Yan Li

Dongxing Zheng

Chen Liu

Chenhui Zhang

Bin Fang

Aitian Chen

Yinchang Ma

Aurélien Manchon

Xixiang Zhang
email: xixiang.zhang@kaust.edu.sa

Current-induced magnetization switching across a nearly room-temperature compensation point in an insulating compensated ferrimagnet

Keywords: Insulating compensated ferrimagnet, spin-orbit torque, perpendicular magnetic anisotropy, spin current

Insulating compensated ferrimagnets, especially hosting room-temperature compensation points, are considered promising candidates for developing ultrahigh-density and ultrafast magnonic devices owing to combining the characteristics of both ferromagnets and antiferromagnets. These intriguing features become outstanding close to their compensation points. However, their spinorbit torque (SOT)-induced magnetization switching, particularly in the vicinity of the compensation points, remains unclear. Herein, we systematically investigated the SOT in insulating compensated ferrimagnetic Gd3Fe5O12/Pt heterostructures with perpendicular magnetic anisotropy. A nearly room-temperature compensation point (Tcomp ~297 K) was consistently identified by the magnetization curves, spin Hall-induced anomalous Hall effect, and spin Hall magnetoresistance measurements, respectively. Moreover, using 100 ns duration pulsed current, deterministic current-induced magnetization switching below and above Tcomp, even at 294 K and 301 K, was achieved with opposite switching polarity. It is found that a large current is required to switch the magnetization in the vicinity of Tcomp although the effective SOT field increases close to Tcomp. Our finding provides alternative opportunities for exploring ultrafast room-temperature magnon-based devices.

INTRODUCTION

Electrical manipulation of the magnetic state through the spin orbit torque (SOT) is of particular significance for both fundamental physics and technological applications. Beyond ferromagnets, the control of the Néel vector via the SOT in antiferromagnetic materials offers potential prospects in exploiting ultrafast and high-density spintronic devices, benefitting from the absence of magnetization and the antiferromagnetic exchange coupling-dominated dynamics. 1,2 Nonetheless, achieving efficient readouts and writing the antiferromagnetic state remains challenging because of the vanishing net magnetization. In some metallic ferrimagnets, such as the rare earth-transition metal alloys CoTb, GdCo, and GdFeCo, the net magnetization can be adjusted to approximately zero by varying the chemical composition or temperature. 3,4 These compensated ferrimagnets possess antiferromagnetic exchange coupling and finite net magnetization, and thus exhibit the combined advantages of both ferro-and antiferromagnets, such as reliable electrical reading and writing, high SOT switching efficiency close to the magnetization compensation point, and ultrafast domain wall velocity at the angular momentum compensation point. [5][6][7][8][9] Note that the intriguing features of these compensated ferrimagnets strongly benefit from their compensation points. To exploit the possible high-performance ferrimagnetic devices, compensated ferrimagnetic materials with room-temperature compensation points are thus highly desired. 9 Electrically insulating compensated ferrimagnets, allowing long-range spin information communication and storage, possess great potential for integrated magnon-based devices beyond conventional metallic ferrimagnetic systems. [10][11][12] However, their SOT switching has been much less addressed so far, particularly in the vicinity of the compensation points. Gd3Fe5O12 (GdIG) is a compensated ferrimagnetic insulator with a high Curie temperature (~550 K). 13 Long spin transmission length and excellent magnon propagation in GdIG, even though not observed previously, are naturally expected in view of its low magnetic damping and absence of Ohmic loss. 14 More strikingly, magnetization compensation temperature of bulk GdIG is close to the room-temperature (Tcomp~295 K). 15,16 The characteristics of GdIG make it a prominent platform for room-temperature, ultrafast, and low-dissipation magnonic applications. In this work, we report the unambiguous observation of a nearly room-temperature compensation point (Tcomp ~297 K) in an insulating compensated ferrimagnetic GdIG film with perpendicular magnetic anisotropy (PMA). In addition, we achieve deterministic current-induced magnetization switching with opposite switching polarity in GdIG/Pt heterostructures at temperatures below 294 K and above 301 K. It is found that a large critical switching current is required in the vicinity of Tcomp although the effective SOT field significantly increases as approaching to Tcomp.

RESULTS AND DISCUSSION

6.5 nm-thick Gd3Fe5O12 (GdIG) films were grown on (111)-oriented Gd3Sc2Ga3O12 (GSGG) substrate by pulsed laser deposition, and then transferred to a magnetron sputter system, in which a 5 nm-thick Pt layer was deposited on the GdIG films. For the electrical transport measurements, the samples were fabricated into Hall bar device, as schematically shown in the bottom panel of Figure 1a. The cross-sectional scanning transmission electron microscopy (STEM) image in the up-right panel of Figure 1a shows the good epitaxial relationship between the GdIG film and the GSGG substrate with sharp interface viewed along the [112 $ ] direction. GdIG consists of three magnetic sublattices: an octahedral Fe sublattice (a-sites), a tetrahedral Fe sublattice (d-sites) and a dodecahedral Gd sublattice (c-sites), as shown in the up-left panel of Figure 1a. The magnetic configurations depend on both magnetic field and temperature, as schematically drawn in Figure 1b; the data originate from references 17,18 . The effective Fe sublattices, which are composed of octahedral Fe sublattice (a-sites) and tetrahedral Fe sublattice (d-sites), are antiferromagnetically coupled to the Gd sublattice with collinear ferrimagnetic configurations at low magnetic fields.

The net moment vanishes at the magnetic compensation temperature Tcomp. Moreover, the magnetic moments of the Fe sublattices do not vary significantly whereas those of the Gd sublattice decrease significantly with increasing temperature. Therefore, the net magnetization is dominated by the Fe sublattices above Tcomp and by the Gd sublattice below Tcomp. In addition, the exchange coupling between the Gd sublattice and effective Fe sublattices is much weaker than the dominant antiferromagnetic coupling between the two Fe sublattices. Thus, a canted magnetic phase is accessible at a large magnetic field [~3 T at 300 K and ~14 T at 280 K (see Figure 1b)], particularly in the vicinity of Tcomp. In this case, the moments of a-Fe and d-Fe are generally antiparallel owing to the strong antiferromagnetic exchange coupling between them. 18 The measured hysteresis loops via sweeping the out-of-plane magnetic field confirm the PMA in the GSGG/GdIG sample at different temperatures, as shown in Figure 2a. Such a PMA is induced by the tensile strain between the GdIG film (lattice constant: 12.480 Å) and GSGG(111) substrate (lattice constant: 12.554 Å). The values of the saturation magnetization 𝑀 ! at various temperatures are extracted from the M-H loops and plotted against temperature in Figure 2d. The net saturation magnetization Ms almost vanishes close to 297 K, which corresponds to the magnetic compensation temperature Tcomp of GdIG. Moreover, a charge current was applied to the Pt layer along the x axis, as shown in Figure 1a; it generated a spin current owing to the spin Hall effect (SHE). The transmission and reflection of the spin current at the GdIG/Pt interface give rise to different effects on the GdIG and Pt sides: 19 the SOT in GdIG layer and the spin Hall-induced anomalous Hall effect (SH-AHE) and spin Hall magnetoresistance (SMR) in Pt layer owing to the simultaneous action of the SHE and inverse SHE. 20,21 According to the SH-AHE theory and previous experiments in magnetic insulator/heavy metal, the SH-AHE signal is proportional to the out-of-plane magnetic moment, 20 which provides a chance to characterize magnetic switching of magnetic insulator. Figure 2b shows the SH-AHE resistance RH after subtracting the linear background from the ordinary Hall effect by sweeping the out-of-plane magnetic field at various temperatures. Evidently, the sign of the RH-H loop is opposite at temperatures above and below Tcomp. Practically, the magnetic moment of Gd ion origins from the inner 4f shell, which is more localized than that of the 3d shell of Fe ions. The transfer of spin angular momentum between Pt and GdIG is therefore dominated by the Fe sublattices via s-d exchange. Furthermore, given that the net magnetization is dominated by the Fe sublattices above Tcomp and the Gd sublattice below Tcomp, the RH-H loops thus change sign across Tcomp.

The angle-dependent magnetoresistance 𝜌(𝜑 "# ) was measured by rotating the sample in the yz plane under the applied magnetic field H (5 T) at various temperatures, as shown in Figure 2c. ∆𝜌 $%& /𝜌 # is defined by [𝜌 # -𝜌(𝜑 "# )]/𝜌 # , where 𝜌 # and 𝜑 '( are the magnetoresistance with respect to the applied magnetic field along the -z axis and the rotation angle in the yz plane with respect to the +z axis, respectively. Far away from Tcomp, the orientation of the net magnetization is approximately along H in a large magnetic field (5 T). Moreover, the measured resistivity at 340 K and 260 K is maximized (minimized) when H is oriented along the z (y) axis, manifesting a standard characteristic of the SMR effect like those in ferromagnetic systems 22 . However, the measured resistivity at 300K is almost minimized (maximized) when H is along z (y) axis, which is similar to the SMR effect in antiferromagnetic films, as observed in α-Fe2O3 with weak ferromagnetism. 23 As shown in Figure 1b, the vector sum of the a-Fe and d-Fe moments under a large magnetic field is nearly perpendicular to H in the vicinity of Tcomp and parallel to H far away from Tcomp. Given that SMR is dominated by the Fe sublattices owing to the weak efficiency of spin current transport between the Gd sublattice and Pt layer, the angular dependence of SMR at 300 K is opposite to these at temperatures far away from Tcomp. In this respect, the effective moment vector of the two Fe sublattices in the vicinity of Tcomp can be treated as the Néel vector for GdIG. Furthermore, the SMR ratio is defined by (𝜌 # -𝜌 " )/𝜌 # , where 𝜌 " is the magnetoresistance with respect to the applied magnetic field along the +y axis. The SMR ratio at different temperatures is also presented in Figure 2d. Far away from Tcomp, the SMR ratio can reach up to ~6 × 10 )* , which is larger than that (~2.5 × 10 )* ) in YIG/Pt. 24 Experimental results of SMR and SH-AHE yield the real ( G + ↑↓ ) and imaginary ( G . ↑↓ ) parts of the spin mixing conductance ( 𝐺 ↑↓ ), G + ↑↓ ≈ 2.3 × 10 /* Ω )/ m )0 and G . ↑↓ ≈ 6.4 × 10 /0 Ω )/ m )0 , indicating substantial spin transparency at the GdIG/Pt interface even though GdIG is an insulator. Pronounced variation in the SMR ratio occur from ~280 K to ~320 K. This suggests that magnetic fluctuations emerge at ~280 K and ~320 K, and the nonlinear magnetic configurations between the Gd and Fe sublattices exist at ~ 300 K at a large external magnetic field. Noteworthily, the net saturation magnetization of GdIG nearly vanishes at ~ 297 K, at which both RH and SMR ratio showed sign-reversal. These experimental observations unambiguously verify that the magnetic compensation temperature is approximately 297 K.

Although charge currents cannot flow in the insulating GdIG films, spin currents generated by the SHE in the Pt layer can exert a torque on the magnetization of GdIG. To determine the currentinduced effective fields and SOT switching efficiency, we performed the angular dependent harmonic Hall measurements. The first (𝑅 1 2 ) and second harmonic resistance (𝑅 1 02 ) upon injecting sinusoidal alternating current 𝐼 > 2 into devices are simultaneously detected when rotating in-plane magnetic field. The rotation angle 𝜑 3' in the xy plane is defined with respect to the +y axis. In addition, the actual temperature is estimated by calibrating the temperature-dependent resistance

Rxx. In an in-plane magnetic field urging single domain approximation, [25][26][27][28] the current-induced field-like effective field HFL and damping-like effective field HDL can be extracted from the angular dependent 𝑅 1 02 with the following expression:

𝑅 1 02 = 𝑅 456 1 !" |1 #$% | cos2𝜑 3' sin𝜑 3' + F & & 0 1 '" |1 #$% |)1 ( + 𝑅 886 G sin𝜑 3' . (1)
Here, Hext, HK, RPHE and RSSE are the in-plane external magnetic field, effective perpendicular magnetic anisotropy field, planar Hall resistance, and spin Seebeck effect-induced resistance, respectively. The amplitudes of the terms cos2𝜑 mT/(10 /@ Am )0 ), is comparable to the reported results (0.06~25 mT/(10 /@ Am )0 )) for TmIG/Pt and (0.1~0.7) for GdFeCo/(BiSb)2Te3. 19,29,30 Noticeably, 𝐻 ;: /𝐽 ? is significantly enhanced nearby Tcomp, which reaches up to 2.1 mT/(10 /@ Am )0 ) at 272 K and 4.3 mT/(10 /@ Am )0 ) at 325 K. In theory, the damping-like torque generated by the injected charge current in the Pt layer can be expressed by 11 𝜏 ;: = -

A )** B +, C ) D -% . E ℏ 0? N𝒎 P × (𝝈 P × 𝒎 P )R. (2)
Here, e, ℏ, 𝜇 @ , 𝛾 ?GG , 𝝈 P , 𝒎 P , 𝐽 ? , 𝜉 ;: , and 𝑡 are the elementary electric charge, reduced Plank constant, vacuum permeability, effective gyromagnetic ratio, polarization of spin, unit vector of net magnetization, charge current density, effective spin Hall angle, and thickness of the magnetic layer, respectively. Therefore, the effective damping-like field should scale linearly with 1/𝑀 H , and thereby diverge from the linear increase when the temperature approaches to Tcomp because the net magnetization at Tcomp is vanishingly small. This 1/𝑀 H dependence has been verified in most metallic ferrimagnetic systems, such as CoTb/Pt, GdFeCo/Pt and GdFeCo/(BiSb)2Te3. 3,30,31 In our experiment, 𝐻 ;: /𝐽 ? is proportional to 1/𝑀 H far away from Tcomp whereas it remarkably deviates from the linear dependence in the vicinity of Tcomp, as shown in Figure 3f. Far away from

Tcomp, the increase in 𝐻 ;: /𝐽 ? with respect to 1/𝑀 H can be explained by the reduction in the net magnetization. When approaching to Tcomp, magnetic fluctuations emerge, which is probably related to the giant enhancement of 𝐻 ;: /𝐽 ? close to Tcomp. Besides, it was reported that the effective damping-like field was significantly enhanced in CoGd/Pt owing to the negative exchange interaction and tilt angle between Co and Gd, thereby following ~ 1/𝑀 ! 0 . 5 In our harmonic measurements, the nonlinear magnetic configurations between Gd and Fe sublattices close to Tcomp are accessible under a large magnetic field, which have also been verified in our SMR measurements. Therefore, the other possible contribution to the enhanced 𝐻 ;: /𝐽 ? could be the negative exchange interaction.

Furthermore, the SOT efficiency can be estimated with the effective spin Hall angle 𝜉 ;: = 0?

ℏ 𝜇 @ 𝑀 H 𝑡𝐻 ;: /𝐽 ? when 𝐻 ;: /𝐽 ? ∝ 1/𝑀 H . 32 As shown in the inset in Figure 3f, 𝜉 ;: is nearly independent of the temperature in the range 𝐻 ;: /𝐽 ? ∝ 1/𝑀 H . Upon increasing temperature, 𝜉 ;:

increases slightly from 0.026 at 221 K to 0.037 at 262 K below Tcomp. Further increasing the temperature above Tcomp, 𝜉 ;: slightly decreases from 0.036 at 335 K to 0.027 at 366 K. The measured 𝜉 ;: is comparable to the reported value of the spin Hall angle in Pt. [32][33][34] In addition, we also calculated 𝜉 ;: approaching to Tcomp using the aforementioned equation. When 𝐻 ;: /𝐽 ? versus 1/𝑀 H deviates from the linear dependence in the vicinity of Tcomp, 𝜉 ;: increases to 0.09 at 273 K and to 0.12 at 325 K, which are even comparable to ~0.13 in topological insulator Bi2Se3 and ~0.14 in two-dimensional material MoS2. 28,30 Such a dramatic increase in 𝜉 ;: may originate from the negative exchange interaction and the existence of magnetic fluctuations close to Tcomp, as mentioned above.

The above-mentioned damping-like SOT field can be utilized to switch the magnetization in GdIG/Pt films. In our SOT switching experiments, a sequence of current pulses with 𝜏 = 100 ns pulse width were injected during the application of an in-plane magnetic field Hx along the x axis.

After the application of the current pulses at periods of 1 s, RH was recorded with a small probe current. Figure 4a presents the reversible current-induced switching with different in-plane magnetic fields 𝐻 3 at T = 280 K. The RH-j loops are clockwise at 𝐻 3 > 0 while anticlockwise at 𝐻 3 < 0. Such a reversed chirality under opposite magnetic field unambiguously demonstrates the deterministic current-induced magnetization switching in GdIG/Pt. Moreover, the SOT-driven RH with the amplitude of ~ 1.3 mΩ corresponds to nearly 100% of magnetization switching. The critical switching current density is about ~ 2 × 10 // A/m 2 , which is comparable to those in TmIG/Pt and metallic ferrimagnet/Pt systems. 3,29 In addition, current-induced SOT switching with different 𝐻 3 values was also realized at T = 310 K, as shown in Figure 4b. Remarkably, at a constant Hx, the RH-j loops at 310 K have opposite polarity to those at 280 K. The reverse of the SOT switching polarity below and above Tcomp is because the transfer of the spin angular momentum between GdIG and Pt is dominated by the s-d exchange coupling between the Fe sublattices and Pt layers. This is consistent with the observations for metallic ferrimagnetic systems, such as CoTb/Pt, CoGd/Pt and GdFeCo/Pt. 3,5,31 The extracted critical switching current density 𝐽 I is presented as a function of Hx in Figures 4c andd. 𝐽 I is ~ 2 × 10 // A/m 2 and decreases with increasing magnetic field. Besides, the asymmetry of the positive and negative critical switching current can be ascribed to the surface tension of domain wall. 35,36 When a current is injected into the devices, Joule heating can result in a large increase of the actual temperature in the magnetic layers. This raises hurdles in detecting the current-indued SOT switching for ferrimagnetic systems, particularly in the vicinity of Tcomp. For instance, the currentswitching polarity was not reported to change across Tcomp in TbIG/W and always happens in the Fe-dominated scenario because the actual measured temperature is always above Tcomp owing to the excessive Joule heating. 37 Co-rich and Tb-rich samples host the same current-switching polarity in ferrimagnetic CoTb owing to the Joule heating effect. 38 Essentially, the large spin transparency at the GdIG/Pt interface can reduce the required injected charge current and decrease the excessive Joule heating in some extent. To evaluate the role of Joule heating in the SOT switching in our experiment, we performed SOT switching measurements with different pulse widths. As shown in Figures 5a andb, the current-switching loops become gradually narrower with increasing pulse width. Figures 5c andd summarize the average critical switching current density 𝐽 I = (𝐽 I J -𝐽 I ) )/2 as a function of pulse width. Here, 𝐽 I J and 𝐽 I ) are positive and negative switching currents, respectively. It can be seen that 𝐽 I decreases with increasing pulse width and becomes gradually saturated. According to the thermal activation model, 39,40 the critical switching current density 𝐽 I can be expressed by

𝐽 I = 𝐽 I@ [1 - / ∆ ln F L L - G] (3)
where 𝐽 I@ is the intrinsic critical switching current density at 0 K; ∆≡ 𝑈/𝑘 M 𝑇 is the thermal stability factor with respect to the energy barrier U; 𝜏 @ , which is assumed to be 1 ns, is the attempt timescale for thermally activated switching. By fitting the experimental results, we obtained 𝐽 I@ = 2.98 × 10 // Am -2 and ∆= 13 for 𝜏 < 2.5 µs while 𝐽 I@ = 1.33 × 10 // Am -2 and ∆ = 75 for 𝜏 > 2.5 µs at 280 K. At 310 K, the fitting results yield 𝐽 I@ = 2.58 × 10 // Am -2 and ∆= 12 for 𝜏 < 2.5 µs. For the long time rang (𝜏 > 2.5 µs) at 310 K, 𝐽 I remain almost unchanged. Furthermore, 𝐽 I@ = 1.17 × 10 // Am -2 is obtained at a fixed value ∆ = 75 for 𝜏 > 2.5 µs. The values of ∆ at 280 K and 310 K are nearly identical for 𝜏 < 2.5 µs. However, the ∆ values are different in the longand short-time ranges. In reality, the actual measured temperature is affected by the long pulse width owing to the excessive Joule heating, further resulting in the variation of the local magnetic properties. This also reduces the switching current threshold. By comparison, the pulsed current with 𝜏 < 2.5 𝜇s can effectively suppress the large increase of the preset temperature.

We next performed current-indued SOT magnetization switching experiments at various temperatures across Tcomp. To reduce the impact of Joule heating, 100 ns duration current pulses was employed here. Figures 6a andb show the deterministic current-induced SOT switching approaching to Tcomp at 𝜇 @ 𝐻 3 = ±50 mT. As expected, the sign reversal of the RH-H loop across

Tcomp in Figure 2b is also observed in the current-induced SOT switching loops, as shown in Figures 6a andb, further verifying that RH is mainly sensitive to the Fe sublattices. In particular, the SOT switching at 294 K and 301 K, which are very close to Tcomp, is realized with reversed switching polarity. Evidently, the critical switching current density at 301 K is larger than those at temperatures far away from Tcomp. Figures 6c andd show the 50 cycles of SOT switching at 294 K and 301 K with 𝜇 @ 𝐻 3 = -50 mT and a successive positive/negative pulsed current sequence.

Switching in the other direction is clearly observed on reversing the pulsed current polarity. The high and low resistance states at 294 K and 301 K have opposite signs at a pulsed current with the identical polarity. The repeatable SOT switching also verify the stability of our experimental method that involves the application of a short pulsed current (pulse width: 100 ns) to minimize the effect of Joule heating. The critical switching current 𝐽 I with respect to the temperature is presented in Figure 6e. Overall, 𝐽 I decreases almost linearly with increasing temperature.

Noticeably, 𝐽 I becomes considerably larger with temperature approaching to Tcomp. Given that the effective damping-like SOT field 𝐻 ;: /𝐽 ? is greatly enhanced near the Tcomp [see Figure 3f], such an increase of 𝐽 I appears counterintuitive. As discussed in SI, magnetic reversal in GdIG/Pt is generally via domain nucleation and domain-wall propagation. Besides, the coherent rotation of the magnetization also happens in the pinned domain. In the macrospin approximation (i.e.

coherent rotation and switching), the intrinsic critical switching current 𝐽 I@ can be expressed by 41 𝐽 I@ = 0?D -% / E ℏB +,

(

1 0 0 - 1 $ √0 ). (4)
For the GdIG/Pt films, the effective perpendicular magnetic anisotropy field 𝐻 O substantially increases whereas the net magnetization 𝑀 H decrease as approaching Tcomp [see Figure S3c in SI].

As shown in Figure 6e, the product of 𝐻 O and 𝑀 H gradually increases as the temperature approaches Tcomp from both sides, which is a possible reason for the enhanced 𝐽 I around Tcomp.

Moreover, thermal fluctuations in the SOT switching experiments can create random domains that are very hard to align together, particularly in the vicinity of Tcomp. Such a variation can increase the domain pinning field given that the magnetic reversal in GdIG/Pt is predominantly mediated by the domain nucleation and domain-wall propagation. In this case, an enhanced 𝐽 I is also expected. Besides, the increased pinning field near the compensation also decreases the the velocity of domain wall to some extent 7 . To summarize, the enhancement of 𝐽 I near Tcomp is ascribed to two possible reasons: the increased 𝐻 O * 𝑀 H product and random domains close to Tcomp. According to the above harmonic Hall measurements, the large damping-like SOT field 𝐻 ;: /𝐽 ? is the direct consequence of the small net magnetization 𝑀 H close to Tcomp. As a result, the larger effective SOT field close to Tcomp does not directly cause a more efficient current-induced SOT switching in ferrimagnetic GdIG-based devices.

CONCLUSION

In summary, the SOT in insulating compensated ferrimagnetic GdIG/Pt heterostructures with PMA was thoroughly studied. We explicitly observed a nearly room-temperature compensation point (~297 K). Considerable spin transparency at the GdIG/Pt interface are consistently confirmed by the SH-AHE, SMR and harmonic measurements, respectively. The SMR experiments in GdIG/Pt exhibit a quasi-antiferromagnetic behavior close to the compensation temperature. More importantly, effectively deterministic current-induced magnetization switching below and above

Tcomp, even at 294 K and 301 K, was realized with thermal stability and opposite switching polarity

METHODS

Sample Fabrication. Gd3Fe5O12 (GdIG, 6.5 nm) films were grown on (111)-oriented Gd3Sc2Ga3O12 (GSGG) substrates by pulsed laser deposition at the laser repetition frequency of 5

Hz. During deposition, the substrate temperature was set to 720 K, and the oxygen pressure was 85 mTorr. After deposition, the samples were cooled down to room temperature at a rate of 10 K/min. Subsequently, the samples were transferred to the magnetron sputter system, in which 5 nm-thick Pt layer was deposited on them at room temperature.

Structural and Magnetic Characterization. Magnetization measurements were measured using a magnetic property measurement system (MPMS3, Quantum Design). The structure characterization was performed using STEM (Titan 80-300, FEI) after the sample was prepared using a focused ion beam (Helios 450, FEI).

Electric

  using 100 ns duration pulsed current. Moreover, the critical switching current increases in the vicinity of Tcomp although the measured effective SOT field from harmonic experiments increases close to Tcomp. Our work deepens the understanding to electrically manipulate the net magnetization of insulating compensated ferrimagnets and offers great prospects for roomtemperature magnon-based magnonics with ultrafast operation.

  Transport Measurements. The films were fabricated into 5 μm wide Hall bar devices by standard photolithography technique and Ar ion milling. Ti(10 nm)/Au(100 nm) layers were deposited as electrical contacts. All electrical transport measurements were performed in a Quantum Design DynaCool. In the SOT switching experiments, switching pulses with different pulse widths were provided by AV-1011B1-B pulse generator (Avtech Electrosystems), and then the Hall resistance is detected by Keithley 2182 voltage source and Keithley 6221 current source upon a small probe current. In the ac harmonic Hall measurements, a Keithley 6221 current source was used to supply an ac current with a frequency of 13.7 Hz. Meanwhile, the in-phase first and out-of-phase second-harmonic voltage signals were probed using two Stanford Research SR830 lock-in amplifiers.

Figure 1 .

 1 Figure 1. (a) Bottom panel: schematic illustration of the transport measurement set-up for GdIG/Pt film grown on GSGG (111). Up-left panel is the schematic of the crystal structure of GdIG with Fe (green), Gd (red), and O (gray) atoms. Octahedral Fe sublattice, tetrahedral Fe sublattice, and dodecahedral Gd sublattice occupy a-site, d-site and c-site in the Wyckoff positions, respectively. Up-right panel is atomic-resolution STEM image. (b) Magnetic phase diagram of GdIG at different magnetic fields and temperatures 17, 18 . The arrows indicate the directions of the moments of the different sublattices.

Figure 2 .

 2 Figure 2. (a) Magnetic hysteresis loops via sweeping out-of-plane magnetic field at various temperatures. For clarity, the curves are vertically shifted. (b) Spin Hall-induced anomalous Hall resistance RH as a function of the out-of-plane magnetic field Hz at different temperatures. The red (navy) arrow represents the moment of the Gd sublattice (effective Fe sublattices). (c) Angulardependent SMR at a fixed magnetic field (5 T) at various temperatures. (d) Extracted saturation magnetization, SH-AHE resistance, and SMR ratio as function of temperature (from Figures. 2 ac).

Figure 3 .Figure 4 .

 34 Figure 3. In-plane angle-dependent planar Hall resistance (a) and second-order harmonic resistance (b) at T=273 K and 𝜇 @ 𝐻 <3= = 2.25 T. In-plane angular dependent planar Hall resistance (c) and second-order harmonic resistance (d) at T=335 K and 𝜇 @ 𝐻 <3= = 2.25 T. (e) Extracted amplitudes of damping-like torque term as a function of 1/(Hext-Hk). (f) 𝐻 ;: /𝐽 as a function of 1/Ms. Inset in (f) shows temperature dependent 𝐻 ;: /𝐽 (black) and 𝜉 ;: (red). The bold green curve is the 1/Ms fitting curve without the points marked in the ellipses.

Figure 5 .Figure 6 .

 56 Figure 5. Current-induced SOT switching for different pulse widths at 280 K (a) and 310 K (b). Extracted critical switching current density 𝐽 I as a function of pulse width at 280 K (c) and 310 K (d). Red dashed lines are fitting curves of the thermal activation model.

  3' sin𝜑 3' and sin𝜑 3' are marked as 𝑅 9: 02 and 𝑅 ;: 02 , respectively. Figures3a and cshow the angle-dependent first harmonic Hall signals 𝑅 1 2 , from which RPHE can be extracted. The observation of RPHE further supports the fact that an SHE-driven spin current can be injected and scattered across the Pt/GdIG interface. Figures3b and dshow the in-plane angular dependent 𝑅 1 02 , which are separated into the cos2𝜑sin𝜑 and sin𝜑 components. |𝐻 <3= | -𝐻 > ), as indicated in Figure3e. The inset in Figure3fpresents the effective dampinglike field per unit current density 𝐻 ;: /𝐽 ? as a function of temperature. Here, 𝐽

	The observed small field-like torque contribution is presented in Supporting Information (SI) [see
	Figure S5]. The damping-like torque contribution can be distinguished via fitting 𝑅 ;: 02 versus
	1/(

? is the applied charge current density. Evidently, 𝐻 ;: /𝐽 ? increases with increasing temperature below Tcomp, and decrease with temperature above Tcomp. The value of 𝐻 ;: /𝐽 ? at 335 K, which is approximately ~1.2

Acknowledgments

This work reported was funded by the King Abdullah University of Science and Technology, Office of Sponsored Research (OSR) under the Award Nos. OSR 2018-3717-CRG7 and OSR 2019-CRG8-4081, respectively.

Supporting Information

The Supporting Information is available free of charge on the ACS Publications website.

Conflict of Interest

The authors declare no competing interests.

Table of Contents

Current


Arnab Ganguly

Ioan Senfu Zhang

Mihai Miron

Jürgen Kosel

Xixiang Zhang

Aurelien Manchon
email: manchon@cinam.univ-mrs.fr

Nirpendra Singh

Dalaver Anjum

Gobind Das
email: gobind.das@ku.ac.ae

Ioan Mihai Miron

Dalver H Anjum

Competition between Chiral Energy and Chiral Damping in the Asymmetric Expansion of Magnetic Bubbles

Keywords: chiral damping, Dzyaloshinskii-Moriya interaction, magnetic bubble expansion

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Magnetic domains are candidate building blocks for modern long-term magnetic data storage [1][2][3]. The out-of-plane magnetic domains with switchable magnetization direction are commonly used as binary memory bits for non-volatile devices [4][5][6]. The ultrahigh mobility of current-driven magnetic domain walls recently observed in non-centrosymmetric heterostructures [7][8][9] opening attractive opportunities for alternative storage and data transfer technologies such as the magnetic racetrack [1,10]. Hence, a precise understanding of the physical characteristic of the dynamics of magnetic domain walls in such heterostructures can substantially enhance the magnetic devices performance [11][12][13][14][15]. The typical system (e.g., Pt/Co/AlOx) consists of a perpendicularly magnetized thin film embedded between dissimilar heavy metals shows current-driven high domain wall velocity up to 400 m/s [7,8]. The high velocity is attributed to the cooperation between damping-like torque arising from the adjacent heavy metals and Dzyaloshinskii-Moriya interaction (DMI) present at the interfaces [16,17]. The magnitude of the damping-like torque is normally assessed through spin-torque or spin-pumping measurements [18][19][20], while magnitude of the DMI is determined by the following ways. Various imaging techniques such as Nitrogen vacancy centers magnetometry [21][22][23], scanning transmission X-ray microscopy [24], electron or X-ray holography [25][26][27][28], and Lorentz microscopy [29][30][31][32] allow for direct observation of the chirality of the domain wall, confirming that interfacial DMI favors Néel configuration over Bloch configuration [33]. Brillouin light scattering [34][35][36] determines the momentum shift of counterpropagative spin waves through inelastic scattering. Finally, several methods have been proposed based on the dynamical characteristics of the domain wall motion. In the simplest model, DMI translates into an effective in-plane magnetic field, which can be determined by recording the velocity shift obtained when applying an external field or probing the asymmetric expansion of magnetic bubbles [37][38][39][40][41]. The asymmetric expansion in the magnetic bubble is driven by a small external magnetic field in the creep regime, i.e., a regime of motion dominated by thermal activation in the presence of a considerable disorder. However, the creep motion is a subtle regime of motion where energy dissipation plays a crucial role. Herein, we propose the symmetry breaking of the system translate into the emergence of a chiral contribution to the magnetic damping. To date, it remains unclear how DMI (chiral energy) and chiral damping compete with each other in the context of creep motion. In this article, we perform a systematic study of field and currentinduced domain wall motion in multilayers with inversion symmetry breaking. We also suggest that both effects (DMI and chiral damping) display quite different domain-velocity dependency on materials. As such, we propose that the asymmetric expansion of the magnetic bubble is dominated by either DMI or chiral damping in opposite limits.

Results

Thin film multilayer of Ta(3 nm)/Pt(3 nm)/Co (0.6 nm)/Pt (dPt)/IrMn(3 nm) is deposited using dc/rf magnetron sputtering. Here, dPt varies from 0 to 1 nm for field induced and 0 to 5 nm for current induced domain wall motion studies. The thin film stack, along with the experimental configuration, is illustrated in fig. 1(a). The sputtering conditions are carefully chosen to obtain perpendicular magnetic anisotropy in these films. The experiment is performed using magnetooptical Kerr effect microscopy in polar geometry [42][43][44][45]. A differential Kerr imaging is performed to observe the magnetic domains and to eliminate the contribution of any nonmagnetic intensities. Square pulses of the magnetic field are applied both in-plane and out-of-plane of the sample using two independent electromagnets. To nucleate a bubble, the thin film magnetization is saturated in one perpendicular direction followed by an out-of-plane field pulse in the opposite direction. The bubbles nucleate from defects or pinning centers present in the sample. The in-plane magnetic field (Hx) alone cannot nucleate or drive bubbles because of strong perpendicular magnetic anisotropy (PMA) of the sample but it induces asymmetric motion when combined with the outof-plane field (Hz). For proper synchronization and temporal overlap between the fields, the inplane pulse is chosen longer than the out-of-plane pulse. We observe that without an in-plane field the bubbles are circular or symmetric with respect to origin. In the presence of an in-plane field, the velocities of ↓↑ and ↑↓ domain walls are very asymmetric along x-direction. The asymmetry changes sign with the reversal of Hx. This asymmetry can be originated in two ways. In the widely accepted scenario, the presence of DMI creates an effective in-plane magnetic field, normal to the domain wall, and favors the Néel configuration [46]. An external magnetic field lowers the energy of one side of the bubble with respect to the other (in one case, Néel wall is enforced, while it is weakened in the other), resulting in an asymmetric creep expansion. Another scenario is possible, though, and does not necessitate the presence of a DM field. If no such field is present, magnetostatics dictates that the magnetic moments at the bubble boundary adopt a Bloch configuration. Applying an in-plane magnetic field therefore promote Neel configuration. Thus, the two opposite sides of the bubble adopt the opposite chirality. If the magnetic damping is sensitive to this chirality [47], then the opposite sides of the bubble are expected to dissipate energy differently, resulting in a different creep velocity and, thereby, an asymmetric expansion. As a general rule, one expects that both effects should coexist, and till now, it remains unclear how to distinguish them. To do so, we analyze the dependence of the velocity of the bubble boundary as a function of the in-plane and out of plane field.

Asymmetric bubble expansion.

In-plane field dependence of domain wall velocity

The variation of domain wall velocities with in-plane field is studied in this section. Figure 2(a-f) shows velocities for ↓↑ and ↑↓ domain walls by red and blue curves plotted on the left side and velocity asymmetry (𝐴 = 2(𝑣 ↓↑ -𝑣 ↑↓ )/(𝑣 ↓↑ + 𝑣 ↑↓ )) on the right side of each figure. The thickness of top Pt, dPt is indicated on each figure. Figure 2(a)-left shows that for dPt =0, the velocity of ↓↑ domain walls (red curve) is larger than that of ↑↓ domain walls (blue curve) at positive in-plane field. Moreover, the former increases with the field value whereas the latter decreases with it. At negative field, we have the opposite scenario. All the curves in Fig. 2 are symmetrically opposite with respect to zero field as the sample does not have any preferential direction. On the right side of Fig. 2(a), the velocity asymmetry A changes sign from positive to negative as the field is reversed from positive to the negative direction. The magnitude of A increases faster at lower field and slows down at higher field, although saturation is not observed until 3 kOe. In Fig. 2(b) for dPt =0.2 nm the velocity of the ↑↓ wall (blue curve) starts to increase after a critical field HC = +2 kOe thus causing a slope reversal in the blue curve as well as in the A curve around the same region (indicated by arrows). At dPt =0.3 nm the feature is observed at a lower field of HC ~1.5 kOe [Fig.

2(c)]

. The velocity of the ↑↓ wall (blue curve) starts increasing dramatically after HC, and overtakes the ↓↑ wall velocity (red curve) at 2 kOe. In this case, A changes sign for the same sign of Hx across 2 kOe. For dPt =0.5 and 0.7 nm, HC is around 0.5 and 0.2 kOe and finally at dPt=1 nm the value is close to zero [Fig. 2(d-f)]. In Fig. 2(f) (dPt=1 nm) the velocity of ↑↓ wall (blue curve) is much higher than that of the ↓↑ wall (red curve) at positive field. The asymmetry is opposite as compared to Fig. 2(a) (dPt=0 nm). Apart from that, another contrast between Figs. 2(a) and 2(f) is the saturation field of asymmetry curves. In the first case no saturation is observed until 3 kOe while in the second case it occurs ~1.2 kOe. The shape of the velocity curves for dPt=0 and 1 nm are completely different. In the former case it is exponential and in the latter case it is linear. From these observations it appears that there is a competition between two effects responsible for the velocity asymmetry, one dominating at lower values of dPt and the other at higher values of dPt.

The chiral contribution to the magnetic energy, i.e., the DMI contribution, can be viewed as an internal in-plane field acting on the domain wall, a change of which causes an opposite lateral shift of in-plane velocity curves for the two opposite walls. Any feature in the velocity curve thus gets laterally shifted and manifested at different field but at same velocity. The chiral contribution to energy dissipation, i.e. the chiral damping, does not impact the magnetic energy itself, rather the attempt frequency controlling the thermal activation [12,40]. This gets the velocity curves shifted vertically in opposite directions, thus the feature manifested at same field but at different velocities [40]. In Fig. 2(a), HC is out of the measurement range and from Figs. 2(b) to (f) HC monotonically decreases close to zero value. This suggests that for dPt =0, we have the highest internal DMI field which progressively vanishes upon increasing the top Pt layer thickness. The observation is consistent with previous literature showing that DMI arising from opposite interfaces tend to cancel each other [38,48]. The exponential variation of the velocity curve in Fig. 2(a) also supports that the asymmetry is coming from energy. In Fig. 2(c) opposite asymmetry is observed across 2 kOe for the same applied field direction as the asymmetry curve crosses the zero line. A mere decrease internal DMI field cannot explain this phenomenon. Indeed, in such case the sign of A would remain the same for a particular direction of Hx This unconventional sign reversal process suggests that a completely different mechanism takes over the DMI field upon increasing dPt. This mechanism is attributed to chiral damping, eventually dominating over the internal DMI field which will be discussed in the later part of the paper. This argument is also supported by the non-exponential velocity curve in Fig. 2(f) that strongly differ from the more exponential dependence observed in Fig. 2 To estimate the values of DMI field and its dependence upon increasing top Pt thickness, currentinduced domain wall motion has been studied in presence of in-plane magnetic field. Thin film micro strips are fabricated using photo-lithography. A transverse domain wall is created on the strip. Simultaneous current and in-plane magnetic field pulse are applied along the length of the film. The current drives the domain wall while the in-plane field either helps or opposes the propagation by favoring one Néel chirality over the other, depending on the direction of the field.

Thus, there exists a compensating field Hx for which the current-induced domain wall velocity vanishes. In that case, the applied field completely opposes the internal DMI field. Thus by measuring the compensation field we extract the DMI field value of the film. Figure 3(a) shows velocity curve as a function of in-plane field for a constant current density. In our experiment a ↓↑ domain wall is driven by current pulses from the left. A field parallel (antiparallel) to the current direction is considered positive (negative). For all different values of dPt, the domain wall velocity changes exponentially with field. In each of the cases, there is a field range for which the velocity of the domain wall is zero and there exists two avalanche fields (Hav) in either side of which domain wall starts to move either along or opposite to the current direction, respectively. It is found that with increasing current density both the Hav's converge to their mean value. That means that the mean value of Hav does not change with current density which is nothing but the DMI field (HD) of the sample. At lower current density the error associated with HD is larger because of the flatness of the curve. On the other hand, at higher current density the probability of nucleation of other domains masking the domain wall of interest increases. Hence, practically the experiment is limited to a certain current density and the corresponding error on HD. The estimated HD is plotted in Fig. 3(b) as a function of the Pt thickness. The experiment confirms the DMI changes sign at dPt =3 nm. From dPt =0 to 1 nm the DMI field decreases but does not change sign to cause opposite asymmetry as observed in Fig. 2. This observation confirms the scenario of the two distinct competing mechanisms.

Out-of-plane field dependence of domain wall velocity

In the previous part, we have discussed asymmetric domain wall motion on qualitative grounds, avoiding entering into the details of the motion regime. General arguments based on the global behavior of the velocity asymmetry led us to postulate the competition between two chiral mechanisms. Let us now provide a more quantitative analysis of these two effects, based on the specific motion regime experienced by the domain wall. In our experiments, the domain wall moves in the thermally activated creep regime. Recent literature by Jué et al. [40] show that the velocity of domain wall in the creep regime can be modeled by creep scaling law as

𝑣 = (𝑑 # 𝑓 # ). 𝑒 $ !" # $% & ' ( ) * %& + ! , -'& . ! , -() (1)
Where, 𝐻 * = 𝐻 + /𝐶 , (𝐶~1 is an empirical constant) and 𝑑 # , 𝑓 # , HP, and UC are the disorder correlation length, de-pinning attempt frequency, pinning field and pinning barrier respectively. In the exponent, the energy barrier 𝑈 -(𝐻 + ) accounts for non-dissipative processes described by the magnetic energy functional. In particular, DMI is one such energy process that is discussed in previous literatures as a factor for controlling the asymmetry of the domain wall velocity [41,[48][49][50][51]. On the other hand, 𝑓 # is inversely proportional to the energy dissipation [52] In other words, a The analysis of current-driven motion (Fig. 3) and field-driven motion (Fig. 4) confirm the competition of two chiral mechanisms that we interpret at DMI field and chiral damping, which dominate at different Pt thicknesses. In Fig. 5, the asymmetry curves reported in Fig. 2

Angle dependence of velocity

To complete this study, we analyze the shape of the magnetic bubbles for various Pt thicknesses.

Figure 6(a) shows bubble expansion in a sample with dPt=0 nm (left) and 1 nm (right) under the same field configuration. Based on the analysis provided above, these two samples correspond to different asymmetry mechanism: the former is dominated by DMI, while the latter is dominated by chiral damping. We immediately observe that the asymmetric bubble expansion in these two regimes is not only opposite but also present quite a different shape. To further analyze this behavior, we study the domain wall velocity as a function of angle θ, with respect to the in-plane field. First, a circular bubble is created by an out-of-plane field and then it is expanded infinitesimally with a short out-of-plane field pulse in presence of an in-plane field. From the differential image shown in Fig. 6(b), displacements at different θ are obtained and summarized in Fig. 6(c-e). For an infinitesimal expansion, the magnetization vector at a certain θ does not change significantly. Thus, the distance measured at an angle θ corresponds to the displacement of a particular magnetization vector at boundary during expansion. Images in Fig. 6(b) correspond to the Pt thickness dPt=0, 0.5 and 1 nm (top, middle and bottom panels) at three different fields Hx=0.5, 1 and 1.5 kOe (left, central and right panels). For dPt=0 nm the expansion is favored on the right side, for dPt=0.5 nm it is more or less symmetric and for dPt=1nm it expands mostly on the left side. Figure 6(c-e) shows normalized polar plot of domain wall velocity as a function of θ at three different Hx, 0.5kOe, 1 kOe and 1.5 kOe (top, middle and bottom panels). Here we clearly see two distinct natures of θ dependence curve for dPt=0 nm (red) and dPt=1nm (magenta). For dPt =1 nm (magenta), the displacement is more sensitive to θ, resulting a sharp structure at 180° whereas for dPt=0 nm (red) the change in displacement is more gradual giving rise to a flatter curve having maxima at 0°. For dPt =0.5 (blue), we see a superposition of these two patterns. At lower field, Hx=0.5kOe the curve is more similar to dPt=0 nm, while with increasing field the curve starts having more similarities with dPt=1nm. From this observation, we can speculate, in line with the above discussion, that the two distinct angular dependence patterns at dPt=0 and 1 nm establish the fact that the asymmetry stems from two fundamentally different phenomena. Now we can identify that the flatter variation is a conscience of the energy related asymmetry and the sharp variation corresponds to the chiral damping. At 0.5 nm both the phenomena are contributing to the opposite asymmetry and thus the superposition effect is observed in angular dependence curve. show the angular displacements of bubbles corresponding to the in-plane fields 0.5, 1 and 1.5kOe. Red, blue and magenta curves correspond to top Pt thickness of 0, 0.5 and 1nm respectively.

Conclusions

In summary, we systematically study field-driven bubble expansion in structure lacking inversion

Figure 1 :

 1 Figure 1: (a) Schematic illustration of sample along with the field configuration of bubble expansion experiment. (b) Kerr microscopy images of magnetic bubbles at different field orientations. The

  Hx and Hz are denoted in the top right corner of each figure. Red and blue arrows indicate the propagation of opposite domain walls from the nucleation center.

Figure 1 (

 1 Figure 1(b) shows differential Kerr images of magnetic bubbles in Ta(3 nm)/Pt(3 nm)/Co(0.6 nm)/IrMn(3 nm) under six different field configurations. The dark and bright contrasts in this image indicate ↓ and ↑ out-of-plane configuration of the magnetization vector. Red and blue arrows indicate the expansion of ↓↑ and ↑↓ domain walls while the black dot between the arrows indicates the nucleation center of the bubbles. Here, a 15 ms long out-of-plane field pulse (Hz =120 Oe) is applied for the expansion of the bubbles. The direction of Hz is shown at the top right corner of each image. An additional in-plane field (Hx=2 kOe) is applied in some cases as indicated in the top right corner of the figures.

  (a).

Figure 2 :

 2 Figure 2: (a-f: left) In-plane field dependent velocity curves of ↓↑ (red) and ↑↓ (blue) domain walls and (a-f: right) corresponding velocity asymmetry for top Pt thicknesses of dPt =0, 0.2, 0.3, 0.5, 0.7 and 1 nm.

Figure 3 :

 3 Figure 3: (a) In-plane field dependent ↓↑ domain wall velocity. Inset shows the positive current and field convention. (b) The DMI field estimated as a function of top Pt thicknesses.

  change in the exponential coefficient reflects a change in the energy functional while a change in the pre-factor indicates a change in the energy dissipation of the system. When the logarithmic velocity is considered with respect to 𝐻 . '//, , the curve is linear in the creep regime with a change in slope indicating change in the energy and vertical shift representing change in the dissipation. In Fig. 4(a-f), logarithmic velocities are plotted with varying out-of-plane field for different top Pt layer thicknesses as mentioned in each figure. The variation is well fitted by straight lines with negative slope (m) confirming that our measurement is in the creep regime. Each velocity curve is measured in presence of a constant Hx indicated next to the curve in Fig. 4a. For each in-plane field, the velocity is measured for ↓↑ and ↑↓ domain walls, reported in red and blue color, respectively. In general, the velocity curves in Fig. 4 are approximately parallel or make a small angle with each other. For dPt=0 [Fig. 4(a)], when an in-plane field is applied along x, the ↓↑ domain wall velocity slope (red curves) is shifted up to higher velocity while the ↑↓ domain wall velocity slope (blue curves) moves down to lower velocity side with respect to zero field curve. In the other cases [Fig. 4(b-f)], when top Pt layer is introduced, Hx causes a positive shift for both ↓↑ and ↑↓ curves. With increasing Pt thickness the ↑↓ (blue) curves experience a dramatic vertical shift achieving higher velocity while the shift for the ↓↑ (red) curves remains very small. This suggests that the chiral damping mechanism, present in the prefactor of Eq. (1), gets activated with the insertion of Pt assisting the ↑↓ (blue) domain wall to move faster than ↓↑ (red) walls and thus altering the asymmetry. In order to provide a synthetic picture of the overall behavior of the velocity asymmetry, Fig. 4(g) displays 𝛿𝑚 = (𝑚 1 -𝑚 2 ), the difference between the slope of the velocity of ↓↑ (red) and ↑↓ (blue) walls as a function of Hx. The colors indicate different values of dPt.as indicated next to each curve The curves are fitted by the phenomenological formula 𝑎(𝑒 '2& / -1) where a and b are constants denoting the amplitude and saturation of the curve. From Fig. 4(g), it is found that the saturation field decreases with Pt thickness very similar to Fig. 3(b). Here the saturation essentially means that the energy difference between the opposite domain walls saturates at a field equal to the DMI field of the sample. As the DMI field decreases with Pt thickness the saturation field decreases. Figure 4(h) shows the vertical shift of the velocity curves in Fig. 4(a-f) with respect to Hx=0 curve at constant fields [Hx=1.5 kOe and 𝜇 # 𝐻 . =0.55 (mT) -1/4 ]. As mentioned above, the asymmetry in the vertical shift is attributed to the chiral contribution in the prefactor of Eq. (1), i.e., to chiral damping. It is found that the ↑↓ (blue) curves get monotonically shifted to higher velocity with Pt thickness while for ↓↑ (red) curves the shift is significantly smaller and weakly depends on the Pt thickness. This suggests that the chiral damping mechanism gets activated with the insertion of Pt assisting the ↑↓ (blue) domain wall to move faster than the ↓↑ (red) one and thus altering the asymmetry. It is intriguing to observe that ↑↓ and ↓↑ domain walls are affected differently by the chiral damping.

Figure 4 :

 4 Figure 4: (a-f) out-of-plane field dependence of the logarithmic velocity of bubble domain. The scattered points are experimentally observed data while the straight lines are the fitted data. The red and blue lines correspond to ↓↑ and ↑↓ domain wall velocities (g) The slope difference for the opposite domain walls obtained from fig. 4(a-f) as a function of in-plane field and (h) velocity shift for the red and blue domain walls with respect to Hx=0 for different Pt thicknesses.

2 8

 2 Fig. 5(a-f). It clearly indicates that chiral damping steadily increases over DMI upon increasing the Pt thickness, indicating a transition from a velocity asymmetry dominated by chiral energy to an asymmetry governed by the chiral dissipation.

Figure 5 :

 5 Figure 5: (a-f) In-plane field dependent asymmetry curves fitted as a combination of DMI (purple) and chiral damping (green) contribution and (g) The ratio of chiral damping and DMI (i.e. weight factor ratio) contributing to the asymmetry for different Pt thicknesses.

Figure 6 :

 6 Figure 6: (a) The shape of bubbles for dPt=0 and 1 nm for the same field configuration, (b) Differential Kerr image of small expansion of a circular bubble for different dPt at different values of Hx and (c-e)

  symmetry. In such samples magnetic bubbles expand asymmetrically in presence of in-plane and out-of-plane field. The velocity of the domain wall in the creep regime can be well fitted by the creep scaling law. The velocity asymmetry can occur along or opposite to the field direction depending on the domain wall chirality and DMI of the sample. Damping and energy are the most important factors which control the asymmetry. Energy related asymmetry corresponds to a change

Acknowledgements

in slope while chiral damping asymmetry can be identified through a vertical shift in the out-ofplane velocity curve. In this study the velocity asymmetry is investigated in Ta(5 nm)/Pt(3 nm)/Co (0.6 nm)/IrMn(3 nm) by systematically inserting thin layer of Pt between Co and IrMn interface.

The thickness of Pt varies from 0 to 1 nm. With no Pt, the asymmetry is dominated by energy having a strong effective internal field. As Pt thickness increases the internal field starts to disappear while at the same time chiral damping appears taking a leading role on asymmetry. The chiral damping asymmetry acts opposite to the energy asymmetry. As a result of these two competing effects, the asymmetry reversal occurs with increasing Pt thickness. The study is helpful for the effective control of magnetic bubbles which can be used for future memory and logic based applications.

Methods

Sample preparation: Thin film multilayer of Ta(5 nm)/Pt(3 nm)/Co (0.6 nm)/Pt(dPt)/IrMn (3 nm) with dPt ranging from 0 to 5 nm were deposited on thermally oxidized Si substrates using Singulus dc/rf magnetron sputtering. The sputtering conditions were carefully chosen to obtain perpendicular magnetic anisotropy in these films. The patterned strip tracks and the electrodes are prepared using lithography and Ar-ion milling.

MOKE measurements:

The experiment was performed using magneto-optical Kerr effect (MOKE) microscopy in polar geometry [42][43][44][45]. To observe the domains differential Kerr imaging was performed which helped us to eliminate nonmagnetic intensities from the image. Square pulses of the magnetic field were applied both in the plane and out-of-plane of the sample using two independent electromagnets. To nucleate a bubble, the thin film magnetization was saturated in one perpendicular direction followed by an out-of-plane field pulse in the opposite direction.

The bubbles nucleate from defects or pinning centers present in the sample. An in-plane field alone cannot nucleate or drive bubbles because of strong PMA but combined with out-of-plane field it induces asymmetric motion. To ensure a proper synchronization and temporal overlap between the fields, in-plane pulse is chosen longer than the out-of-plane pulse.