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Saccone M, Caravelli F, Hofhuis K, Dhuey S, Scholl A, Nisoli C, Farhan A. Real-space observation of ergodicity transitions in artificial spin ice. Nat Commun 2023; 14:5674. [PMID: 37704596 PMCID: PMC10499874 DOI: 10.1038/s41467-023-41235-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2022] [Accepted: 08/23/2023] [Indexed: 09/15/2023] Open
Abstract
Ever since its introduction by Ludwig Boltzmann, the ergodic hypothesis became a cornerstone analytical concept of equilibrium thermodynamics and complex dynamic processes. Examples of its relevance range from modeling decision-making processes in brain science to economic predictions. In condensed matter physics, ergodicity remains a concept largely investigated via theoretical and computational models. Here, we demonstrate the direct real-space observation of ergodicity transitions in a vertex-frustrated artificial spin ice. Using synchrotron-based photoemission electron microscopy we record thermally-driven moment fluctuations as a function of temperature, allowing us to directly observe transitions between ergodicity-breaking dynamics to system freezing, standing in contrast to simple trends observed for the temperature-dependent vertex populations, all while the entropy features arise as a function of temperature. These results highlight how a geometrically frustrated system, with thermodynamics strictly adhering to local ice-rule constraints, runs back-and-forth through periods of ergodicity-breaking dynamics. Ergodicity breaking and the emergence of memory is important for emergent computation, particularly in physical reservoir computing. Our work serves as further evidence of how fundamental laws of thermodynamics can be experimentally explored via real-space imaging.
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Affiliation(s)
- Michael Saccone
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
| | - Francesco Caravelli
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Kevin Hofhuis
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093, Zurich, Switzerland
- Laboratory for Multiscale Materials Experiments (LMX), Paul Scherrer Institute, 5232, Villigen PSI, Switzerland
| | - Scott Dhuey
- Molecular Foundry, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA, 94720, USA
| | - Andreas Scholl
- Advanced Light Source, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA, 94720, USA
| | - Cristiano Nisoli
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Alan Farhan
- Department of Physics, Baylor University, Waco, TX, 76798, USA.
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Magnetization dynamics of weakly interacting sub-100 nm square artificial spin ices. Sci Rep 2019; 9:19967. [PMID: 31882867 PMCID: PMC6934880 DOI: 10.1038/s41598-019-56219-y] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2019] [Accepted: 12/06/2019] [Indexed: 12/02/2022] Open
Abstract
Artificial Spin Ice (ASI), consisting of a two dimensional array of nanoscale magnetic elements, provides a fascinating opportunity to observe the physics of out-of-equilibrium systems. Initial studies concentrated on the static, frozen state, whilst more recent studies have accessed the out-of-equilibrium dynamic, fluctuating state. This opens up exciting possibilities such as the observation of systems exploring their energy landscape through monopole quasiparticle creation, potentially leading to ASI magnetricity, and to directly observe unconventional phase transitions. In this work we have measured and analysed the magnetic relaxation of thermally active ASI systems by means of SQUID magnetometry. We have investigated the effect of the interaction strength on the magnetization dynamics at different temperatures in the range where the nanomagnets are thermally active. We have observed that they follow an Arrhenius-type Néel-Brown behaviour. An unexpected negative correlation of the average blocking temperature with the interaction strength is also observed, which is supported by Monte Carlo simulations. The magnetization relaxation measurements show faster relaxation for more strongly coupled nanoelements with similar dimensions. The analysis of the stretching exponents obtained from the measurements suggest 1-D chain-like magnetization dynamics. This indicates that the nature of the interactions between nanoelements lowers the dimensionality of the ASI from 2-D to 1-D. Finally, we present a way to quantify the effective interaction energy of a square ASI system, and compare it to the interaction energy computed with micromagnetic simulations.
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Chen XM, Farmer B, Woods JS, Dhuey S, Hu W, Mazzoli C, Wilkins SB, Chopdekar RV, Scholl A, Robinson IK, De Long LE, Roy S, Hastings JT. Spontaneous Magnetic Superdomain Wall Fluctuations in an Artificial Antiferromagnet. PHYSICAL REVIEW LETTERS 2019; 123:197202. [PMID: 31765174 DOI: 10.1103/physrevlett.123.197202] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2018] [Revised: 10/16/2019] [Indexed: 06/10/2023]
Abstract
Collective dynamics often play an important role in determining the stability of ground states for both naturally occurring materials and metamaterials. We studied the temperature dependent dynamics of antiferromagnetically ordered superdomains in a square artificial spin lattice using soft x-ray photon correlation spectroscopy. We observed an exponential slowing down of superdomain wall motion below the antiferromagnetic onset temperature, similar to the behavior of typical bulk antiferromagnets. Using a continuous time random walk model we show that these superdomain walls undergo low-temperature ballistic and high-temperature diffusive motions.
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Affiliation(s)
- X M Chen
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Department of Electrical and Computer Engineering, University of Kentucky, Lexington, Kentucky 40506, USA
| | - B Farmer
- Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA
| | - J S Woods
- Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - S Dhuey
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - W Hu
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - C Mazzoli
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - S B Wilkins
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - R V Chopdekar
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - A Scholl
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - I K Robinson
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
- London Centre for Nanotechnology, University College, Gower Street, London WC1E 6BT, United Kingdom
| | - L E De Long
- Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA
| | - S Roy
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - J T Hastings
- Department of Electrical and Computer Engineering, University of Kentucky, Lexington, Kentucky 40506, USA
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Pancaldi M, Leo N, Vavassori P. Selective and fast plasmon-assisted photo-heating of nanomagnets. NANOSCALE 2019; 11:7656-7666. [PMID: 30951080 DOI: 10.1039/c9nr01628g] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Thermal relaxation of nanoscale magnetic islands, mimicking Ising macrospins, is indispensable for studies of geometrically frustrated artificial spin systems and low-energy nanomagnetic computation. Currently-used heating schemes based on contact to a thermal reservoir, however, lack the speed and spatial selectivity required for the implementation in technological applications. Applying a hybrid approach by combining a plasmonic nanoheater with a magnetic element, in this work we establish the robust and reliable control of local temperatures in nanomagnetic arrays by contactless optical means. Plasmon-assisted photo-heating allows for temperature increases of up to several hundred kelvins, which lead to thermally-activated moment reversals and a pronounced reduction of the magnetic coercive field. Furthermore, the polarization-dependent absorption cross section of elongated plasmonic elements enables sublattice-specific heating on sub-nanosecond time scales. Using optical degrees of freedom, i.e. focal position, polarization, power, and pulse length, thermoplasmonic heating of nanomagnets offers itself for the use in flexible, fast, spatially-, and element-selective thermalization for functional magnetic metamaterials.
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Loreto RP, Nascimento FS, Gonçalves RS, Borme J, Cezar JC, Nisoli C, Pereira AR, de Araujo CIL. Experimental and theoretical evidences for the ice regime in planar artificial spin ices. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:025301. [PMID: 30521491 DOI: 10.1088/1361-648x/aaeeef] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
In this work, we explore a kind of geometrical effect in the thermodynamics of artificial spin ices (ASI). In general, such artificial materials are athermal. Here, We demonstrate that geometrically driven dynamics in ASI can open up the panorama of exploring distinct ground states and thermally magnetic monopole excitations. It is shown that a particular ASI lattice will provide a richer thermodynamics with nanomagnet spins experiencing less restriction to flip precisely in a kind of rhombic lattice. This can be observed by analysis of only three types of rectangular artificial spin ices (RASI). Denoting the horizontal and vertical lattice spacings by [Formula: see text] and [Formula: see text], respectively, then, a RASI material can be described by its aspect ratio [Formula: see text]. The rhombic lattice emerges when [Formula: see text]. So, by comparing the impact of thermal effects on the spin flips in these three appropriate different RASI arrays, it is possible to find a system very close to the ice regime.
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Affiliation(s)
- R P Loreto
- Laboratory of Spintronics and Nanomagnetism (LabSpiN), Departamento de Física, Universidade Federal de Viçosa, 36570-900, Viçosa, Minas Gerais, Brazil
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