Controlling the influence of elastic eigenmodes on nanomagnet dynamics through pattern geometry
Introduction
Understanding nanomagnet dynamics in densely packed arrays is important due to their potential applications in next generation spintronic devices. A number of experiments can be employed for this purpose including ferromagnetic resonance [1], Brillouin light scattering [2], x-ray spectroscopy [3], and the time-resolved magneto-optic Kerr effect (TR-MOKE) [4], [5], [6], [7], [8]. Each has their own benefits and drawbacks, and involves various techniques such as rf magnetic fields [1], spin polarized currents [9], [10] and picosecond acoustic pulses [11] for instigating magnetization precession in order to gain insight into the underlying mechanisms governing the motion of the spins. In all-optical TR-MOKE the precession is initiated by optical excitation with femtosecond pump pulses that are absorbed by the magnetic material. This method provides high spatial and temporal resolution. While the intrinsic magnetic response of a nanomagnet is most naturally studied using a single element [4], measurements on arrays are valuable as they may be the only way to generate large enough magneto-optical signals to observe the dynamics of a given system and because they provide a complementary set of information that helps identify extrinsic effects due to inter-element variations and interactions. However, a side effect in regularly patterned arrays is the simultaneous generation of surface acoustic waves (SAWs) due to the thermal expansion of the elements upon irradiation with the pump pulse. These SAWs exist at specific frequencies and have been extensively investigated recently due to the emerging field of phononic bandgap materials. In these systems, the phononic band structure is a function of material properties as well as the position and size of elements in arrays which create stopbands in the spin-wave spectrum [12], [13], [14]. Time-resolved studies on periodic arrays of Al nanoelements revealed that the SAW frequencies depend inversely on the array pitch [15]. The interplay of mechanical and magnetic oscillations in arrays has been investigated as well [16]. Specifically, optically generated SAWs can drive the magnetization dynamics in nanostructured arrays via magneto-elastic coupling. This causes the spin precession resonances to be pinned at the SAW frequencies over an extended applied field range around the point where the two resonances are degenerate. While this opens up the possibility for utilizing SAWs as an extra degree of freedom for investigating nanomagnet arrays, the SAW induced magnetization dynamics complicate the extraction of the intrinsic magnetic response. Here, we demonstrate a method for suppressing the laser-induced SAW influence on magnetization dynamics. By altering the array geometry from a periodic to a randomized pattern, the effect of the SAWs on the magnetization dynamics can be mitigated, thereby restoring the intrinsic magnetic response. Using spatial Fourier analysis, we quantify the efficacy of the approach and show that it is limited by residual correlations in structures with a finite filling factor. The approach is powerful enough to permit the observation of the field-dependent Kittel mode and the extraction of the effective damping in densely packed nano-elements using all-optical pump-probe methods.
Section snippets
Experimenal details
Fig. 1(a) shows SEM images of the two samples investigated, exhibiting a periodic (top) and an aperiodic (bottom) pattern, respectively. They were fabricated using electron beam lithography on a (100) Si substrate capped by a 110 nm thick hafnium oxide antireflection coating as previously reported [16], [17], [18]. They are both comprised of 30 nm thick 156 nm wide polycrystalline Ni squares. In the periodic array the elements have a pitch of 330 nm corresponding to a fill factor of 0.22. This same
Results and discussion
In order to understand the influence of the nanomagnet array geometry on the generation of SAWs, it is instructive to analyze the array geometry in Fourier space. Fig. 1(b) shows the two-dimensional spatial Fourier transforms of the two samples under investigation. In the periodic array, the regular arrangement of elements in particular directions manifests itself as discrete points in Fourier space. The spacing of these points is a function of the array pitch. Each point corresponds to a
Conclusion
In conclusion, we have demonstrated a method for drastically reducing the influence of SAWs on the magnetization dynamics in densely packed arrays. By randomizing the array geometry, the constructive mechanical interaction between individual elements can be reduced which leads to a near-complete elimination of the magneto-elastic interactions within the elements. This allows for the determination of intrinsic material parameters such as the Kittel mode and the effective damping in densely
Acknowledgement
This work was supported by the National Science Foundation under Grants No. DMR-1311744, DMR-1506104 and ECCS-1509020 and by the German Research Foundation (DFG) under Grant No. AL618/21-1. Work at the Molecular foundry, Lawrence Berkeley National Laboratory was supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. We acknowledge T. Yuzvinsky and the W.M. Keck Center for Nanoscale Optofluidics at the
References (24)
J. Magn. Magn. Mater.
(1996)- et al.
Phys. Rev. Lett.
(2007) - et al.
Phys. Rev. B
(2011) - et al.
Phys. Rev. Lett.
(2009) - et al.
Nano Lett.
(2006) - et al.(2012)
- et al.
Phys. Rev. B
(2001) - et al.
Phys. Rev. B
(2005) - et al.
Appl. Phys. Lett.
(2011) - et al.
Nature
(2003)
Phys. Rev. Lett.
Phys. Rev. B
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