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

Artificial spin ice is a frustrated magnetic two-dimensional nano-material, recently employed to study variety of tailor-designed unusual collective behaviours. Recently proposed extensions to three dimensions are based on self-assembly techniques and allow little control over geometry and disorder. We present a viable design for the realization of a three-dimensional artificial spin ice with the same level of precision and control allowed by lithographic nano-fabrication of the popular two-dimensional case. Our geometry is based on layering already available two-dimensional artificial spin ice and leads to an arrangement of ice-rule-frustrated units, which is topologically equivalent to that of the tetrahedra in a pyrochlore lattice. Consequently, we show, it exhibits a genuine ice phase and its excitations are, as in natural spin ice materials, magnetic monopoles interacting via Coulomb law.

[1]  M. Tarzia,et al.  Thermal phase transitions in artificial spin ice. , 2013, Physical review letters.

[2]  R. Moessner,et al.  Spin Ice, Fractionalization, and Topological Order , 2011, 1112.3793.

[3]  Aaron Stein,et al.  Thermal ground-state ordering and elementary excitations in artificial magnetic square ice , 2011 .

[4]  Michel J. P. Gingras,et al.  Spin Ice State in Frustrated Magnetic Pyrochlore Materials , 2001, Science.

[5]  Andrew G. Glen,et al.  APPL , 2001 .

[6]  Laura J. Heyderman,et al.  Exploring hyper-cubic energy landscapes in thermally active finite artificial spin-ice systems , 2013, Nature Physics.

[7]  V. Novosad,et al.  Oscillatory thickness dependence of the coercive field in magnetic three-dimensional antidot arrays , 2006 .

[8]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[9]  Gia-Wei Chern,et al.  Crystallites of magnetic charges in artificial spin ice , 2013, Nature.

[10]  C. Nisoli.  On thermalization of magnetic nano-arrays at fabrication , 2012, 1201.2832.

[11]  R. Moessner,et al.  Magnetic monopoles in spin ice , 2007, Nature.

[12]  S. Greaves,et al.  Formation of thermally induced ground states in two-dimensional square spin ices , 2012 .

[13]  Long-range order at low temperatures in dipolar spin ice. , 2000, Physical review letters.

[14]  Roderich Moessner,et al.  Colloquium: Artificial spin ice : Designing and imaging magnetic frustration , 2013 .

[15]  W. Kwok,et al.  Realization of artificial ice systems for magnetic vortices in a superconducting MoGe thin film with patterned nanostructures. , 2013, Physical review letters.

[16]  W. A. Moura-Melo,et al.  Conditions for free magnetic monopoles in nanoscale square arrays of dipolar spin ice , 2010, 1001.0748.

[17]  Muir J. Morrison,et al.  Degeneracy and criticality from emergent frustration in artificial spin ice. , 2012, Physical review letters.

[18]  A. Libál,et al.  Realizing colloidal artificial ice on arrays of optical traps. , 2006, Physical review letters.

[19]  Jie Li,et al.  Ground state lost but degeneracy found: the effective thermodynamics of artificial spin ice. , 2007, Physical review letters.

[20]  J. Cumings,et al.  Direct observation of the ice rule in an artificial kagome spin ice , 2008, 0802.0034.

[21]  Ludovic D. C. Jaubert,et al.  Monopole and Dirac string Dynamics in Spin Ice , 2009, 0903.1074.

[22]  D. Menzel,et al.  Three-dimensional artificial spin ice in nanostructured Co on an inverse opal-like lattice , 2013 .

[23]  R. Moessner,et al.  Magnetic multipole analysis of kagome and artificial spin-ice dipolar arrays , 2009, 0906.3937.

[24]  W. A. Moura-Melo,et al.  Efficient demagnetization protocol for the artificial triangular spin ice , 2013, 1306.3947.

[25]  R. Chopdekar,et al.  Thermalized ground state of artificial kagome spin ice building blocks , 2012 .

[26]  Paolo Vavassori,et al.  Exploring thermally induced states in square artificial spin-ice arrays , 2013 .

[27]  Muir J. Morrison,et al.  Unhappy vertices in artificial spin ice: new degeneracies from vertex frustration , 2012, 1210.7843.

[28]  R Moessner,et al.  Artificial square ice and related dipolar nanoarrays. , 2006, Physical review letters.

[29]  C. Reichhardt,et al.  Creating artificial ice states using vortices in nanostructured superconductors. , 2008, Physical review letters.

[30]  Jie Li,et al.  Effective temperature in an interacting vertex system: theory and experiment on artificial spin ice. , 2010, Physical review letters.

[31]  V. Crespi,et al.  Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands , 2006, Nature.

[32]  Eiji Saitoh,et al.  Magnetic interactions in a ferromagnetic honeycomb nanoscale network , 2006 .

[33]  Gia-Wei Chern,et al.  Two-stage ordering of spins in dipolar spin ice on the kagome lattice. , 2009, Physical review letters.

[34]  H. Zabel,et al.  Charge ordering of magnetic dipoles in artificial honeycomb patterns , 2010, 1004.0855.

[35]  B. V. Costa,et al.  Magnetic monopole and string excitations in two-dimensional spin ice , 2008, 0809.2105.