The generalization of the extended Stevens operators to higher ranks and spins, and a systematic review of the tables of the tensor operators and their matrix elements

Rudowicz, Czesław; Chung, C.Y.

doi:10.1088/0953-8984/16/32/018

Cited by 143 publications

(96 citation statements)

References 60 publications

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“…Further restriction comes about because the crystalline electric field environment is symmetric under operations of the point group D 3d . Here we use [6,91,92,93…”

Section: Single Ion Propertiesmentioning

confidence: 99%

New physics in frustrated magnets: Spin ices, monopoles, etc. (Review Article)

Zvyagin

2013

Low Temperature Physics

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During recent years the interest to frustrated magnets has grown considerably. Such systems reveal very peculiar properties which distinguish them from standard paramagnets, magnetically ordered regular systems (like ferro-, ferri-, and antiferromagnets), or spin glasses. In particular great amount of attention has been devoted to the socalled spin ices, in which magnetic frustration together with the large value of the single-ion magnetic anisotropy of a special kind, yield peculiar behavior. One of the most exciting features of spin ices is related to low-energy emergent excitations, which, from many viewpoints can be considered as analogies of Dirac's monopoles. In this article we review the main achievements of theory and experiment in this field of physics.

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“…Further restriction comes about because the crystalline electric field environment is symmetric under operations of the point group D 3d . Here we use [6,91,92,93…”

Section: Single Ion Propertiesmentioning

confidence: 99%

New physics in frustrated magnets: Spin ices, monopoles, etc. (Review Article)

Zvyagin

2013

Low Temperature Physics

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“…For this purpose, the extended Stevens (ES) operators, which include both the positive and negative q components, have been defined and their transformation properties worked out [19]. Note that the ES operators ) ( O q k X have recently been generalized to any rank k and quantum number X of the angular momentum operator X = S, J, or L [32].…”

Section: Basic Nomenclature and Theoretical Aspectsmentioning

confidence: 99%

“…triclinic, site symmetry the spin Hamiltonian, including the Zeeman electronic (Ze) terms and ZFS ones in the ES operators notation [3,19,32], is defined by [1][2][3][4][5]: …”

Section: Basic Nomenclature and Theoretical Aspectsmentioning

confidence: 99%

Alternative zero-field splitting (ZFS) parameter sets and standardization for Mn2+ ions in various hosts exhibiting orthorhombic site symmetry

Kripal

Yadav

Gnutek

et al. 2009

Journal of Physics and Chemistry of Solids

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A c c e p t e d m a n u s c r i p t

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“…Optical absorption spectroscopy in geosciences has been reviewed with focus on the basic concepts of crystal field theory [17] and quantitative aspects of crystal fields [18]. Generalization of the extended Stevens operators to higher ranks and spins and systematic review of the tables of the tensor operators and their matrix elements are provided in [19].…”

Section: Conclusion and Further Readingsmentioning

confidence: 99%

Noether's theorem and low symmetry aspects concerning the crystal (ligand) field Hamiltonians and spin Hamiltonians

Rudowicz

Qin

2006

J. Phys.: Conf. Ser.

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Noether's theorem and low symmetry aspects concerning the crystal (ligand) field Hamiltonians and spin Hamiltonians An important theorem and a conjecture on the conserved quantities stipulated by Noether's theorem for the Hamiltonians in question formulated by us helps to elucidate the interrelationships and deeper meaning of the concepts involved. Implications of the existence of the conserved quantities for interpretation of experimental CF parameter (CFP) datasets are encapsulated in five corollaries. These considerations reveal that the feasibility of determination of CFPs from fitting experimental spectra and the reduction of the existing higher-order rotational invariants for hexagonal type II and cubic symmetry require reinterpretation. This novel approach enables adoption of better fitting strategies utilizing welldefined conserved quantities, which are invariant under CRS. The advantages of this approach are illustrated using the CFP datasets reported in literature for RE 3+ (4f N ) ions in LiYF 4 . This review deals also with the fundamental intricate aspects, hitherto not fully understood, concerning the CF Hamiltonians for the 'low symmetry' cases, including the CRS cases as well as orthorhombic ones. This includes: (1) selection of the axis systems, (2) types of CF parameters and their properties, (3) introduction of a new notion of a nominal axis system for the fitted CFP datasets, (4) implications of the Noether's theorem and the AS of CF Hamiltonians, (5) correlation properties among CFP datasets, (6) the rotational degrees of freedom and the reduction of the number of independent CFPs, and (7) extension of the multiple correlated fitting technique. Clarification of these intricate aspects enables us to provide a general framework aimed at achieving an increased compatibility and reliability of CFP datasets for transition ions at low symmetry sites in crystals. IntroductionSpectroscopic properties of the transition ions, especially iron-group ions and lanthanides, at low symmetry sites in crystals play important role for various technologically important materials (for references, see [1][2][3][4][5]). The trivalent rare-earth (RE) 4f N ions have been most extensively studied due to applications in laser host and optoelectronic materials. The experimental techniques employed to investigate the CF/LF effects, majority of which are 'non-directional' techniques -unlike those used in the EMR (electron magnetic resonance) studies [6,7], were discussed in [3]. During our recent CF/LF studies of transition ions in crystals [1-5] we have encountered several intricate low symmetry aspects. The motivation to clarify these aspects has prompted us to embark on a comprehensive project aimed at increasing the compatibility and reliability of the crystal field parameter (CFP) datasets. This review presents a concise summary of the major findings arising from our studies concerning the intricate low symmetry properties of CF/LF Hamiltonians and spin Hamiltonians (SHs). To facilitate broad understanding, a bir...

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The generalization of the extended Stevens operators to higher ranks and spins, and a systematic review of the tables of the tensor operators and their matrix elements

Cited by 143 publications

References 60 publications

New physics in frustrated magnets: Spin ices, monopoles, etc. (Review Article)

New physics in frustrated magnets: Spin ices, monopoles, etc. (Review Article)

Alternative zero-field splitting (ZFS) parameter sets and standardization for Mn2+ ions in various hosts exhibiting orthorhombic site symmetry

Noether's theorem and low symmetry aspects concerning the crystal (ligand) field Hamiltonians and spin Hamiltonians

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