Impact of the skyrmion spin texture on magnetoresistance Andr´e Kubetzka, Christian Hanneken, Roland Wiesendanger, and Kirsten von Bergmann∗ Department of Physics, University of Hamburg, D-20355 Hamburg, Germany (Dated: February 1, 2017) We investigate the impact of the local spin texture on the differential conductance by scanning tunneling microscopy. In the focus is the previously found non-collinear magnetoresistance, which originates from spin mixing effects upon electron hopping between adjacent sites with canted mag- netic moments. In the present work it is studied with lateral resolution both for the zero magnetic fieldspinspiralstateaswellasforindividualmagneticskyrmionsatdifferentmagneticfieldvalues. We analyze in detail the response of the differential conductance and find different dependencies of 7 peak energy and peak intensity on the local properties of the non-collinear spin texture. We find 1 that in the center of a skyrmion the peak energy and intensity scale roughly linear with the angle 0 between nearest neighbor moments. Elsewhere in the skyrmion, where the non-collinearity is not 2 isotropic and the magnetization quantization axis varies, the behavior of the peak energy is more complex. n a J I. INTRODUCTION (NCMR), see sketch in inset to Fig.1(a), arises due to 1 spin mixing effects because of electron hopping between 3 atoms with canted magnetic moments, as demonstrated When magnetic materials are involved in transport ] measurements the spin has an impact on the resis- by two-band tight-binding as well as ab-initio DFT cal- ci tance, in general coined magnetoresistance (MR). The culations. These theoretical approaches for the system s of a PdFe bilayer on Ir(111) have demonstrated that the most prominent example is the giant magnetoresistance - l (GMR)1,2, whichoccurswhencurrentflowsbetweentwo electronic band structure of this material is different for r collinear versus non-collinear spin configurations9. This t magnetic electrodes separated by a non-magnetic metal- m explainstheexperimentalobservationthatskyrmionsare lic spacer. A similar setup is used to measure tunneling . magnetoresistance (TMR)3, where the metallic spacer is electronically different compared to their ferromagnetic t a exchanged with an insulating tunnel barrier. Because in surrounding, enabling an all-electrical detection scheme. m NCMRisageneraleffect,butitisnotalwaysstraight- bothcasestheconductancedependsontherelativealign- - ment of the magnetization in the two electrodes, one of forward to disentangle from other MR effects, in par- d ticular the TAMR, which typically leads to a maximal them can be used to read out the magnetic state of the n MR change for perpendicular magnetization quantiza- o other one. The TMR can be exploited in a spatially tion axes. While the TAMR originates from SOC and c resolvedscanningtunnelingmicroscopy(STM)measure- [ ment, when the tip is spin-polarized; such spin-polarized is thus usually limited to a few percent, the NCMR re- STM measurements can reveal spin structures at sur- sultsfromaspinmixingandvaluesupto50%havebeen v1 faces down to the atomic scale4,5. Changes in MR can found experimentally for PdFe9, with MR defined by: 7 bedescribedinscatteringmodels6 orbasedonelectronic (dI/dU) −(dI/dU) 7 bandstructureeffects7. Becauseinscanningtunnelspec- MR= FM NC ×100%, (1) (dI/dU) 0 troscopy (STS) the differential conductance (dI/dU) re- FM 9 flects the vacuum local density of states (LDOS), STM where dI/dU is the differential conductance signal at a 0 can be used to study the latter. Recently, the MR non-collinear(NC)orferromagnetic(FM)positionofthe . 1 changeduetothepresenceofadomainwallhasbeendis- spin texture. Furthermore, whereas the TAMR is an on- 0 cussed6,8. However, different types of MR are expected site effect, which depends on the local quantization axis 7 inthepresenceofadomainwall, andaseparationofdif- of the magnetization, NCMR is governed by the details 1 : ferenteffectsisexperimentallydifficultbecausethemea- of the spin texture in the local environment. v suredsignalisacombinationofseveraleffects. Duetoits A theoretical investigation including SOC of a closely i X spatialresolutionSTMhasbeenakeymethodtounravel related PdFe system, i.e. with a different stacking of the changes of the vacuum LDOS of a domain wall: the the Pd layer, has evaluated the contributions of non- r a differencebetweenthecenterofthewall(in-planemagne- collinearityandSOCtotheenergy-dependentMRinthe tization) and a domain (out-of-plane) was detected with skyrmioncenter: althoughbothcontributionsarecompa- a non-magnetic tip and it was pinned down by accom- rableforextremelysmallskyrmions,theSOChasaminor panying density functional theory (DFT) calculations of effectformorerealisticallysizedskyrmions,however,the theelectronicbandstructuretoamixingofstatesdueto effect of the non-collinearity was found to be as large as spin-orbitcoupling(SOC),resultingintunnelanisotropic 20%10. Othertheoreticalstudiesofspinspiralsinatomic magnetoresistance (TAMR)7. chains11 and films12 have also found that the impact of Recently, STM measurements have identified an MR SOC on the total MR is less than 10%, and that the effect,whichoriginatesfromthenon-collinearityofaspin conductance change due to the non-collinearity is domi- texture9. The observed non-collinear magnetoresistance nating the transport. Recent experimental studies have 2 shown that discrete jumps in magnetic field dependent a MR can be linked to the appearance and disappearance 50 nm R M of individual skyrmion tubes in a wire13. C e- e- PdFe N In this work we extend the investigation of the previ- ously studied system of PdFe on Ir(111) and present a more detailed analysis, in particular of the central find- Fe Fe Ir ing of the response of a susceptible peak in the differen- tialconductanceanditsrelationtothenon-collinearity9. Ir Ir First, we present data which demonstrates that the Fe NCMR effect occurs also for the zero magnetic field spin PdFe spiralgroundstateandinbothstackingsofthePdonFe. PdFe Then we turn to the magnetic skyrmions, that arise in Fe thissystemuponapplicationofaperpendicularmagnetic field14. Welookcloselyintothemagneticfielddependent details of the skyrmion spin texture15 and correlate the evolution of the peak energy as well as its intensity with b the different parameters that characterize the local spin configuration. We conclude with a discussion about the B = 0T differentlocalcontributionstothetotalMRinthesenon- collinear spin textures. hcp PdFe fcc PdFe II. EXPERIMENTAL DETAILS 20 nm c The experiments were performed in a multi-chamber ultra-high vacuum system with separate chambers for B = -2.5T substrate cleaning, metal deposition, and STM measure- ments. The Ir crystal was cleaned by repeated cycles of sputtering and annealing, and from time to time heating in oxygen. Iron was deposited onto the Ir(111) surface atelevatedtemperaturetoobtainstep-flowgrowthofthe fccstacking16andsubsequentlyPdwasdeposited14. Two d e spin spiral max spin spiral min differentSTMswereusedwithbasetemperaturesof4.2K ) ferromagnet and8K,andthetipmaterialwaseitherCrorW.Mapsof nits skyrmion differential conductance (dI/dU) were measured simul- u b. taneously to constant-current (I) topographic images at r a identical sample bias voltage (U) with closed feedback U ( loop. Scanning tunnel spectroscopy (STS), dI/dU(U), d was performed with open feedback loop; the stabiliza- Id/ tionparameters(U andI )beforeswitchingoffthe hcp PdFe fcc PdFe stab stab feedback loop were chosen with particular care to ensure 0 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 1 thatthetip-sampledistancedoesnotdependonthemag- sample bias (V) sample bias (V) netic state of the sample, i.e. in first approximation the laterally-resolvedspectroscopicdatarepresentsconstant- FIG. 1. (a) Pseudo-3D STM topography of a typical sample heightspectroscopy. ThedI/dU signalwasmeasuredvia of Pd and Fe on Ir(111), colorized with the differential con- lock-in technique where the bias voltage was modulated ductancesignal;theinsetisasketchoftheNCMReffectfora with U at a frequency of about 2.6kHz. mod planar tunnel junction: the resistance/conductance between a non-magnetic electrode and a magnetic electrode is differ- ent for a collinear compared to a non-collinear spin texture. III. EXPERIMENTAL RESULTS (b)dI/dU mapoftheareaindicatedbytheblackrectanglein (a) showing NCMR contrast for the spin spiral ground state in both stackings of the Pd on Fe. (c) dI/dU map of the The system of the atomic bilayer PdFe on Ir(111) same area as in (b) in applied magnetic field with individual serves as our model system and Fig.1(a) shows an magnetic skyrmions imaged by NCMR. (d,e) dI/dU spec- overviewSTMconstant-currentimage,colorizedwiththe traofthedifferentmagneticstatesascolor-codedin(b,c)for simultaneously obtained dI/dU signal. The measure- both stackings of PdFe. Measurement parameters for (a-c): ment was performed with a non-magnetic tip and the U =+0.7V,I =1nA,U =40mV;for(d,e)U =−1V, mod stab dark irregular stripes connected to the step edges of the I =1nA, U =7mV; all T =4.2K. stab mod Ir(111) substrate indicate the Fe monolayer grown in fcc 3 sptaatcckhiensg.anTdhediiffslearnednstosnigntoapl sotfrethnegtFhesainredimcaotneoldaiyffeerrePndt a B = -1.75 T d 0 1.00 T stackings. A dI/dU map of the area indicated by the outside (°)q 3600 12..7550 TT black rectangle is shown again in Fig.1(b) with an hcp e PdFeislandontheleftandanfccPdFestripetotheright. rim ngl 90 In addition to the different contrast levels due to the Pd center ar a120 stackingonecanobserveastripepatternindicativeofthe ol spinspiralstates: theobserveddI/dU contrastoriginates p150 from the NCMR at this sample bias of +0.7V. Because 180 ofthenon-negligibleout-of-planeanisotropyofPdFe15,17 4 nm e V)0.9 thespinspiralisinhomogeneousandthedI/dU signalis y ( htitnwhig-eephmelena9rn.nefoeNmrigoahotgbuenot-terohtinfiac-gtpmlwamnohameigleenrneetgtthsiicoewnrmesitoihwsmiltneahonrgtsseemxrataaeslnrlencgroalemlasnmpbgaaelregteswndeebteteinoc- arb. u.)b68 orciemuntstiedre angle (°)a112500 peak energ00..780 a10c (°)20 field applied this is not the virgin state and some inter- ct. ( 4 an 5 connected in-plane rings have remained after a previous du B = 1.75 T me magnetic field sweep. on 2 0 c pliWedhseinngalenmeaxgtenrentaicl smkyargmneiotincsocuatn-obfe-pfloaunnedfiienldPdisFeapo-f diff. 00 0.2 0.4 0.6 0.8 1 f 4 11..0705 TT bothstackings,seeFig.1(c)foradI/dU mapofthesame sample bias (V) °) 2.50 T area at B = −2.5T. At this magnetic field strength the c 2 nm (sa 3 skyrmions appear as dark spots due to the NCMR (see v. B = 1.75 T e 2 d dotted circles); the skyrmions form due to the interface- d. inducedDzyaloshinskii-Moriyainteractionandthushave n 1 a uniquerotationalsenseandareofcycloidalnature5,14,17. st 0 To study the electronic states of PdFe in the different 0 g magnetic phases local STS has been employed: Fig.1(d) 1.00 T and (e) show spectra at positions of highest and lowest 0.2 1.75 T dI/dU signal of the spin spiral (compare colored circles 2.50 T q0.4 in (b)) as well as for the ferromagnetic region and the 2s skyrmion center (compare colored circles in (c)) for hcp co0.6 and fcc PdFe, respectively. All spectra are featureless at negativesamplebias(notshown)butshowcharacteristic 0.8 peaks in the unoccupied states: the ferromagnetic states 1 haveasinglepeakataround+0.7V,whichshiftstowards 0 1 2 3 4 5 6 distance (nm) higher energy for the spin spiral states and the skyrmion centers; at the same time the intensity of this peak de- creases. As demonstrated previously9 a two peak struc- FIG. 2. (a) dI/dU map of a single skyrmion in PdFe on Ir(111)atB =−1.75TmeasuredwithaWtip(U =+0.7V, ture is found for the skyrmion center of the hcp PdFe, I =1nA,U =20mV,T =8K).(b)dI/dU spectrataken andthischangeoftheelectronicstructurehasbeenmod- mod atdifferentpositionswithintheskyrmion(seecolor-codedcir- eled by tight-binding based on density function theory cles in (a); U = −0.3V, I = 0.2nA, U = 20mV, stab stab mod (DFT)calculationsfortheferromagneticstatewhichne- T = 8K). (c) Sketch of a skyrmion at 1.75 T, the cones glectSOC9andhasbeenshowntooriginatefromNCMR. representatomicmagneticmoments,theirdirectionspointin Inaddition,thevacuumLDOS,whichcorrelateswiththe the direction of magnetization, and the color-scale indicates experimentallymeasureddI/dU,hasbeenobtainedfrom the out-of-plane magnetization component (red down, blue these DFT calculations for the ferromagnetic state and up). (d)-(g) Magnetic field dependent properties of indi- a spin spiral with a period of 5.14nm, very similar to vidual magnetic skyrmions in PdFe as a function of distance the experimentally observed one. For both stackings the from the skyrmion center: (d) the polar angle of the spins in a skyrmion; (e) the mean angle between a spin and its agreementbetweenthecalculatedvacuumLDOSandthe six neighbors and (f) standard deviation of this mean angle; experimentallyobtainedspectraisverynice,exceptfora (g)themagneticquantizationaxisvariesfromout-of-planein rigidshiftbyabout0.2V9,18. OtherDFTcalculationsfor the center of a skyrmion via in-plane back to out-of-plane in extremelysmallskyrmionsforfccPdFe,thistimeinclud- its surrounding. ingSOC,havebeenpublishedinRef.10andshowapeak at about 0.6V for the ferromagnetic state, which shifts to smaller energies upon introducing non-collinearity, in contrasttotheexperimentallyobservedshiftofthepeak at 0.7V to higher energies. 4 The question arises how the spectra spatially evolve alsotwoobviousdifferences: first,thevariationinthesix between the skyrmion center and the ferromagnetic en- nearest-neighboranglesα,whichcanbequantifiedbythe vironment and if their characteristics can be directly standard deviation σ of the mean angle α, is different α correlated with the non-collinearity. A high resolution (comparealsodistance-dependentplotsforselectedmag- dI/dU map of a single skyrmion in the hcp PdFe at neticfieldsinFig.2(f)). Naturallythestandarddeviation B = −1.75T measured with a non-magnetic W tip σ is zero for the collinear state outside the skyrmion as α is shown in Fig.2(a). Spectra taken at different posi- well as for the symmetric spin arrangement in the center tions within this skyrmion are displayed in Fig.2(b), see of the skyrmion. However, at all other positions within color coding in (a) for the positions with respect to the the skyrmion it is finite. The second apparent difference skyrmion center. From previous SP-STM studies15 the for the two positions with the same mean angle is the details of the spin texture of magnetic skyrmions in the quantizationaxisofthemagnetization,whichisreflected hcp PdFe bilayer as a function of external magnetic field by γ =cos2(θ) as plotted in Fig.2(g): the magnetization are known and Fig.2(c) displays a sketch of the atomic quantizationaxiscanalsomodifyelectronicstatesdueto magnetic moments within a magnetic skyrmion for an SOC, resulting in TAMR7,19. In a magnetic skyrmion a externalmagneticfieldof1.75T.Thecirclesindicatethe potential TAMR contribution γ is identical in its center positions where the spectra displayed in Fig.2(b) were and outside, and it is maximal different for the in-plane obtained. The evolution of the size and shape of mag- spins, cf. Fig.2(g). Because for the spectra displayed in netic skyrmions in PdFe as a function of external mag- Fig.2(b) in the center of the skyrmion with γ = 1 and netic field can be characterized by the polar angle θ of nearthein-planeregionwithγ =0thereisalsoachange magnetization,asdisplayedinFig.2(d)forselectedmag- inσ from0◦ toabout4◦,wecannotunambiguouslyiden- netic fields as a function of distance from the skyrmion tifytheoriginofthischange, i.e.whetheritisduetothe center. This plot demonstrates that the diameter (de- change in σ or γ = 0. However, experimentally we find finedasdistancefromin-planetoin-plane)changesfrom a significant difference in the spectra in the center and about 4nm at 1T to about 2nm at 2.5T, and that also outside the skyrmion, where σ = 0◦ and γ = 1 in both the general shape of the skyrmion changes with external cases, which thus originates only from the change in the magnetic field. non-collinearity α. Previous analysis9 has revealed that the peak energy For a more detailed analysis of the changes of the inthecenterofaskyrmionscalesroughlylinearwiththe electronic states due to the spin texture we measure nearest-neighbor angle α , see inset to Fig.2(e). While the laterally-resolved spectra across a skyrmion with the c for a spin in the center of a skyrmion the angle α to same tip and identical parameters at different magnetic all six nearest-neighbors on the hexagonal lattice is the field values. Figure3(a) shows a waterfall plot of the same (α ), i.e. the environment is symmetric, the situ- respective data set for a skyrmion at B = −1.75T, c ation is different for other positions within a skyrmion, where each horizonal line is a single dI/dU spectrum compare configurations indicated by circles in the sketch and the color code indicates the intensity; the center of of the spin structure of a magnetic skyrmion at 1.75T the skyrmion is indicated by the dashed line. We find in Fig.2(c). To account also for such inhomogeneous en- that the peak at around +0.7V in the ferromagnetic re- vironments with different nearest-neighbor angles α, we gionoutsidetheskyrmionshiftstowardshigherenergyin calculate the mean angle α to the six nearest neighbors thecenteroftheskyrmionandatthesametimechanges from the given spin texture and plot it as a function of its intensity. A plot of the evolution of peak energy and distance from the skyrmion center, see Fig.2(e). This intensity for three different magnetic field values as a parameterαcanbeinterpretedasthegeneralizeddegree function of distance to the skyrmion center is shown in of non-collinearity, and we find that its maximum value Fig.3(b) and (c); the same data points are plotted both movestowardsthecenteroftheskyrmionastheexternal in one direction across the skyrmion and vice versa, i.e. magnetic field is increased. The question arises, whether theyaremirroredatthecenteroftheskyrmion;thelines the peak energy directly reflects the local mean angle α, areguidestotheeye. Forsmallskyrmionsthemaximum assuggestedbythedirectcorrelationofpeakenergyand peakenergyisinthecenteroftheskyrmion, whereasfor nearest-neighbor angle α in the center of the skyrmion, a large skyrmion at B = −1T a slight reduction of the c see inset to Fig.2(e). We can crosscheck this for the peak energy is found near the center. The peak inten- 1.75T skyrmion: both in the center of the skyrmion as sities, Fig.3(c), show a local maximum in the center of well as at a distance of about 1.6nm from the center α the skyrmion for both −1T and −1.75T (not the entire is about 15◦. However, comparison of the experimental data set measured at −2.5T can be analyzed quantita- spectra obtained at the respective positions within the tively due to a defect near the center of the skyrmion skyrmion (Fig.2(b) center and rim) reveals that such a which seems to have an impact on the intensity, and the strictcorrelationbetweenpeakenergyandmeanangleα unreliable data points are plotted as empty circles). In cannot be confirmed. the following we try to correlate this magnetic field de- pendent evolution of peak energy and intensity with the Although the two selected positions within the 1.75T details of the local spin texture. skyrmion(comparegroupsofatomsindicatedbythecir- cles in Fig.2(c)) have the same mean angle α there are In our previous publication9 it was demonstrated that 5 0 dI/dU (arb. units) 10 b a 1.00 T b 1.00 T 1.75 T 1.75 T a V) 0.85 2.50 T nits) 2.50 T nergy (V) 00..885 ak energy ( 0.8 nsity (arb. u 78 e e e eak p 0.75 ak int 6 p 0.75 e p 0 5 10 15 20 25 0 5 10 15 20 25 1.00 T mean angle a (°) mean angle a (°) 1.75 T c 2.50 T FIG. 4. (a) Evolution of the peak energy (data of Fig.3) s) nit as a function of mean angle at the respective position in the u skyrmion, lines are guides to the eye. (b) Same as (a) but arb. 8 for the peak intensity; the empty circles at the bottom mark y ( data points that are considered unreliable due to a defect. sit 7 n e a b 2 nm eak int 6 0.85 (°)sa 2cosq p V) a (°) a (°) y ( 0 0.2 0.4 0.6 0.8 1 -6 -4 -2 0 2 4 6 g sample bias (V) distance (nm) ener 0.8 k a e p FIG. 3. (a) Spatially-resolved dI/dU spectra across a 0.75 skyrmion at B = −1.75T measured with a W tip (U = stab −0.3V, I =0.2nA, U =20mV, T =8K); the dashed stab mod lineindicatestheskyrmioncenter. (b)Evolutionofthepeak 0.7 0 5 10 15 20 0 5 10 15 20 energyasafunctionofdistancefromtheskyrmioncenterfor mean angle a (°) mean angle a (°) different magnetic fields as labeled with the same W tip; all datapointsarealsomirroredattheskyrmioncenter,linesare FIG. 5. Data as in Fig.4(a) together with the evolution of guidestotheeye. (c)Sameas(b)butforthepeakintensity; (a)thedegreeofinhomogeneityσ and(b)thequantization α theemptycirclesatthebottomindicatedatapointsthatare axis cos2(θ) in addition to the mean angle; insets show the considered unreliable due to a defect. separate contributions of σ and cos2(θ) as a function of the α mean angle. thepeakenergyinthecenterofaskyrmionscalesroughly linearly with the external magnetic field and thus with zation was found to be proportional to the inverse of the the nearest-neighbor angle α , see also inset to Fig.2(e); spin spiral wave length, i.e. proportional to the nearest c the same was found for the full tight-binding calcula- neighbor angles of a spin spiral. tions with small deviations at small angles9. It is nat- In contrast, there are strong systematic deviations ural to try to generalize this dependence for the mean from a linear behavior for the peak energy, see Fig.4(a): angle α when considering arbitrary positions within the except for the positions in the skyrmion center the peak skyrmion. To analyze the relation between the exper- energy is significantly lower than the fit line, and even imentally observed peak energy and intensity with the nearly constant for mean angles between 5 − 15◦ at degree of non-collinearity, we plot these parameters not B = −1T. For a change of the angle in the skyrmion as a function of the distance from the skyrmion center, center of 10◦ we find a peak shift of about 60mV; how- but as a function of α at the respective position, see ever, we can find the same peak shift for different posi- Fig.4(a,b). The three data points for the center of the tions within a skyrmion that have the same mean angle, skyrmions at the different magnetic field values are indi- e.g. α = 15◦ at B = 1.75T (at the skyrmion center and cated by crosses, and the black line represents a linear about 1.6nm away from it, see also red dot in Fig.2(e)). fit to these data points and the ferromagnetic reference. We now come back to the details of the skyrmion spin While the data points for the intensity (b) have the ten- texture, cf. Fig.2(c): different positions can be charac- dencytobebelowtheline,weconcludethatthepeakin- terized by the polar angle of the magnetization θ, the tensity in first approximation scales with α, irrespective mean angle α, the degree of inhomogeneity σ , and the α of the applied field and the detailed spin configuration. quantizationaxisgivenbycos2(θ). Becauseαalonedoes Thismightbelinkedtoaprevioustheoreticalfindingre- notdescribetheevolutionofthepeakenergy,weanalyze portedinRef.12,inwhichtheleadingordercontribution whetheroneofthelattertwoparametersalsoplaysarole: to the relative MR change due to the rotating magneti- the insets to Fig.5(a,b) show σ and cos2(θ) as a func- α 6 tionofthemeanangle,andthemainpanelsdemonstrate variation of the density of states from site to site across that either one can, together with the linear dependence the skyrmion. While this has a direct effect on the band onα,describethegeneraltrendofthepeakenergyforall structure, also a more indirect effect is possible: when three magnetic field values. While the agreement using the bands that are altered by SOC are also involved in σ seemstobebetterforpositionsclosertotheferromag- the NCMR, a slight modification of electronic states due α netic surrounding, the shape of the cos2(θ) fits slightly toSOCmayleadtoasignificantchangeofthedensityof better towards the center of the skyrmion. states when the spin bands mix with each other, result- inginanenhancedNCMRsignal. Thispossibleinterplay alsoimpliesthattherelevanteffectsdeterminingthepeak IV. CONCLUSION shift need not be additive, as suggested by the simplistic illustration of Fig.5, but can induce more complicated Wehavestudiedthemagneticfielddependentvacuum behavior of the LDOS. dI/dU ofskyrmionsinthesystemofPdFeonIr(111)and Thepresenteddetailedexperimentalstudycanserveas analyzed in more detail the previously observed peak, a benchmark for future theoretical studies regarding the whichissensitivetothelocalspintexture, regardingthe magnetoresistive properties of non-collinear states. Re- energy and the intensity. The peak intensity is found gardlessofthedetailsofthemechanismforthepeakshift to be roughly linear with the local mean angle between andintensitychangethevariationoftheMRislargeand neighboring magnetic moments, reflecting the degree of weproposetouseitasameanstodetectandinvestigate non-collinearity. In contrast, while the peak energy in the spin texture of non-collinear states. the skyrmion center is proportional to its magnetic field dependent mean angle, we observe significant deviations from a linear behavior of the peak energy elsewhere in ACKNOWLEDGMENTS the skyrmion. We demonstrate that this could be at- tributed either to the inhomogeneity of the local spin WethankS.Heinze,N.Romming,andB.Dup´eforin- textureasrepresentedbythestandarddeviationofnear- sightful discussions. Financial support from the German est neighbor spin angles, or to the mixing of states due ResearchFoundation(DFG:GrK1286andSFB668-A8) to SOC, as manifested in TAMR. The latter depends on andtheEuropeanUnion(FET-OpenprojectMAGicSky the local magnetization quantization axis and leads to a No. 665095) is gratefully acknowledged. ∗ [email protected] B 247, 2594 (2010). 1 M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, 12 K.M.Seemann,F.Garcia-Sanchez,F.Kronast,J.Miguel, F. Petroff, P. Etienne, G. 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