Artificial spin ice comprises a class of frustrated arrays of interacting single-domain ferromagnetic nanostructures. Previous studies of artificial spin ice have focused on simple lattices based on natural frustrated materials. Here we experimentally examine artificial spin ice created on the shakti lattice, a structure that does not directly correspond to any known natural magnetic material. On the shakti lattice, none of the near-neighbour interactions is locally frustrated, but instead the lattice topology frustrates the interactions leading to a high degree of degeneracy. We demonstrate that the shakti system achieves a physical realization of the classic six-vertex model ground state. Furthermore, we observe that the mixed coordination of the shakti lattice leads to crystallization of effective magnetic charges and the screening of magnetic excitations, underscoring the importance of magnetic charge as the relevant degree of freedom in artificial spin ice and opening new possibilities for studies of its dynamics.
At a glance
- Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands. Nature 439, 303–306 (2006). et al.
- Artificial spin ice: Designing and imaging magnetic frustration. Rev. Mod. Phys. 85, 1473–1490 (2013). , &
- Artificial ferroic systems: Novel functionality from structure, interactions and dynamics. J. Phys. Condens. Matter 25, 363201 (2013). &
- Spin ice state in frustrated magnetic pyrochlore materials. Science 294, 1495–1501 (2001). &
- Spin ice, fractionalization, and topological order. Ann. Rev. Condens. Matter Phys. 3, 35–55 (2012). , &
- Geometrical frustration in the ferromagnetic pyrochlore Ho2Ti2O7. Phys. Rev. Lett. 79, 2554–2557 (1997). , , , &
- Zero-point entropy in ‘spin ice’. Nature 339, 333–335 (1999). , , , &
- Absence of Pauling’s residual entropy in thermally equilibrated Dy2Ti2O7. Nature Phys. 9, 353–356 (2013). et al.
- Magnetic monopoles in spin ice. Nature 451, 42–45 (2008). , &
- Dirac strings and magnetic monopoles in the spin ice Dy2Ti2O7. Science 326, 411–414 (2009). et al.
- Magnetic Coulomb phase in the spin ice Ho2Ti2O7. Science 326, 415–417 (2009). et al.
- Measurement of the charge and current of magnetic monopoles in spin ice. Nature 461, 956–959 (2009). et al.
- Magnetic multipole analysis of kagome and artificial spin-ice dipolar arrays. Phys. Rev. B 80, 140409 (2009). &
- Two-stage ordering of spins in dipolar spin ice on the kagome lattice. Phys. Rev. Lett. 106, 207202 (2011). , &
- Direct entropy determination and application to artificial spin ice. Nature Phys. 6, 786–789 (2010). et al.
- Direct observation of the ice rule in an artificial kagome spin ice. Phys. Rev. B 77, 094418 (2008). , &
- Comparing artificial frustrated magnets by tuning the symmetry of nanoscale permalloy arrays. Phys. Rev. B 81, 092406 (2010). et al.
- Artificial kagome arrays of nanomagnets: A frozen dipolar spin ice. Phys. Rev. Lett. 106, 057209 (2011). et al.
- Direct observation of magnetic monopole defects in an artificial spin-ice system. Nature Phys. 6, 359–363 (2010). , , , &
- Real-space observation of emergent magnetic monopoles and associated Dirac strings in artificial kagome spin ice. Nature Phys. 7, 68–74 (2011). et al.
- Nanoscale structure of the magnetic induction at monopole defects in artificial spin-ice lattices. Phys. Rev. B 83, 174431 (2011). , , , &
- Ground state lost but degeneracy found: The effective thermodynamics of artificial spin ice. Phys. Rev. Lett. 98, 217203 (2007). et al.
- Disorder strength and field-driven ground state domain formation in artificial spin ice: Experiment, simulation, and theory. Phys. Rev. Lett. 109, 037203 (2012). et al.
- Thermal ground-state ordering and elementary excitations in artificial magnetic square ice. Nature Phys. 7, 75–79 (2011). , , &
- Melting artificial spin ice. New J. Phys. 14, 035009 (2012). et al.
- Exploring thermally induced states in square artificial spin-ice arrays. New J. Phys. 15, 055012 (2013). , , &
- Exploring hyper-cubic energy landscapes in thermally active finite artificial spin-ice. Nature Phys. 9, 375–382 (2013). et al.
- Direct observation of thermal relaxation in artificial spin ice. Phys. Rev. Lett. 111, 057204 (2013). et al.
- Crystallites of magnetic charges in artificial spin ice. Nature 500, 553–557 (2013). et al.
- Artificial square ice and related dipolar nanoarrays. Phys. Rev. Lett. 96, 237202 (2006). &
- Unhappy vertices in artificial spin ice: New degeneracies from vertex frustration. New J. Phys. 15, 045009 (2013). , &
- Degeneracy and criticality from emergent frustration in artificial spin ice. Phys. Rev. Lett. 111, 177201 (2013). , &
- 1982). Exactly Solved Models in Statistical Mechanics (Academic,
- 1971). & in Phase Transitions and Critical Phenomena Vol. 1 (eds Domb, C. & Green, M. S.) (Academic,
- Disorder regimes and equivalence of disorder types in artificial spin ice. J. Appl. Phys. 111, 07E109 (2012). , &
- Real and effective thermal equilibrium in artificial square spin ices. Phys. Rev. B 87, 024405 (2013). et al.
- http://arxiv.org/abs/1306.6154 (2013). & Magnetic monopole polarons in spin ice with mixed coordination numbers. Preprint at
- Supplementary Information (947KB)