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The nonlinear vibrational properties of a periodic micromechanical oscillator array have been measured. For sufficiently large amplitude of the driver, the optic mode of the di-element cantilever array becomes unstable and breaks up into excitations ranging over only a few cells. A driver-induced locking effect is observed to eternalize some of these intrinsic localized modes so that their amplitudes become fixed and the modes become spatially pinned. DOI: 10.1103/PhysRevLett.90.044102 PACS numbers: 05.45.-a, 05.45.Xt, 63.20.Pw, 85.85.+j Intrinsic localized modes (ILMs) which extend over only a few lattice sites of a periodic nonlinear lattice have been examined theoretically in a variety of systems [1][2][3][4]. Although the smallest excitations would be in a quantum lattice [5], there are still interesting issues in classical models to be explored experimentally such as mobility [6], discrete lattice potential [7], and interaction among ILMs [8], as well as the long-time behavior of a driver-induced modulational instability for a dissipative system. Thus the exploration of amplitude-dependent features is one of the important experimental issues at the present time.Although some experimental studies have been reported for large scale mechanical systems [9], for somewhat smaller Josephson-junction arrays [10,11] and optical waveguides [12,13], and for nanoscale lattices [14 -16] none of these systems are, as yet, appropriate for studying the detailed motion of large numbers of ILMs in the presence of a driver. Recently, microelectro-mechanical system (MEMS) silicon technology has matured sufficiently [17] so that we can make a few hundred coupled cantilever oscillators [18]. In this Letter we describe our experimental investigation of ILM creation and locking for a cantilever array in the presence of damping, disorder, and a driver.Our cantilever array is produced from a photoresist mask over a silicon nitride layer on a silicon substrate. This is exposed and then etched via a CF 4 plasma in a reactive ion chamber. The silicon substrate is undercut using an anisotropic KOH etch, thus releasing the silicon nitride cantilevers. A 3D rendition of one unit cell of the resulting array is shown in Fig. 1(a). Such cantilevers have a hard nonlinearity. To achieve the large amplitude uniform mode instability required to produce ILMs one needs to drive the highest frequency uniform mode of the system [19]. In order to accomplish this when using a piezoelectric transducer (PZT) driver, two different length cantilevers per unit cell have been constructed as shown in Fig. 1(a). With this di-element array the dispersion curve is folded over so that the highest frequency vibrational mode is now at the zone center. The room temperature quality factor of this mode is about 8000.Figure 1(b) shows the experimental setup for measuring ILM dynamics and mobility versus time. A cylindrical lens is used to focus a He-Ne laser line image on the static array. The reflected beam is then incident on a 1-D CCD camera. The PZT is driven...

Inelastic neutron measurements of the high temperature lattice excitations in NaI show that in thermal equilibrium at 555 K an intrinsic mode, localized in three dimensions, occurs at a single frequency near the center of the spectral phonon gap, polarized along [111]. At higher temperatures the intrinsic localized mode gains intensity. Higher energy inelastic neutron and x-ray scattering measurements on a room temperature NaI crystal indicate that the creation energy of the ground state of the intrinsic localized mode is 299 meV.

In a strongly nonlinear discrete system, the spatial size of an excitation can become comparable to, and influenced by, the lattice spacing. Such intrinsic localized modes (ILMs)--also called 'discrete breathers' or 'lattice solitons'--are responsible for energy localization in the dynamics of discrete nonlinear lattices. Their energy profiles resemble those of localized modes of defects in a harmonic lattice but, like solitons, they can move (although, unlike solitons, some energy is exchanged during collisions between them). The manipulation of these localized energy 'hotspots' has been achieved in systems as diverse as annular arrays of coupled Josephson junctions, optical waveguide arrays, two-dimensional nonlinear photonic crystals and micromechanical cantilever arrays. There is also some evidence for the existence of localized excitations in atomic lattices, although individual ILMs have yet to be identified. Here we report the observation of countable localized excitations in an antiferromagnetic spin lattice by means of a nonlinear spectroscopic technique. This detection capability permits the properties of individual ILMs to be probed; the disappearance of each ILM registers as a step in the time-dependent signal, with the surprising result that the energy staircase of ILM excitations is uniquely defined.

Intrinsic localized modes ͑ILMs͒ have been observed in micromechanical cantilever arrays, and their creation, locking, interaction, and relaxation dynamics in the presence of a driver have been studied. The micromechanical array is fabricated in a 300 nm thick silicon-nitride film on a silicon substrate, and consists of up to 248 cantilevers of two alternating lengths. To observe the ILMs in this experimental system a line-shaped laser beam is focused on the 1D cantilever array, and the reflected beam is captured with a fast charge coupled device camera. The array is driven near its highest frequency mode with a piezoelectric transducer. Numerical simulations of the nonlinear Klein-Gordon lattice have been carried out to assist with the detailed interpretation of the experimental results. These include pinning and locking of the ILMs when the driver is on, collisions between ILMs, low frequency excitation modes of the locked ILMs and their relaxation behavior after the driver is turned off. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1540771͔An advance of the theory of nonlinear excitations in discrete lattices was the discovery that some localized vibrations in perfectly periodic but nonintegrable lattices could be stabilized by lattice discreteness. The modulational instability of extended large amplitude vibrational modes has been proposed as a mechanism for the realization of dynamical localization on the scale of the lattice constant. Although theoretically a variety of methods to excite the instability of a homogeneous vibrational mode have been proposed, these ideas have yet to be tested experimentally. Since the observation of nanoscale localized vibrational modes still cannot be achieved there is definite advantage to examining a macroscopic array, which is small enough so that the entire time dependence of the instability dynamics occurs in a practical measurement interval. This has been accomplished by using micromechanical silicon technology to fabricate up to 248 identical cantilevers with a 40 micron lattice constant. Optical techniques have been used to track the motion of individual cantilevers in the presence of an inertial driver. In addition to experimentally characterizing the modulational instability and identifying the best method for producing intrinsic localized modes a new discovery is the locking of the local mode amplitude with the driver frequency. Numerical simulations have been used to better understand the nature of this synchronization effect.

The existence of anharmonic localization of lattice vibrations in a perfect 3-D diatomic ionic crystal is established for the rigid-ion model by molecular dynamics simulations. For a realistic set of NaI potential parameters, an intrinsic localized gap mode vibrating in the [111] direction is observed for fcc and zinc blende lattices. An axial elastic distortion is an integral feature of this mode which forms more readily for the zinc blende than for the fcc structure. Molecular dynamics simulations verify that in each structure this localized mode may be stable for at least 200 cycles.It has been proposed [1,2] and numerically demonstrated [3] that a large amplitude vibration in a perfect 1-D lattice can localize because of anharmonicity. More detailed analytical and numerical investigations of classical 1-D anharmonic chains made possible by simple eigenvalue generating recursion relations have revealed a variety of stable intrinsic localized modes with frequencies outside of the plane wave bands [3][4][5][6][7][8]. Recently quantum mechanical aspects of ILMs (Intrinsic Localized Modes) have been considered [9,10]. Some progress also has been reported for higher dimensional classical crystal lattices with simple nearest-neighbor model interactions [11,12]. Particularly important has been the recognition that diatomic crystal potentials like the Born-Mayer-Coulomb in 1-D produces an intrinsic gap mode (IGM) between the optic and acoustic branches instead of an ILM above the plane wave spectrum [13]. The possibility of IGMs in 3-D anharmonic lattices with realistic potentials has remained elusive. One approach has been to focus on crystal surfaces and edges where harmonic localization already plays an important role [14][15][16].In this Letter we demonstrate with molecular dynamics simulations that, for sufficiently large vibrational amplitude, anharmonicity can stabilize an IGM in a 3-D uniform diatomic crystal with rigid ion NaI potential arranged in either the fcc or zinc blende structure. By developing a self-consistent numerical technique for finding an intrinsic localized mode eigenvector, we have been able to show that for a given gap mode amplitude with the same potential that the localization is much stronger for a T d symmetry site when compared to an O h one.To construct the stationary localized mode eigenvector for the nonlinear 3-D diatomic lattice with long range interactions, we build on techniques which have been used successfully to identify 1-D anharmonic modes [13], one of which is the rotating wave approximation. A Fourier extension of that idea for vibration in a stationary periodic mode with fundamental frequency, ω, which includes the static and second harmonic for the i th particle displacement, r i (t), iswhere ri , is the distorted equilibrium position of the i th particle, and the r (n) i 's are the time-independent amplitudes of the different harmonics. The force acting on the i th particle can also be represented by a similar Fourier series. Substituting the coordinate and force Fou...

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The far-infrared conductivity of CePd 3 has been obtained from temperature-dependent reflectivity measurements between 0.4 and 400 meV. The low-temperature results are consistent with simple Fermi-liquid ideas, even though the conduction-carrier density is less than 0.3 electron per formula unit.