A strategy for fast and precise control of polarity and chirality in magnetic vortices

Abstract

Magnetic vortices hold great promise for advanced information storage applications due to their quartet degenerate states and high topological stability. The key to their application lies on meticulous control of its polarity and chirality, which traditionally relies on magnetic fields, currents, and spin waves. However, the vortex core’s intrinsic precession under these stimuli hampers fast switching of the polarity and chirality. Here, we demonstrate a fast and precise control of polarity and chirality in magnetic vortices using combined femtosecond (fs) laser and tiny magnetic fields via micromagnetic simulations on Permalloy nanodisks. The fs laser pulse induces an ultrafast quench effect to establish the initial paramagnetic state, while the simultaneously applied magnetic fields precisely target the final vortex structure. Intriguingly, a 110 mT out-of-plane field and a 7 mT in-plane circular field are sufficient to realize precise control of the polarity and chirality on sub-nanosecond time scale, respectively, which are much lower than that of the previous work. Our approach guarantees fast and reliable switching of magnetic vortex polarity and chirality, paving the groundwork for a high-speed quaternary data storage and contributing a novel perspective to the fundamentals of spintronics.

Graphical abstract

Keywords

magnetic vortex / chirality switching / polarity switching / femtosecond laser quenching / micromagnetic simulation

1 Introduction

As fundamental topological objects in mesoscopic patterned structures, magnetic vortices are characterized by their integer winding number and in-plane chiral spin configurations with a tiny out-of-plane magnetization at the core due to geometric constraints [1, 2]. These topological structures exhibit two degrees of freedom: chirality (c = ±1), denoting the magnetization’s in-plane circulation as either clockwise (CW, c = –1) or counterclockwise (CCW, c = 1) around the nanodisk circumference, and polarity (p = ±1), which designates the out-of-plane core magnetization direction (upward for p = 1, downward for p = –1), yielding four degenerate states that possess potential in multi-bit information storage applications [3−6]. Particularly, a wide array of vortex-based devices have been proposed by utilizing structural switching between the degenerate states, such as racetrack memories [7−11], logical devices [12−16], quantum computing [17−19], and microwave oscillators [20−25]. Therefore, precise control of the degrees of freedom in a magnetic vortex is essential for vortex-based functional devices.

To achieve reliable control of the polarity and chirality of magnetic vortices, methods including electrical current [26−33], magnetic field [34−41], and spin-wave [42, 43] have been attempted, which make precession of the vortex core and switch the chirality or polarity. Moreover, switching of polarity and chirality has been achieved through the application of localized or pulsed fields together with designing samples with particular shapes [39, 41, 44−47]. Although these approaches are effective, they are limited by the initial magnetic structure and specific geometrical configurations, posing challenges to practical applications and the miniaturization of devices with decreasing sample sizes. Moreover, chirality switching is generally confined to nanosecond timescales under pulsed magnetic fields due to the inherent precession of the vortex core prior to final switching [39, 48, 49], and polarity reversal in symmetric systems driven by electric currents typically necessitates tens of nanoseconds [27, 37, 50]. Consequently, achieving fast and precise control of vortex degrees of freedom in small samples with symmetric geometries continues to pose a significant challenge.

The femtosecond (fs) lasers has opened up new possibilities for ultrafast switching of magnetic structures [51−56]. For example, the photothermal effect of ultrafast fs lasers can lead to the ultrafast formation of multi-magnetic vortices, revealing hidden topological states in topological magnetic structures [56]. Moreover, it has been indicated that fs lasers can significantly reduce the magnetic field required to reverse the core of magnetic vortices near the Curie temperature (T_C) [57]. Consequently, fs laser-assisted methods are more advantageous than the traditional methods in manipulating magnetic structures.

In this study, we introduce a fs laser-assisted approach enabling fast and precise control of degrees of freedom in magnetic vortices, illustrated by micromagnetic simulations on permalloy (Py) nanodisks. This method combines fs lasers with small magnetic fields, utilizing the disordered paramagnetic state induced by the fs laser’s photothermal effect as the initial structure and simultaneously applying small magnetic fields with milliteslas of magnitude to it to control the chirality and polarity of the final vortex in the subsequent remagnetization relaxation process. This research demonstrates the reformation of magnetic vortex with desired chirality and polarity from a paramagnetic state within a few nanoseconds in a geometrically symmetric disk. Moreover, our approach eliminates the requirement for prior knowledge of the initial vortex’s chirality or polarity, enabling the desired vortex state to be achieved without pre-measurements. Therefore, the method proposed in this work provides a rapid and efficient manner for controlling vortex chirality and polarity in symmetric disks, holding great potential for applications in magnetic vortex-based spintronic devices.

2 Basic principle

To demonstrate the feasibility of the basic ideal, micromagnetic simulations were carried out on circular Py nanodisks using the open-source OOMMF software created by NIST (URL: math.nist.gov/oommf/oommf_cites.html), which is based on the Landau–Lifshitz–Gilbert (LLG) equation [58, 59]:

(1){\mathrm{\partial }}_t\mathit{m}= -{\gamma }_0\left(\mathit{m}\times {\mathit{h}}_{\mathrm{e}\mathrm{f}\mathrm{f}}\right)+ \alpha \left(\mathit{m}\times {\mathrm{\partial }}_t\mathit{m}\right),

where \mathit{m} is the reduced magnetization (i.e., \mathit{m}=\mathit{M}/M_{\mathrm{s}}), {\mathit{h}}_{\mathrm{e}\mathrm{f}\mathrm{f}} is the effective field, {\gamma }_0 is the absolute gyroscopic ratio, and \alpha is the damping constant. In this work, the used material parameters are typical for Py, namely, saturation magnetization M_{\mathrm{s}}= 800\mathrm{k} \mathrm{A}/\mathrm{m}, exchange constant A=13\mathrm{p}\mathrm{J}/\mathrm{m}, Gilbert damping constant \alpha =0.05, and magnetic anisotropy constant is zero. The magnetic parameters employed in our micromagnetic simulation are derived from previous studies on laser excitation [56, 60]. Following a similar assumption and methodology [56, 60], we focused solely on the photothermal effect during the interaction between the laser pulse and the magnetization. When the fluence is sufficient to raise the temperature above the T_C, the magnetization becomes disordered. As the sample cools down after the pulse excitation, the system relaxes into a vortex state. Based on this premise, the most straightforward approach was to randomize the magnetization and allow the system to relax using various random seeds. The Py nanodisk has a diameter of 500 nm and a thickness of 30 nm. In our simulation, we assumed that the laser uniformly excites the entire sample into a randomly magnetized state, effectively disregarding temperature gradients. The cell size was set to 5 nm× 5 nm× 30 nm, and other cell sizes were also utilized, such as a 5 nm× 5 nm× 15 nm mesh grid, which underwent a similar relaxation process. Furthermore, the mesh size employed in this study is consistent with previous research [56]. To determine the critical magnetic fields for polarity and chirality control during the fs laser quench, 30 runs of simulations for controlling polarity and chirality were performed, respectively. In each simulation, a distinct initial random spin configuration induced by fs laser pulse was used to relax under different magnetic fields.

The transient temperature evolution of the nanodisk after a fs laser pulse excitation was evaluated by a two-temperature model (TTM) [56, 61]. The diameter of the fs laser spot was usually 40 µm, which is much larger than sample and makes sure the uniform excitation of the sample [56]. To achieve the desired temporal resolution in the simulation, the TTM considers the material as a dual system, encompassing both lattice and electrons while taking into account their interactions [61]. The electrons absorb the majority of the energy delivered by the fs laser, rapidly elevating their temperature. Subsequently, the electrons transfer their energy to the lattice through electron−phonon coupling, resulting in an elevation of the lattice temperature. For the TTM calculation, the parameters of electron heat capacity, lattice heat capacity, and electron–phonon coupling factor are derived from previous research [61]. At a laser fluence of appropriate pulse energy, the Py disks could be heated above T_C rapidly, and then cooled down to T_C through local equilibration with background in tens of picoseconds [56]. On longer time scales, the system returns to room temperature due to the slower lateral heat dissipation with the surrounding environment.

Fig.1(a) presents the principle of a two-step manipulation approach for the four energy degenerate states of the magnetic vortex. Upon excitation by a single-shot fs laser pulse (with 515 nm wavelength and 300 fs pulse duration) with sufficient energy, the magnetic vortex rapidly transitions into a paramagnetic state. The externally applied out-of-plane and in-plane magnetic fields, control the polarity and chirality of magnetic vortices in the subsequent relaxation process, respectively, leading to transitions among the four degenerate energy states [Fig.1(b)]. Notice that, since the external magnetic field only plays a critical role in the fast relaxation process after the laser pulse excitation, the duration of the magnetic field could be relatively long and only depends on the repetition rate of the fs laser pulse applied. The temperature variations of the Py nanodisk during fs laser excitation were calculated using the TTM [56, 61], as illustrated in Fig.1(c). Due to the fs laser quenching effect [56], with a certain fluence the fs laser pulse could raise the sample’s temperature to above T_C and result in a transient paramagnetic state on the fs time scale. Note that, in real experiment the laser fluence should be carefully optimized to make sure full demagnetization of the vortex state, but preventing damage to the sample. The sample’s temperature surpasses its T_C of ~850 K upon the single-shot fs laser pulse excitation, causing the original magnetic vortex to transform into a transient paramagnetic state that serves as the initial condition in the simulation. Then the sample temperature rapidly decreases within a few picoseconds. This phenomenon is termed as the fs laser quench effect. Considering the generation of the disordered state within a few picoseconds and the subsequent remagnization relaxation occuring within one nanosecond, in our simulation a magnetic field with relative long duration, namely, static magnetic field, was applied throughout the simulation process to ensure the applied magnetic field acts on the whole relaxation process of the disordered state.

3 Results and discussion

3.1 Fast control of magnetic vortex polarity with combined fs laser quenching and out-of-plane magnetic field

Our micromagnetic simulations show that the polarity of the magnetic vortex can be precisely controlled by applying an out-of-plane magnetic field during the single-shot fs laser quench of the sample. The dynamic process of a magnetic vortex formation after the laser pulse quench is as follows: when a fs laser irradiates a magnetic vortex, the vortex transitions into a disordered state due to the fs laser pulse injected energy into the system, in which the temperature is transiently above T_C. The initial thermal perturbation makes the magnetic moment undergoes disordered motion and reaches the paramagnetic state with the highest energy (Fig. S1). The simultaneous application of a magnetic field gradually aligns the direction of the magnetic moment during its evolution, causing it to precess around the effective field direction, namely, Larmor precession. Note that, the external magnetic field plays a major role in the first 200 ps, during which the vortex–antivortex pair forms rapidly. As the magnetic structure further relaxes, the adjacent vortices and antivortices inside the disk move closer and annihilate in pairs over time. While for the half-vortices at the disk’s edge, the nearby internal vortices move towards the centers of the adjacent half-vortices, and they annihilate upon collision, as indicated by the dashed circles in Fig.2(a) and (b). The spin system’s energy decreases continuously during the annihilation process of vortex-antivortex pairs until it reaches the lowest energy state of a single magnetic vortex state after 800 ps (see Fig. S1). Throughout the relaxation process, the exchange interaction energy and demagnetization energy play major roles due to the vortex formation mechanism, and the winding number remains unchanged with w = 1, a fact that has been experimentally illustrated [56].

Fig.2(a) and (b) illustrate the transition of the magnetic structure from a random paramagnetic state to a specific polarity vortex state under an out-of-plane magnetic field with opposite directions. Fig.2(a) illustrates the time-dependent evolution of the magnetic structure under an applied magnetic field in the +z direction. The high fluence of the laser employed in this study elevates the sample temperature above the T_C, leading to a random magnetization state that disrupts the spin configuration of the initial magnetic vortex and can easily overcomes the geometric constraints. This phenomenon is advantageous for sample preparation in experiments involving various geometries, such as polygons, Pac-Man disks, and thickness-asymmetric samples [34, 39, 41]. As shown, vortex–antivortex pairs gradually form between 0 and 200 ps, and from 200 to 800 ps these pairs coalesce and annihilate, resulting in a single vortex with an off-centered core. During this process, the target vortex state is established, and there is no gyrotropic precession of the vortex core as that in the conventional magnetic field pulse or current pulse induced vortex switching. Subsequently, over a period of up to 7 ns, the magnetic vortex further relaxes, with the vortex core shifting toward the center. Ultimately, this process results in a vortex with desired upward polarity. Fig.2(b) shows the transition from a paramagnetic state to a downward polarity magnetic vortex under a magnetic field applied in the –z direction. This dynamical process is similar to that in Fig.2(a), including the movement and annihilation of vortex–antivortex pairs, and finally stabilizing into a vortex with a downward polarity. Notice that, the polarity manipulation processes shown in Fig.2(a) and (b) are completed within a few nanoseconds, leading to the possibility for high-speed information processing. For practical application, the fast reversal of out-of-plane magnetic field could be obtained by a high frequency electrical current-induced magnetic field [37, 39] or a microwave magnetic field [62]. Interestingly, we found that when a shorter duration magnetic field is applied, the relaxation process of the magnetic vortex also changes. Figure S2 illustrates a single-pulse out-of-plane magnetic field with a duration of ~0.1 ns, resulting in a full relaxation dynamical process of ~11 ns, which means the entire remagnetization process significantly slows down. Therefore, to be more efficient, the magnetic field duration should be longer enough to cover the time window of the remagnetization relaxation process (at least longer than 1 nanosecond), as shown in Fig.2(a) and (b).

To determine the threshold of the out-of-plane field required for effectively and precisely manipulating the vortex polarity, an out-of-plane magnetic field along the +z direction was applied with a range from 60 to 500 mT. As illustrated in Fig.2(c), the controllability was less effective under magnetic fields below 110 mT. Specifically, at 60 and 78 mT, the probability of achieving upward polarity was 80% and 86.7%, respectively, as indicated by the arrows in Fig.2(c). The slight dip observed in Fig.2(c) is probably related to the number of the calculations. With an increase in the number of simulations, the dip is expected to flatten out. A remarkable enhancement in the control of vortex polarity is observed with increasing magnetic field strength. For instance, at 90 mT the controllability significantly increased to 96.7%, demonstrating effective manipulation. Further increase of the magnetic field strength above 110 mT maintains the controllability reach 100%. Thus, the magnetic field strength in the +z direction is crucial for achieving the desired upward polarity. Fig.2(d) presents the corresponding chirality distribution across the 60 to 500 mT out-of-plane magnetic fields. It is evident that the distributions of CCW and CW chirality are approximately 50%. Despite occasional deviations from this average in some magnetic fields, the average proportions of both CCW and CW chirality consistently converge to ~50% with increasing the out-of-plane field to above 110 mT.

Applying a perpendicular magnetic field along the –z direction also plays a similar crucial role for controlling the sample’s downward polarity during the fs laser quench process, as shown in Fig.2(e) and (f). Given that the laser spot is significantly larger than the sample diameter and Py has excellent thermal conductivity, the effects of upward and downward magnetic fields on polarity control should be equivalent. Therefore, the critical field required to control the downward polarity (above –110 mT) is comparable to that of the upward. We found that the threshold magnetic field is independent on the sample diameter (see Fig. S3), but increases with the magnetic constants of the sample material (see Fig. S4).

The results in Fig.2 suggest that out-of-plane magnetic fields can effectively control the polarity of magnetic vortices during the fs laser quench process. Notably, the critical magnetic field for control polarity effectively is ~110 mT, significantly lower than the previously established threshold of 250 mT [20] required for switching of vortex polarity using out-of-plane magnetic field only. This reduction is due to the energy transfer of fs laser pulse to the vortex, substantially lowering the critical energy barrier. The mechanism of the vortex polarity control in this condition can be understood as follows. The fs laser pulse excites the Py nanodisk above the T_C, leading to rapid demagnetization of the initial magnetization state within a few picoseconds. Subsequently, remagnetization occurs as the temperature decreases below the T_C. During the remagnetization process, the simultaneously applied out-of-plane magnetic field determines the polarity direction of the final magnetic vortex. Based on these insights, we propose a strategy that integrates optical quench with out-of-plane magnetic field-assisted manipulation of magnetic vortex polarity for fast information storage, as schematically shown in Fig.2(g). This methodology adeptly harnesses magnetic vortex polarity (upward and downward) for binary data encoding, representing “1” and “0”.

3.2 Fast control of magnetic vortex chirality with combined fs laser quenching and in-plane magnetic field

We further investigate the relationship between the chirality and in-plane magnetic field in the fs laser pulse quench process, and find that the precise chirality control can be achieved by applying a circular in-plane magnetic field. The circular in-plane magnetic field can be in principle obtained by applying a certain perpendicular current in the nanodisk [63]. For the micromagnetic simulations in this section, magnetic fields with identical magnitudes but opposing directions were applied to a random paramagnetic state in the Py nanodisk. Fig.3(a) illustrates the transition process from a disordered paramagnetic state to a CCW chirality vortex under a circular in-plane magnetic field along the CCW direction (8 mT). As shown clearly, vortex-antivortex pairs form gradually between 0 and 200 ps, and then from 200 ps to 800 ps these pairs coalesce and annihilate, resulting in a single vortex with an off-centered core. Finally, the vortex further relaxes to the ground state with the time elapsing more than one nanosecond. Fig.3(b) depicted the similar evolution process from a paramagnetic state to a CW chirality vortex under a CW-directed circular in-plane magnetic field (–8 mT). Therefore, the time required for the transition from a disordered state to the magnetic vortex state with a definite chirality is ~1.4 ns.

To determine the threshold of the in-plane circular magnetic field required for the controllable vortex chirality manipulation, magnetic fields with strengths ranging from 3 to 90 mT were applied in the CCW direction. The statistical results for the final chirality distribution are presented in Fig.3(c). At a magnetic field of 3 mT, the probability of the CCW chirality for the magnetic vortex is ~86.6%. With increasing the field strength, the proportion of the CCW chirality improves. At 7 mT, CCW chirality is observed in all the simulations. Further elevation of the in-plane CCW magnetic field strength sustains the chirality control at ~100%, demonstrating the high robustness of the in-plane CCW-oriented magnetic field in regulating the vortex CCW chirality. Notably, the in-plane CCW magnetic field does not apparently affect the polarity of the vortices, as depicted in Fig.3(d), which shows that the polarity statistics of up and down remain around 50% across the varying in-plane CCW magnetic fields.

Similar micromagnetic simulations were conducted with an in-plane CW magnetic field applied in the Py nanodisk ranging from –3 to –90 mT, and the results are shown in Fig.3(e) and (f). It can be found that magnitude of the critical field (about –7 mT) required to control the CW chirality is similar to that of the CCW case. Based on these insights, we introduce an approach for rapid switching of magnetic vortex chirality by employing optical quench in conjunction with in-plane circular magnetic field assistance, as depicted in Fig.3(g). This methodology proceeds information storage based on the efficient fast control of the chirality (CCW and CW) of magnetic vortices, encoded as binary “1” and “0”.

3.3 Simultaneous fast control of polarity and chirality of magnetic vortex combing fs laser quenching with out-of-plane and in-plane magnetic fields

The results in Fig.2 and Fig.3 show that the independent fast control of polarity/chirality is feasible using the application of an out-of-plane/in-plane magnetic field during the fs laser quench of the Py nanodisk. These results are intriguing, because the unique quench of the fs laser pulse makes the polarity and chirality switching of magnetic vortex efficiently controllable via very low critical out-of-plane and in-plane magnetic fields, respectively. Therefore, based on these findings, we propose a strategy to realize fast four-bit data memory by simultaneously applying both the small out-of-plane magnetic field (regulating the polarity) and the in-plane circular magnetic field (controlling the chirality) in conjunction with the fs laser quench.

As schematically shown in Fig.4(a), an fs laser pulse is used to ultrafast erase the magnetic vortex in the Py nanodisk, while two small magnetic fields (out-of-plane and circular in-plane ones) are simultaneously applied to determine the polarity and chirality of the newly formed magnetic vortex after the quench. To verify the feasibility of this strategy, we performed systematic micromagnetic simulations, in which a ±135 mT out-of-plane magnetic field and a ±8 mT in-plane circular magnetic field were exerted on the circular Py nanodisk with an initial fs laser pulse-induced paramagnetic state. To accumulate statistically meaningful data quantitatively, the simulation was repeated 100 times with different initial paramagnetic states for each out-of-plane/in-plane magnetic field setting. As shown in Fig.4(b), the four energy degeneracy states can be effectively controlled with the percentage of each desired final state reaching ~100%.

Based on the simulation results, the concept schematic of the proposed fast quaternary information storage is depicted in Fig.4(c). The quaternary data information in one magnetic vortex can be encoded in the four states with specific polarity and chirality, namely, “00”, “01”, “10”, and “11”, and the data writing/erasing is accomplished by controlling the switch between the four states via simultaneously optical quench and in-plane/out-of-plane magnetic field assist. As depicted in Fig.2 and Fig.3, the time scale for the fs laser pulse to excite magnetic vortex to a disordered state is a few picoseconds, while that for the disordered state to revert into a vortex state with target chirality/polarity is within a few nanoseconds. Therefore, the advantage of this quaternary-bit data storage strategy is that it has substantially high information storage capacity and fast information processing speed. Regarding the practical implementation of quaternary-bit data storage devices, it is proposed that the signals of the four energy-degenerate vortex states could be measured with an electrical readout, such as a nanovoltmeter [64] represented as “V” with a bridge in Fig.4(c). The implementation of these devices can be achieved by delivering fs lasers to magnetic vortex structures using an optical objective and optical fiber, both of which are widely utilized [65, 66]. Recent studies have investigated the potential of magnetic vortices as qubits [17−19], highlighting the need for precise control over their polarity and chirality. By employing focused lasers, it is possible to excite these structures, thereby enabling the development of quaternary memory and qubits based on magnetic vortices for future applications.

4 Conclusion and outlook

In summary, we have successfully demonstrated a fast-controllable method for switching both the polarity and chirality of magnetic vortices. By utilizing the random magnetization induced by fs laser excitation as the initial state, the polarity and chirality can be efficiently manipulated with out-of-plane and in-plane circular magnetic fields, respectively. Our method requires a significantly lower critical magnetic field than the previous studies and is not constrained by the initial state or geometry of the Py nanodisk. Specifically, an out-of-plane magnetic field of about 110 mT can achieve the desired polarity, while an in-plane circling magnetic field of about 7 mT can set the chirality. The substantially reduced critical magnetic field and efficiently fast switching of polarity and chirality in magnetic vortices are advantageous for low-power consumption and high-speed spintronic devices. Our work presents a new avenue for fast manipulating topological spin textures, such as vortices, merons, and skyrmions, which has significant implications for future spintronic devices. In addition, short pulsed magnetic fields could induce different phenomena in magnetic vortices compared to the static magnetic fields, such as dynamic excitations in radially symmetric modes [67]. Therefore, combining short pulsed magnetic fields with fs laser via different interaction mechanisms may result in more complex and interesting phenomena in the transition dynamics of magnetic vortices, which would further enrich the dynamic regulation and study of topological spin textures.

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