Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands

Wang, R. F.; Nisoli, Cristiano; Freitas, R. S.; Li, J.; McConville, W.; Cooley, Benjamin; Lund, Michael S.; Samarth, N.; Leighton, Chris; Crespi, Vincent H.; Schiffer, P.

doi:10.1038/nature04447

Cited by 831 publications

(975 citation statements)

References 23 publications

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“…Artificial spin-ice systems 14,15 consist of regular arrays of magnetic squares 15 or honeycomb lattices 16 , with dimensions in the 100-1,000 nm range, small enough to ensure singledomain behaviour but with sufficient magnetic volume for stable room-temperature ferromagnetism. These systems show ice-rule behaviour 16 but direct observation of monopole defects is lacking.…”

Section: (R Ijmentioning

confidence: 99%

Direct observation of magnetic monopole defects in an artificial spin-ice system

et al. 2010

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Free monopoles have fascinated and eluded researchers since their prediction by Dirac 1 in 1931. In spin ice, the bulk frustrated magnet, local ordering principles known as ice rules-two-in/two-out for four spins arranged in a tetrahedron-minimize magnetic charge. Remarkably, recent work 2-5 shows that mobile excitations, termed 'monopole defects', emerge when the ice rules break down 2 . Using a cobalt honeycomb nanostructure we study the two-dimensional planar analogue called kagome or artificial spin ice. Here we show direct images of kagome monopole defects and the flow of magnetic charge using magnetic force microscopy. We find the local magnetic charge distribution at each vertex of the honeycomb pins the magnetic charge carriers, and opposite charges hop in opposite directions in an applied field. The parameters that enter the problem of creating and imaging monopole defects can be mapped onto a simple model that requires only the ice-rule violation energy and distribution of switching fields of the individual bars of a cobalt honeycomb lattice. As we demonstrate, it is the exquisite interplay between these energy scales in the cobalt nanostructure that leads to our experimental observations.The dipolar interactions of a given spin with all of its nearest neighbours cannot be satisfied on a triangular lattice, resulting in a frustrated magnetic state with strong correlations and a local ordering principle, but no long-range order. Owing to its equivalence to the electrical charge distribution in water ice 6 , the materials are known as 'spin ices' and the local ordering scheme as the 'ice rules'. Spin-ice materials such as Dy 2 Ti 2 O 7 have been subject to an intense research effort 7,8 and frustrated magnetism has evolved into a deeply interdisciplinary field, providing model systems for complex biological problems and a mathematical basis for the neural network algorithm from the Sherrington-Kirkpatrick model 9 .A powerful way to understand spin ice is to consider the magnetic dipole as a positive and negative magnetic charge (±q) separated by one lattice spacing. The ice rule can then be described as the local minimization at each lattice site i of the total magnetic charge (Q i, = q i ). Predictions suggest that the magnetic properties can be fractionalized, with mobile excitations carrying magnetic charge, rather than spin, and their interactions being described by a magnetic Coulomb's law 2 (equation (1))where V 0 is the self-energy and r ij is the separation. Although these topological excitations are confined to the dipole lattice, and they are compatible with Maxwell's equations 10 , their free magnetic charge character has led to the nomenclature magnetic Blackett Laboratory, Imperial College, Prince Consort Road, London SW7 2AZ, UK. *e-mail: W.Branford@imperial.ac.uk.monopole defects. Recent studies 3-5,10 in rare-earth pyrochlores strongly suggest that monopole defects exist in bulk spin ice 10 .Creating an odd number of intersecting dipoles, as in 'kagome spin ice' 11 , is interesting becaus...

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Section: (R Ijmentioning

confidence: 99%

Direct observation of magnetic monopole defects in an artificial spin-ice system

et al. 2010

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“…Arrays of lithographically fabricated single-domain nanoscale ferromagnets can be designed to frustrate inter-island magnetostatic interactions, in analogy to the spin-spin interactions in frustrated magnetic materials 1 . A wide range of interesting behavior 2,3 can be observed in these artificial frustrated magnets by tuning the geometry of square [4][5][6][7] , triangular 8,9 , hexagonal (and kagome) [10][11][12][13][14][15][16][17][18][19][20] and brickwork lattices, as well as isolated clusters 21 .…”

Section: Figmentioning

confidence: 99%

Magneto-optical Kerr effect studies of square artificial spin ice

Kohli

Balk

et al. 2011

Phys. Rev. B

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We report a magneto-optical Kerr effect (MOKE) study of the collective magnetic response of artificial square spin ice, a lithographically-defined array of single-domain ferromagnetic islands. We find that the anisotropic inter-island interactions lead to a non-monotonic angular dependence of the array coercive field. Comparisons with micromagnetic simulations indicate that the two perpendicular sublattices exhibit distinct responses to island edge roughness, which clearly influence the magnetization reversal process. Furthermore, such comparisons demonstrate that disorder associated with roughness in the island edges plays a hitherto unrecognized but essential role in the collective behavior of these systems.

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“…inhomogeneities in the magnetization field [7,10,11]. This method therefore allows for the identification of the magnetization orientation of individual islands by detecting the magnetic flux emanating from the island ends.…”

Section: Introductionmentioning

confidence: 99%

“…An attractive alternative to the pyrochlore class of spin-ice systems is provided by 'artificial spin ice'-regular nanolithographic arrays of in-plane magnetized nanoscale magnets. This line of research has been initiated by Wang et al [7], who demonstrated the experimental feasibility of preparing a square lattice of elongated permalloy islands in a state characterized by two-in-two-out ice rules at the vertices where the ends of four islands meet. These artificial spin-ice systems have the advantage that, in contrast to the pyrochlore systems, the anisotropy barriers stabilizing a particular magnetic state are of the order of 10 4 K. Hence they offer the appealing possibility of observing some of the exciting phenomena predicted for pyrochlore spin ice at room temperature.…”

Section: Introductionmentioning

confidence: 99%

Artificial kagome spin ice: dimensional reduction, avalanche control and emergent magnetic monopoles

Hügli

Duff

O'Conchuir

et al. 2012

Phil. Trans. R. Soc. A.

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Artificial spin-ice systems consisting of nanolithographic arrays of isolated nanomagnets are model systems for the study of frustration-induced phenomena. We have recently demonstrated that monopoles and Dirac strings can be directly observed via synchrotronbased photoemission electron microscopy, where the magnetic state of individual nanoislands can be imaged in real space. These experimental results of Dirac string formation are in excellent agreement with Monte Carlo simulations of the hysteresis of an array of dipoles situated on a kagome lattice with randomized switching fields. This formation of one-dimensional avalanches in a two-dimensional system is in sharp contrast to disordered thin films, where avalanches associated with magnetization reversal are twodimensional. The self-organized restriction of avalanches to one dimension provides an example of dimensional reduction due to frustration. We give simple explanations for the origin of this dimensional reduction and discuss the disorder dependence of these avalanches. We conclude with the explicit demonstration of how these avalanches can be controlled via locally modified anisotropies. Such a controlled start and stop of avalanches will have potential applications in data storage and information processing.

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Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands

Cited by 831 publications

References 23 publications

Direct observation of magnetic monopole defects in an artificial spin-ice system

Direct observation of magnetic monopole defects in an artificial spin-ice system

Magneto-optical Kerr effect studies of square artificial spin ice

Artificial kagome spin ice: dimensional reduction, avalanche control and emergent magnetic monopoles

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