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Packwood DM, Reaves KT, Federici FL, Katzgraber HG, Teizer W. Two-dimensional molecular magnets with weak topological invariant magnetic moments: mathematical prediction of targets for chemical synthesis. Proc Math Phys Eng Sci 2013; 469:20130373. [PMID: 24353469 DOI: 10.1098/rspa.2013.0373] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2013] [Accepted: 08/27/2013] [Indexed: 11/12/2022] Open
Abstract
An open problem in applied mathematics is to predict interesting molecules that are realistic targets for chemical synthesis. In this paper, we use a spin Hamiltonian-type model to predict molecular magnets (MMs) with magnetic moments that are intrinsically robust under random shape deformations to the molecule. Using the concept of convergence in probability, we show that for MMs in which all spin centres lie in-plane and all spin centre interactions are ferromagnetic, the total spin of the molecule is a 'weak topological invariant' when the number of spin centres is sufficiently large. By weak topological invariant, we mean that the total spin of the molecule depends only upon the arrangement of spin centres in the molecule, and is unlikely to change under shape deformations to the molecule. Our calculations show that only between 20 and 50 spin centres are necessary for the total spin of these MMs to be a weak topological invariant. The robustness effect is particularly enhanced for two-dimensional ferromagnetic MMs that possess a small number of spin rings in the structure.
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Affiliation(s)
- D M Packwood
- WPI-Advanced Institute for Materials Research , Tohoku University , 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan
| | - K T Reaves
- WPI-Advanced Institute for Materials Research , Tohoku University , 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan ; Materials Science and Engineering , Texas A&M University , College Station, TX 77843-3003, USA
| | - F L Federici
- WPI-Advanced Institute for Materials Research , Tohoku University , 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan ; Department of Physics and Astronomy , University College London , Gower Street, London WC1E 6BT, UK
| | - H G Katzgraber
- Materials Science and Engineering , Texas A&M University , College Station, TX 77843-3003, USA ; Department of Physics and Astronomy , Texas A&M University , College Station, TX 77843-4242, USA
| | - W Teizer
- WPI-Advanced Institute for Materials Research , Tohoku University , 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan ; Materials Science and Engineering , Texas A&M University , College Station, TX 77843-3003, USA ; Department of Physics and Astronomy , Texas A&M University , College Station, TX 77843-4242, USA
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Affiliation(s)
- B Yucesoy
- Physics Department, University of Massachusetts, Amherst, Massachusetts 01003, USA
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Katzgraber HG, Pázmándi F, Pike CR, Liu K, Scalettar RT, Verosub KL, Zimányi GT. Reversal-field memory in the hysteresis of spin glasses. Phys Rev Lett 2002; 89:257202. [PMID: 12484912 DOI: 10.1103/physrevlett.89.257202] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2002] [Indexed: 05/24/2023]
Abstract
We report a novel singularity in the hysteresis of spin glasses, the reversal-field memory effect, which creates a nonanalyticity in the magnetization curves at a particular point related to the history of the sample. The origin of the effect is due to the existence of a macroscopic number of "symmetric clusters" of spins associated with a local spin-reversal symmetry of the Hamiltonian. We use first order reversal curve (FORC) diagrams to characterize the effect and compare to experimental results on thin magnetic films. We contrast our results on spin glasses to random magnets and show that the FORC technique is an effective "magnetic fingerprinting" tool.
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Affiliation(s)
- H G Katzgraber
- Department of Physics, University of California, Davis 95616, USA
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