Relations between arbitrary symmetry spin-hamiltonian parameters Bkq and bkq in Various Axis Systems

Rudowicz, Czesław

doi:10.1016/0022-2364(85)90156-8

Cited by 21 publications

(8 citation statements)

References 35 publications

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“…The dashed and solid arrows indicate x and z axis are not fixed within the plane perpendicular to yaxis. Rudowicz et al [50,51] has demonstrated that within the 15 CEF parameters, certain rotations exists along y-axis that make one of the CEF parameters 0 . Here we deploy the transformation of rotating the CEF coordination system w.r.t local y-axis by an angle α such that B 0 2 is 0 for all the solutions.…”

Section: Examplesmentioning

confidence: 99%

CrysFieldExplorer: a software for rapid optimization of crystal field Hamiltonian

Qian¹,

Bai²,

Feng³

et al. 2023

Preprint

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We present a new lite python-based program, CrysFieldExplorer, for fast optimizing crystal electric field (CEF) parameters to fit experimental data. The main novelty of CrysFieldExplorer is the development of a unique loss function, referred to as the Spectrum-Characteristic Loss (L Spectrum ), which is defined based on the characteristic polynomial of the Hamiltonian matrix. Particle Swarm Optimization and Covariance matrix adaptation evolution strategy are used to find the minimum of the total loss function. We demonstrate that CrysFieldExplorer can performs direct fitting of CEF parameters to any experimental data such as neutron spectrum, susceptibility, magnetizations etc. CrysFieldExplorer can handle a large amount of none-zero CEF parameters and reveal multiple local and global minimum solutions. Detailed crystal field theory, description of the loss function, implementation and limit of the program are discussed within context of two examples.

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Section: Examplesmentioning

confidence: 99%

CrysFieldExplorer: a software for rapid optimization of crystal field Hamiltonian

Qian¹,

Bai²,

Feng³

et al. 2023

Preprint

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“…for the spin S>7/2 systems. Note that the transformation properties of the ES operators and parameters have been worked out [47,48]. ∑ (L or J) in the literature [2,[15][16][17].…”

Section: Major Reference Notationmentioning

confidence: 99%

“…for the spin S>7/2 systems. Note that the transformation properties of the ES operators and parameters have been worked out [47,48]. The parameters q k b with the consistent definition of the factors [2,15]: f 2 = 1/3, f 4 = 1/60, f 6 = 1/1260, would be preferable.…”

Section: Major Reference Notationmentioning

confidence: 99%

“…Stevens, who stated in his recent book: 'There is a problem over listing the replacement angular momentum operators and their matrix elements because of the diversity of the definitions and errors in the tabulated matrix elements. The reader is therefore advised to consult the papers by C. Rudowicz,particularly,[Refs 47,48, for a critical account of the current literature and for proposals for future standardization in the definitions and notations. A step forward would seem to be to adopt his suggestions'.…”

Section: Supplemental Reference Notationmentioning

confidence: 99%

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Current Status of the Proposals for Unification of Notations and Guidelines for Data Presentation in the EMR Area. Blueprint for Future Actions

Rudowicz

2003

ChemInform

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“…31) Other important computer tools developed by us include the CF analysis (CFA) package [32][33][34] for the 3d N ions at arbitrary symmetry sites in crystals and the CST package for conversions, standardization and transformations of the spin Hamiltonian and the crystal-field Hamiltonian. [35][36][37] The fundamentals of the theory underlying the CST package may be found in references indicated -concerning transformations of the extended Stevens and related operators, 38,39) whereas standardization of orthorhombic 40) and monoclinic 41,42) Hamiltonians. Concerning other pertinent topics, it is worth mentioning of the following recent books, reviews, and papers.…”

Section: Outline Of the Theoretical Backgroundmentioning

confidence: 99%

Characteristics of the Magnetically Ordered High-SpinS=2 Fe²⁺Ion Systems Potentially Suitable for High-Magnetic-Field and High-Frequency EMR Studies

Rudowicz

Sung

2003

J. Phys. Soc. Jpn.

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This review is the first one in a planned series on the systems potentially suitable for highmagnetic-field and high-frequency electron magnetic resonance (HMF-EMR) studies. Such systems must best exhibit large or very large zero-field splitting (ZFS). The transition metal 3d 4 and 3d 6 ions with an orbital singlet ground state (OSGS) with the spin S=2 in some crystals may provide most suitable examples for applications of the HMF-EMR techniques. The compounds for which an evidence of an OSGS (S=2) exists can be classified into the following groups: (a) magnetically ordered at low temperatures, (b) magnetically ordered at higher temperatures, and (c) not ordered magnetically down to very low temperatures. Our literature search has also identified other groups of the 3d 4 and 3d 6 ions: (d) magnetically ordered compounds but exhibiting substantial orbital degeneracy and (e) biological systems. The largest sub-class of the S=2 systems consists of the high-spin Fe 2+ ion systems. To conform to the main theme of the Workshop, this review focuses on the magnetically ordered high-spin S=2 Fe 2+ ion systems potentially suitable for HMF-EMR studies. The data for the group (a) are presented in the form of a detailed review. For each ion/compound system we provide (i) brief characteristics, (ii) survey of the experimental as well as theoretical methods employed so far, especially those used for determination of the ZFS parameters, and (iii) selected major references as 'pointers' for further studies and literature searches. The groups (b) and (d) are not of prime interest for the present study, however, summary tables with basic pertinent data are included for completeness. The groups (c) and (e) deserve separate reviews. The data collected and analysed in this review may provide guidance for future HMF-EMR studies as well as enable correlation of the experimental ZFS data with the predictions of the microscopic spin Hamiltonian theory developed by us.KEYWORDS: magnetic materials, high-magnetic-field and high-frequency electron magnetic resonance, Fe 2+ ions, orbital singlet ground state, high spin S=2, very large zero-field splitting

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Relations between arbitrary symmetry spin-hamiltonian parameters Bkq and bkq in Various Axis Systems

Cited by 21 publications

References 35 publications

CrysFieldExplorer: a software for rapid optimization of crystal field Hamiltonian

CrysFieldExplorer: a software for rapid optimization of crystal field Hamiltonian

Current Status of the Proposals for Unification of Notations and Guidelines for Data Presentation in the EMR Area. Blueprint for Future Actions

Characteristics of the Magnetically Ordered High-SpinS=2 Fe²⁺Ion Systems Potentially Suitable for High-Magnetic-Field and High-Frequency EMR Studies

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Relations between arbitrary symmetry spin-hamiltonian parameters Bkq and bkq in Various Axis Systems

Cited by 21 publications

References 35 publications

CrysFieldExplorer: a software for rapid optimization of crystal field Hamiltonian

CrysFieldExplorer: a software for rapid optimization of crystal field Hamiltonian

Current Status of the Proposals for Unification of Notations and Guidelines for Data Presentation in the EMR Area. Blueprint for Future Actions

Characteristics of the Magnetically Ordered High-SpinS=2 Fe2+Ion Systems Potentially Suitable for High-Magnetic-Field and High-Frequency EMR Studies

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Characteristics of the Magnetically Ordered High-SpinS=2 Fe²⁺Ion Systems Potentially Suitable for High-Magnetic-Field and High-Frequency EMR Studies