Photothermal skyrmion tweezer: programmable optical manipulation of magnetic topological quasiparticles

Domain: physics
Published: 2025-12-13
Editorial outcome: minor_revision

Abstract
Magneticskyrmions,astopologicalquasiparticles,haveshowngreatpotential asinformationcarriersfornext-generationspintronictechnologies,including memory,logic,andcomputingdevices.Whiletheirnon-trivialtopological dynamicsandinteractionshavebeenextensivelyexplored,experimental controlofindividualskyrmionshassofarreliedmainlyonglobalstimulisuch aselectriccurrents,magneticfields,andsurfaceacousticwaves.Effortsto achievepreciseskyrmionpositioningaresignificantlyhamperedbythesky- rmionHalleffectanddefectpinning.Here,wedemonstratehigh-precision trappingandtransportofindividualskyrmionsusingaphotothermalpotential well,therebyextendingopticalmanipulationintothequasiparticlerealm. Moreover,byintegratingdeterministicopticalskyrmioncreationandannihi- lationwithphotothermalandconventionalelectricaltransportmethods, weestablishafullyprogrammableplatformforsystematicinvestigationof skyrmiondynamicsandinteractions.Thisapproachopensnewavenues towardsreconfigurableandscalablearchitecturesforfutureskyrmionic deviceapplicationsandenrichesstudiesoflight–quasiparticleinteractions insolid-statesystems.

Introduction
Magnetic skyrmions are topologically nontrivial quasiparticles characterized by a swirling spin configuration. Their robustness against externalperturbations1andhighelectricalmobilityunderlowcurrent density2makeskyrmionsstrongcandidatesforenergy-efficientinfor- mationcarriersinmemorydevices,logics,andunconventionalcom- putingarchitectures3–8.Anotherdistinctivefeatureofskyrmionsisthe emergentmagneticfieldoriginatingfromtheirtopology,whichgives risetophenomenasuchastheskyrmionHalleffect9,10andthetopo- logical Hall effect11,12. Suppressing the skyrmion Hall effect13–15 is necessaryforefficientskyrmiontransport;thetopologicalHalleffect of electrons enables all-electrical skyrmion detection16. Recently, interactions of skyrmions with spin textures17,18, magnons19,20, and photons21havebeenreported,leadingtovariousemergentphenom- enaanalogoustoparticle–antiparticleinteractions,Landaulevels,and band structure reconstruction. Consequently, magnetic skyrmions provideapromisingplatformnotonlyfordemonstratingadvanced spintronicdevicesbutalsoforthestudyofrichdynamicsandfunda- mentalphysicsoftopologicalquasiparticles.

Precise and programmable control of individual skyrmions is crucialbothforsystematicstudiesoftheirfundamentalbehaviorand forthereliableoperationofskyrmionicdevices.Conventionalelectric current-driven techniques, however, face significant limitations: the appliedcurrentactsonmultipleskyrmionssimultaneously,reducing experimental selectivity and flexibility22,23. In addition, electrical transportandmanipulationofmagneticskyrmionsareconstrainedby theskyrmionHalleffect,whichinherentlydeflectstheirtrajectories9,10, and defect pinning, which leads to unpredictable stochastic motion24,25.Alternativemethodsbasedonsurfaceacousticwaves26or heatflow27,28presentsimilardrawbacks.Arecentapproachutilizinga magneticfieldgradientfromamagneticforcemicroscopyprobe29has demonstratedsingle-skyrmionmanipulation,butitisconstrainedby slow operation speed and the inability to control and observe sky- rmionssimultaneously.

Optical tweezers, first demonstrated by Ashkin in 198630,31, use tightlyfocusedlaserbeamstoprovidenoncontactandprecisecontrol over physical objects, ranging from microspheres32,33 and cells34 to individualatoms35,36,advancingresearchinbiology37,chemistry33,38,and quantumsciences39,40.Withopticaltweezers,particleensemblescanbe assembled on demand, enabling experiments from two-particle interactions38,41tomany-bodyphysics42,43.Extendingsuchcapabilities toemergentquasiparticlesisthereforeanaturalandtimelypursuit.To date,opticaltrappingandtransporthavebeenexperimentallyrealized formagneticbubblesinrelativelythickmagneticfilms44andforAbri- kosovvorticesinsuperconductors45.Formagneticskyrmions,however, opticaltweezinghassofarremainedtheoretical,requiringextremely localized optical fields and strong magnetoelectric coupling46. Other theoreticalworkshaveexploredskyrmionmanipulationusingmoving trapsortips,aswellasskyrmiondynamicsinperiodicordisordered pinning landscapes47–49. Aside from optical tweezing, another line of research,opticalgenerationofskyrmionictextures,hasrecentlybeen demonstrated50–52.Althoughultrafastlaserheatingproducesmultiple skyrmionssimultaneously,theirnumberandpositionaredetermined stochastically.Achievingprogrammablecreationandcontrolofindivi- dualskyrmionswouldextendthewell-establishedparadigmofoptical tweezers to topological quasiparticles, establishing a powerful new platformforcontrolledstudiesofspintextures.

In this work, we introduce optical manipulation of skyrmions, magnetictopologicalquasiparticlesinaspinsystem,anddemonstrate theiruniqueadvantages.Amicron-scalephotothermalpotentialwell, inducedbyfocusedlaserincidence,enablesprecisetwo-dimensional tweezingandisolationofindividualskyrmions,evenovercomingthe spin–orbit torque generated by electric current pulses. Beyond the reach of conventional optical tweezers,thisphotothermalapproach enables deterministic creation and annihilation of individual sky- rmions.Byintegratingthisopticalcontrolwithelectricaltransport,we establish fully programmable manipulation of skyrmions in two dimensions,providinga versatileplatform forsystematicstudiesof skyrmiondynamicsandinteractions,andopeningnewavenuestoward reconfigurablearchitecturesforquantumspintronicapplications.

Results
Photothermaltrapforspintextures
Thecoreofouropticalmanipulationapproachofindividualskyrmions is a micrometer-scale photothermal potential well generated by focused laser incidence (Fig. 1a). In magnetic systems with the presence of the interfacial Dzyaloshinskii–Moriya interaction (DMI)andtheperpendicularmagneticanisotropy(PMA),theenergy densitpyffiffiffioffiffiffifffiffiffiffiffia chiral domain wall (DW) can be expressed as53,54 U=4 AK (cid:1)πD+ln2μ M2d.Here,Aistheexchangestiffness,K is eff π 0 s eff the effective PMA energy density per volume, D is the DMI energy densitypersurface,M s isthesaturationmagnetization,anddisthe film thickness. As the temperature increases, thermal fluctuations disrupt magnetic ordering, reducing key magnetic parameters55. AccordingtoBloch’slaw,thesaturationmagnetizationM s decreases as the temperature approaches the Curie temperature, whereas A scales as55 M2 s. Similarly, both K eff and D decrease due to thermal agitation56,57. Consequently, while the DMI energy density ((cid:1)πD) increases,allothercontributionstototalenergydensitydecreasein totalenergydensitywithtemperature.BymeasuringK eff andM sasa function of temperature, we confirmed that the dominant factor driving the reduction in totalenergy density is the decreasein K eff (SupplementaryNote1).

A focused laser with a Gaussian beam profile locally heats the magnetic medium, producing a Gaussian temperature distribution thatformsaphotothermalpotentialwell,asconfirmedbyfiniteele- ment simulations (see Supplementary Note 2 for details). Skyrmion dynamicswithinthisphotothermalpotentialcanbedescribedbythe Thiele equation, where the anisotropy gradient induced by local heating serves as the driving force (see Supplementary Note 3). By steeringthelaserbeam,individualskyrmionscanbeselectivelydrag- gedtodesiredlocationsorpinnedataspecificsite,effectivelycoun- teractingmotioninducedbyelectriccurrents(Fig.1b,c).Wenotethat thermomagnetic torques arising from thermal gradients may also influenceskyrmionmotion27,buttheircontributionistypicallyweaker thanthatofthephotothermalpotential58,59.

The photothermal effect induced by a high-intensity laser pro- videsanotheropportunitytoengineerindividualskyrmions,enabling theirselectivecreationorannihilation(Fig.1d,e).Whenlocalheating exceeds a certain threshold temperature, the irradiated region undergoes demagnetization. Because the heated area has much reducedcoercivity,thelocalmagnetizationflipsduetothesmallstray field from the surrounding magnetic domains and stabilizes into a skyrmion.Moreover,bybringingoneskyrmionclosetoanotherwith ourphotothermaltweezer,wecaninducecontactbetweentheirDWs, causingthemtomergeintoasingleskyrmion.Thesizeandshapeof themergedskyrmionthenrapidlyrelaxtothosecharacteristicofthe hostmagneticmedium.

Inthiswork,weexaminedskyrmionsinamultilayerstackcom- prisingMgO(1nm)/Ta(0.1nm)/Co 20 Fe 60 B 20 (1.2nm)/W(3nm)/TaO x (3nm)onaSi/SiO substrate(forfurtherdetails,seethe“Methods” 2 section).TheTalayerwasintroducedtofinelytunethePMA,whilethe W/CoFeBinterfacegeneratesDMIstrongenoughtostabilizethesky- rmionic textures. The W layer also supports spin–orbit torques for electriccurrent-drivenmanipulationofskyrmions.Amagneto-optical Kerreffect(MOKE)microscopysetupwasusedtovisualizemagneti- zationstatesinrealtime,wheredarkandlightregionscorrespondto magnetizationalongthe−zand+zdirections,respectively.

A small perpendicularmagnetic fieldof2.56Oe was applied to optimize the size and density of skyrmions. The resulting skyrmion diameterrangedfrom2.0to5.0μm,makingthemclearlyresolvable underanopticalmicroscope.TheMOKEimage(Fig.1f)revealssuffi- ciently well-separated skyrmions, allowing individual manipulation without interference from neighboring skyrmions. A skyrmion Hall effectmeasurementconfirmsthetopologicalnatureofourmagnetic textures, validating them as magnetic skyrmions (Supplemen- taryNote4).

Skyrmiontweezers
Wefirstdemonstratetheuseofthephotothermaltweezerfordragging a single magnetic skyrmion along the laser beam’s sweep direction (Fig.2a).Onceasingleskyrmionistrappedwithinthebeamspotbythe photothermalpotential,wemovethesamplerelativetothefixedlaser position, and then, the skyrmion is transported accordingly. This functionality enables precise control over the arrangement of sky- rmions, enabling the creation of arbitrary patterns of skyrmions (Fig.2b).Thepotentialwelllandscaperesultingfromthetemperature gradientisuniversalforanyspintextures,regardlessoftheirdetailed distributions,aslongasthePMAenergyremainsdominant.Asaresult, wecancontrolmagneticDWs,notjustindividualskyrmions(Supple- mentaryNote5).Fromatopologicalperspective,achiralDWwitha semicircularshapecarriesatopologicalchargeof±1/2,oftenreferred toasa“halfskyrmion”60,61.Wecanextractahalfskyrmionnotonly from bulk domain structures but also from a single skyrmion, by selectivelydraggingoneofitsends(SupplementaryNote5).

Theprobabilityofstableskyrmiontransport,definedasthelike- lihood that a target skyrmion remains intact without elongation or pinningtoalocaldefect,wasmeasuredbyvaryingthesweepingspeed (v sw)andlaserbeampower(Fig.2c).Stronglocalmaterialdefectscan pin or deform skyrmions during photothermal tweezing. For each combinationofsweepingspeedandlaserbeampower,weconducted 20trialsandrecordedthesuccessprobabilityoftransportingasingle skyrmionoveradistanceof10μm.Atasweepingspeedof120nm/s andalaserpowerof6.02mW,wewereabletodragindividualsky- rmions with a high probability of 85%, which could be further enhancedbyfabricatingmagneticfilmswithlowerdefectdensities.As expected, the higher the sweeping speed, the lower the trapping probability, because the decline in trapping probability at higher sweeping speeds is attributed to skyrmion inertia, which hinders immediatecouplingwiththedynamicpotentialoftheopticaltweezer.

The transport of skyrmions controlled by the photothermal tweezercanbeunderstoodasathermallyactivatedhoppingprocess betweenintrinsicpinningsitesinthemagneticfilm.Thephotothermal potentialwithasufficientlystrongdrivingforceenablestheskyrmion toovercome pinning potentialswithoutdeformation,butthe prob- abilistic nature of creep motion determines the success of these “jumps,”whichdependsonthedrivingduration.Ifthesweepingspeed istoohigh,skyrmionsdonothavesufficienttimetojumpandfollow the laser beam.The maximum sweeping speed allowable for jumps withthedesiredtransportprobabilityisinverselyproportionaltothe probabilistic activation time, which follows the Arrhenius equation: v sw /exp (cid:1) k B ðT E 0 b +αPÞ ,whereE bistheactivationenergybarrier,k Bis theBoltzmannconstant,Pisthelaserpower,αistheheatingcoeffi- cient,andT istheambienttemperature.TheresultsinFig.2cprovide 0 approximatebutcompellingsupportforthisinterpretation(Supple- mentary Note 6). We note that, beyond this stochastic regime, the skyrmion velocity is ultimately bounded by two factors: a practical limit, determined by the maximum anisotropy gradient and local pinningdensity(SupplementaryNote3),andafundamentallimit,set by the magnon group velocity62,63. Under our current experimental conditions, however, the skyrmion speed is governed primarily by localpinning.

Wealsodemonstratethatthephotothermalpotentialwellcanpin a selected skyrmion at a desired position, preventing displacement under external electric current injection. We tracked the motion of severalskyrmionsunderelectriccurrentpulseinjection(Fig.3a):free skyrmions(coloredblue,yellow,andorange),askyrmionpinnedata persistent intrinsic defect (colored green), and a selected skyrmion trapped by the photothermal tweezer (colored red). While all free skyrmionsmovealongthedirectionoftheinjectedcurrentpulses,the photothermally trapped skyrmion, confined by a 6.5mW laser, remainsstationary,similartotheskyrmionpinnedatthedefectsite. Thedisplacementoftheskyrmionsfromtheirinitialpositionsisshown inFig.3b.Whilethelaserforthephotothermalpotentialwason,forthe firstfivecurrentpulses(N=1–5),thephotothermallypinnedskyrmion remainedstationary,whilethefreeskyrmionsmoved2.4μmper pulse on average. We turned off the laser before applying the sixth pulse (N=6),afterwhich the previously photothermally pinned skyrmion started to move freely, whilethe defect-pinned skyrmion remained stationary. Here, the applied electric pulses were square-shaped with 7.79×109A/m2 currentdensityand100msduration.

Higher laser power enhances the depth of the photothermal potentialwell,therebyincreasingtheskyrmionresistancetoexternal driving current.Westatisticallyanalyzedthedisplacementofasky- rmioninducedbyasingleelectricpulsedependingonthelaserpower andthecurrentdensity.Figure3cshowsboxplotsofthefirstandthird quartiles,alongwiththemedian,basedon20trialspercondition.To minimize inhomogeneous spatial variations in intrinsic pinning, all measurementswereperformedonskyrmionsatthesamelocation(for furtherdetails,seethe“Methods”section).Skyrmiontransportunder currentpulsesexhibitsathresholdbehavior,inwhichthetotalpinning potential,thesumoftheintrinsicandphotothermalpotentials,must beovercome.Withoutlaserpinning,skyrmionsremainpinnedunless thecurrentdensityexceedsathresholdof4.24×109A/m2(bluedashed line).Whenthelaserpinningisturnedon,theadditionalphotothermal potential well increases the threshold current density required for skyrmion motion to 4.56×109A/m2 at a laser power of 4.14mW (orangedashedline)andtoover5.19×109A/m2at5.06mW.Thisresult demonstrates the capability of the photothermal effect to locally engineerthepotentiallandscapeforskyrmions,offeringprecisecon- trol over their dynamics. Finally, we confirmed the stability of the skyrmion topology under both elevated uniform temperatures and localized photothermal gradients by examining spin–orbit torque- driventransport(SupplementaryNote7).

Fullyprogrammableskyrmionmanipulation
Thephotothermaleffectenablesthedeterministiccreationofaniso- lated skyrmion at a desired position. Localized heating from the focused laser beam reduces the material’s magnetic properties, includingmagnetizationandcoercivity,andlowerstheenergybarrier formagnetizationreversal(SupplementaryNote8).Theflippedmag- netization is stabilized by the stray field from neighboring magnetizations64.Theresultingbubbledomainadoptsaskyrmionic texture, because the equilibrium state of DWs in our sample is chiral65,66. The process of optical skyrmion generation is shown in Fig.4a.Theinitialstateoftheuniformlymagnetizeddomainisshown inthefirstpanel,withtheredcircleindicatingthepositionofthelaser beaminadvance.Thedeterministiccreationofasingleskyrmionatthe irradiatedlocationisshowninthesecondpanel.Thegeneratedsky- rmionhasthesamesizeandshapeastheoriginalskyrmionsand,as showninthethirdpanelofFig.4a,itexhibitsidenticalmotionwhenwe appliedanelectricpulse(3.14×109A/m2currentdensityand100ms duration). Next, the skyrmion Hall effect for optically created sky- rmionswasmeasured,confirmingtheirdeflectionfromthedirection oftheinjectedcurrentpulseandvalidatingtheirtopologicalnature andnonzerowindingnumber(SupplementaryNote4).

The probabilityofskyrmiongenerationasafunctionoftheinci- dentlaserpowerisshowninFig.4b.Thelaserwasappliedfor1s,and theprobabilitywasevaluatedover20trialsatdifferentlocationsfor eachpowerlevel.Below3mW,noskyrmionsweregenerated,whereas above4mW,theskyrmionformationprobabilityincreaseddramati- cally, ultimately reaching deterministic creation. This result demonstratesthatphotothermalskyrmiongenerationrequiresalaserpower exceedingacertainthreshold,anditcanbeexplainedwithanArrhe- nius equation (see supplementary Note 8 for details). Conventional skyrmioncreationmethodsusingexternalmagneticfields65,66,ultra- fast lasers51,52, and electrical current pulses64, are limited to either generatingalargenumberofskyrmionsstochasticallyorrestricting theirformationtopredefinedlocationssuchaselectrodesortracks.By contrast,photothermalgenerationenablespreciseanddeterministic skyrmioncreationatarbitrarypositions,makingitaversatiletoolfor potentialquantumandspintronicapplications.Furthermore,atsuffi- cientlyhighlaserpower,twoskyrmionscanbeinducedtomergeintoa single skyrmion, enabling selective annihilation (Supplemen- taryNote9).

Byintegratingthetechniquesoutlinedabove,wedemonstrated fully programmable control over the motion of an individual sky- rmionthroughsuccessiveoperationsofthephotothermaltweezer. As shown in Fig. 4c, the comprehensive manipulation, including skyrmioncreation,pinning,transport,andannihilation,withina5×5 cellarraywasexperimentallydemonstrated.Eachunitcellmeasures 4.3μm×4.3μm,aspacingdeterminedbythetypicaldisplacementof a skyrmion induced by an electrical pulse (3.14×109A/m² current densityand100msduration).Startingfromaninitialconfiguration with two preexistingskyrmions (coloredblue), and usingthepho- tothermal effects, a new skyrmion (colored red) was created at a target position. The created skyrmion was pinned with a photo- thermaltweezer,whereasthetwopreexistingskyrmionswereshifted byanelectricpulse.Subsequently,thecreatedskyrmionwastrans- portedindependentlytoothercellsusingthephotothermaltweezer. Unlike electrical current-driven motion, which is restricted to pre- determined directions, the photothermal tweezer enables flexible two-dimensional skyrmion positioning with high spatial precision. Finally,thecreatedskyrmionwasdraggedtoapreexistingskyrmion, and as they approached closer, the DWs separating them became demagnetizedbythethermaleffect.Thisoperationprovidedenough energytobreakthetopologicalbarrier,mergingthemintoasingle skyrmion.Theabilitytocontrolthebirth,movement,andannihilation of individualskyrmions shows the potential ofadvanced two- dimensionalspintronicapplication67,68.

Methods
Samplefabrication
Themagneticthinfilms,consistingofanMgO(1nm)/Ta(0.1nm)/ Co 20 Fe 60 B 20 (1.2nm)/W(3nm)/TaO x (3nm)stack,weredepositedon aSi/SiO substratebyDC/RFmagnetronsputtering.Afterdeposition, 2 thesampleunderwentapost-annealingprocessat350°Cfor1hunder a 1×10−7Torr vacuum. For electrical transport measurements of magneticskyrmions,electrodescomposedofTi(2nm)/Au(50nm) were fabricated using photo-lithography and a lift-off process. We prepared two identical samples grown under the same fabrication conditions.Sample#1wasusedfortheexperimentsshowninFig.2a,c, aswellasFig.3a,b,whileSample#2wasusedforthoseinFig.2b, Fig.3c,andFig.4.Thisseparationwasintendedtoavoidinaccuracies duetopotentialsampledegradationfromrepeatedexperimentsused forstatisticalanalysis.Weconfirmedtheequivalenceofthemagnetic properties of the two samples (see Supplementary Note 1 for more details).

Experimentalsetup
Local photothermal heating was achieved using a focused 638nm continuous-wave(CW)laser.Thediameterofthefocusedlaserbeam was2.4μm,comparabletothetypicalskyrmionsizeinthemagnetic films studied. The magneto-optical Kerr effect (MOKE) microscopy setup for real-time skyrmion motion measurements consisted of a 530nm light-emitting diode (LED) for illumination and an electron- multiplying charge-coupled device (iXon DU-897). A piezoelectric translation stage was used to precisely move the sample in two dimensions,allowingthefocusedbeamtosweeprelativetothesam- ple. Custom-built electromagnets were used to apply both in-plane andout-of-planemagneticfieldssimultaneously.Forallexperiments shown in the main manuscript, an out-of-plane magnetic field of 2.56Oewasappliedtotuneskyrmionsize.Anin-planemagneticfield wasappliedonlyduringtheinitialnucleationofskyrmionsfromthe stripedomainstateacrossthesampleandwasthensettozeroduring allothermeasurements.

Photothermalpinningmeasurement
Forstatisticalanalysisofthemotionofphotothermallypinnedsky- rmions per electrical current pulse (Fig. 3c in the main text), we examined skyrmions created at the same predefined position and minimizeddifferencesarisingfromspatialinhomogeneityacrossthe sample.Thephotothermaleffectenabledthedeterministiccreation of a skyrmion at a fixed position, carefully selected to avoid any persistent intrinsic defects that might skew the statistical results. Instanceswherethetargetskyrmionwasannihilatedbyhigh-current- densityelectricalpulseswereexcludedfromthestatisticalanalysis. ThemotionofskyrmionswastrackedinrealtimeusingtheMOKE microscopeandquantitativelyanalyzedusingtheTrackMateplugin inImageJsoftware(NationalInstitutesofHealthandtheLaboratory for Optical and Computational Instrumentation, University of Wisconsin).

Dataavailability
Thedatathatsupportthefindingsofthisstudyareavailablefromthe correspondingauthoruponreasonablerequest.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript demonstrates the control of skyrmions using a focused continuous-wave (CW) laser. The concept of trapping and transporting individual skyrmions via a photothermal potential well is intriguing. However, the work currently lacks detailed quantitative analysis of experimental phenomena. Key comments are as follows:\n1. The title should be more precise. The generalization from skyrmions to topological particles lacks justification, as the study focuses specifically on skyrmions.\n2. The authors discuss the temperature dependence of anisotropy, a critical ingredient for skyrmion control. However, the manuscript does not characterize the temperature distribution induced by laser heating. An interpretation in terms of temperature (rather than laser power) would be more theoretically sound, but requires supporting data on thermal profiles.\n3. Unclear theoretical basis in supporting information. The authors provide an Arrhenius equation-based explanation for laser sweeping in the Supporting Information, but:\n- What is the activation energy barrier used in this model?\n- How is the choice of this parameter theoretically or experimentally justified?\n4. The spin dynamics governing skyrmion generation, motion, and annihilation remain unclear. The manuscript should:\n- Elaborate on the spin dynamics of generation and annihilation processes, including characteristic timescales.\n- Clarify the dynamic mechanism driving skyrmion displacement under the applied temperature distribution (e.g., origin of driving force, motion equations).\n5. I think the upper limit of skyrmion motion speed needs to be addressed. This physical constraint is critical for evaluating the method’s scalability.\n6. Thermal control is inherently susceptible to stochasticity, raising concerns:\n- How is the topological stability of skyrmions ensured under temperature gradients? Experimental or theoretical evidence of structural resilience is needed.\n- Given the authors’ claim of “robust, reversible, and scalable” manipulation, what strategies mitigate the stochastic nature of thermal control to ensure repeatability and robustness?", "reviewer_2": "Manipulating individual or groups of particles by optical means, particularly with optical tweezers, goes back to Ashkin, and since that time, this technique has been widely applied to biological systems, soft matter, condensed matter, and atomic systems. An interesting question is whether optical tweezer techniques can also be used to manipulate emergent quasiparticles such as skyrmions, magnetic textures, magnetic vortices, and other particle textures that arise in condensed matter.\nHere, the authors use a photothermal optical tweezer to trap and move, create and annihilate skyrmions. The ability to radially manipulate skyrmions on the individual level opens up new device possibilities as well as new methods for understanding skyrmion dynamics and skyrmion-skyrmion interactions. Additionally, this technique could be extended to examine many of the same effects that have been explored in colloidal systems, such as trap arrays, ratchets, holographic traps, dynamic traps, Bessel beams, and so on, which could open up a new field of optico-skyrmionics.\nIn addition to manipulating the skyrmions, the authors discuss issues directly relevant to the skyrmion systems. In colloidal systems, the substrate is often smooth; however, in the skyrmion case, there can be quenched disorder or pinning effects on the skyrmions, and the authors study how often the skyrmion needs to be dragged, which in some cases occurs 85% of the time. They also find sweep rate dependence and discuss the role of local heating from the photothermal trap.\nAnother feature that makes this work different from optical tweezer studies in other systems, such as colloids and atomic systems, is that the authors demonstrate that this technique can be used to individually create and delete skyrmions, which is relevant for devices.\nOverall, the work is very strong, opens a new aspect of research for skyrmion physics, and describes a technique that could be used for other emergent particle-like textures. The text is clear, and Figure 1 is particularly elucidating as it nicely summarizes the four main aspects of the work: moving, pinning, creation, and annihilation of skyrmions. The authors also show how potential devices could be made using a grid-like trapping system.\nI have some comments for the authors to address, after which the paper can be published, where I expect it could have a very high impact.\n(1) There has been some previous theory work describing how skyrmions could be manipulated with optical tweezers that should be mentioned.\nWang et al propose that skyrmions could be manipulated with optical tweezers and used micromagnetic simulations to confirm this.\nThe optical tweezers of skyrmions\nXi-Guang Wang, Levan Chotorlishvili, Vitalii K. Dugaev, Arthur Ernst, Igor V. Maznichenko, Nikita Arnold, Chenglong Jia, Jamal Berakdar, Ingrid Mertig & Józef Barnaś\nnpj Computational Materials volume 6, Article number: 140 (2020)\nAdditionally, there have been some numerical studies on the individual manipulation of skyrmions with moving traps or tips for different sweep rates and types of pinning. This work mentions that such manipulation could be achieved with optical trapping or some kind of magnetic tip.\nDynamics and nonmonotonic drag for individually driven skyrmions\nC. Reichhardt and C. J. O. Reichhardt\nPhys. Rev. B 104, 064441 (2021)\nCommensuration effects on skyrmion Hall angle and drag for manipulation of skyrmions on two-dimensional periodic substrates\nC. Reichhardt and C. J. O. Reichhardt\nPhys. Rev. B 105, 214437 (2022)\nAlso the following review article discussing skyrmion pinning has a section discussing manipulation of a single skyrmion with some form of local tip or with optical means.\nStatics and dynamics of skyrmions interacting with disorder and nanostructures\nC. Reichhardt*, C. J. O. Reichhardt†, and M. V. Milošević‡\nRev. Mod. Phys. 94, 035005 – Published 20 September, 2022\nFor experiments the closest thing I could find was\nOgawa, N., W. Koshibae, A. J. Beekman, N. Nagaosa, M. Kubota, M.\nKawasaki, and Y. Tokura, 2015, “Photodrive of magnetic bubbles\nvia magnetoelastic waves,” Proc. Natl. Acad. Sci. U.S.A. 112,\n8977–8981.\n(2) The authors do a nice job of discussing the optical manipulation with optical tweezers for colloids, atoms, and biological systems. They could mention the original work of Ashkin work for this. For a nice overview, see:\nA. Ashkin.\n“History of optical trapping and manipulation of small-neutral particle, atoms, and molecules.”\nIEEE J. Sel. Top. Quantum Elec.6, 841–856 (2000).\n(3) The authors could also mention some new directions, which could include optical arrays, ratchets, holographic traps, and so on, similar to the optical tweezers work done in colloidal systems.\nA revolution in optical manipulation,\nD. G. Grier, Nature 424, 810-816 (2003).\n(4) The authors should mention some experiments showing optical manipulation for single vortices in type-II\nsuperconductors, which have also been used to spell out letters.\nOptical manipulation of single flux quanta\nI. S. Veshchunov, W. Magrini, S. V. Mironov, A. G. Godin, J.-B. Trebbia, A. I. Buzdin, Ph. Tamarat & B. Lounis\nNature Communications volume 7, Article number: 12801 (2016)", "reviewer_3": "Kim and coworkers report an experimental study of optical manipulation of spin textures in a CoFeB thin film with interface-induced antisymmetric exchange interactions. These spin textures are topologically nontrivial and can be treated as skyrmion quasiparticles. The authors focus on the dynamics of skyrmion quasiparticles controlled by an optical tweezer and demonstrated a high precision trapping and transport of skyrmions via laser-induced photothermal potentials. The authors also demonstrated that the photothermal effect can lead to the creation or annihilation of a single individual skyrmion. They show a programmable control of skyrmions in two dimensions can be realized by combining optical and electric manipulations. They suggested the programmable creation, annihilation, and manipulation of individual skyrmions will be useful device applications, such as probabilistic computing and reconfigurable logic computing. I think this manuscript is well written, and the study on the precise control of particle-like skyrmions through optical methods is both interesting and valuable to the skyrmion community. Since the initial observation of skyrmions in chiral magnets, most research in the field has focused on controlling and manipulating skyrmions using electric currents, magnon currents, and thermal currents. As far as I am aware, there are only a few reports on the creation and manipulation of skyrmions using optical lasers. However, as the authors mentioned in the introduction, optical tweezers have actually been used in many different fields to control particle-like objects. I therefore agree with the authors that the optical manipulation of skyrmion quasiparticles is worth exploring. For the above reasons, I think this manuscript is suitable for publication in the journal. Before acceptance, the manuscript could be improved through a minor revision; see comments below.\n1. The authors should highlight relevant published studies on the optical manipulation of magnetic bubbles and skyrmions in the introduction, and clearly make a link to what they are exploring and indicate how their study advances the field. There are some important references, for example, see https://www.pnas.org/doi/10.1073/pnas.1504064112,\nhttps://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.054421, and\nhttps://pubs.acs.org/doi/abs/10.1021/acs.nanolett.8b03653.\n2. The role of temperature gradient–induced forces (e.g., magnonic spin Seebeck effect or thermomagnonic torques) is not fully disentangled from the optical potential mechanism. The authors attribute skyrmion motion primarily to an attractive photothermal potential well. However, skyrmions are known to exhibit drift under thermal gradients due to magnon currents. Could the authors clarify whether such effects contribute to the observed dynamics? Have control experiments (e.g., different laser spot sizes or reversed gradients) been performed to isolate this effect?"}, "author_response": "Response to the Reviewer #1\nGeneral Comment:\nThe manuscript demonstrates the control of skyrmions using a focused continuous-wave (CW) laser.\nThe concept of trapping and transporting individual skyrmions via a photothermal potential well is\nintriguing. However, the work currently lacks detailed quantitative analysis of experimental\nphenomena. Key comments are as follows\nResponse to General Comment:\nWe thank Reviewer #1 (R1) for all the comments and suggestions. We are glad to see that R1 finds\nthe interest and potential of our work. We have addressed all of the points and queries raised by R1 in\na point-by-point fashion and revised the manuscript accordingly, as listed below. In particular, we have\nincorporated additional and more detailed quantitative analyses of the experimental phenomena in both\nthe revised main manuscript and the supplementary notes to address the reviewer’s main concern.\nComment 1:\nThe title should be more precise. The generalization from skyrmions to topological particles lacks\njustification, as the study focuses specifically on skyrmions.\nResponse to Comment 1:\nWe thank R1 for the valuable comment. We agree that our study focuses specifically on skyrmions\nand that we have not explicitly demonstrated our photothermal tweezer scheme for other topological\nquasiparticles. However, the underlying mechanism of reducing magnetic ordering through localized\nheating can, in principle, be generalized to other spin textures such as antiskyrmions, merons, and\nhopfions, since their energy densities are governed by magnetic interactions in a manner similar to\nskyrmions.\nFollowing the reviewer’s suggestion, we revised the title as, “Photothermal skyrmion tweezer:\nProgrammable optical manipulation of magnetic topological quasiparticles”. To clarify the scope and\npotential of our study, we also added the following sentence to the conclusion section of the main\nmanuscript\n(page 10, paragraph 2, line 9):\n“The concept of photothermal tweezers may also be extended to other magnetic quasiparticles, such\nas hopfions, antiskyrmions, and merons, as their magnetic ordering decreases upon heating in a manner\nsimilar to skyrmions.”\nComment 2:\nThe authors discuss the temperature dependence of anisotropy, a critical ingredient for skyrmion\ncontrol. However, the manuscript does not characterize the temperature distribution induced by laser\nheating. An interpretation in terms of temperature (rather than laser power) would be more theoretically\nsound, but requires supporting data on thermal profiles.\nResponse to Comment 2:\nWe thank R1 for the valuable comment.\nIn response, we performed two complementary calculations to characterize the temperature\ndistribution induced by laser heating. First, we used the transfer matrix methodS6 (TMM) to calculate\nthe optical absorption within each layer of the thin-film heterostructure for a 638 nm laser wavelength.\nThe absorbed power values obtained from the TMM calculation were then used as input for finite\nelement method (FEM) simulations to model the steady-state temperature profile and heat transfer as a\nfunction of laser power. For the FEM simulations, we applied air convection at the top surface with a\nheat transfer coefficient of 10 W/(m²·K), while the bottom substrate and side boundaries were treated\nas infinite. The initial temperature of the materials was set to 293.15 K.\nThe resulting temperature increment profile, as shown in Figs. S5a and S5b, exhibits a Gaussian\ndistribution with a full width at half maximum (FWHM) of approximately 2.7 µm, which is broader\nthan the laser beam diameter of 2.4 µm due to heat diffusion. As shown in Fig. S5c, the temperature\nincrement T at the beam centre is less than 50 K even at a laser power of 7 mW, resulting in an absolute\ntemperature well below the Curie temperature reported for CoFeBS2, S3. The temperature increase is\nlinear with the laser power with a heating coefficient of 6.35 K/mW. In addition, time-dependent\nsimulations of transient heating and cooling of materials (Fig. S5d) show that the system reaches\nthermal equilibrium within 200 ns, regardless of the laser power. This rapid equilibration confirms that\nthe skyrmion transport described in the main manuscript occurs in a quasi-steady-state regime.\nFigure S5. Simulated steady-state and transient temperature profiles induced by laser heating. (a)\nTemperature increment landscape when a 638-nm laser with a power of 7 mW is irradiated on the sample. The\nincident laser beam has a diameter of 2.4 µm, while the resulting steady-state temperature profile exhibits a full\nwidth at half maximum (FWHM) of approximately 2.7 µm due to heat diffusion. Scale bar, 1 m. (b) Cross-\nsectional distributions of the temperature increment and its gradient as a function of incident laser power P. (c)\nTemperature increment at the beam center as a function of laser power. (d) Time-dependent temperature increment\nat the beam center. The material was heated from room temperature (293.15 K) and the laser heating was turned\noff at 1.0 s.\nTo reflect the reviewer’s comment, we added a new section in Supplementary Information and\nreferenced it in the main manuscript as follows:\n(page 4, paragraph 2, line 1)\n“A focused laser with a Gaussian beam profile locally heats the magnetic medium, producing a\nGaussian temperature distribution that forms a photothermal potential well, as confirmed by finite\nelement simulations (see Supplementary Information S2 for details).”\nReferences\n[S2] Lee, K-M., Choi, J.W., Sok, J. & Min, B-C. Temperature dependence of the interfacial magnetic\nanisotropy in W/CoFeB/MgO. AIP Adv.7, 065107 (2017)\n[S3] Yamanouchi, M. et al. Domain Structure in CoFeB Thin Films With Perpendicular Magnetic\nAnisotropy. IEEE Magn. Lett. 2, 3000304 (2011)\n[S6] Knittl, Z. Optics of Thin Films: An Optical Multilayer Theory (Wiley, London, 1976)\nComment 3:\nUnclear theoretical basis in supporting information. The authors provide an Arrhenius equation-based\nexplanation for laser sweeping in the Supporting Information, but:\n- What is the activation energy barrier used in this model?\n- How is the choice of this parameter theoretically or experimentally justified?\nResponse to Comment 3:\nWe appreciate the thoughtful comment of R1.\nIn our analysis (S6 in the revised Supplementary Information; S4 in the original Supplementary\nInformation), we obtained the activation energy barrier by fitting the experimentally extracted results\nwith the Arrhenius equation: , where , P, , and E are the room\nb\ntemperature, the incident laser power, the heating coefficient, and the activation energy barrier,\n𝑣𝑠𝑤 = 𝑣0exp(−𝐸𝑏/𝑘𝐵(𝑇0+𝛼𝑃)) 𝑇0\nrespectively. The value of the heating coefficient was calculated from the FEM simulation as\n(see our response to Comment 2 of R1). The acquired activation energy from fitting the\nα =\nmodel was 1.57 eV, which is in excellent agreement with the previously reported activation energy of\n6.3506 K/mW\n1.56 eV for thermal depinning of skyrmions in a CoFeB/Ta/MgO stackS12. This close agreement\nsupports the physical validity of our activation energy estimate.\nFigure S8 Arrhenius equation-based analysis of photothermal skyrmion transport. (Top panel) Magnified\nplot of the experimental data from Fig. 2c in the main manuscript. The probability of successfully transporting a\nsingle skyrmion over a 10 μm distance as a function of the incident laser power and sweeping speed, based on 20\ntrials per condition. (Bottom panel) Exponential dependence of the sweeping speed on incident laser power. The\nlaser power required to achieve a skyrmion transport probability of = 0.1 is estimated for different sweeping\nspeeds, varying from 120 nm/s to 2.4 μm/s.\n𝑝\nTo reflect the reviewer’s comment, we added the aforementioned details and the relevant reference\nin Supplementary Information S6 as follows:\n“We used a heating coefficient of , obtained from\nthe FEM simulation in Supplementary Information S2. The fitted activatio−n4 energy was determined to\n𝛼 = 6.35 K/mW (𝑘𝐵𝛼 = 5.47×10 eV/mW)\nbe 1.57 eV, in close agreement with the previously reported value of 1.56 eV for thermal depinning of\nskyrmions in a CoFeB/Ta/MgO stackS13.”\nReference\n[S13] Zázvorka, J. et al. Thermal skyrmion diffusion in a reshuffle device. Nat. Nanotechnol.14,\n658–661 (2019).\nComment 4:\nThe spin dynamics governing skyrmion generation, motion, and annihilation remain unclear. The\nmanuscript should:\n- Elaborate on the spin dynamics of generation and annihilation processes, including characteristic\ntimescales.\n- Clarify the dynamic mechanism driving skyrmion displacement under the applied temperature\ndistribution (e.g., origin of driving force, motion equations).\nResponse to Comment 4:\nWe thank Reviewer 1 for this important and constructive comment. In particular, the reviewer\nrequested clarification of the spin dynamics governing skyrmion generation and annihilation, including\ntheir characteristic timescales, as well as the dynamic mechanism that drives skyrmion displacement\nunder applied temperature gradients. To address these points, we have expanded our discussion and\nsupplemented the manuscript with additional analysis. Specifically, our response is organized into three\nparts: (1) photothermal generation of skyrmions, (2) photothermal annihilation of skyrmions, and (3)\nthe equation of motion of skyrmions in a photothermal potential.\n(1) Photothermal generation of skyrmion\nPhotothermal heating lowers the energy barrier for magnetization reversalS12 by changing magnetic\nparameters, most notably reducing the anisotropy energy density (See also Supplementary Information\nS1). The dipole field from the surrounding domain then induces local magnetization reversal and\nstabilizes the reversed region into a bubble domain with an optimum radius . In our sample, this\nbubble exhibits the chiral spin texture of a Néel-type skyrmion due to the interfacial Dzyaloshinskii-\n𝑟opt\nMoriya interaction (DMI)S12 (See also Supplementary Information S4). When the laser beam radius is\nmuch larger than the , multiple skyrmions nucleate stochastically within the illuminated regionS16.\nBy contrast, when the beam radius is comparable to or smaller than , only a single bubble domain\n𝑟opt\n𝑟opt\nis stabilized, confined to the heated spot. Thus, photothermal tweezers enable deterministic and\nprogrammable skyrmion creation at the laser focus. We describe the mechanism in detail below.\nThe energy of a bubble-shaped domain arises from several competing contributions: domain wall\nenergy, dipole interaction energy, and Zeeman energy from the external field . The domain wall\nenergy increases with bubble size, whereas the dipole interaction energy decreases. In the presence of\n𝐻𝑧\n, a magnetic bubble of radius R, illustrated in Fig. S11a, has an excess energy relative to the\nuniform domain state:\n𝐻𝑧 Δ𝐸\n2 2 8𝑅 2\nwhere d is the magn𝛥e𝐸ti(c𝑅 f)ilm= t2h𝜋ic𝑅k𝑑ne𝜎s 𝑑 s 𝑤 , −2𝜇is 0 𝑀th 𝑠 e 𝑅d𝑑omlanin( wall )en+er 2gy𝜋 𝜇d 0 e𝑅nsi𝑑ty 𝑀, a 𝑠 n𝐻d 𝑧 is the saturation\n√𝑒𝑑\nmagnetization, under the assumption that the domain wall width is negligible compared to the bubble\n𝜎𝑑𝑤 𝑀𝑆\ndiameterS16, S17. In our sample, the domain wall width is ~49 nm, more than 20 times smaller\nthan the typical skyrmion radius (1–2 m). 𝜋√𝐴/𝐾eff\nThe domain wall energy density for a Néel-type skyrmion is given by\n, where A is the exchange stiffness, is the effective anisotropy\n𝜎\ne𝑑n𝑤erg\n=\ny\n4\nd\n√\nen\n𝐴\ns\n𝐾\niteyf,f a\n−\nnd\\𝜋 𝐷\nD\n+ is\nl t n he 2 DMI2 constantS4. The local minimum of determines the optimum bubble size. Using the\n𝜋\n𝜇0𝑀𝑠𝑑 𝐾eff\nmeasured parameters for our sample ( , , ) and the\n𝛥𝐸(𝑅)\nDMI constant ( ) reported for W/CoFeB5/MgOS18, we find that choosing\n𝑀s = 7.43×10 A/m 𝑑 = 1.2 nm 𝜇0𝐻𝑧 = 2.56 Oe\nyields an optimum bubble radiu2s of , consistent with the experimentally measured radii\nD = 0.73 mJ/m 𝐴 = 16 pJ/m\nof intrinsic, magnetic-field-induced skyrmions (1–2 m) at room temperature. The calculated\n𝑟opt ~1.33 μm\ncurves at various temperatures are shown in Fig. S11b, assuming dominantly changes with heating\n𝛥𝐸(𝑅)\n(as confirmed in Supporting Information S1). The radius corresponding to the local maximum of\n𝐾eff\ndefines the critical radius . Bubbles with , even if nucleated, are unstable and\ncollapse into the uniform state again, whereas those with relax to the bubble with . The\n𝜟𝑬(𝑹)= 𝑬𝑩 𝒓𝒄 𝑹 < 𝒓𝒄\nenergy at the local maximum thus corresponds to the energy barrier for stable bubble formation.\n𝑹 > 𝒓𝒄 𝑹 = 𝒓𝒐𝒑𝒕\n𝑬𝑩\nFigure S11 Excess energy of a magnetic bubble depending on its radius. (a) Schematic illustration of a\nmagnetic bubble in the presence of an external field. (b) Excess energy of magnetic bubbles as a function of\nradius and temperature. Triangular and circular markers denote the local maximum and minimum of at\neach temperature. The orange dashed line indicates the laser spot radius.\n𝜟𝑬(𝑹)\nAs the temperature increases, decreases, which lowers ;consequently decreases and\nincreases with temperature (Fig. S11b). However, the actual skyrmion size under photothermal\n𝐾eff 𝜎𝑑𝑤 𝐸𝐵 𝑟opt\ntweezing does not increase significantly (Fig. S12). This discrepancy arises because the laser-induced\ntemperature profile is highly localized (see also Supplementary Information S2), thereby confining the\nskyrmion within the photothermal potential against the cooler surroundings.\nFigure S12 Skyrmion size under photothermal tweezing. (a, b) Magnetization profile of an intrinsic,\nmagnetic-field induced skyrmion (a) without and (b) with focused laser incidence. Laser power is 5.06 mW.\nScale bar, 5 m.\nThe energy barrier decreases exponentially with increasing the temperature (Fig. S13a). Using an\nArrhenius equation, the characteristic creation time is estimated as , where\n𝐸𝐵\nis the prefactor for microscopic magnetization reversal, typically sS19, S20. With\nτcreation = 𝜏0exp(𝐸𝐵/𝑘𝐵𝑇)\n, the characteristic creation time falls significantly below 1 s, the d−u1r0ation o−f 8the laser irradiation\n𝜏0 10 −10 𝜏0 =\nemployed in the experiments, once the temperature exceeds 313 K (Fig. S13b), indicating that skyrmion\n1 ns\nnucleation becomes deterministically accessible. This theoretical estimate closely matches the creation\nprobability in Fig. 4b of the main manuscript, where the probability sharply increases above the same\ntemperature threshold.\nFigure S13 Energy barrier and characteristic timescale for magnetic bubble creation. (a) Energy barrier\nas a function of temperature. (b) Corresponding creation timescale as a function of temperature and laser\npower (black dots), compared with the measured probability of photothermal skyrmion creation (red triangles)\n𝑬fro𝑩m Fig. 4b of the main manuscript.\nReferences\n[S4] Yang, S. et al. Magnetic Skyrmion Transistor Gated with Voltage-Controlled Magnetic\nAnisotropy. Adv. Mater.35, 2208881 (2023)\n[S12] Yang, S. et al. Electrical generation and deletion of magnetic skyrmion-bubbles via vertical\ncurrent injection. Adv. Mater.33, 2104406 (2021)\n[S16] Je, S.-G. et al. Creation of magnetic skyrmion bubble lattices by ultrafast laser in ultrathin films.\nNano Lett. 18, 7362–7371 (2018).\n[S17] Büttner, F., Lemesh, I. &Beach, G. S. D. Theory of isolated magnetic skyrmions: From\nfundamentals to room temperature applications. Sci. Rep.8, 4464 (2018)\n[S18] Jaiswal, S., et al. Investigation of the Dzyaloshinskii-Moriya interaction and room temperature\nskyrmions in W/CoFeB/MgO thin films and microwires. Appl. Phys. Lett.111, 022409 (2017)\n[S19] Weller, D., & Moser, A. Thermal Effect Limits in Ultrahigh-Density Magnetic Recording. IEEE\nTrans. Magn.35, 4423-4439 (1999)\n[S20] Lederman, M., & Schultz, S. Measurement of Dynamics of the Magnetization Reversal in\nIndividual Single-Domain Ferromagnetic Particles. Phys. Rev. Lett.73, 1986-1989 (1994)\nTo reflect the reviewer’s comment, we added a new section in Supplementary Information and\nreferenced it in the main manuscript as follows:\n(page 8, paragraph 2, line 2)\n“…from the focused laser beam reduces the material’s magnetic properties, including magnetization\nand coercivity, and lowers the energy barrier for magnetization reversal (Supplementary Information\nS8).”\n(page 9, paragraph 1, line 4)\n“This result demonstrates that photothermal skyrmion generation requires a laser power exceeding a\ncertain threshold, and it can be explained with an Arrhenius equation (See Supplementary Information\nS8 for details).”\n(2) Photothermal annihilation of skyrmion\nTwo neighbouring skyrmions generally repel each other, which prevents their overlap1. This\nrepulsive interaction grows exponentially as the distance between skyrmions decreases2, 3. Elevated\ntemperature from photothermal heating reduces the repulsive potential exponentially3, allowing the\nphotothermal tweezer to drag one skyrmion much closer to another than is possible at room temperature.\nOnce the temperature exceeds a critical threshold, the separating domain wall becomes unstable and\ntwo skyrmions begin to collapse and merge into a single state. This annihilation corresponds to a\nrelaxation from a higher-energy configuration with two confined skyrmions to a lower-energy state with\na single skyrmion, where the excess domain wall energy is released. Figure S14 shows the observation\nof photothermal annihilation of two skyrmions step by step.\nFigure S14 Photothermal skyrmion annihilation. (a, b) A single skyrmion is trapped by the photothermal\ntweezer and dragged toward another skyrmion. (c) The domain walls separating the two skyrmions becomes\ndemagnetized by local photothermal heating. (d) The merged skyrmion relaxes to the characteristic size and shape\nof typical skyrmions in our sample. Incident laser power, 11.8 mW; Sweeping speed, 360 nm/s.\nWe acknowledge that, unfortunately, our current experimental setup cannot resolve the detailed spin\ndynamics and characteristic timescales of annihilation. Direct measurement would require a time-\nresolved imaging system with sub-nanosecond temporal resolution and nanometer-scale spatial\nprecision, sufficient to capture the rapid evolution and collapse of domain wall textures. Such\ncapabilities are beyond the scope of this study. Nevertheless, we view the reviewer’s suggestion as\nhighly valuable and inspiring. Future works employing pump-probe magneto-optical microscopy, such\nas time-resolved X-ray MOKE microscopy4, 5, will allow direct observation of transient skyrmion\nannihilation dynamics and provide deeper insight into the microscopic mechanisms involved.\nReferences\n[1] Ge, Y., et al. Constructing coarse-grained skyrmion potentials from experimental data with Iterative\nBoltzmann Inversion Commun. Phys6, 30 (2023)\n[2] Brearton, R., van der Laan, G. & Hesjedal, T. Magnetic skyrmion interactions in the micromagnetic\nframework. Phys. Rev. B101, 134422 (2020)\n[3] Wang, Y., Wang, J., Kitamura, T., Hirakata, H. & Shimada, T. Exponential temperature effects on\nskyrmion-skyrmion interaction. Phys Rev. Applied11, 225-228 (2015)\n[4] Büttner, F., et al. Dynamics and inertia of skyrmionic spin structures. Nat. Phys.11, 225-228 (2015)\n[5] Donnelly, C., et al. Time-resolved imaging of three-dimensional nanoscale magnetizations\ndynamics. Nat. Nanotechnol.15, 356-360 (2020)\nTo reflect the reviewer’s comment, we added Figure S14 to Supplementary Note and referenced it in\nthe main manuscript as follows:\n(page 9, paragraph 1, line 11)\n“Furthermore, at sufficiently high laser power, two skyrmions can be induced to merge into a single\nskyrmion, enabling selective annihilation (Supplementary Information S9).”\n(3) Equation of motion of skyrmion in a photothermal potential\nThe key mechanism driving skyrmion dynamics in our system is the spatial gradient of the uniaxial\nanisotropy energy induced by localized laser heating, as described in Supplementary Information S1.\nThe anisotropy gradient imposes an effective force on skyrmions, thereby producing directed motion.\nThiscan be described within the framework of the Thiele equationS7, S8:\n𝑀𝑠𝑑 𝛼𝐺𝑀𝑠𝑑\nwhere is the electron gyromagnet𝐆ic ×ra𝐯tio−, is the𝑫 G∙i𝐯lb−ert∇ d𝐸aamnipsi=ng0 parameter,\n𝛾𝑒 𝛾𝑒\nis the gyroscopic vector, and is the dissipative tensor. A\n𝛾𝑒 𝛼𝐺 𝐆 = 𝐳̂∫𝐦∙\nsingle isolated skyrmion possess cylindrical symmetry, which reduces the dissipative tensor to\n(𝜕𝑥𝐦×𝜕𝑦𝐦) d𝐴 𝐷ij = ∫𝜕𝑖𝐦∙𝜕𝑗𝐦 d𝐴\ndiagonal form with nonzero elements . The gyroscopic vector is related to the\nskyrmion’s topological charge Q as . The anisotropy energy is given by\n𝐷𝑥𝑥 = 𝐷𝑦𝑦 = 𝐷0\n, where is the uniaxial anisotropy constant.\n𝐆 = 4π𝑄 𝐳̂ 𝐸anis =\nSolving th2e Thiele equation provides the radial and azimuthal components of the skyrmion velocity\n𝐾𝑢∫(1−𝑚𝑧) 𝑑𝑉 𝐾𝑢\nin cylindrical coordinates , under the condition that the laser-induced temperature profile is\nazimuthally isotropic ( ):\n(𝑠,𝜙,𝑧)\n𝜕𝐸anis/𝜕𝜙 = 0\n𝛾𝑒 𝐷0𝛼𝐺 ∂𝐾𝑢 2\n𝑣𝑠 = − 2 2 ∫(1−𝑚𝑧) 𝑑𝑉\n𝑀𝑠𝑑[(𝐷0𝛼𝐺) +(4𝜋𝑄) ] ∂𝑠\n𝛾𝑒 4𝜋𝑄 ∂𝐾𝑢 2\nHere, describes the d𝑣ri𝜙ft =mo−tion toward the2 laser spot 2centre, ∫wh(1ile− 𝑚 𝑧c)o r𝑑r𝑉esponds to the skyrmion\n𝑀𝑠𝑑[(𝐷0𝛼𝐺) +(4𝜋𝑄) ] ∂𝑠\nHall effect motion (rotation around the photothermal potential).\n𝑣𝑠 𝑣𝜙\nTo evaluate the integrals in the Thiele equation, we adopt a simplified ansatz for the Néel-type\nskyrmion magnetization profile:\nwith\n𝐦= sin𝜃(𝑠)𝐬̂+cos𝜃(𝑠)𝒛̂\n𝜋, for 𝑠 < 𝑅−𝜟/2\n𝜋 𝑅−𝑠 𝜟\n𝜃(𝑠)= { +𝜋( ), for 𝑅− < 𝑠 < 𝑅+𝜟/2,\nwhere R is the skyrmion radius a2nd is thΔe domain wall width2. Substituting this profile allows\n0, for 𝑠 > 𝑅+𝜟/2\nexplicit evaluation of the integrals, giving , ,\nΔ\n𝑄, a=nd± 1 𝐆 = 𝐳̂∫𝐦∙(𝜕𝑥𝐦×𝜕,𝑦 w𝐦h ) e rde𝐴 d =is ±th4e𝜋 f𝐳îlm𝐷 0 =\n3\nthickness. The skyrmion velocity compo 𝜋 ne 𝑅 nts then become2 depending on size parameters as:\n∫𝜕𝑥𝐦∙𝜕𝑥𝐦 d𝐴= ∫𝜕𝑦𝐦∙𝜕𝑦𝐦 d𝐴 = Δ ∫(1−𝑚𝑧) 𝑑𝑉 = 𝜋𝑅𝑑Δ\n(𝑅,Δ)\n4 2\n𝜋 𝑅 𝛾𝑒 𝛼𝐺 ∂𝐾𝑢\n𝑣𝑠(𝑅,Δ)= − 6 2\n𝑀𝑠 𝜋 𝑅 2 2 ∂𝑠\n[ 2 𝛼𝐺 +16𝜋 ]\nΔ\n2\n4𝜋 𝑅𝛾𝑒Δ 1 ∂𝐾𝑢\n𝑣𝜙(𝑅,Δ)= ∓ 6 2\n𝑀𝑠 𝜋 𝑅 2 2 ∂𝑠\n[ 2 𝛼𝐺 +16𝜋 ]\nΔ\nSince and the variation of M with temperature is negligible (Supplementary\ns\n1 2\nInform𝐾aetifofn= S𝐾1𝑢),− w\n2\ne𝜇 0a𝑀pp𝑠roximate . Using the measured linear dependence of on\n∂𝐾𝑢 ∂𝐾eff\ntemperatures (Supplementary Information S1) and the temperature profile from FEM simulation\n∂𝑠 ≈ ∂𝑠 𝐾eff\n(Supplementary Information S2), we estimate to be at a laser power of 7 mW.\nUsing the experimental parameters and the Gi ∂ lb 𝐾𝑢 ert damping param10eter o4f 0.015S9, S10, the radial and\n∂𝑠 1.59×10 J/m\nazimuthal velocities are calculated to be ~35 m/s and ~41 m/s, respectively. These calculated velocities\nare significantly higher than the experimentally observed values of ~1 m/s obtained with our\nphotothermal tweezer. This significant discrepancy reflects the strong influence of local pinning and\nmaterial disorder. These theoretical values represent an idealized defect-free case, where such\ndissipative effects are absent.\nReferences\n[S7] Thiele, A. A. Steady-state motion of magnetic domains. Phys. Rev. Lett. 30,230 (1973).\n[S8] de Assis, I. R., Mertig, I. & Göbel, B. Skyrmion motion in magnetic anisotropy gradients:\nAcceleration caused by deformation. Phys. Rev. B108, 144438 (2023)\n[S9] Ilhama, S., et al. Gilbert damping constants of Ta/CoFeB/MgO(Ta) thin films measured by optical\ndetection of precessional magnetization dynamics. Phys. Rev. B 89, 174416 (2014).\n[S10] Lattery, D. M., et al. Low Gilbert Damping Constant in Perpendicularly Magnetized\nW/CoFeB/MgO Films with High Thermal Stability. Sci. Rep. 8, 13395 (2018).\nTo address the reviewer’s comment and clarify these points, we added a new section including the\nequation of motion in Supplementary Information and revised the main manuscript as follows:\n(page 4, paragraph 2, line 3)\n“Skyrmion dynamics within this photothermal potential can be described by the Thiele equation,\nwhere the anisotropy gradient induced by local heating serves as the driving force (See Supplementary\nInformation S3).”\nComment 5:\nI think the upper limit of skyrmion motion speed needs to be addressed. This physical constraint is\ncritical for evaluating the method’s scalability.\nResponse to Comment 5:\nWe appreciate the valuable comment and inspiration of R1.\nThe Thiele equation analysis, as discussed in our response to Comment 4, provides the practical upper\nbound for skyrmion velocity under our present experimental conditions. This bound is estimated to be\n~35 m/s in an ideal defect-free medium, determined by the maximum anisotropy gradient achievable\nwith our current laser power and material parameters (see also Supplementary Information S3). The\nspeed could be increased by enhancing the anisotropy gradient, either through materials with a stronger\ntemperature dependence of anisotropy or by raising the incident laser power. In our current experimental\nsetup, stronger laser power leads to higher attainable skyrmion speeds without reaching an upper limit\n(Fig. 2c in the main manuscript).\nBeyond this practical regime, there exists a theoretical limit to skyrmion velocity, set by the\nmaximum group velocity of magnons, analogous to the relativistic limit for magnetic solitons63, 64. This\nlimiting velocity is formulated as2:\n2\nwhere A is the exchange stiffness, is\n𝑣\nt0h\n=\nthe e√le\n2\nc\n𝜇\ntr0o\n𝐴\nn\n𝛾\n𝑒g y\n,\nromagnetic ratio, and is the vacuum\npermeability. For our CoFeB material, with an estimated exchange stiffness of (see our\n𝛾𝑒 𝜇0\nresponse to Comment 4 of R1), the magnon group velocity is calculated to be m/s.\n𝐴 = 16 pJ/m\nskyrmion dragging velocity of ~1 m/s demonstrated by our photothermal tweezer. In real materials,\nthe effective velocity is predominantly limited by pinning interactions with local defects. Since\ndepinning (escape from pinning sites) is a thermally activated process, increasing the sample\ntemperature and incident laser power can help skyrmions overcome pinning barriers more rapidly and\nenhance the attainable transfer speed. Furthermore, employing materials with smaller activation\nenergies and lower defect densities will enable access to the intrinsic upper limit of skyrmion motion\nspeed. Inspired by the reviewer’s comment, we plan to pursue future studies aimed at systematically\nprobing and challenging the upper velocity limit of skyrmion transport by photothermal tweezers.\nReferences\n[63] Caretta, L. et al. Relativistic kinematics of a magnetic soliton. Science370, 1438-1442 (2020)\n[64] How, H., O’Handley, R. C. & Morgenthaler, F. R. Soliton theory for realistic magnetic domain-\nwall dynamics. Phys. Rev. B40, 4808-4817 (1989)\nTo reflect the reviewer’s comment, we added the following sentence and relevant references in the\nmain manuscript as follows:\n(page 7, paragraph 1, line 2)\n“…We note that, beyond this stochastic regime, the skyrmion velocity is ultimately bounded by two\nfactors: a practical limit, determined by the maximum anisotropy gradient and local pinning density\n(Supplementary Information S5), and a fundamental limit, set by the magnon group velocity63, 64. Under\nour current experimental conditions, however, the skyrmion speed is governed primarily by local\npinning.”\nComment 6:\nThermal control is inherently susceptible to stochasticity, raising concerns:\n- How is the topological stability of skyrmions ensured under temperature gradients? Experimental\nor theoretical evidence of structural resilience is needed.\n- Given the authors’ claim of “robust, reversible, and scalable” manipulation, what strategies mitigate\nthe stochastic nature of thermal control to ensure repeatability and robustness?\nResponse to Comment 6:\nWe appreciate R1 for raising the important points.\nThermal stability of topological textures is indeed crucial for further application of photothermal\ntweezers. To verify that skyrmions maintain their topological integrity under elevated temperatures and\nthermal gradients, we performed spin-orbit torque (SOT)-driven transport measurements. The response\nof skyrmions to SOT is highly sensitive to their topological structure, particularly the chirality of in-\nplane spins at the domain wallS14. For example, Néel-type skyrmions move parallel to the electric\ncurrent, and Bloch-type skyrmions drift in the orthogonal directionS15. Nontopological magnetic\nbubbles will not move efficiently under SOTS14.\nFigure S9 shows SOT-driven motion of skyrmions at 297 K and 350 K. In both cases, the skyrmions\nmove consistently in the direction parallel to the current, and their speed increases with temperature.\nNotably, 350 K exceeds the maximum temperature reached under laser heating at 7 mW (see our\nresponse to Comment 2 of R1 and Supplementary Information S2), which is higher than the laser powers\nused in the main manuscript. This confirms that the topological structure of skyrmions in the employed\nmagnetic material remains stable within the temperature range generated by laser heating in our\nphotothermal tweezer experiments.\nFigure S9 SOT-driven transport of skyrmions at elevated temperature (a, b) Skyrmion motion at (a) 297 K,\nand (b) 350 K per single electric current pulse. is the pulse duration. Scale bar, 5 m. is the external\nmagnetic field.\n𝝉 𝝁𝟎𝑯𝒛\nWe also examined the topological stability of skyrmions under the thermal gradient generated by the\nphotothermal tweezer (Fig. S10), using data from the photothermal pinning experiments presented in\nFig. 3 of the main manuscript. In each case, a single skyrmion was trapped using the tweezer with\ndifferent laser powers corresponding to distinct potential well depths: 4.14 mW for a shallower potential\nwell (Fig. S10a) and 5.06 mW for a deeper potential well (Fig. S10b), and its SOT-driven response was\nmeasured. In the shallower well, the skyrmion escaped the confinement, whereas in the deeper well, it\nremained trapped but exhibited a small displacement within the well. These results, together with the\nelevated-temperature stability test in Fig. S9, confirm that skyrmions maintain their topological\nstructure under both uniform heating and localized photothermal gradients.\nFigure S10 SOT-driven motion of skyrmions under photothermal pinning. (a, b) Images of skyrmion before\n(left) and after (right) a single electric current pulse in the (a) shallow potential well, obtained with a tweezer laser\npower of 4.14 mW, and (b) deep potential well, obtained with a tweezer laser power of 5.06 mW. The current\npulse has a magnitude of and a duration of 100 ms. Scale bar, 10 m.\n𝟗 𝟐\n𝟓.𝟏𝟗×𝟏𝟎 𝐀/𝐦\nReferences\n[S14] Jiang, W. et al. Blowing magnetic skyrmion bubbles Science. 349, 283-286 (2015).\n[S15] Dai, B. et al. Electric field manipulation of spin chirality and skyrmion dynamic. Sci. Adv.9,\neade6836 (2023).\nTo reflect the reviewer’s comment, we added a new section in Supplementary Information containing\nthe aforementioned details and referenced it in the main manuscript.\n(page 8, paragraph 1, line 8)\n“Finally, we confirmed the stability of the skyrmion topology under both elevated uniform\ntemperatures and localized photothermal gradients by examining spin–orbit torque-driven transport\n(Supplementary Information S7).”\nWe also acknowledge that our original description may have overstated the robustness of\nphotothermal tweezers, given the stochastic nature of thermal effects. While thermal effects can in\ngeneral introduce variability, our approach mitigates this by enabling controlled and repeatable\npreparation of skyrmion ensembles through localized and programmable heating. This reconfigurability\nnot only ensures experimental repeatability but also allows prompt adaptation to different skyrmion-\nhosting materials. Nonetheless, reflecting the reviewer’s comment, we revised and toned down the\nrelevant sentence in the manuscript as:\n(page 1, paragraph 1, line 11)\n“This approach opens new avenues towards reconfigurable and scalable architectures for future\nskyrmionic device applications and enriches studies of light–quasiparticle interactions in solid-state\nsystems.”\nResponse to the Reviewer #2\nGeneral Comment:\nManipulating individual or groups of particles by optical means, particularly with optical tweezers,\ngoes back to Ashkin, and since that time, this technique has been widely applied to biological systems,\nsoft matter, condensed matter, and atomic systems. An interesting question is whether optical tweezer\ntechniques can also be used to manipulate emergent quasiparticles such as skyrmions, magnetic\ntextures, magnetic vortices, and other particle textures that arise in condensed matter.\nHere, the authors use a photothermal optical tweezer to trap and move, create and annihilate\nskyrmions. The ability to radially manipulate skyrmions on the individual level opens up new device\npossibilities as well as new methods for understanding skyrmion dynamics and skyrmion-skyrmion\ninteractions. Additionally, this technique could be extended to examine many of the same effects that\nhave been explored in colloidal systems, such as trap arrays, ratchets, holographic traps, dynamic traps,\nBessel beams, and so on, which could open up a new field of optico-skyrmionics.\nIn addition to manipulating the skyrmions, the authors discuss issues directly relevant to the skyrmion\nsystems. In colloidal systems, the substrate is often smooth; however, in the skyrmion case, there can\nbe quenched disorder or pinning effects on the skyrmions, and the authors study how often the skyrmion\nneeds to be dragged, which in some cases occurs 85% of the time. They also find sweep rate dependence\nand discuss the role of local heating from the photothermal trap.\nAnother feature that makes this work different from optical tweezer studies in other systems, such as\ncolloids and atomic systems, is that the authors demonstrate that this technique can be used to\nindividually create and delete skyrmions, which is relevant for devices.\nOverall, the work is very strong, opens a new aspect of research for skyrmion physics, and describes\na technique that could be used for other emergent particle-like textures. The text is clear, and Figure 1\nis particularly elucidating as it nicely summarizes the four main aspects of the work: moving, pinning,\ncreation, and annihilation of skyrmions. The authors also show how potential devices could be made\nusing a grid-like trapping system.\nI have some comments for the authors to address, after which the paper can be published, where I\nexpect it could have a very high impact.\nResponse to General Comment:\nWe sincerely thank Reviewer #2 (R2) for the thoughtful comments and constructive assessment of\nour work. We are glad to see that R2 finds the significance and potential of our approach and inspires\nthe suggestions for extending our technique to trap arrays, ratchets, holographic and dynamic traps, and\nBessel beams. We also agree that these concepts, which have been demonstrated in the colloidal\nsystems, are natural and promising extensions of our platform to explore in future studies. We have\naddressed all the comments given by R2 and revised the manuscript to contain all the suggested\nreferences, based on his/her suggestions as listed below.\nComment 1:\nThere has been some previous theory work describing how skyrmions could be manipulated with\noptical tweezers that should be mentioned.\nWang et al propose that skyrmions could be manipulated with optical tweezers and used\nmicromagnetic simulations to confirm this.\nThe optical tweezers of skyrmions, Xi-Guang Wang, Levan Chotorlishvili, Vitalii K. Dugaev, Arthur\nErnst, Igor V. Maznichenko, Nikita Arnold, Chenglong Jia, Jamal Berakdar, Ingrid Mertig & Józef\nBarnaś, npj Computational Materials volume 6, Article number: 140 (2020)\nAdditionally, there have been some numerical studies on the individual manipulation of skyrmions\nwith moving traps or tips for different sweep rates and types of pinning. This work mentions that such\nmanipulation could be achieved with optical trapping or some kind of magnetic tip.\nDynamics and nonmonotonic drag for individually driven skyrmions, C. Reichhardt and C. J. O.\nReichhardt, Phys. Rev. B 104, 064441 (2021)\nCommensuration effects on skyrmion Hall angle and drag for manipulation of skyrmions on two-\ndimensional periodic substrates, C. Reichhardt and C. J. O. Reichhardt, Phys. Rev. B 105, 214437\n(2022)\nAlso the following review article discussing skyrmion pinning has a section discussing manipulation\nof a single skyrmion with some form of local tip or with optical means.\nStatics and dynamics of skyrmions interacting with disorder and nanostructures, C. Reichhardt,\nC. J. O. Reichhardt, and M. V. Milošević, Rev. Mod. Phys. 94, 035005 – Published 20 September,\nOgawa, N., W. Koshibae, A. J. Beekman, N. Nagaosa, M. Kubota, M. Kawasaki, and Y. Tokura,\n2015, “Photodrive of magnetic bubbles via magnetoelastic waves,” Proc. Natl. Acad. Sci. U.S.A. 112,\n8977–8981.. The current pulse has a magnitude of 5.19 × 10⁹ A/m² and a duration of 100 ms.\nResponse to Comment 1:\nWe thank R2 for pointing out the relevant theoretical studies on the optical manipulation of magnetic\nskyrmions, as well as a related experimental work on magnetic bubbles. In response, we have cited\nthese works, together with an additional relevant reference that we found, and revised the introduction\nand conclusion of the main manuscript to acknowledge their contributions, as detailed below.\n(page 3, paragraph 1, line 3)\n“… Extending such capabilities to emergent quasiparticles is therefore a natural and timely pursuit.\nTo date, optical trapping and transport has been experimentally realized for magnetic bubbles in\nrelatively thick magnetic films44 and for Abrikosov vortices in superconductors45. For magnetic\nskyrmions, however, optical tweezing has so far remained theoretical, requiring extremely localized\noptical fields and strong magnetoelectric coupling46. Other theoretical works have explored skyrmion\nmanipulation using moving traps or tips, as well as skyrmion dynamics in periodic or disordered pinning\nlandscapes47–49.”\n(page 10, paragraph 2, line 15)\n“In particular, holographic photothermal tweezers could provide a powerful platform for studying\nskyrmions dynamics on engineered periodic or disordered pinning landscapes47–49.”\nReferences\n[44] Ogawa, N., et al. Photodrive of magnetic bubbles via magnetoelastic waves. Proc. Natl. Acad.\nSci. U.S.A.112, 8977-8981 (2015).\n[45] Veshchunov, I. S., et al. Optical manipulation of single flux quanta. Nat. Commun. 7, 12801\n(2016).\n[46] Wang, XG., et al. The optical tweezer of skyrmions. npj Comput. Mater6, 140 (2020)\n[47] Reichhardt, C. & Reichhardt, C. J. O. Dynamics and nonmonotonic drag for individually driven\nskyrmions. Phys. Rev. B104, 064441 (2021).\n[48] Reichhardt, C. & Reichhardt, C. J. O. Commensuration effects on skyrmion Hall angle and drag\nfor manipulation of skyrmions on two-dimensional periodic substrates. Phys. Rev. B105, 214437\n(2022).\n[49] Reichhardt, C., Reichhardt, C. J. O. & Milošević, M. V. Statics and dynamics of skyrmion\ninteracting with disorder and nanostructures. Rev. Mod. Phys.94, 035005 (2022).\nComment 2:\nThe authors do a nice job of discussing the optical manipulation with optical tweezers for colloids,\natoms, and biological systems. They could mention the original work of Ashkin work for this.\nA. Ashkin. History of optical trapping and manipulation of small-neutral particle, atoms, and\nmolecules.” IEEE J. Sel. Top. Quantum Elec.6, 841–856 (2000).\nResponse to Comment 2:\nWe appreciate R2’s comment and agree that including the original work by Ashkin is important for\ncontext. We have therefore added the relevant references to the main manuscript.\n(page 2, paragraph 3, line 1)\n“Optical tweezers, first demonstrated by Ashkin in 198630, 31, use tightly focused laser beams to provide\nnoncontact and precise control over physical objects…”\nReferences\n[30] Ashkin, A., Dziedzic, J. M., Bjorholm, J. E. & Chu, S. Observation of a single beam gradient\nforce optical trap for dielectric particles. Opt. Lett.11 288-290 (1986)\n[31] Ashkin, A. History of optical trapping and manipulation of small-neutral particle, atoms, and\nmolecules. IEEE J. Sel. Top. Quantum Elec.6 841-856 (2000)\nComment 3:\nThe authors could also mention some new directions, which could include optical arrays, ratchets,\nholographic traps, and so on, similar to the optical tweezers work done in colloidal systems.\nA revolution in optical manipulation, D. G. Grier, Nature 424, 810-816 (2003).\nResponse to Comment 3:\nWe thank R2 for the insightful suggestion. In the revised manuscript, we have added a sentence on\npotential new directions, inspired by optical tweezer studies in colloidal systems, to the conclusion of\nthe main manuscript as\n(page 10, paragraph 2, line 11)\n“Furthermore, advances in wavefront engineering with spatial light modulators could enable\nphotothermal tweezers with complex configurations such as trap arrays, ratchets, and tailored beam\nprofiles68 opening opportunities for sophisticated studies of skyrmion interactions and coupling with\nother spin textures.”\nReference\n[68] Grier, D. G. A revolution in optical manipulation. Nature.424, 810-816 (2003).\nComment 4:\nThe authors should mention some experiments showing optical manipulation for single vortices in\ntype-II superconductors, which have also been used to spell out letters.\nOptical manipulation of single flux quanta, I. S. Veshchunov, W. Magrini, S. V. Mironov, A. G.\nGodin, J.-B. Trebbia, A. I. Buzdin, Ph. Tamarat & B. Lounis, Nature Communications volume 7, Article\nnumber: 12801 (2016)\nResponse to Comment 4:\nWe thank R2 for pointing out this important work on optical manipulation of single vortices in type-\nII superconductors. We have cited this study and added a sentence to the introduction of the main\nmanuscript.\n(page 3, paragraph 1, line 4)\n“To date, optical trapping and transport has been experimentally realized for magnetic bubbles in\nrelatively thick magnetic films44 and for Abrikosov vortices in superconductors45.”\nReference\n[44] Ogawa, N., et al. Photodrive of magnetic bubbles via magnetoelastic waves. Proc. Natl. Acad.\nSci. U.S.A.112, 8977-8981 (2015).\n[45] Veshchunov, I. S., et al. Optical manipulation of single flux quanta. Nat. Commun.7, 12801 (2016).\nResponse to the Reviewer #3\nGeneral Comment:\nKim and coworkers report an experimental study of optical manipulation of spin textures in a CoFeB\nthin film with interface-induced antisymmetric exchange interactions. These spin textures are\ntopologically nontrivial and can be treated as skyrmion quasiparticles. The authors focus on the\ndynamics of skyrmion quasiparticles controlled by an optical tweezer and demonstrated a high precision\ntrapping and transport of skyrmions via laser-induced photothermal potentials. The authors also\ndemonstrated that the photothermal effect can lead to the creation or annihilation of a single individual\nskyrmion. They show a programmable control of skyrmions in two dimensions can be realized by\ncombining optical and electric manipulations. They suggested the programmable creation, annihilation,\nand manipulation of individual skyrmions will be useful device applications, such as probabilistic\ncomputing and reconfigurable logic computing. I think this manuscript is well written, and the study on\nthe precise control of particle-like skyrmions through optical methods is both interesting and valuable\nto the skyrmion community. Since the initial observation of skyrmions in chiral magnets, most research\nin the field has focused on controlling and manipulating skyrmions using electric currents, magnon\ncurrents, and thermal currents. As far as I am aware, there are only a few reports on the creation and\nmanipulation of skyrmions using optical lasers. However, as the authors mentioned in the introduction,\noptical tweezers have actually been used in many different fields to control particle-like objects. I\ntherefore agree with the authors that the optical manipulation of skyrmion quasiparticles is worth\nexploring. For the above reasons, I think this manuscript is suitable for publication in the journal. Before\nacceptance, the manuscript could be improved through a minor revision; see comments below.\nResponse to General Comment:\nWe sincerely thank Reviewer #3 (R3) for the thoughtful comments and constructive assessment of\nour work. We are glad to see that R3 found the significance and potential of our approach to the\nskyrmion community. We have addressed all the comments given by R3 and revised the manuscript\naccordingly, as listed below.\nComment 1:\nThe authors should highlight relevant published studies on the optical manipulation of magnetic\nbubbles and skyrmions in the introduction, and clearly make a link to what they are exploring and\nindicate how their study advances the field. There are some important references, for example, see\nhttps://www.pnas.org/doi/10.1073/pnas.1504064112,\nhttps://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.054421, and\nhttps://pubs.acs.org/doi/abs/10.1021/acs.nanolett.8b03653.\nResponse to Comment 1:\nWe appreciate the reviewer’s comment. To reflect the reviewer’s comment, we added some important\nreferences and brief introductions on them, especially for optical manipulation of magnetic bubbles and\nlaser-induced creation of nucleation of skyrmions, in main manuscript.\n(page 3, paragraph 1, line 3)\n“Extending such capabilities to emergent quasiparticles is therefore a natural and timely pursuit. To\ndate, optical trapping and transport has been experimentally realized for magnetic bubbles in relatively\nthick magnetic films44 and for Abrikosov vortices in superconductors45. For magnetic skyrmions,\nhowever, optical tweezing has so far remained theoretical, requiring extremely localized optical fields\nand strong magnetoelectric coupling46. Other theoretical works have explored skyrmion manipulation\nusing moving traps or tips, as well as skyrmion dynamics in periodic or disordered pinning landscapes47–\n49. Aside from optical tweezing, another line of research, optical generation of skyrmionic textures,\nhas recently been demonstrated50–52. Although ultrafast laser heating produces multiple skyrmions\nsimultaneously, with their number and position determined stochastically. Achieving programmable\ncreation and control of individual skyrmions would extend the well-established paradigm of optical\ntweezers to topological quasiparticles, establishing a powerful new platform for controlled studies of\nspin textures.”\nReferences\n[44] Ogawa, N., et al. Photodrive of magnetic bubbles via magnetoelastic waves. Proc. Natl. Acad.\nSci. U.S.A.112, 8977-8981 (2015).\n[45] Veshchunov, I. S., et al. Optical manipulation of single flux quanta. Nat. Commun. 7, 12801\n(2016).\n[46] Wang, XG., et al. The optical tweezer of skyrmions. npj Comput. Mater6, 140 (2020)\n[47] Reichhardt, C. & Reichhardt, C. J. O. Dynamics and nonmonotonic drag for individually driven\nskyrmions. Phys. Rev. B104, 064441 (2021).\n[48] Reichhardt, C. & Reichhardt, C. J. O. Commensuration effects on skyrmion Hall angle and drag\nfor manipulation of skyrmions on two-dimensional periodic substrates. Phys. Rev. B105, 214437\n(2022).\n[49] Reichhardt, C., Reichhardt, C. J. O. & Milošević, M. V. Statics and dynamics of skyrmion\ninteracting with disorder and nanostructures. Rev. Mod. Phys.94, 035005 (2022).\n[50] Fujita, H. & Sato, M. Ultrafast generation of skyrmionic defects with vortex beams: Printing\nlaser profiles on magnets. Phys. Rev. B 95, 054421 (2017).\n[51] Khela, M. et al. Laser-induced topological spin switching in a 2D van der Waals magnet. Nano\nLett. 14, 1378 (2023).\n[52] Fujita, H. & Sato, M.Ultrafast generation of skyrmionic defects with vortex beams: Printing\nlaser profiles on magnets. Phys. Rev. B 95, 054421 (2017).\nComment 2:\nThe role of temperature gradient–induced forces (e.g., magnonic spin Seebeck effect or\nthermomagnonic torques) is not fully disentangled from the optical potential mechanism. The authors\nattribute skyrmion motion primarily to an attractive photothermal potential well. However, skyrmions\nare known to exhibit drift under thermal gradients due to magnon currents. Could the authors clarify\nwhether such effects contribute to the observed dynamics? Have control experiments (e.g., different\nlaser spot sizes or reversed gradients) been performed to isolate this effect?\nResponse to Comment 2:\nWe thank Reviewer 3 for this insightful comment. Temperature gradients can drive skyrmion motion\nvia two different mechanisms: (i) entropic torques, arising from the temperature dependence of\nmagnetic parameters and the resulting change in free energy1, 2, and (ii) thermomagnonic torques,\nassociated with angular momentum transfer from thermal magnon currents3–5. In our manuscript, the\nterm “photothermal potential” refers to the entropic torque mechanism, i.e., the reduction of free energy\nupon local heating, which we identify as the dominant driving force in our optical tweezer scheme. It\nis unfortunately difficult to completely rule out the contribution of thermomagnonic torques in our\ncurrent experiments, since both mechanisms generally act in the same direction, driving skyrmions\ntoward the hotter region4, 5. However, multiple theoretical studies of domain wall motion under thermal\ngradients have consistently shown that entropic torques dominate over momentum transfer from\nmagnons1–5.\nFor a quantitative comparison between the contributions of magnonic and entropic torques, we\nestimate the velocity of a domain wall under magnonic spin-transfer torque as6:\n𝛽 𝛾𝑒ℏ\nwhere , , , , and J are the non𝑣a⃗dMia=ba−ticity par a𝐽⃗mmeter, the Gilbert damping parameter, the\nm 𝛼G 𝑀s\ngyromagnetic ratio, the saturation magnetization, and the magnon current density, respectively. Since\n𝛼G 𝛾e 𝑀s\ngenerally has the same order of magnitude as , . The thermally induced magnon current\ndensity is given by\n𝛽 𝛼G 𝛽/𝛼G ≈ 1\n𝑘𝐵 𝐹0\nwhere is the magnon wavelength, is𝐽⃗ mthe= te−mper2ature gr∇a𝑇dient, and is a coefficient from the\n6𝜋 λℏ𝛼G\nkinetic theory of magnonic spin transfer torque6. The magnon wavelength is expressed as7, 8:\n𝜆 ∇𝑇 𝐹0 ≈ 1\n2𝑔𝜇B𝐴\n𝜆 = √\nwhere is the exchange stiffness, is the Landé\n𝑀\nf𝑠a\n𝑘\nc𝐵to\n𝑇\nr, and is the Bohr magneton. Using\nfor the exchange stiffness (see our response to Comment 4 of Reviewer 1 and Supplementary\n𝐴 𝑔 𝜇B 𝐴 =\nInformation S8 for details), we estimate . For of ~23.5 at a laser power of 7\n16 pJ/m\nmW (Supplementary Information S2), this yields and . This\n𝜆 ≈ 0.43 𝑛𝑚 ∇𝑇 K/μm\nmagnonic velocity is more than two orders of magnitude sma2l7ler −th2an− 1the entropic-torque-driven\n𝐽m ≈ 8.1×10 m s 𝑣⃗M ≈0.20 m/s\nvelocity of ~35 m/s under the same conditions (see our response to Comment 4 of Reviewer 1 and\nSupplementary Information S3).\nWe note that thermomagnonic-torque-driven motions of domain walls or skyrmions have been\nexperimentally observed in magnetic insulators, but only under extremely small thermal gradients (~10\nmK/mm) and very low damping ( )6,10. In such cases, slowly varying temperature profiles\nsuppress entropy gradients across magnetic spin structures, while long magnon lifetime allows\n𝛼G < 0.008\nmagnonic torques to dominate. In our study, on the other hand, highly localized thermal gradients (>104\nK/nm) within the laser spot induce substantial entropy changes across the skyrmion and its domain wall\nstructure, strongly modifying magnetic parameters and maximizing the entropic torque contribution.\nFor aforementioned reasons, we conclude that entropic torques provide the dominant driving force\nin our optical tweezer, with thermomagnonic contributions negligible under our conditions.\nNevertheless, we agree that quantitative comparison is important and view this as a valuable direction\nfor future studies. Control experiments are currently challenging due to defect pinning and limited\nmeasurement capabilities, but employing low-damping magnetic insulators in future could allow direct\ncomparison of global thermomagnonic torque and localized entropic torques, and even enable the\nconcept of magnonic trapping of skyrmions.\nReferences\n[1] Moretti, S., Raposo, V., Martinez, E. & Lopez-Diaz, L. Domain wall motion by localized\ntemperature gradients. Phys. Rev. B95, 064419 (2017).\n[2] Schlickeiser, S., Ritzmann, U., Hinzke, D. & Nowak, U. Role of Entropy in Domain Wall Motion\nin Thermal Gradients. Phys. Rev. Lett.113, 097201 (2014).\n[3] Ritzmann, U., Hinzke, D. & Nowak, U. Propagation of thermally induced magnonic spin currents.\nPhys. Rev. B89, 024409 (2014).\n[4] Wang, X. S. & Wang, X. R. Thermodynamic theory for thermal-gradient-driven domain-wall\nmotion. Phys. Rev. B90, 014414 (2014).\n[5] Kim, S. K. & Tserkovnyak, Y. Landau-Lifshitz theory of thermomagnonic torque. Phys. Rev. B92,\n020410 (2015).\n[6] Jiang, W., et al. Direct Imaging of Thermally Driven Domain Wall Motion in Magnetic Insulators.\nPhys. Rev. Lett. 110, 177202 (2013).\n[7] Cornelissen, L. J., et al. Magnon spin transport driven by the magnon chemical potential in a\nmagnetic insulator. Phys. Rev. B94, 014412 (2016).\n[8] Šipr, O., Mankovsky, S. & Ebert, H. Spin wave stiffness and exchange stiffness of doped permalloy\nvia ab initio calculations. Phys. Rev. B100, 024435 (2019).\n[9] K-W. Moon, et al. A spin torque meter with magnetic facet domains. Nat. Commun. 9, 3788 (2018)\n[10] Yu, X., et al. Real-space observations of 60-nm skyrmion dynamics in an insulating magnet under\nlow heat flow. Nat. Commun.12, 5079 (2021)\nAs we responded to the comment, although a detailed analysis of magnon contributions remains\noutside the scope of this study, we have revised the manuscript with relevant references as follows:\n(page 4, paragraph 2, line 7)\n“We note that thermomagnonic torques arising from thermal gradients may also influence skyrmion\nmotion58, but their contribution is typically weaker than that of the photothermal potential59, 60.”\nReferences\n[58] Yu, X., et al. Real-space observations of 60-nm skyrmion dynamics in an insulating magnet under\nlow heat flow. Nat. Commun.12, 5079 (2021)\n[59] Moretti, S., Raposo, V., Martinez, E. & Lopez-Diaz, L. Domain wall motion by localized\ntemperature gradients. Phys. Rev. B95, 064419 (2017).\n[60] Schlickeiser, S., Ritzmann, U., Hinzke, D. & Nowak, U. Role of Entropy in Domain Wall Motion\nin Thermal Gradients. Phys. Rev. Lett.113, 097201 (2014).\nAdditional minor changes\nWe additionally revise the main manuscript with minor changes to improve the English and phrasing,\nas follows:\n(page 1, paragraph 1, line 3)\n“…experimental control of individual skyrmions has so far relied mainly on global stimuli such as\nelectric currents, magnetic fields, and surface acoustic waves. Efforts to achieve precise skyrmion\npositioning are significantly hampered by the skyrmion Hall effect and defect pinning. Here, we\ndemonstrate high-precision trapping and transport of individual skyrmions using a photothermal\npotential well, thereby extending optical manipulation into the quasiparticle realm.”\n(page 2, paragraph 1, line 1)\n“Magnetic skyrmions are topologically nontrivial quasiparticles characterized by a swirling spin\nconfiguration. Their robustness against external perturbations1 and high electrical mobility under low\ncurrent density2 make skyrmions strong candidates for energy-efficient information carriers in memory\ndevices, logics, and unconventional computing architectures3–8. Another distinctive feature of\nskyrmions is the emergent magnetic field originating from their topology, which gives rise to\nphenomena such as the skyrmion Hall effect9, 10 and the topological Hall effect11, 12. Suppressing the\nskyrmion Hall effect13–15 is necessary for efficient skyrmion transport, the topological Hall effect of\nelectrons enables all-electrical skyrmion detection16. Recently, interactions of skyrmions with spin\ntextures17, 18, magnons19, 20, and photons21 have been reported leading to various emergent phenomena\nanalogous to particle–antiparticle interactions, Landau levels, and band structure reconstruction.\nConsequently, magnetic skyrmions provide a promising platform not only for demonstrating advanced\nspintronic devices and but also for the study of rich dynamics and fundamental physics of topological\nquasiparticles”\n(page 2, paragraph 2, line 1)\n“Precise and programmable control of individual skyrmions is crucial both for systematic studies and\nfor the reliable operation of skyrmionic devices. Conventional electric current-driven techniques,\nhowever, face significant limitations: the applied current acts on multiple skyrmions simultaneously,\nreducing experimental selectivity and flexibility22, 23. In addition, electrical transport and manipulation\nof magnetic skyrmions are constrained by the skyrmion Hall effect, which inherently deflects their\ntrajectories9, 10, and defect pinning, which leads to unpredictable stochastic motion24, 25. Alternative\nmethods based on surface acoustic waves26 or heat flow27,28 present similar drawbacks. A recent\napproach utilizing a magnetic field gradient from a magnetic force microscopy probe29 has\ndemonstrated single-skyrmion manipulation, but it is constrained by slow operation speed and the\ninability to control and observe skyrmions simultaneously.”\n(page 3, paragraph 1, line 2)\n“With optical tweezers, particle ensembles can be assembled on demand, …”\n(page 3, paragraph 2, line 1)\n“In this work, we introduce optical manipulation of skyrmions, magnetic topological quasiparticles\nin a spin system, and demonstrate its unique advantages. A micron-scale photothermal potential well,\ninduced by focused laser incidence, enables precise two-dimensional tweezing and isolation of\nindividual skyrmions, even overcoming the spin–orbit torque generated by electric current pulses.\nBeyond the reach of conventional optical tweezers, this photothermal approach enables deterministic\ncreation and annihilation of individual skyrmions. By integrating this optical control with electrical\ntransport, we establish fully programmable manipulation of skyrmions in two dimensions, providing a\nversatile platform for systematic studies of skyrmion dynamics and interactions, and opening new\navenues toward reconfigurable architecturesfor quantum spintronic applications”\n(page 4, paragraph 1, line 1)\n“The core of our optical manipulation approach of individual skyrmions is a micrometer-scale\nphotothermal potential well generated by focused laser incidence (Fig. 1a). In magnetic systems with\nthe presence of the interfacial Dzyaloshinskii–Moriya interaction (DMI) and the perpendicular\nmagnetic anisotropy (PMA), the energy density of a chiral domain wall (DW) can be expressed as53, 54\n. Here, is the exchange stiffness, is the effective PMA energy\ndensity per volume, is ln t 2 he DM2I energy density per surface, is the saturation magnetization, and d\n𝑈 = 4√𝐴𝐾eff−𝜋𝐷+ 𝜋 𝜇0𝑀𝑠𝑑 𝐴 𝐾eff\nis the film thickness. As the temperature increases, thermal fluctuations disrupt magnetic ordering,\n𝐷 𝑀𝑠\nreducing key magnetic parameters55. According to Bloch’s law, the saturation magnetization\ndecreases as the temperature approaches the Curie temperature, whereas scales as55 . Similarly,\n𝑀𝑠\nboth and decrease due to thermal agitation56, 57. Consequently, while the DMI ene2rgy density\n𝐴 𝑀𝑠\n( ) increases, all other contributions to total energy density decrease in total energy density with\n𝐾eff 𝐷\ntemperature. By measuring and as a function of temperature, we confirmed that the dominant\n−𝜋𝐷\nfactor driving the reduction in total energy density is the decrease in (Supplementary Information\n𝐾eff 𝑀𝑠\nS1).”\n𝐾eff\n(page 4, paragraph 2, line 5)\n“By steering the laser beam, individual skyrmions can be selectively dragged to desired locations or\npinned at a specific sites, effectively counteracting motion induced by electric currents (Figs. 1b and\n1c).”\n(page 4, paragraph 3, line 2)\n“When local heating exceeds a certain threshold temperature, the irradiated region undergoes\ndemagnetization. Because the heated area has much reduced coercivity, the local magnetization flips\ndue to the small stray field from the surrounding magnetic domains and stabilizes into a skyrmion.\nMoreover, by bringing one skyrmion close to another with our photothermal tweezer, we can induce\ncontact between their DWs, causing them to merge into a single skyrmion. The size and shape of the\nmerged skyrmion then rapidly relax to those characteristic of the host magnetic medium.”\n(page 7, paragraph 2, line 2)\n“… preventing displacement under external electric current injection.”\n(page 7, paragraph 2, line 8)\n“The displacement of the skyrmions from their initial positions is shown in Fig. 3b.”\n(page 7, paragraph 3, line 1)\n“…thereby increasing the skyrmion resistance to external driving current. We statistically analyzed\nthe displacement of a skyrmion induced by a single electric pulse depending on the laser power and the\ncurrent density. Figure 3c shows box plots of the first and third quartiles, along with the median, based\non 20 trials per condition. To minimize inhomogeneous spatial variations in intrinsic pinning, all\nmeasurements were performed on skyrmions at the same location (for further details, see the Methods\nsection). Skyrmion transport under current pulses…”\n(page 9, paragraph 1, line 1)\n“The probability of skyrmion generation as a function of the incident laser power is shown in Fig.\n4b. The laser was applied for 1 s, and the probability was evaluated over 20 trials at different locations\nfor each power level. Below 3 mW, no skyrmions were generated, whereas above 4 mW, the skyrmion\nformation probability increased dramatically, ultimately reaching deterministic creation. This result\ndemonstrates that photothermal skyrmion generation requires a laser power exceeding a certain\nthreshold, and it can be explained with an Arrhenius equation (See supplementary Information S8 for\nmore details). Conventional skyrmion creation methods using external magnetic fields66, 67, ultrafast\nlasers51, 52, and electrical current pulses65, are limited to either generating a large number of skyrmions\nstochastically or restricting their formation to predefined locations such as electrodes or tracks.”\n(page 10, paragraph 2, line 7)\n“By combining collective electric transport for large-scale skyrmion motion with targeted\nphotothermal manipulation of selected skyrmions, we achieved efficient, fully programmable two-\ndimensional manipulation.”\n(page 10, paragraph 2, line 11)\n“Finally, the programmable creation, manipulation, and annihilation of individual skyrmions will\nexpand…”\nResponse to the Reviewer #1\nGeneral Comment:\nThe authors addressed my concerns. I support the publication of this manuscript.\nResponse to General Comment:\nWe are delighted that Reviewer #1 found our revisions satisfactory and recommended our manuscript\nfor publication. We are grateful for his/her insightful comments and suggestions, which substantially\nenhanced the clarity and quality of our work.\nResponse to the Reviewer #2\nGeneral Comment:\nThe authors have satisfactorily addressed all of the referee comments. I recommend the paper for\npublication without further change.\nResponse to General Comment:\nWe are pleased to see that Reviewer #2 was satisfied with our responses and has recommended the\npublication of our revised manuscript. We sincerely appreciate his/her valuable comments and\nsuggestions, which have greatly helped us improve the quality of our results and the manuscript.\nResponse to the Reviewer #3\nGeneral Comment:\nThe authors have made significant revisions regarding all the comments by the referees. Now the\nmanuscript looks much better and can be published in NC.\nResponse to General Comment:\nWe are glad to see that Reviewer #3 found our revisions satisfying and recommended the publication\nof our manuscript. We also respond his/her last technical suggestion as below.\nComment 1:\nBy the way, I suggest the authors cite the following papers on programmable control of skyrmion on\ngrid-like trapping systems?\nCommunications Physics 4, 255 (2021).\nhttps://www.nature.com/articles/s42005-021-00761-7\nApplied Physics Letters 125, 032404 (2024).\nhttps://doi.org/10.1063/5.0215267\nResponse to Comment 1:\nWe thank the reviewer for suggesting these highly relevant references. We have added them to the\nmain text as follows:\n(page 10, paragraph 1, line 3)\n“The ability to control the birth, movement, and annihilation of individual skyrmions shows the\npotential of advanced two-dimensional spintronic application68, 69”\nAdditional minor changes\nWe additionally revise the main manuscript with minor changes for editorial requests:\n(page 3)\nAdded the sub heading\n“Results”\n(page 10)\nChange the sub heading from ‘Conclusion’ .\n“Discussion”\n(page 16)\nAdded the ‘competing interests’ section.\n“Competing interests\nThe authors declare no competing interests.”\n(page 16)\nModified the author contribution to name all the authors.\n“…wrote the manuscript with the assistance ofC. H., D. K., C. K., and all other authors.”\n(page 18)\nModified the Fig. 2 caption for readability.\n“…laser power and sweeping speedv , based on 20 trials for each condition.”"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors addressed my concerns. I support the publication of this manuscript.", "reviewer_2": "The authors have satisfactorily addressed all of the referee comments. I recommend the paper for publication without further change.", "reviewer_3": "The authors have made significant revisions regarding all the comments by the referees. Now the manuscript looks much better and can be published in NC. By the way, I suggest the authors cite the following papers on programmable control of skyrmion on grid-like trapping systems?\nCommunications Physics 4, 255 (2021).\nhttps://www.nature.com/articles/s42005-021-00761-7\nApplied Physics Letters 125, 032404 (2024).\nhttps://doi.org/10.1063/5.0215267"}, "author_response": ""}]

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