved: the current density required to write magnetic bits becomes prohibitively high as bit dimensions are reduced. Recently, spin–orbit torques and the spin-Hall effect in particular have attracted significant interest, as they enable magnetization reversal without high current densities running through the tunnel barrier. For perpendicularly magnetized layers, however, the technological implementation of the spin-Hall effect is hampered by the necessity of an in-plane magnetic field for deterministic switching. Here we interface a thin ferromagnetic layer with an anti-ferromagnetic material. An in-plane exchange bias is created and shown to enable field-free S HE-driven magnetization reversal of a perpendicularly magnetized Pt/Co/IrMn structure. Aside from the potential technological implications, our experiment provides additional insight into the local spin structure at the ferromagnetic/anti-ferromagnetic interface.

Creating an in-plane EB in samples with perpendicular magnetic anisotropy (PMA) is more difficult, as the intrinsic anisotropy field needs to be overcome to force the magnetization of the Co layer in the in-plane direction during field-cooling. We therefore applied a large in-plane field of 2.0 T while heating the sample to 225 °C and field-cooling over a period of 30 minutes.

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Supplementary Note 4. Magnetic reversal without exchange bias
As discussed in the main text, gradual magnetization reversal is observed when sweeping the current density from high negative to high positive values and back, even in the presence of additional in-plane magnetic fields. We proposed that the local spin structure of the IrMn causes a distribution of effective local magnetic fields. To test this hypothesis, we created a Hall cross sample without an anti-ferromagnetic layer, composed of Ta (4) / Pt (3) / Co (1.2) / Ta (5), with nominal thicknesses in nm. In this sample switching is found to be abrupt (Supplementary Figure   5), suggesting rapid domain wall propagation across the measured region. This is markedly different from the exchange-biased samples, where no evidence of coherent domain wall propagation was found. Even if slow domain wall propagation occurs, the steps must be far below the submicron range accessible in the Kerr microscope, in agreement with existing studies on similar bilayers 1,2 . We conclude that the gradual magnetization reversal is not related to domain wall motion (or device geometry in general) and results directly from the IrMn layer.
with the attempt frequency 0 = 10 9 s -1 , E b the energy barrier for anti-ferromagnetic grain reversal, k B Boltzmann's constant and T the temperature. We know that our samples are stable for at least several weeks at room temperature, so that ~ 10 s at 300 K, yielding b 34.5 . At a temperature of 650 K, we find ~ 10 ms (see Supplementary Figure 7), which is three orders of magnitude larger than the current pulse duration.
Still, we cannot exclude that briefly approaching the Néel temperature has an instantaneous, reversible effect on the exchange bias. One could speculate, for instance, that this would reduce the effective exchange bias due to a reduction of the anti-ferromagnetic ordering within grains, as illustrated in Supplementary Figure 8. This would contribute towards our findings that the effective exchange bias measured in our switching experiments (roughly 5 mT) is lower than the 50 mT value we measured in thin films at room temperature. However, to our knowledge, such an effect has never been reported on before.   Deposition starts with a Ta seed layer, which is commonly used to improve film quality 5 and was found to significantly increase the PMA in our samples. The thickness of this buffer layer was minimized to reduce current shunting effects. This reduces the PMA, but we found that a 1 nm Ta seed layer suffices for our measurements.
The Pt thickness of 3 nm maximizes the spin-Hall effect (SHE); see Supplementary Note 8.
The Co layer was chosen as thin as possible, to maximize both the PMA and the susceptibility to spin currents injected from the interface. MOKE measurements were performed on a sample with a variable Co thickness, which was subjected to the in-plane field cooling process. As shown in Supplementary Figure 12 The thickness of the IrMn layer is crucial to obtain a large and stable EB. We created a sample with a variable IrMn thickness, and annealed it at 225°C in a 0.2 T out-of-plane magnetic field for 30 minutes. This allows us to measure the EB and coercivity as a function of IrMn thickness using polar MOKE, which we found to be a good measure for the properties of an in-plane annealed sample. As shown in Supplementary Figure 13, the highest EB is obtained for an IrMn thickness of 6 nm. Note that the coercivity peak and negligible EB indicate that the EB is unstable for reduced thicknesses. The reduction in EB observed at higher thicknesses can probably be attributed to changes in microstructure or domain structure in the IrMn 6 . A 0.3 nm Pt dusting layer was inserted between the Co and IrMn layers to increase the PMA of the Co layer. Interestingly, this dusting layer was found to significantly reduce the chance of device breakdown at high current densities. Note that this thin layer is not expected to contribute significantly to the net spin current due to scattering, as discussed in Supplementary Note 8.
Finally, the stack is capped with a 1.5 nm Ta layer which is allowed to oxidize naturally, producing a protective yet transparent and non-conductive capping layer.

Supplementary Note 8. Spin current considerations
Owing to the spin-Hall effect, a vertical spin current density J s can be generated from a planar charge current J e in materials with a nonzero bulk spin-Hall angle SH ≡ s e ⁄ . For our thin Pt films, we use the reported 7 value of SH = 0.07. Note that extensive debate exists on this subject, which is beyond the scope of this publication.
where d is the Pt layer thickness. From this perspective, a thicker Pt layer is beneficial as it improves the net spin current. However, this also increases the total electric current I e required to produce a certain current density J e , which increases Joule heating and thus the risk of device breakdown. To solve this trade-off, we compute the spin current J s as a function of Pt thickness d while constraining J e to maintain a constant total current I e . The result of this computation is shown in Supplementary Figure 14. Current shunting through other metallic layers in the stack is taken into account, using a basic calculation where the stack is regarded as a parallel resistor network with appropriate resistances based on bulk conductivities. The optimum value for the Pt thickness is thus determined to be between 3 and 4 nm. In our calculations, we only take into account the spin current generated from the thick Pt layer. This is justified, as contributions from the other layers are negligible. By the diffusion mechanism here, the contribution from the 0.3 nm Pt dusting layer is about thirty times smaller than the contribution from the 3 nm Pt layer. The Ta seed layer is also very thin, and its local conductivity will be significantly reduced due to elastic scattering at the substrate interface.
Finally, although IrMn may exhibit a spin-Hall angle comparable to Pt 8 , its conductivity is more than an order of magnitude lower. Therefore, its contribution to the total current density and total spin current is negligible compared to the Pt.

Supplementary Note 9. Simulation details
As discussed in the main text, following the approach of our earlier work 9 , magnetization dynamics are simulated by solving the Landau-Lifshitz-Gilbert (LLG) equation 10 : with M the free layer magnetization, γ the electron gyromagnetic ratio,  0 the vacuum permeability, H eff the effective magnetic field, α the Gilbert damping coefficient, and ≡ | | the saturation magnetization. The spin-Hall torque coefficient is given by ħ / where θ and ψ are the azimuthal and elevation angle with respect to the direction, respectively.
The resulting distribution is constrained to 45° offset angles from the direction, as illustrated in