Square Array Of Antidots Research Articles

Commensurability resonances in two-dimensional magnetoelectric lateral superlattices

Hybrid lateral superlattices composed of a square array of antidots and a periodic one-dimensional magnetic modulation are prepared in $\mathrm{Ga}[\mathrm{Al}]\mathrm{As}$ heterostructures. The two-dimensional electron gases exposed to these superlattices are characterized by magnetotransport experiments in vanishing average perpendicular magnetic fields. Despite the absence of closed orbits, the diagonal magnetoresistivity in the direction perpendicular to the magnetic modulation shows pronounced classical resonances. They are located at magnetic fields where snake trajectories exist which are quasicommensurate with the antidot lattice. The diagonal magnetoresistivity in the direction of the magnetic modulation increases sharply above a threshold magnetic field and shows no fine structure. The experimental results are interpreted with the help of numerical simulations based on the semiclassical Kubo model.

Nonlinear magnetotransport in a two-dimensional electron system in a square array of antidots in GaAs/AlAs heterostructures

Nonlinear magnetotransport of two-dimensional electrons in square antidot lattices prepared on the basis of selectively doped GaAs/AlAs heterostructures with the period that is much less than the electron mean free path in the initial GaAs quantum wells but is much larger than their Fermi wavelength has been studied. It has been shown that the character of the nonlinear transport of the two-dimensional electrons in the lateral lattices under study changes from classical to quantum with the decrease in the antidot radius. It has been found that the quantum lifetime increases in the magnetic field corresponding to the condition of equality of the cyclotron diameter of two-dimensional electrons and the antidot lattice period.

Visualizing the ac magnetic susceptibility of superconducting films via magneto-optical imaging

We have established a link between the global ac response and the local flux distribution of superconducting films by combining magnetic ac susceptibility, dc magnetization, and magneto-optical measurements. The investigated samples are three Nb films: a plain specimen, used as a reference sample, and other two films patterned with square arrays of antidots. At low temperatures and small ac amplitudes of the excitation field, the Meissner screening prevents penetration of flux into the sample. Above a certain ac drive threshold, flux avalanches are triggered during the first cycle of the ac excitation. The subsequent periodic removal, inversion, and rise of flux occurs essentially through the already-created dendrites, giving rise to an ac susceptibility signal weakly dependent on the applied field. The intradendrite flux oscillation is followed, at higher values of the excitation field, by a more drastic process consisting of creation of new dendrites and antidendrites. In this more invasive regime, the ac susceptibility shows a clear field dependence. At higher temperatures a smooth penetration occurs, and the flux profile is characteristic of a critical state. We have also shown that the regime dominated by vortex avalanches can be reliably identified by ac susceptibility measurements.

High field vortex matching effects in superconducting Nb thin films with a nanometer-sized square array of antidots

Nb thin films containing a regular square array of antidots with 17 nm diameter and 50 nm spacing have been fabricated using a relatively simple lithographic process. The critical current density jc(H) curves, obtained here by electric transport measurements, exhibit commensurability effects with pronounced maxima just above the expected μ0H1=0.830 T and μ0H1/2=0.415 T matching fields, down to temperatures as low as 2.3 K. The behavior of jc(H) as well as the position of the maxima are consistent with the ones calculated in the framework of the time dependent Ginzburg–Landau model.

Fractional matching effect of vortices in [formula omitted] with square lattice of antidots

In order to study the influence of artificial pinning centers on vortex behavior in high-Tc superconductors, we have measured vortex-flow resistance in Bi2Sr2CaCu2O8+y single-crystal thin films with a square array of antidots. In addition to the integer matching effect, which is expected at integer multiples of the first matching field H1, fractional matching effects have been found as fine dip structures at fields Hf(=fH1) (f: fractional number). The observed values of f are 1/6, 1/4, 1/3, 1/2, 2/3, and 3/4. While a square lattice of vortices (or unoccupied antidots) can fit on the antidot array for the cases of 1/4 and 1/2 (3/4), different vortex configurations are required to explain for the other fractions, viz., a stripe pattern at 1/3.

Strain-Induced Fermi Contour Anisotropy of GaAs 2D holes

We report measurements of magnetoresistance commensurability peaks, induced by a square array of antidots, in GaAs (311)A two-dimensional holes as a function of applied in-plane strain. The data directly probe the shapes of the Fermi contours of the two spin subbands that are split thanks to the spin-orbit interaction and strain. The experimental results are in quantitative agreement with the predictions of accurate energy band calculations, and reveal that the majority spin subband has a severely distorted Fermi contour whose anisotropy can be tuned with strain.

Non commensurate vortex lattices in a composite antidot lattice or dc current

Within the phenomenological Ginzburg–Landau theory we investigate the effect of a composite antidot lattice and small dc applied current to the stability of commensurate and non commensurate vortex structures in perforated type-II superconducting samples in the weak pinning regime. We found that a composite antidot lattice, consisting of small and big antidots in the unit cell, considerably increases the probability to find square pinned vortex lattice as compared to a sample with a regular square array of antidots. An applied current also favors the square pinned vortex states. These results indicate that both the applied current and a composite pinning array distort the broad local minimum in the free energy which keeps the vortices away from the pinning centers.

Aharonov–Bohm-type effects in different arrays of antidots

We have investigated Aharonov–Bohm-type oscillation in the quantum Hall plateau transition region in three types of square arrays of antidots; a large ( 50 × 160 antidots) array, a small ( 5 × 10 antidots) array, and the sample with antidots placed only near the side edges. The temperature dependence of the amplitude confirmed that the oscillation originates from the fine structure in the density of single particle states circumnavigating around each antidot. In addition, we have also observed Altshuler–Aronov–Spivak oscillation near zero magnetic field in square arrays of antidots.

A micromagnetic study of the hysteretic behavior of antidot Fe films

We report on the results of a micromagnetic study of the magnetization reversal process taking place in square arrays of antidots lithographed in Fe thin films. Our study focuses on the influence on the reversal process of the antidot diameter and the distance between adjacent antidots. It is shown that the minimization of the dipolar energy term of the total system energy originates inhomogeneous moment distributions at the antidot surfaces, and that these structures and their coupling rule the reversal process. We also show that the variation of the interantidot distance in the range of a few units of the exchange length allows varying the coercive force value by a factor of four approximately.

Vortex imaging and local magnetization studies in HTS by scanning Hall probe microscopy

We have used scanning Hall probe microscopy to correlate vortex images and local magnetisation measurements in two different high temperature superconducting samples. Near the edge of a continuous YBCO thin film we have observed local hysteresis inversion and negative remanent fields, which can be semi-quantitatively explained in terms of a theoretical model of flux penetration in an infinitely long superconducting strip. In a YBCO film containing a regular square array of antidots we have further find that vortices trapped at antidots exhibit an unusual behaviour upon field sweep reversal.

In-plane anisotropic vortex motion induced by a square array of antidots

We report on electro-transport measurements on a Pb thin film with a square array of antidots, for the whole angular range of in-plane current orientations. We demonstrate that the interaction of a moving flux line lattice with a periodic pinning potential, breaks the rotational symmetry and induces a guided vortex motion along the principal symmetry orientations of the pinning array. As a consequence, we found that for orientations different than the symmetry directions, the vortex velocity is not aligned with the Lorentz force. We show that this anisotropic vortex motion is temperature dependent and progressively fades out when approaching the normal state.

Ac response of Pb thin films with a periodic pinning potential

We have studied the dynamic response of Pb thin films with a square array of antidots by means of ac susceptibility χ( T, H) measurements. For low amplitudes h of the ac excitation, the field dependence of the ac susceptibility exhibits a series of distinctive features associated with the presence of different dynamic regimes. For fields below a certain characteristic field H s, vortices strongly pinned by the antidots perform an oscillatory movement inside the pinning potential induced by the external ac drive. For fields between H s and H p, interstitial vortices, performing an intra-valley motion in the weak potential wells produced by the repulsive interaction of their pinned neighbors, dominate the ac response. For H p< H< H t, the interstitial vortices are driven out of their pinning sites while vortices in the antidots remain trapped. For higher fields all vortices are set in motion and a critical state develops. We show that the characteristic h-independent field H s allows one to clearly identify the maximum number of flux quanta per hole. Unlike H s, the fields H p and H t, signaling the onset of motion of interstitial vortices and vortices trapped by the antidots, respectively, strongly depend on h.

Guided vortex motion in superconductors with a square antidot array

We have measured the in-plane anisotropy of the vortex mobility in a thin Pb film with a square array of antidots. The Lorentz force, acting on the vortices, was rotated by adding two perpendicular currents and keeping the amplitude of the net current constant. One set of voltage probes was used to detect the vortex motion. We show that the pinning landscape provided by the square antidot lattice influences the vortex motion in two different ways. First, the modulus of the vortex velocity becomes angular dependent with a lower mobility along the diagonals of the pinning array. Second, the vortex displacement is preferentially parallel to the principal axes of the underlying pinning lattice, giving rise to a misalignment between the vortex velocity and the applied Lorentz force. We show that this anisotropic vortex motion is temperature dependent and progressively fades out when approaching the normal state.

X-ray photoemission electron microscopy investigation of magnetic thin film antidot arrays

Periodic square arrays of antidots in 10 nm-thick cobalt films have been investigated with antidot periods, p, ranging from 2 μm down to 200 nm and various ratios of antidot size to antidot separation, w/d. For p=2 μm, the extent of modification of the thin film magnetic domain structure increases with increasing w/d, forming domains pinned diagonally between antidots for w/d⩾0.2 and resulting in a two-dimensional periodic checked domain contrast commensurate with the antidot lattice for w/d⩾0.9. As p is decreased while maintaining d≈w, we observe a dramatic change in the magnetic domain configuration at p=400 nm resulting in chains of magnetic domains running parallel to the intrinsic hard axis and with lengths corresponding to a multiple of the antidot period.

Vortex avalanches in a Pb film with a square antidot array

We have performed magnetization measurements on a Pb thin film perforated by a square array of antidots in a broad temperature range. For temperatures below 6 K, we observe magnetization jumps at low fields. In the film with the antidot lattice, the region in the field-temperature plane, where the jumps are observed, is substantially enlarged but the relative jump size is smaller compared to a reference film without any nanostructuring. Also, the width of the magnetization loops for the perforated film is much smaller than that for the plain film at very low temperatures. These results can be understood by taking into account the existence of a multiterrace critical state induced by the antidot array. The size distributions of the magnetization jumps do not follow the power-law decay expected in the case of self-organized criticality.

Unexpected fourfold symmetry in the resistivity of patterned superconductors

We report the magneto-optical observation of a surprising fourfold symmetry of the flux penetration in a superconducting ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ thin-film disk containing a square array of antidots, leading to an angular variation of the critical current by a factor of nearly 2. This behavior is explained using a vortex channeling model. Potential applications in superconducting devices are discussed

Dynamic regimes in films with a periodic array of antidots

We have studied the dynamic response of Pb thin films with a square array of antidots by means of ac susceptibility chi(T,H) measurements. At low enough ac drive amplitudes h, vortices moving inside the pinning potential give rise to a frequency- and h-independent response together with a scarce dissipation. For higher amplitudes, the average distance travelled by vortices surpasses the pinning range and a critical state develops. We found that the boundary h*(H,T) between these regimes smoothly decreases as T increases whereas a step-like behavior is observed as a function of field. We demonstrate that these steps in h*(H) arise from sharp changes in the pinning strength corresponding to different vortex configurations. For a wide set of data at several fields and temperatures in the critical state regime, we show that the scaling laws based on the simple Bean model are satisfied.

Vortex confinement by regular pinning arrays

The pinning of vortices is studied in a superconducting Pb film with a regular array of submicron dots (Co dots with in-plane magnetization and Co/Pt dots with out-of-plane magnetization) or antidots. Matching anomalies are observed in the critical current and magnetization behavior at integer and rational multiples of the first matching field, corresponding to stable vortex configurations. The pinning force of Co dots with a single-domain state is enhanced compared to multi-domain dots. For Co/Pt dots with out-of-plane magnetisation a clear asymmetry is present in the magnetisation curves due to the direct interaction of the vortices with the magnetic moment of the dots. In superconducting films with a square array of antidots, Shapiro voltage steps are observed in the voltage-current characteristics in the presence of rf-radiation. These steps clearly reveal the presence of mobile interstitial vortices coexisting with immobile vortices strongly pinned at the antidots.

Quantum lifetimes in antidot arrays

Magnetotransport in GaAs/Ga 1− x Al x As heterostructures with a square array of antidots has been investigated. Quantum lifetimes τ q are estimated from the amplitudes of Shubnikov–de Haas oscillations and two values of τ q are found at low and high magnetic fields. The critical field at which τ q changes corresponds to the magnetic field where the cyclotron diameter 2 R c is almost equal to the effective constriction length L c between two antidots. This suggests that the influence of scattering from antidots on τ q is different in the regions where 2 R c> L c and where 2 R c< L c.

Single-particle relaxation times in antidot arrays

Magnetotransport in GaAs/Ga 1− x Al x As heterostructures with a square array of antidots has been investigated. Single-particle relaxation times τ s are estimated from the amplitudes of Shubnikov–de Haas oscillations and two values of τ s are found at low and high magnetic fields. The critical field at which τ s changes corresponds to the magnetic field where the cyclotron diameter 2 R c is almost equal to the effective constriction length L c between two antidots. This suggests that the influence of scattering from antidots on τ s is different in the region where 2 R c> L c and where 2 R c< L c.