Disentangling factors governing Dzyaloshinskii domain wall creep in Co/Ni thin films using Pt x Ir 1−x seedlayers
Derek Lau, James Price Pellegren, Hans Nembach, Justin Shaw, Vincent Sokalski
DDisentangling factors governing Dzyaloshinskii domain wall creep in Co/Ni thin filmsusing Pt x Ir − x seedlayers D. Lau, J.P. Pellegren, H.T. Nembach, J.M. Shaw, and V. Sokalski ∗ Department of Materials Science & Engineering,Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, CO 80305, USA (Dated: August 17, 2018)We characterize asymmetric growth of magnetic bubble domains in perpendicularly magnetizedCo/Ni multi-layers grown on Pt x Ir − x seedlayers by application of perpendicular and in-plane mag-netic fields. Using a refined model of domain wall creep that incorporates contributions from theanisotropic elastic energy, ε , and a chirality-dependent prefactor, v , we elucidate factors that governthe mobility of Dzyaloshinskii domain walls as a function of seedlayer composition. The interfacialDzyaloshinskii-Moriya Interaction magnitude is found to decrease monotonically with x Ir , whichis independently confirmed by Brillouin light scattering (BLS). Moreover, the persistence of signif-icant asymmetry in velocity curves across the full composition range supports previous assertionsthat a chirality-dependent attempt frequency akin to chiral damping could play a critical role inthe observed trends. This work helps resolve fundamental questions about the factors governingDzyaloshinskii DW creep and demonstrates varying Pt-Ir seedlayer composition as a method totune DMI. Recent observations that topologically protected mag-netic features like skyrmions and chiral domain walls(DWs) can be manipulated with spin current has re-newed interest in developing spintronic devices for en-ergy efficient nonvolatile memory and logic applications[1–6]. These topological structures are stabilized bythe Dzyaloshinskii-Moriya Interaction, DMI, which isan anti-symmetric exchange energy that scales as E = − D · ( S × S ) leading to chiral winding configurationsas the ground state.[7, 8] Here, S represents the spin an-gular momentum of neighboring electrons and D is theDMI vector. Prospects for future thin film engineering inthis area were bolstered by the discovery of an interfacialDMI, iDMI, that exists in ultrathin heavy metal / fer-romagnet heterostructures because of their structural in-version asymmetry (SIA).[9] In this case, D is restrictedto lie in the plane of the film with direction given by D = D (ˆ r × ˆ z ) where ˆ r and ˆ z are the unit vectors from S to S and the film normal, respectively. The impact ofseveral seedlayers and their thickness have been exploredexperimentally in an effort to control the strength of thiseffect.[10–14] However, to date there have only been the-oretical investigations on the composition dependence ofthe iDMI, which we present here for Pt-Ir alloys.[15] Inthin films with a perpendicular magnetization, D canbe described by an effective field, µ o H DMI = D/ ( M s λ ),that acts on the internal magnetization of a DW favoringthe N´eel configuration over the in the out-of-plane ge-ometry magnetostatically favored Bloch type, where M s and λ are the saturation magnetization and Bloch wallwidth, respectively.[10, 11, 16] It is now well-establishedthat the combination of H DMI and an in-plane field H x leads to a wall energy that is highly anisotropic withrespect to the DW normal’s spatial orientation about H x . [17–19] This break in symmetry results in asym- FIG. 1. Illustration of the impact of the anisotropic elasticenergy (a) and chiral weight (b) on velocity vs µ H x withtheir combined effect shown in (c). d-f) The correspondingeffects on A creep . Most notable is the convergence of ↑↓ (blue)and ↓↑ (red) domain walls at large µ H x for the case of elasticenergy alone. This convergence is absent for a non-zero chiralweight. metric expansion of magnetic bubble domains when sub-jected to a perpendicular driving field.[10, 11, 20, 21] Forsmall driving fields, the motion is thermally activatedwith velocity described by the Arrhenius creep scalinglaw, v = v o e ζH − / z , where ζ has built in the activationenergy for DW propagation and is proportional to thefourth root of the DW elastic energy, ε / . The pref-actor, v , is the corresponding attempt frequency forDW propagation.[22, 23] Although asymmetric domaingrowth has become the predominant technique for ex-tracting D , fundamental questions remain about how tointerpret creep velocity changes with H x in ultrathin fer-romagnetic films with appreciable iDMI.Initial work on this topic suggested that ε is equiva- a r X i v : . [ c ond - m a t . m t r l - s c i ] A ug FIG. 2. Experimental v vs. µ H x for seedlayers with varying x Pt with representative MOKE images. Dashed lines are fitsfrom equation 1. The center grey of the Kerr images represent the initial bubble shape while the white region is the domainafter growth under both µ H x and µ H z , which was fixed at 7 mT. lent to σ , the wall energy, and was the factor govern-ing DW velocity. Assuming constant λ , σ vs. H x issymmetric about a maximum that occurs when H x = H DMI and was proposed to correspond to a minimumin velocity.[10, 11] Significant asymmetric deviationsfrom this idealized shape observed experimentally led tospeculation about other possible factors that could becontributing.[21, 24–26] This included chiral damping,which would impact v instead of ε and depend only onthe orientation of the DW internal magnetization.[25] Itwas also later identified that ε is actually given by thestiffness, ˜ σ (Θ) = σ (Θ) + σ (cid:48)(cid:48) (Θ), which should reside inthe exponent of the creep law instead of σ (Θ).[19] HereΘ denotes the angle between the DW normal and H x .In the isotropic case, σ (cid:48)(cid:48) (Θ) = 0. However, in cases ofanisotropic DW energy as found in Dzyaloshinskii DWssubject to H x here, σ (cid:48)(cid:48) (Θ) becomes comparable in magni-tude σ (Θ). This description based only on elastic energyof the domain wall demonstrated that significant curveasymmetry should exist due exclusively to iDMI and wasable to explain some of the perplexing experimental data.In this paper, we use an augmented model forDzyaloshinskii DW creep to fit experimental measure-ments of asymmetric domain growth in Co/Ni multi-layers grown on Pt-Ir alloy seedlayers. The model in-corporates elastic energy of the domain wall based on itsdispersive stiffness [19] and also allows for a chirality de-pendent prefactor that would occur in the case of chiraldamping given by v ( H x ) = v ∗ (1 + α cd cos ( φ eq ( H x ) − Θ))where α cd is a parameter from -1 to 1 that characterizesthe weight of this effect - hereafter referred to as the chi-ral weight. φ eq is the equilibrium internal magnetizationorientation with respect to H x as calculated in Pellegrenet al.[19] v ∗ is the attempt frequency absent any chiral ef-fects. For calculations of v , we only consider the case ofΘ = 0 or π to account for fits to the left and right veloci- ties of the bubble domains. The resulting creep equationdescribing DW velocity as a function of H x is given asfollows: v = v ( H x ) exp (cid:20) κ ˜ σ ( H x )˜ σ ( H x = 0) H − / z (cid:21) (1)where κ is a creep scaling constant that does not de-pend on H x . ˜ σ is calculated using the dispersive stiffnessmodel of Pellegren et al. in the limit of a vanishinglysmall deformation lengthscale, L as justified later.[19]The effects of elastic energy and chiral weight on theshape of velocity curves is shown qualitatively in Figure1. The asymmetric component, A creep = ln( v ↑↓ /v ↓↑ ),is included to further highlight experimental signaturesassociated with the different mechanisms. ( v ↑↓ and v ↓↑ are the domain wall velocities, where the magnetizationtransitions from up to down and down to up, respectively.In the case where only elastic energy is considered, v ↑↓ and v ↓↑ converge (i.e. A creep = 0) as H x → ∞ . For anon-zero α cd , A creep saturates when H x > H DMI + H DW where H DW is the DW anisotropy field.Co/Ni films were prepared using DC magnetronsputtering from 5 in. targets onto 3 in. Si(001) substrates with native oxide. The work-ing pressure was fixed at 2.5 mTorr Ar. Thefilm stack is Substrate/TaN(3)/Pt(3.5)/Pt x Ir − x (1.2)/[Co(0.2)/Ni(0.6)] /Co(0.2)/Ta(0.8)/TaN(6), with unitsin nanometers. The Pt x -Ir − x seedlayer is prepared usinga combinatorial sputtering technique where the substrateis moved between two targets rapidly, depositing < M − H loops measured using alternatinggradient field magnetometry (AGFM) and vibrating sam-ple magnetometry (VSM) across the composition gradi-ent indicate a saturation magnetization, M s ∼ kA/m ,and in-plane saturation field, µ H k ∼ . T , which haslittle dependence on Pt x Ir − x seedlayer composition (seesupplemental information (S1)). Measurement of domaingrowth was performed using a wide-field white light Kerrmicroscope. The microscope is fit with an in-plane elec-tromagnet capable of producing static in-plane fields upto µ H x ∼
250 mT as well as a perpendicular coil thatcan generate up to µ H p ∼
20 mT magnetic pulses downto 1 ms. As described in [17, 19], a Ga + ion beam is usedto selectively damage portions of a sample film, where ini-tial bubble domains of approximately 20 µ m can be nu-cleated. Velocity was determined by two images showingthe difference in domain wall positions before and aftera single pulse. The pulse length ranged from 1-20ms andwas chosen so that an appreciable displacement wouldoccur.We used Brillouin Light Scattering spectroscopy (BLS)to establish an independent measure of the magnitudeof the DMI. The laser had a wavelength of 532 nm.Damon-Eshbach spin-waves experience a non-reciprocalfrequency-shift ∆ f DMI = | g || µ B h | sgn ( M ) DM s k in the pres-ence of DMI. The spectroscopic splitting factor is esti-mated as g || = 2 .
19 [28], µ B is the Bohr Magneton, h isPlanck’s constant and k is the spin-wave wavevector with | k | = 16 . µm − . We measured the spin-wave frequencyfor the two opposite directions of the magnetization todetermine ∆ f DMI . The measured | ∆ f DMI | was between0.1 GHz and 0.8. GHzFigure 2 shows representative Kerr images as a func-tion of in-plane field ( H x ) and seedlayer composition withcorresponding v vs H x curves. As seen in previous stud-ies, the domain shape is highly non-elliptical evolvingfrom a flattened shape at low field to a teardrop shapeat higher field.[17, 21, 29] The field at which this occursis found to be directly related to the amount of Pt inthe seedlayer (see supplementary info for additional Kerrimages). To separate the effects of elastic energy andchiral weight, we examine the shape of v vs H x and thecalculated A creep (Figure 3). In all cases, the velocitycurve is asymmetric about a minimum in velocity. Thisleads to a reversal in the preferred expansions directionin the Pt-rich compositions, which is indicated by the in-tersection of the velocity curves in figure 2 and by thezero crossing of A creep in figure 3 a. As identified pre-viously, a change in sign of A creep at non-zero H x couldbe explained using a larger deformation lengthscale, L,in the dispersive stiffness model.[19] However, the obser-vation that A creep tends to saturate rather than returnto zero suggests this is not the case. Therefore, we limitour fitting to the case of L →
0, which is consistent withthe expectation that pinning sites in sputtered thin filmsare densely distributed. We note that as the composi-
FIG. 3. a) A creep vs. µ H x as a function of X Pt . b) Extractedvalues of D and α cd vs X Pt based on fits to A creep . Closedblue (dark) circles represent fits extracted from the elasticdomain wall model. Open blue (light) circles represent D values characterized using BLS demonstrated by Nembach etal.[12] tion shifts from x P t = 1 to 0, the minimum in velocityshifts towards H x = 0 and changes sign near x P t = 0 . D does not actually change sign and only approaches 0for the case of pure Ir. This result is in stark contrast tothe aforementioned creep models based only on the wallenergy, which would have given the incorrect sign of D in this range.[10, 11]Even as D decreases with decreasing x P t , the asym-metry of the curve is preserved suggesting that its originis not exclusively due to iDMI. Indeed, A creep appearsto saturate in all cases even though its magnitude is re-duced for increasing Pt content. The results of the fitto the velocity curves are shown in Figure 3b highlight-ing that significant α cd is needed to explain the data ofFigures 2/3a and dominates the trend for large X Ir .To further examine the impact of chi-ral weight and iDMI via the elastic en-ergy, we have prepared the following films:TaN(3)/Pt(2.5)/[Co(0.2)/Ni(0.6)] /Co(0.2)/Ir(2.5)/TaN(6)and the same stack with Pt and Ir positions swapped.These are referred to as Pt-seed/Ir-cap and Ir-seed/Pt-cap, respectively. Velocity curves and asymmetryfor these samples are shown in Figure 4. We notethat the magnitude of D measured here should notbe compared with the results tabulated in Figure 3because we have significantly increased the effectivemagnetic layer thickness by replacing the Ta cap(known to create a magnetic dead layer) with eitherPt or Ir (both known to have a proximity inducedmagnetization). Indeed, we see that the sign of D is reversed between these two cases with comparablemagnitudes as expected. The Pt seed/Ir cap favorsleft-handed N´eel walls ( D = − . ± . mJ/m )and the Ir seed/Pt cap favors right-handed N´eelwalls ( D = 0 . ± . mJ/m ). It is interestingthat despite the expected change in sign of D , α cd remains nearly the same ( α cd,P t − seed = 0 . ± . α cd,Ir − seed = 0 . ± . α cd depended exclusivelyon the elements present and interface orientation, weshould see a change in sign upon reversal of the filmstack. The absence of this reversal suggests that therecould be a contribution to the chiral weight that isintrinsic to the Co/Ni stack even though it is nominallysymmetric. Just as Pt/Co/Pt films are known to haveSIA, it is conceivable that the Co/Ni/Co/Ni/Co filmstack itself could be structurally asymmetric if thelattice evolves through the thickness and/or the top andbottom Co/Ni interfaces are not identical. This assertionrequires further investigation as it is also possible thatthe chiral weight contributions from Pt and Ir changewhen used as seed vs cap layers.In summary, we have shown a monotonic increase of D with X P t in Pt x Ir − x seedlayer alloys. Moreover, weshow that the impact of DMI on elastic energy is in-sufficient to explain the trends in velocity curves seenexperimentally. The results are fit well when a chirality-dependent attempt frequency is included in the model— something speculated to originate from chiral damp-ing or, more recently, a chiral gyromagnetic ratio.[25, 30]However, it remains unclear if the 10-100x increase in ve-locity is consistent with these mechanisms. We also showdefinitively that reversal of Pt and Ir stack sequence in-deed reverses the sign of D , but does not change thesign of α cd . This suggests that there could be a mecha-nism for chiral effects built into the Co/Ni multi-layersthemselves. 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