Los Alamos National Laboratory Artificial Spin Ice: From Toy to Material by Design? Cristiano Nisoli Los Alamos National Laboratory

Frustration Frustration: a set of constraints not all of which can be satisfied at the same time

Frustration Frustration: a set of constraints not all of which can be satisfied at the same time Compromises: Attempt to optimize gains vs. sacrifices

Frustration Frustration: a set of constraints not all of which can be satisfied at the same time Compromises: Attempt to optimize gains vs. sacrifices Manifold of Choices Something between order and disorder

Geometric Frustration Interesting because… The collective and correlated local compromises compose into a degenerate ensemble that is disordered (extensive entropy) yet not random. Order is boring. Randomness is death. Life happens somewhere in between. Life needs susceptibility, response.

Geometric Frustration G. H. Wannier Phys. Rev. 79, 357 (1950)

Ice Rule in Water Ice and Spin Ice

Ice Rule in Water Ice and Spin Ice

Ice Rule in Water Ice and Spin Ice

Ice Rule in Water Ice and Spin Ice

Monopoles

Monopoles

Monopoles

Ice Rule in Water Ice and Spin Ice "Magnetic monopoles in spin ice." Nature 451.7174 (2008): 42-45.

Ice Rule in Water Ice and Spin Ice "Measurement of the charge and current of magnetic monopoles in spin ice." Nature 461.7266 (2009): 956-959. "Magnetic monopoles in spin ice." Nature 451.7174 (2008): 42-45.

Reviews of Modern Physics 85 (4), 1473 (2013) Artificial Spin Ice: Interacting Magnetic Nanoislands Direct Imaging of magnetic degrees of freedom Designing the low energy dynamics for the collective behavior of interacting nanostructures Nature 439, 303-306 (2006) Reviews of Modern Physics 85 (4), 1473 (2013)

Out of equilibrium statistical mechanics Artificial Spin Ice: Early Fun Out of equilibrium statistical mechanics Possibility to test directly a theoretical framework Phys. Rev. Lett. 98 (21), 217203 (2007) Phys. Rev. Lett. 105, 047205 (2010)

Out of equilibrium statistical mechanics Artificial Spin Ice: Early Fun Out of equilibrium statistical mechanics Possibility to test directly a theoretical framework Phys. Rev. Lett. 98 (21), 217203 (2007) Phys. Rev. Lett. 105, 047205 (2010)

ASI Developing into a multidisciplinary field Hexagonal Geometry: extensive degeneracy Phys. Rev. B 73, 052411, 2006 Phys. Rev. B 77, 094418, 2008

ASI Developing into a multidisciplinary field Hexagonal Geometry: extensive degeneracy Phys. Rev. B 73, 052411, 2006 Phys. Rev. B 77, 094418, 2008 Field Reversal and monopole imaging Nature Physics 6, 359, 2010 Nature Physics 7, 68, 2011

ASI Developing into a multidisciplinary field Hexagonal Geometry: extensive degeneracy Phys. Rev. B 73, 052411, 2006 Phys. Rev. B 77, 094418, 2008 Field Reversal and monopole imaging Nature Physics 6, 359, 2010 Nature Physics 7, 68, 2011 Direct Extraction of Entropy/Shannon Information theory Nature Physics 6, 786, 2010

Topological Hall Effect Science 335, 1597, 2012 ASI Developing into a multidisciplinary field Hexagonal Geometry: extensive degeneracy Phys. Rev. B 73, 052411, 2006 Phys. Rev. B 77, 094418, 2008 Field Reversal and monopole imaging Nature Physics 6, 359, 2010 Nature Physics 7, 68, 2011 Direct Extraction of Entropy/Shannon Information theory Nature Physics 6, 786, 2010 Topological Hall Effect Science 335, 1597, 2012

Thermal ensembles Nature Physics 7, 75, 2011 New J. Phys. 14, 035009, 2012

Artificial Spin ice, Emergence, Subtle Exotic States Nature 500, 553–557 2013 However it became clear that higher level of controls were necessary to reveal emergence. The problem was solved in 2012-2013 when we developed new protocols capable to reach lower entropy states of these materials, and access new emergent phenomena. This meant that my job had to change. The material was now mature to go from descriptive science to design science and hypothesis-driven design and research. Phys. Rev. Lett. 106, 207202 2011 New J. Phys. 14 035017 2012 http://web.ornl.gov/info/news/pulse/no398/story3.shtml

Geometric Frustration G. H. Wannier Phys. Rev. 79, 357 (1950)

New Theoretical Directions: DESIGNING EMERGENCE That is what finally convinced me that the material could be used not only to access delicate exotic states, but to design them. My job had changed. It was not to make more vague proposal for realization and then explain the results in a situation where so many variables were unforeseeable. Now the doors to emergence by design were open. This is more rewarding but also more risky. We started

New Theoretical Directions: DESIGNING EMERGENCE That is what finally convinced me that the material could be used not only to access delicate exotic states, but to design them. My job had changed. It was not to make more vague proposal for realization and then explain the results in a situation where so many variables were unforeseeable. Now the doors to emergence by design were open. This is more rewarding but also more risky. We started

New Journal of Physics 15 (4), 045009 2013 New Theoretical Directions: DESIGNING EMERGENCE That is what finally convinced me that the material could be used not only to access delicate exotic states, but to design them. My job had changed. It was not to make more vague proposal for realization and then explain the results in a situation where so many variables were unforeseeable. Now the doors to emergence by design were open. This is more rewarding but also more risky. We started New Journal of Physics 15 (4), 045009 2013

New Theoretical Directions: DESIGNING EMERGENCE That is what finally convinced me that the material could be used not only to access delicate exotic states, but to design them. My job had changed. It was not to make more vague proposal for realization and then explain the results in a situation where so many variables were unforeseeable. Now the doors to emergence by design were open. This is more rewarding but also more risky. We started

New Theoretical Directions: DESIGNING EMERGENCE That is what finally convinced me that the material could be used not only to access delicate exotic states, but to design them. My job had changed. It was not to make more vague proposal for realization and then explain the results in a situation where so many variables were unforeseeable. Now the doors to emergence by design were open. This is more rewarding but also more risky. We started

New Theoretical Directions: DESIGNING EMERGENCE Physical Review Letters 111, 177201 2013

New Theoretical Directions: DESIGNING EMERGENCE Nature Physics 10, 670–675 (2014)

New Theoretical Directions: DESIGNING EMERGENCE Nature Physics 10, 670–675 (2014)

New Theoretical Directions: DESIGNING EMERGENCE

New Theoretical Directions: DESIGNING EMERGENCE

New Theoretical Directions: DESIGNING EMERGENCE Nature Physics, under review

New Theoretical Directions: DESIGNING EMERGENCE

New Theoretical Directions: DESIGNING EMERGENCE

Conclusions Artificial spin ice was introduced initially to mimic the frustration of spin ice and to realize celebrated model of statistical mechanics It became a fruitful ground to study diverse novel phenomena and exotic states Advances in control and manufacturing have opened the way to a material-by-design in magnetism Useful or exotic magnets are rare and found serendipitously in nature. They are based on localized, dipolar degrees of freedom. Emergent properties are at low T New materials based on delocalized, monopolar degrees of freedom could be a game changer for high T emergence The field is now mature for designing emergence

Collaborators Peter Schiffer UI Urbana Ian Gilbert NIST Sheng Zhang Argonne Vincent Crespi Penn State Paul Lammert Penn State Gia-Wei Chern LANL Muir Morrison Caltech Tammie Nelson LANL