Realization of Artificial Ice Systems for Magnetic Vortices in a Superconducting MoGe Thin Film with Patterned Nanostructures

Abstract

We report an anomalous matching effect in MoGe thin films containing pairs of circular holes arranged in such a way that four of those pairs meet at each vertex point of a square lattice. A remarkably pronounced fractional matching was observed in the magnetic field dependences of both the resistance and the critical current. At the half matching field the critical current can be even higher than that at zero field. This has never been observed before for vortices in superconductors with pinning arrays. Numerical simulations within the nonlinear Ginzburg-Landau theory reveal a square vortex ice configuration in the ground state at the half matching field and demonstrate similar characteristic features in the field dependence of the critical current, confirming the experimental realization of an artificial ice system for vortices for the first time.PACS numbers: 74.78. Na, 74.40.Gh Artificial ice systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14] that can have properties similar to atomic spin ices [15][16][17][18][19][20] have been gaining tremendous interest in recent years in areas ranging from solid state systems, magnetism, and soft matter. Among them the two-dimensional (2D) artificial spin ices created using e.g., nanomagnetic arrays [1-8] and charged colloidal particle assemblies [9][10][11][12][13][14] have opened a new avenue in the study of novel phenomena such as geometrical frustration [7,8,[15][16][17][18][19][20][21][22][23][24] which can elucidate, e.g., exotic spin states, [16] charge quantization in magnetic monopoles, [21,22] and mechanisms of high-T c superconductivity. [24] In artificial nanomagnetic square spin ices, [1,8] however, the ice rule states with spin arrangements following "two spins in, two spins out" orders [17] have been only partially observed, which could be due to the weak interactions between the magnetic islands.Vortex matter in a superconductor has much stronger interactions relative to the pinning strength due to the much smaller size scale of the pinning array and could therefore permit a true ice rule obeying ground state. In a recent theoretical work Libal et al. proposed to create artificial square and Kagome ices with vortices in superconductors containing nanostructured arrays of pinning centers.[25] Using elongated double-well pinning sites arranged in a square lattice, for example, they were able to obtain the ground state of a square vortex ice which follows the "two vortices in, two vortices out" rule at each vertex, where the state of each double-well site is defined as "in" if the vortex sits close to the vertex and "out" otherwise. Such vortex systems can offer several advantages over the other artificial ices: [25] i) the ground state can be reached more rapidly as compared to nanomagnet systems due to the larger vortex-vortex interaction strength; ii) defect formation processes can be studied by changing the magnetic field to create vacancies or interstitials that locally break the ice rules; iii) different dynamical annealing protocols can be real...

Mapping degenerate vortex states in a kagome lattice of elongated antidots via scanning Hall probe microscopy

“…Because the thickness of the sample is sufficiently small, the variations of the order parameter and currents along the thickness can be neglected. randomly generated initial conditions [9]. Then we can obtain many vortex ground and metastable states.…”

“…The physics of quantized units of flux in a superconductor interacting with a pinning landscape continues to attract considerable academic interest due to the implications largely transcending the domain of superconductivity, such as Bose condensates [1,2], colloids [3,4], semiconductors [5,6], Mott insulator transition [7], vortex ice, spin ice, and charge ice [8][9][10][11][12], skyrmions [13,14], cold-atom trapping [15], etc. The appeal and advantage of superconducting systems is that the size and number of the particles can be tuned by changing the temperature and the magnetic field, respectively.…”

Realizing three-dimensional artificial spin ice by stacking planar nano-arrays

“…Because of their nano-scale interaction energies (∼ 10 3 − 10 5 K depending on the size of the nanomagnet and mutual spacing) they reveal, at accessible temperatures, emergent features which in natural materials are seen only at very low temperature. Following the pioneering work of Wang et al on the two-dimensional square-ice array [7,8], artificial spin ices have been proposed and studied in diverse types of physical systems [9][10][11][12] and geometries such as honeycomb (kagome ice) [13][14][15][16][17][18][19][20], brickwork [21], triangular [22][23][24], and pentagonal lattices [25]. A systematic approach for designing 2D arrays with emergent ice-type frustration has also been proposed [26,27], and recently realized experimentally [29].…”

Emergent geometric frustration of artificial magnetic skyrmion crystals

“…Alternative realizations of the artificial spin ice system can be created using colloids in arrays of elongated optical traps [58,59] or vortices in superconducting films with arrays of pinning defect sites [60][61][62]. In these two particle analogues, the effective spin vector is defined according to the position of a colloid or vortex in a double-well potential well.…”

“…Although the naturally occurring spin ices exhibit interesting types of topological monopole defects and "ice-rule" states [39,40], the frustrated behaviors occur only at very low temperatures and the individual spin ordering or defects cannot be directly visualized on the atomic scale size. Recent advances in nanofabrication technology have permitted the creation of artificial ice systems [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62] that mimic the behavior of geometrically frustrated atomic spin ices at much larger length scales and higher temperatures, where direct visualization of the microscopic effective spin configurations under controlled conditions is possible.…”