The domain wall spin torque-meter
I.M. Miron, P.-J. Zermatten, G. Gaudin, S. Auffret, B. Rodmacq, A. Schuhl
TThe domain wall spin torque-meter
I.M. Miron, P.-J. Zermatten, G. Gaudin, S. Auffret, B. Rodmacq, and A. Schuhl
SPINTEC, CEA/CNRS/UJF/GINP,INAC, 38054 Grenoble Cedex 9, France (Dated: November 6, 2018)
Abstract
We report the direct measurement of the non-adiabatic component of the spin-torque in domainwalls. Our method is independent of both the pinning of the domain wall in the wire as well asof the Gilbert damping parameter. We demonstrate that the ratio between the non-adiabatic andthe adiabatic components can be as high as 1, and explain this high value by the importance ofthe spin-flip rate to the non-adiabatic torque. Besides their fundamental significance these resultsopen the way for applications by demonstrating a significant increase of the spin torque efficiency.
PACS numbers: 72.25.Rb,75.60.Ch,75.70.Ak,85.75.-d a r X i v : . [ c ond - m a t . o t h e r] O c t he possibility of manipulating a magnetic domain wall via spin torque effects whenpassing an electrical current through it opens the way for conceptually new devices such asdomain wall shift register memories[1]. Early spin-torque theories[2, 3, 4] were based on aso called adiabatic approximation which assumed that the incoming electron’s spin followsexactly the magnetization as it changes direction within the domain wall. Nevertheless, theobserved critical currents needed to trigger the domain wall motion were lower than thevalue predicted within this framework[5]. As first predicted by Zhang[6], the existence of anon-adiabatic term in the extended Landau-Lifshitz-Gilbert equation leads to the vanishingof the intrinsic critical current. The action of this non-adiabatic torque on a DW is expectedto be identical to that of an easy axis magnetic field. Micromagnetic simulations have beenused to predict the velocity dependence on current for a DW submitted to the action of thetwo components of the spin-torque[7]. The quantitative measurement of this non-adiabatictorque can be achieved either by demonstrating the equivalence of field and current ina static regime, or by observing the complex dynamic behavior[7]. The main difficultyof these measurements comes from the pinning of the DW by material imperfections. Itmasks the existence of the intrinsic critical current, and in addition, above the depinningcurrent, obscures the DW velocity dependence on current. Moreover, most of the DWvelocity measurements were done using materials with in-plane magnetization[5, 8, 9, 10,11], where the velocity can also depend on the micromagnetic structure of the wall[12](transverse wall or vortex wall). Despite the simpler micromagnetic structure of the DWs,very few results were reported[13] for Perpendicular Magnetic Anisotropy (PMA) materials.In this case the intrinsic pinning is much stronger, probably due to a local variation ofthe perpendicular anisotropy. Up to now, none of the measurements were able to clearlyevidence the equivalence between field and current, nor to reproduce the predicted dynamicbehavior; hence the value of the non-adiabatic torque is still under debate.In this letter we use a novel approach for the measurement of the non-adiabatic componentof spin-torque. Instead of measuring the DW velocity, we perform a quasistatic measurementof its displacement under current and magnetic field. In principle this method is similar toany quasi-static force measurement: a small displacement is created, first with the unknownforce and then with a known reference force. In our case the unknown force is caused bythe electric current passing through the DW while the reference force is due to an appliedmagnetic field. By comparing the two displacements one directly compares the applied2 IG. 1: Schematic representation of the experimental setup. The inset shows an SEM picture of asample. forces. Due to the high sensitivity of our method (able to detect DW motion down to ∼ − nm[14]) we can study the displacement of the DW inside its pinning center. Since themeasurement relies on the comparison to a reference force, the method is independent ofthe strength of the pinning. Moreover, as the field and current are applied quasi-statically,the damping parameter does not play any role.According to recent theories[6, 15, 16] that derived the value of the spin torque, β (theratio between the non-adibatic and adiabatic torques) is given by the ratio between therate of the spin-flip of the conduction electrons and that of the s-d exchange interaction.Generally, two conditions must be fulfilled to obtain a high spin-flip rate. First it is necessaryto have a strong crystalline field inside the material. The electric fields will yield a magneticfield in the rest frame of the moving electrons. Second, a breaking of the inversion symmetryis needed. Otherwise the total torque of the magnetic field on the electron spin averagesout, and the spin-flip may only occur during momentum scattering[17].In order to highlight these effects we have patterned samples from a Pt /Co /(AlO x ) layer[18]. In this case the symmetry is broken by the presence of the3lO x on one side of the Co layer, and of the heavy Pt atoms on the other[19, 20]. Wewill emphasize the importance of the spin-flip interaction to spin torque by comparingresults from these samples with those for samples fabricated from a symmetric Pt /Co /Pt layer[21], where a much smaller spin-flip rate is expected. As the only differ-ence between the two structures is the upper layer, we expect similar growth properties forthe Co layer. Both samples exhibit PMA and a strong Anomalous Hall Effect (AHE)[22].The films are patterned into the shape depicted in Figure 1. This shape is well suited for aquasi static measurement as a constriction is created by the presence of the four wires usedfor the AHE measurement (figure 1 inset). This way a DW can be pinned in a positionwhere changes in the out of plane component of the magnetization (i.e. DW motion) canbe detected by electrical measurements. A current is passed through the central wire. Thiscurrent will serve to push the domain wall as well as to probe the eventual displacement.In the case where the DW does not move under the action of the current, the transverseresistance remains unchanged and the voltage measured across the side wires (AHE) will belinear with the current. If the DW moves due to the electric current, the exciting force willcreate resistance variations, causing a nonlinear relationship between the measured voltageand the applied current. A simple way to detect such nonlinearities is to apply a perfectlyharmonic low frequency (10 Hz) ac current, and look at the first harmonic in the Fast FourierTransform (FFT) of the measured voltage. Its value is a measure of the amplitude of theDW displacement at the frequency of the applied current. To quantitatively compare theaction of a magnetic field to that of an electric current, the magnetic field is applied atthe same frequency and in phase (or opposition of phase) with the electric current. Byapplying current and field simultaneously, we ensure that their corresponding torques act onthe same DW configuration. In addition to the displacement provoked by the current, thefield induced displacement will add to the value of the first harmonic, which can be eitherincreased if the field and current push the wall in the same direction, or decreased if theyact in opposite directions.Figure 2 shows the dependence of the resistance variation at the frequency of the current(∆R f ) on the current amplitude for different values of the field amplitude. First, at lowcurrent and field amplitudes the displacement is almost linear ( ∼ A/cm ), but for highervalues, the ∆R f varies more rapidly. A simple estimation based on the value of the resistancevariation compared to the total Hall resistance of a cross (1 Ω) yields ∼ IG. 2: (a) Dependence of the resistance variation on the current amplitude for several fieldamplitudes (Pt/Co/AlO x sample). The inset shows a possible nonlinear and asymmetricpotential well. The energy landscape can be modeled by an effective out of plane magneticfield that has negative values on one side of the equilibrium position and positive valueson the other. (b) A zoom on the small amplitude regime. The inset shows the perfectsuperposition obtained by shifting the curves horizontaly with 1.25 · Acm − Oe − .5aximum amplitude of the DW motion in the first regime and ∼ ∼ f on current and field (figures 2 and 3) is in perfectagreement with the characteristic features of the non-adiabatic component of the spin-torque.First, we do not observe any critical current down to the lowest current value (10 A/cm -figure 4 in [14]). Futhermore, by extrapolating the amplitude of the DW displacement (figure2), when the current is reduced, the displacement goes to zero as the current goes to zero,in agreement with the absence of the critical current.However, the most important feature of the ∆R f behavior is that the curves obtainedfor any field amplitude can be obtained from the curve corresponding to zero field just byshifting it horizontally (in current): towards the lower current values when the field andcurrent act in the same direction on the DW and towards higher values when their actionsare opposed. This means that any displacement of the DW can also be achieved with adifferent current if a magnetic field is added. The difference in current is compensated bythe magnetic field. The value of this horizontal shift gives the field to current correspondence.The inset of figure 1b shows that all the curves corresponding to different field amplitudeshave the same shape; by shifting them horizontally (using the field-current correspondence),they all collapse on the zero field amplitude curve. This shows that independently of thedirection or strength of the applied current and field, as predicted by the theories, their effecton the DW is fundamentally similar. Moreover, further evidence that this correspondence isintrinsic and not influenced by pinning is that its value remains the same within the differentamplitude regimes as well as when the local potential well is tuned by a constant bias field.6 IG. 3: The nonlinear regime (Pt/Co/AlO x sample). When an external bias field is added,the effective pinning field changes (inset) and the nonlinear regime is reached for differentcurrent and field amplitudes. However, this does not cause any change in the field to currentcorrespondence: the horizontal distance between the curves remains the same.7ince the motion of the DW is quasi-static the magnetization can be considered to beat equilibrium during motion. In this case the sum of all torques must be zero. In orderfor the DW to remain at rest, the torque from the applied current must be compensatedby the torque generated by the magnetic field. The upturn observed on the -60 Oe curve(figure 2b) determines the position of the zero amplitude point. Note that the position ofthis point is in perfect agreement with the field to current correspondence obtained from thehorizontal shifting of the curves. By taking into account the micromagnetic structure of theDW (very thin 5nm Bloch wall) the two torques are integrated over the width of the wall,and by comparing their values (the field torque is easily calculated; [14]) the non-adiabaticterm of the spin-torque is determined. In the case of Pt/Co/AlO x stacks the current-fieldcorrespondence is approximately 1.25 10 A/cm to 1Oe, corresponding to a value of β = 1.Similar measurements (figure 1 in [14]) were also performed in the saturated state (with-out the DW). They confirm that there is no contribution to the signal from the ordinaryHall effect, but indicate a small contribution from thermoelectric effects - the Nernst-Ettingshausen Effect(NEE)[24]. The contribution from DW motion to ∆R f is much higherthan the NEE for the Pt/Co/AlO x stack. In the case of Pt/Co/Pt layers we find that theamplitude of the current induced DW motion is much smaller and entirely masked by theNEE. When a DW is moving inside the perfectly harmonic region at the bottom of the po-tential well, its displacement depends linearly on the applied force. In such a scenario, thecurrent induced DW motion and the NEE are indistinguishable. They both lead to a lineardependence of the ∆R f response on current. The only possibility to separate these effects,for the Pt/Co/Pt layer, is to attain the high amplitude nonlinear regime of DW motion.This is done by keeping the current amplitude constant and varying the field amplitude.When the current and field push the wall in the same direction, the nonlinear regime shouldbe reached for smaller field amplitudes, than if their actions were opposed.In the presence of current induced displacements, the nonlinearities observed in the∆R f versus field amplitude curve should be asymmetric. Moreover the asymmetry shoulddepend on the current value. Such an asymmetry is observed (inset of figure 4) in the caseof Pt/Co/AlO x samples. In contrast to this behavior, a fully symmetric dependence thatdoes not depend on the current amplitude is measured for the Pt/Co/Pt samples (figure 4).We conclude that in this case the spin torque induces DW displacements smaller than theresolution limit of this method. This limit value leads to (supplementary notes) β ≤ IG. 4: The nonlinear response of a DW to magnetic field. (a) ∆R f vs. the amplitude of the fieldfor three different current densities in the case of Pt/Co/Pt layers (inset Pt/Co/AlO x ).(b)Derivative of ∆R f vs. the field amplitude for a Pt/Co/Pt sample (inset Pt/Co/AlO x ).Theoretical estimations[6] based on a spin-flip frequency of 10 Hz yield a value β =0.01.To clarify the difference of the spin-torque efficiency in the two samples, the symmetrybreaking due to the presence of the AlO x surface must be taken into account. As a metallicfilm gets thinner, the conduction electron’s behavior resembles more and more to that of atwo-dimensional electron gas. When such a gas is trapped in an asymmetric potential well,9he spin-orbit coupling is much stronger than in the case of a symmetric potential due tothe Rashba interaction[25]. This effect was first evidenced in nonmagnetic materials wherethis interaction leads to a band splitting (0.15 eV for the surface states of Au (111)[26]).In the case of ferromagnetic metals this effect was already proposed to contribute as aneffective magnetic field[27] for certain DW micromagnetic structures, but should not haveany effect for Bloch walls in PMA materials. The simple 1D representation used in thiscase[27] to model the DW accounts for the coherent rotation of the spins of the incomingelectrons around the effective field, but excludes any de-coherence between electrons havingdifferent k-vector directions on the Fermi sphere (different directions of the Rashba effectivefield) as well as possible spatial inhomogeneities of this field (surface roughness). Since thespin-torque is caused by the cumulative action of all conduction electrons [6], the relevantparameter is not the spin-flip rate of a single electron but the relaxation rate of the outof equilibrium spin-density [6]. In a more realistic 2D case, in the presence of the abovementioned strong decoherence effects, the relaxation rate of the out of equilibrium spin-density approaches the rate of spin precession around the Rashba effective field. The abovevalue of the measured spin-orbit splitting (0.15 eV) will yield in this case an effective spin-flip rate of 30 · Hz, which is in excellent agreement with the order of magnitude of themeasured non-adiabatic parameter, supporting this scenario.In summary, a technique that allows the direct measurement of the torque from anelectric current on a DW was developed. 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