Surface acoustic waves increase magnetic domain wall velocity Surface acoustic waves increase magnetic domain wall velocity

Domain walls in magnetic thin films are being explored for memory applications and the speed at which they move has acquired increasing importance. Magnetic fields and currents have been shown to drive domain walls with speeds exceeding 500 m/s. We investigate another approach to increase domain wall velocities, using high frequency surface acoustic waves to create standing strain waves in a 3 micron wide strip of magnetic film with perpendicular anisotropy. Our measurements, at a resonant frequency of 248.8 MHz, indicate that domain wall velocities increase substantially, even at relatively low applied voltages. Our findings suggest that the strain wave derived effective magnetic field acts as an additional driver for domain wall motion. The growing promise of racetrack memory technology 1 has led to an explosion in the investigation of the motion of domain walls (DW) in magnetic nanostructures. Defect free thin films, higher fields, and current 2–4 have all been shown to increase DW velocities, but the latter two approaches increase overall power requirements, an undesirable trait. Here we show that strain in the form of high frequency surface acoustic waves (SAW) result in a substantial increase in the DW velocity in a 3 μ m wide frequency SAW driven magnetic resonances in Ni films 8 and (Ga,Mn)(As,P) 9 show that the direction of magnetization can be

The growing promise of racetrack memory technology 1 has led to an explosion in the investigation of the motion of domain walls (DW) in magnetic nanostructures. Defect free thin films, higher fields, and current [2][3][4] have all been shown to increase DW velocities, but the latter two approaches increase overall power requirements, an undesirable trait.
Here we show that strain in the form of high frequency surface acoustic waves (SAW) result in a substantial increase in the DW velocity in a 3μm wide magnetic stripe of a [Co/Pt]5 multilayer with perpendicular magnetic anisotropy. The stripe is parallel to the propagation direction of the SAW and lies between two identical interdigital transducers (IDT) each with 100 finger pairs, all patterned via photolithography on a 128 ○ Y cut LiNbO 3 substrate. The two IDTs are spaced an integer number of wavelengths apart and excited in parallel, generating a standing wave between them. Figures 1a and 1b show the geometry and coordinate system, the sample structure and the SAW wavelength. The frequency response of the reflection and transmission parameters, shown in Figures 1c and 1d, are measured using a spectrum analyzer (Agilent E7402A) and a bidirectional coupler (Mini-Circuit ZFBDC20-62HP+). The response of all four S-parameters over the frequency range 240-260 MHz are measured to obtain the SAW resonance frequency (f 0 ) of 248.8 MHz.
The interaction between strain and magnetism is encompassed in the magneto-elastic constants and the free energy terms associated with them viz.
where B 1 and B 2 are the longitudinal and shear magneto-elastic constants which are material dependent, e ii and e ij constitute the longitudinal and shear strains in the magnetic film and the α i are the direction cosines of the magnetization. The directions x, y, and z are as defined in Figures 1a and 1b, with the z axis perpendicular to the plane of the sample and the x axis parallel to the propagation direction of the SAW. Previous experiments that explore the coupling between strain and magnetism include SAW driven magnetization rotation in cobalt microstructures 5 and a lowered coercivity in inplane Galfenol (FeGa) films 6 and out of plane (Ga,Mn)(As,P). 7 High frequency SAW driven magnetic resonances in Ni films 8 and (Ga,Mn)(As,P) 9 show that the direction of magnetization can be reversed with appropriate control of the SAW pulse width. Our previous paper 10 had shown that SAW were efficient drivers of DWs in a large area thin film. In this manuscript, we make detailed and wide-ranging measurements of the effects of SAW on DW velocity in a microscopic strip that restricts the direction of DW motion and allows us to quantitatively model the effects of the SAW. Measurements of the DW velocity are made using a MOKE microscope and a pulsed magnetic field. The velocity measurements with SAW are performed using pulsed magnetic fields in the presence of a continuously driven SAW at the resonance frequency. The stripe is first saturated at a field of -750 Oe, followed by a nucleation field of 177 Oe. The DW nucleates in the reservoir close to the left end of the stripe and successive field pulses expand the domain along the stripe. We perform more than 10 measurements for each field to obtain the average velocity and standard error. Typical MOKE images of DW motion are shown in Figure 2. The motion of the DW in the absence of SAW is shown in Figure 2(a) with 20 ms field pulses of 142 Oe. Successive 20 ms pulses move the DW from left to right through the length of the magnetic stripe and the velocity is obtained by measuring the position of the domain wall after every pulse. A good measure of the increase in DW velocity can be seen in the number of pulses it takes to move the DW through the length of the stripe. In the absence of SAW, it takes ninety-seven 20-ms long pulses to move the DW across the stripe. In contrast, in the presence of a continuous SAW excitation of 4 V, (Figure 2b) the DW moves across the stripe in only sixteen pulses. This factor of 6 decrease in the number of pulses implies a 6-fold increase in the velocity. Videos of the DW propagation along the stripe at a field of 142 Oe with SAW excitations of 0 V, 2 V and 4 V are presented in supplementary material videos S1, S2 and S3, respectively.
We repeat the set of measurements at field values ranging from 118 to 190 Oe, and with SAW excitations ranging from 0 to 4 V. The velocity as a function of field with no SAW is shown in Figure 3(a) and displays the expected increase in velocity with increasing field. A plot of Ln(v) vs H -1/4 in the inset displays the linear dependence that would be expected in the creep regime 11,12 i.e., Here, vo is a scaling parameter, Uc is the depinning potential, H dep is the depinning field at 0K and μ=1/4 is the critical exponent. We extract the scaling parameter ln[voin μm/s] = 62.0 ± 0.9 and depinning parameter, U c k B T (H dep ) 1/4 = 201.3 ± 3.1(Oe) 1/4 from the fit of the straight line in the inset. These numbers (derived for zero SAW excitation) characterize the average, overall pinning landscape seen by the DWs and we use them for fitting the SAW data. Experiments measuring the effects of DC strain on creep behavior have shown 12 that strain does not alter these parameters in any substantial fashion.
DW velocity data as a function of increasing SAW amplitudes are shown in Figure 3 Figure 4a for each SAW voltage shows sets of parallel lines, indicating that we remain in the creep regime. We model the effect of the SAW as an additional field and insert this effective field into the creep equation to fit the increased SAW driven velocity.
We start by simplifying the magneto-elastic terms in the free energy (Eq. (1)) for 128 ○ Y cut LiNbO 3 and the magnetization of the sample. The out-of-plane anisotropy of the film ensures that αx=0 everywhere except at DWs. Moreover, if we assume a Néel DW (as is commonly accepted) αy = 0 everywhere. Because the surface is stress free, the ezz term arises only from the effective Poisson ratio for a [Co/Pt] layer on LiNbO 3 , calculated to be 13 ν eff = -0.4. Previous calculations 10 indicate that propagation along the x axis in 128 ○ Y cut LiNbO 3 results in shear strains that are substantially (>20 times) lower than exx. Hence the magneto elastic term in the free energy with the spatial and time dependence of the standing wave, may be approximated as where e 00 is the strain amplitude per unit voltage. Simulations have shown 14 that the strain gradient is the leading driving term   Fig. 3(a)).
for DWs, implying that DWs will be driven most strongly at the nodes of the standing wave. Our data do not show any spatial dependence, perhaps due to the fairly low resonance frequency, which will limit the magnitude of the strain gradient. Moreover, because we are in the creep regime, the velocity changes we see are driven by the ability of DWs to depin from the pinning potential landscape.
The amplitude of the strain derived effective field is a derivative of the magneto-strictive free energy FME and is given by An absolute measure of this field is difficult to obtain because the conversion between voltage and strain field, the exact value for B 1 and direction of magnetization (αx, αz) inside the domain wall are subject to some uncertainty. However, we can assume that the strain is proportional to applied voltage. Both in-plane and out of plane fields are relevant to the depinning as has been shown in previous measurements. 15 The ratio of Hz/Hx depends on αx and αz which vary across the DW, but we can assume that both are nonzero and both are proportional to V, so that the direction of the SAW induced field is somewhere in the x-z plane. Hence the net effective field for domain wall motion is given by the vector addition of the applied field (Happ in the z direction) and the SAW derived field (H SAW ), viz. ⃗ where γ = 2B 1 e 00 α x M s encompasses the magneto-elastic constant, αx and the conversion between applied voltage and strain amplitude and β = Hz/Hx accounts for the direction of H SAW . The entire set of velocity data is modelled using β and γ as free parameters and the previously obtained ν 0 and U c k B T (H dep ) 1/4 from the data without SAW excitation. Figure 4(b) shows that the entire data set collapses onto a single curve, that of the V= 0 line, with the best fit (χ 2 = 1.24) obtained for values of β=0.2 and γ = 11.7 Oe/V. The small value for β implies an effective field close to the x axis direction. The total effective field per unit voltage produced by this particular set of SAW transducers HSAW = √ (Hx) 2 + (Hz) 2 = γ √ 1 + β 2 = 11.9 Oe/V.
In summary, we have investigated the effects of SAW on domain wall velocities in multilayers of [CoPt]5 over a wide range of field and SAW excitations. Domain wall velocities shows a dramatic 3-8 fold increase with SAW voltage. Modelling the SAW as an effective field collapses all the SAW data onto a single curve in the creep regime, manifesting the effectiveness of our model. The coupling parameter between SAW voltage and field is found to be 11.9 Oe/V, for this particular set of IDTs. Increasing the number of fingers and better impedance matching will contribute to higher SAW derived effective fields and hence higher DW velocities.
See supplementary material videos S1, S2 and S3 for domain wall propagation along the stripe at a field of 142 Oe and SAW voltages of 0V, 2V, and 4V, respectively. This work was supported by NSF (DMR-1409622) and NSF Nebraska MRSEC (DMR-1420645). The research was performed in part in the Nebraska Nanoscale Facility: National Nanotechnology Coordinated Infrastructure and the Nebraska Center for Materials and Nanoscience, which are supported by the National Science Foundation under Award ECCS: 1542182, and the Nebraska Research Initiative.