Oscillatory spin-orbit torque switching induced by field-like torques

Deterministic magnetization switching using spin-orbit torque (SOT) has recently emerged as an efficient means to electrically control the magnetic state of ultrathin magnets. The SOT switching still lacks in oscillatory switching characteristics over time, therefore, it is limited to bipolar operation where a change in polarity of the applied current or field is required for bistable switching. The coherent rotation based oscillatory switching schemes cannot be applied to SOT because the SOT switching occurs through expansion of magnetic domains. Here, we experimentally achieve oscillatory switching in incoherent SOT process by controlling domain wall dynamics. We find that a large field-like component can dynamically influence the domain wall chirality which determines the direction of SOT switching. Consequently, under nanosecond current pulses, the magnetization switches alternatively between the two stable states. By utilizing this oscillatory switching behavior we demonstrate a unipolar deterministic SOT switching scheme by controlling the current pulse duration.

oscillatory switching behavior we demonstrate a unipolar deterministic SOT switching scheme by controlling the current pulse duration.

Introduction
Magnetism plays a key role in modern data storage and advanced spintronics devices as non-volatile information can be encoded in the magnetization state of a nanoscale magnet. Over the last two decades, electrical methods to control the magnetization state have received immense research attention to meet the demand for the reduction in the size and energy consumption of magnetic storage cells and devices. As a result, remarkable developments have been made in switching the magnetization electrically using spin-transfer torque (STT) [1][2][3][4][5] , electric field [6][7][8][9][10] , and the recently discovered spin-orbit torque (SOT) [11][12][13][14][15] . The operation principle of majority of these electrical techniques is based on the control of the polarity of the external force, such as an electric current or magnetic field, to achieve switching between two magnetic states (bipolar switching techniques).
On the other hand, magnetization switching techniques with a fixed polarity of the external force (unipolar operation) are receiving immense attention because of their scientific interest as well as their potential to significantly increase the scalability of spintronics devices by replacing transistors with diodes 10,16 . It is possible to achieve unipolar magnetization switching by exploiting the temporal evolution of magnetization switching, or, in other words, the magnetization dynamics. For example, in the context of STT or electric field induced magnetization switching, unipolar operation was previously demonstrated 7,9,[16][17][18][19] by driving the magnetization into coherent precessional motion between the two stable states and then precisely controlling the time duration for which the external force of fixed polarity was applied. As the time varying magnetization trajectory oscillates between the two potential minima (stable states), switching was accomplished by removing the external force at the appropriate time to release the magnetization at the desired final state. This oscillatory behavior was also theoretically predicted in the SOT driven switching 20,21 . However, it must be emphasized that the above described oscillatory switching scheme for unipolar operation requires strong coherency of the magnetic moments or, in other words, the magnetization should be kept uniformly aligned throughout the rotational switching process. The coherency of the magnetization is very sensitive to thermal agitations 22 and also relatively weak [23][24][25] in magnetic structures with perpendicular magnetic anisotropy (PMA) which are required for high density applications.
Here, we report our experimental discovery of an alternative method to achieve the oscillatory switching behavior in the scenario of incoherent magnetization switching in PMA structures driven by SOT. The SOT is an electric current induced phenomenon that utilizes spin currents generated by spin orbit interactions to efficiently manipulate and switch the magnetization of an ultrathin magnet [11][12][13][14][15] . While its microscopic origin is still controversial 26-29 , SOT is known to be composed of two components, namely, the damping-like torque (DLT),   can be considered as equivalent field with y m symmetry (HDLT) and ŷ symmetry (HFLT), respectively 30 .
Unless the lateral dimensions of the ultrathin magnet are extremely small (< 40 nm), the SOT induced magnetization switching in PMA structures is an incoherent process 31 . In the incoherent regime, the switching happens by depinning of a reversed magnetic domain followed by its expansion 24,[30][31][32][33][34][35] . Due to the torque symmetries, the general consensus till now is that the DLT is responsible to drive the domain expansion in SOT switching 30 and the role of FLT in deterministic switching is usually neglected and not well understood 25,30 . On the contrary, our studies reveal that in PMA structures with large FLT, the SOT driven incoherent magnetization dynamics and the deterministic switching are greatly influenced by FLT.

Nanosecond pulse current induced SOT switching
We explore the SOT driven magnetization switching dynamics under the application of nanosecond current pulses in Ta/CoFeB/MgO structures, whose FLT is large and is of opposite sign to that of DLT 27,36 (FLT/DLT = -3.2, see Methods for our sign conventions). As shown in In order to study the SOT switching dynamics, we have measured the probability of magnetization switching by applying current pulses with the initial state of the magnetization as 'up' (+z-direction). Figure 1b shows the two dimensional diagram of the measured switching probability (Psw) as a function of current density (J) and pulse duration (t) at a fixed H = 1191 Oe. We have also measured the Psw vs.  24,[30][31][32][33][34][35] rather than coherent magnetization rotation, which is also expected from the size of the studied structure.

Oscillatory switching behavior induced by FLT
Beyond the first switching boundary, the Psw is expected to remain at 100 % and does not change, since the existing theories and experimental results indicate that the DLT driven incoherent SOT switching is a deterministic process 24,30,31 . On the contrary, as seen in Figs In order to obtain more insights on the backward switching, we have measured Psw for different θH as shown in Fig. 1d. Interestingly, the observed 'down' to 'up' backward switching exhibits significant asymmetric behavior with respect to θH, compared to the 'up' to 'down' forward switching. The backward switching is suppressed or enhanced, as the H is tilted towards (θH < 180°) or away from (θH > 180°) the +y-direction, respectively. This asymmetric behavior implies that an equivalent field with y-symmetry gives rise to the observed backward switching, and this y-symmetry coincides with the direction of HFLT. The harmonic Hall voltage measurements in the Ta/CoFeB/MgO structure have shown that a large HFLT exists in the -ydirection when a positive current (along the +x-direction) is applied 27,36 . The observed backward switching in Fig. 1d is suppressed when the effective HFLT is reduced by applying an external transverse field along the +y-direction (θH < 180°) opposite to the SOT induced HFLT (along the - Similarly, we have determined the VDW during the observed backward switching using the relation, , as the backward switching follows the first forward switching in time. The tc,bck represents the time corresponding to Psw = 50% during the backward switching. Interestingly, the estimated VDW,bck also shows monotonic increase with respect to J and H (Figs. 2a and 2b) and an asymmetric behavior as a function of θH (Fig. 2c), implying that the backward switching also arises from the spin torque driven domain expansion similar to the case of the first forward switching but in an opposite manner. However, VDW,bck is smaller than VDW,fwd because the domain expansion in the backward switching is energetically unfavorable as discussed later. However, this annihilation process is followed by a nucleation of a DW with an inverted chirality

One-dimensional micromagnetics simulations of domain walls
) which can be understood as a reflection of the DW on the structure edge 40,41 . This DW with an inverted chirality is not energetically favorable and follows damped motion over time to revert back its chirality due to the applied H along the -x-direction. However, a sufficiently large HFLT in the -y-direction can give dynamic stability to the DW with inverted chirality with a lifetime of several nanoseconds. As this metastable DW's center is along the +x-

Unipolar SOT switching
Finally, utilizing the observed oscillatory characteristics, we show a deterministic unipolar SOT switching scheme which reversibly controls the magnetization configuration under a constant J and H of a fixed polarity and changing t only. This is demonstrated using a series of current pulses with alternating lengths of 2.5 ns and 7.5 ns with a fixed current density of 79.4 × 10 6 A cm -2 under a constant H of 1067 Oe. After each pulse injection, the magnetization state is monitored using the anomalous Hall resistance (RAHE) measurement. As shown in Fig. 4, the deterministic SOT switching consistently occurs by the unipolar current pulses. The initial state of the magnetization is pointing 'up' and the pulse of 2.5 ns always switches the magnetization to 'down', while the magnetization is always brought to 'up' state with the pulse of 7.5 ns.

Discussion
The role of FLT has not been paid much attention in the majority of SOT switching experiments and thus, the SOT switching and domain wall dynamics have been mainly discussed using the DLT alone. The FLT was claimed to induce a partial decrease in the SOT switching probability (decreased to ~60% after achieving full 100% switching) 44 . However, another work reported a similar backward SOT switching that was attributed to a small tilt of in-plane assist field along the out-of-field direction 45 . With these two different interpretations, the role of FLT in SOT dynamics and the underlying physics of the backward SOT switching still remain vague.
In this regard, our experiments bring to light the crucial role of FLT in breaking the determinism in SOT driven incoherent switching dynamics which results in oscillatory magnetization switching characteristics with respect to the current pulse duration. We make use of this observed oscillatory behavior to demonstrate a unipolar deterministic SOT switching scheme which operates by controlling the duration of the current pulses, while keeping the magnitudes and polarities of the current and the assist-field constant. Our study provides the missing piece in the physics of SOT switching dynamics and offers novel strategies for magnetization switching with unipolar operation. We studied total 9 devices with varying the dot diameter and ferromagnet thickness.

Sample preparation and measurements
Every device showed the backward switching with quantitative difference in the switching phase diagram that is attributed to the deviation in effective anisotropy and depinning sites.

Intrinsic switching current density from the macrospin switching model The intrinsic
switching current density from the macrospin-like rotation switching model is calculated 46 using Note 8). The corresponding FLT/DLT ratio is -3.2. For the current pulse, both rise and fall times are 100 ps. In our sign convention, a negative DLT efficiency (cDLT < 0) induces an 'up'-to-'down' switching for J > 0 and H < 0 (θH = 180°). The considered geometry has dimension of 220 nm × 80 nm × 2.5 nm and the unit cell size of 2 nm × 80 nm × 2.5 nm. The initial magnetization direction of majority part of the considered geometry is 'up' (along +zdirection) with reversed 'down' domain formed at one edge. The DMI effective field (HDMI) is estimated using the following relation 30