Second-order Zero-field Splitting Research Articles

Theoretical investigations of the spin-Hamiltonian parameters and local structural distortion of Fe3+: ZnAl2O4 crystals

The relations between the spin-Hamiltonian (SH) parameters and the structural parameters of the Fe(3+) ions in Fe(3+): ZnAl2O4 crystals have been established by means of the microscopic spin Hamiltonian theory and the superposition model (SPM). On the basis of this, the local structure distortion, the second-order zero-field splitting (ZFS) parameter D, the fourth-order ZFS parameter (a-F), and the Zeeman g-factors g factors: g//, g⊥, and Δg(=g//-g⊥) for Fe(3+) ions in Fe(3+): ZnAl2O4 crystals, for the first time taking into account the electronic magnetic interactions, i.e. the spin-spin (SS), the spin-other-orbit (SOO), and the orbit-orbit (OO) interactions, besides the well-known spin-orbit (SO) interaction, are theoretically investigated using complete diagonalization method (CDM). This investigation reveals that the local structure distortion effect plays an important role in explaining the spectroscopic properties of Fe(3+) ions in Fe(3+): ZnAl2O4 crystals. The theoretical second-order ZFS parameter D, the fourth-order ZFS parameter (a-F), and the Zeeman g-factors: g//, g⊥, and Δg of the ground state for Fe(3+) ion in Fe(3+): ZnAl2O4 crystals yield a good agreement with experiment findings by taking into account the lattice distortions: ΔR=0.0191nm and Δθ=0.076°. In conclusion, our research shows that there is a slight local structure distortion for Fe(3+) ions in Fe(3+): ZnAl2O4 crystals, but the site of Fe(3+) still retains D3d symmetry. On the other hand, it is found for Fe(3+) ions in Fe(3+): ZnAl2O4 crystals that the SO mechanism is the most important one, whereas the contributions to the SH parameters from other four mechanisms, including the SS, SOO, OO, and SO∼SS∼SOO∼OO mechanisms are not appreciable, especially for the ZFS parameter D.

Local structure distortion and the spin-Hamiltonian parameters for Fe3+-doped ZnGa2O4 crystal materials

Relations between the spin-Hamiltonian (SH) parameters including the second-order zero-field splitting (ZFS) parameter D, the fourth-order ZFS parameter (a-F), the Zeeman g-factors: g//, g, g(=g//-g) and the structural parameters of ZnGa2O4:Fe3+ crystals have been established by means of the microscopic spin Hamiltonian theory and Newman's crystal field (CF) superposition model. On the basis of this, the SH parameters for Fe3+ magnetic ions in ZnGa2O4:Fe3+ crystals are investigated theoretically using the CFA/MSH (crystal field analysis/microscopic spin-Hamiltonian) software based on the full configuration complete diagonalization method. It is found that the theoretically calculated parameters including the ZFS parameters D, (a-F), and the Zeeman g-factors: g//, g, g(=g//-g) for ZnGa2O4:Fe3 + crystals are in good agreement with experimental data when taking into account the lattice distortions: R=0.0487 nm and =0.192. This investigation reveals that there is a slight local structure distortion due to Fe3 + ions in ZnGa2O4:Fe3+ crystals, but the site of Fe3+ still retains D3d symmetry. On the other hand, it is found for Fe3+ ions in ZnGa2O4:Fe3+ crystals that the contribution to the SH parameters from the spin-orbit (SO) mechanism is the most important one, whereas the contributions to the SH parameters from other four mechanisms, including the spin-spin (SS), spin-other-orbit (SOO), orbit-orbit (OO), and SO-SS-SOO-OO mechanisms, are small.

Zero-field splitting of the ground state and local lattice distortions for Fe3+ ions at the tetragonal FeF5O cluster center in Fe3+:KMgF3 crystals

Abstract The relations between the zero-field splitting (ZFS) parameters and the structural parameters of the tetragonal FeF 5 O cluster center in Fe 3+ :KMgF 3 crystals have been established by means of the microscopic spin Hamiltonian theory and the superposition model (SPM). On the basis of this, the local structure distortions, the second-order ZFS parameter D , the fourth-order one ( a + 2 F /3), and the energy level separations Δ 1 and Δ 2 of the ground spin state for Fe 3+ ion doped in Fe 3+ :KMgF 3 crystals are theoretically investigated. We use complete diagonalization method (CDM) and take into account the electronic magnetic interactions, i.e. the spin–spin (SS), the spin-other-orbit (SOO), and the orbit–orbit (OO) interactions, besides the well-known spin–orbit (SO) interaction. This investigation reveals that the replacement of O 2− for F − and the induced lattice relaxation Δ R 2 (O), combined with an inward relaxation of the nearest five fluorine ions Δ R 1 (F) give rise to a strong tetragonal crystal field, which yields the large ZFS of the ground state. The theoretically calculated parameters D , ( a + 2 F /3), Δ 1 , and Δ 2 for Fe 3+ :KMgF 3 crystals are in good agreement with experimental ones when the five F − ions move toward Fe 3+ by |Δ R 1 (F)| = 6.40 × 10 −4 nm and the O 2− ion toward Fe 3+ by |Δ R 2 (O)| = 10.55 × 10 −3 nm.

Local structure distortion and spin Hamiltonian parameters of oxide-diluted magnetic semiconductor Mn-doped ZnO

The local structure distortion, the spin Hamiltonian (SH) parameters, and the electric fine structure of the ground state for Mn2+ (3d5) ion in ZnO crystals are systematically investigated, where spin–spin (SS), spin–other-orbit (SOO) and orbit–orbit (OO) magnetic interactions, besides the well-known spin-orbit (SO) coupling, are taken into account for the first time, by using the complete diagonalization method. The theoretical results of the second-order zero-field splitting (ZFS) parameter D, the fourth-order ZFS parameter (a-F), the Zeeman g-factors: g// and g⊥, and the energy differences of the ground state: δ1 and δ2 for Mn2+ in Mn2+: ZnO are in good agreement with experimental measurements when the three O2– ions below the Mn2+ ion rotate by 1.085° away from the [111]-axis. Hence, the local structure distortion effect plays an important role in explaining the spectroscopic properties of Mn2+ ions in Mn2+: ZnO crystals. It is found for Mn2+ ions in Mn2+: ZnO crystals that although the SO mechanism is the most important one, the contributions to the SH parameters, made by other four mechanisms, i.e. SS, SOO, OO, and SO∼SS∼SOO∼OO mechanisms, are significant and should not be omitted, especially for calculating ZFS parameter D.

Theoretical study of spin-singlet contributions to zero-field splitting of a 3d6 ion in a trigonal ligand field and applications to Fe2+ in FeSiF6 · 6H2O and FeCO3

The complete energy matrix (210 × 210) for d6(d4) configuration ions in a trigonal ligand field is constructed. The energy levels and zero-field splitting parameters in ferrous fluosilicate and ferrous carbonate are studied. The contributions of spin singlets to zero-field splitting parameters in a trigonal ligand field are investigated for the first time. The calculation results indicate that the spin-singlet contribution to second-order zero-field splitting parameter D is negligible, but the contributions to fourth-order zero-field splitting parameter a − F cannot be neglected. Moreover, it is found that the stronger the trigonal ligand field, the larger are the spin-singlet contributions to the zero-field splitting parameters.

Origin of magnetization tunneling in single-molecule magnets as determined by single-crystal high-frequency EPR

Abstract We review an extensive body of single-crystal high-frequency electron paramagnetic resonance (HFEPR) data in order to determine the transverse spin Hamiltonian parameters that control the tunneling of the direction of magnetization in a variety of integer and half-integer-spin single-molecule magnets (SMMs). The SMMs studied are members of the following families: S = 9/2 [Mn4O3Cl]6+; S = 5 [Mn3NiO4]6+; S = 6 [Mn3ZnO4]6+; and S = 4 [Ni4(OR)4]4+. HFEPR spectra for the half-integer S = 9/2 Mn4 complexes that have C3 symmetry do not provide measurable evidence for transverse spin Hamiltonian terms. This finding is consistent with the relatively large coercive field seen in the magnetization hysteresis loops for these complexes. On the other hand, a low symmetry S = 9/2 complex exhibits a much faster rate of ground-state magnetization tunneling, in agreement with HFEPR spectra for a powder sample that gives a rhombic zero-field splitting (ZFS) parameter of E = 0.140 cm−1. The S = 5 Mn3Ni systems exhibit magnetization tunneling that is much faster than seen for the high-symmetry S = 9/2 Mn4 complexes. This can be attributed to their integer-spin ground states. Like the C3 symmetry Mn4 SMMs, the HFEPR spectra for high-symmetry Mn3Ni complexes do not provide measurable evidence for transverse ZFS terms. However, the spectra exhibit broad peaks, suggesting distributions in the local molecular environments brought about by disordered solvate molecules. This disorder likely explains the fast tunneling in the high-symmetry S = 5 Mn3Ni systems, though one cannot rule out fourth- (and higher-) order interactions that cannot be detected by HFEPR due to the broad resonances. The one S = 6 Mn3Zn complex shows an even faster rate of tunneling compared to the isostructural S = 5 Mn3Ni complex. Finally, the S = 4 [Ni(hmp)(dmb)Cl]4 complex provides unique insights into the origin of fourth- (and higher-) order interactions found for many SMMs on the basis of analysis using a giant spin Hamiltonian (GSH) approximation. We conclude that the fourth-order anisotropy found for the S = 4 ground state of [Ni(hmp)(dmb)Cl]4 originates from the second-order ZFS interactions associated with the individual NiII ions, but only as a result of higher-order processes that occur via S-mixing between the ground state and higher-lying (S

Mechanisms of Spin-Mixing Instabilities in Antiferromagnetic Molecular Wheels

The microscopic theory of field-induced spin-mixing instabilities in antiferromagnetic molecular wheels CsFe8 is proposed. The basic features of magnetic torque measurements [O. Waldmann, Phys. Rev. Lett. 96, 027206 (2006)] are well explained by the interplay of three basic ingredients: the spin-mixing vibronic interaction with field-dependent vibronic constants, cooperative elastic interactions, and spin-mixing interactions independent from vibrations. The main contribution to spin mixing comes from second-order zero-field splitting mechanisms. At variance with previous interpretations, we find that the observed anomalies are not associated with a phase transition.

Theoretical investigation of zero-field splitting and local structure distortion for a substitution of Fe 3+ ion in CdCl 2 crystal

A theoretical method for studying the inter-relation between electron and molecule structure is proposed on the basis of the complete energy matrices of the electron-electron repulsion, the ligand-field and the spin-orbit coupling for d(5) configuration ion in a trigonal ligand-field. As an application, the local distortion structure of (FeCl6)(3-) coordination complex for Fe3+ ions doped into CdCl2 is investigated. Both the second-order zero-field splitting parameter b(2)(0) and fourth-order zero-field splitting parameter b(4)(0) are considered simultaneously in the structural investigation. By diagonalizing the complete energy matrices, the local structure distortion parameters Delta R = -0.24 angstrom, Delta theta = 2.137 degrees at 26 K and Delta R = -0.203 angstrom, Delta theta = 2.515 degrees at 225 K for Fe3+ ions in CdCl2 are determined. These results elucidate a microscopic origin of various ligand-field parameters which are usually used empirically for the interpretation of electron paramagnetic resonance results. It is found that the theoretical results are in good agreement with the experimental values. (C) 2007 Elsevier Ltd. All rights reserved.

Theoretical Investigation of Electron Paramagnetic Resonance Spectra and Local Structure Distortion for Mn2+ Ions in CaCO3:Mn2+ System: A Simple Model for Mn2+ Ions in a Trigonal Ligand Field

This paper reports on a novel application of a ligand field model for the detection of the local molecular structure of a coordination complex. By diagonalizing the complete energy matrices of the electron-electron repulsion, the ligand field and the spin-orbit coupling for the d5 configuration ion in a trigonal ligand field, the local distortion structure of the (MnO6)10- coordination complex for Mn2+ ions doped into CaCO3, have been investigated. Both the second-order zero-field splitting parameter b(0)2 and the fourth-order zero-field splitting parameter b(0)4 are taken simultaneously in the structural investigation. From the electron paramagnetic resonance (EPR) calculations, the local structure distortion, DeltaR=-0.169 A to -0.156 A, Deltatheta=0.996 degrees to 1.035 degrees for Mn2+ ions in calcite single crystal, DeltaR=-0.185 A to -0.171 A, Deltatheta=3.139 degrees to 3.184 degrees for Mn2+ ions in travertines, and DeltaR=-0.149 A to -0.102 A, Deltatheta=0.791 degrees to 3.927 degrees for Mn2+ ions in shells are determined, respectively. These results elucidate a microscopic origin of various ligand field parameters which are usually used empirically for the interpretation of EPR and optical absorption experiments. It is found that the theoretical results of the EPR and optical absorption spectra for Mn2+ ions in CaCO3 are in good agreement with the experimental findings. Moreover, to understand the detailed physical and chemical properties of the doped CaCO3, the theoretical values of the fourth-order zero-field splitting parameters b(0)4 for Mn2+ ions in travertines and shells are reported first.

SUPERPOSITION MODEL ANALYSIS FOR THE ZERO-FIELD SPLITTING OFMn2+IN SOME CRYSTALS

The Newman superposition model has been applied to second-order zero-field splitting parameter [Formula: see text] taken from the literature for Mn2+in Hg(ClO4)2· 6 H2O , M ″ SiF6·6 H2O (M ″= Fe, Co, Zn ) and M ″ NbOF5·6 H2O (M ″= Co, Zn ). In the calculations, the local lattice relaxation has been taken into account. It is shown that nearly the same value of intrinsic parameter b2=-0.057(8) cm-1is obtained.

Multifrequency EPR Study of Metallofullerenes: Eu@C82 and Eu@C74

In this work, the cage structure of a family of europium metallofullerenes, Eu@C74 and three isomers of Eu@C82, were investigated. The analogy of the electronic states of three isomers of Eu@C82 with those of three isomers of Ca@C82 was confirmed by UV−vis−near-IR absorption spectra. The symmetries Cs, C2, and C2v were assigned for three isomers of Eu@C82 by comparing each corresponding isomer of Ca@C82. The D3h cage structure of Eu@C74, which is expected only for the C74 from the isolated pentagon rule, was also confirmed by comparing its photoabsorption spectrum with that of Ca@C74. Multifrequency electron paramagnetic resonance (EPR) spectroscopy was employed to determine the zero-field splitting (ZFS) parameters of the metallofullerenes, which are closely related to the surrounding cage structures. The experimental X- and W-band EPR spectra were completely reproduced by computer simulations based on a spin Hamiltonian considering the ZFS terms up to fourth order. The introduction of the fourth-order ZFS terms into the Hamiltonian resulted in a precise determination of the second-order ZFS terms. A nonvanishing rhombicity parameter E of Eu@C74 demonstrated the reduction of the symmetry from D3h to C2v due to the positioning of Eu2+ ion at the off-center of C74 cage. Moreover, in this work, the semiphenomenological superposition-exchange model (SPEM) was invoked to examine a relationship between the molecular structures and ZFS parameters. All of the experimental ZFS parameters were satisfactory reproduced in terms of the SPEM, leading to confirmation of the molecular symmetries. The semiphenomenological analysis also enabled us to select the most appropriate cage for Eu@C82 with C2 symmetry from among three possible isomers.

Superposition model calculation ofzero-field splitting of Fe3+ in LiTaO3 crystal

The second-order zero-field splitting (ZFS) parameter b20 ofthe Fe3+ ion centre at the Li site, the Ta site and thestructural vacancy site in the LiTaO3 crystal are calculatedusing the empirical superposition model. The fourth-orderZFS parameters b40, b43 andb4-3 are also calculated at the Li and Ta site,respectively. The calculated b20 of Fe3+ ion atthe Li site agrees well with the experimental one. It isconcluded that the Fe3+ replaces the Li+ ionrather than the Ta5+ ion in the LiTaO3 crystal. This conclusion confirms the site assignment from the electronnuclear double resonance experiments.

EPR study of Gd3+ in a ferroelastic BiVO4 single crystal

Electron paramagnetic resonance of the Gd3+ ion in a ferroelastic BiVO4 single crystal with a single domain, grown by the Czochralski method, has been investigated at room temperature using a Q-band spectrometer. The rotation patterns of the resonance fields measured in the crystallographic planes are analyzed using a monoclinic spin Hamiltonian. The principal Z-axis of the second-order zero-field splitting tensorD is found to be along the crystallographicb-axis. Spin Hamiltonian parameters together with the principal axes ofg andD tensors in the monoclinic plane show that the local site symmetry of Gd3+ ion in BiVO4 crystal is monoclinic and that the Gd3+ ion substitutes for Bi3+ ion.

Charge-compensation models of four and four centres in

An overall comparison between the principal-axis orientations of the -tensors and the second-order zero-field-splitting (ZFS) tensors for four and four centres reported on in our previous studies has been made. One direction of the principal axes of the -tensor is nearly the same as one of those of the second-order ZFS tensor for centres, but a similar direction does not exist for centres. It is also found that one direction of the principal axes of the second-order ZFS tensors for centres is similar to one of those for the centres. It is suggested that ions substituted for in tetrahedra play the role of positive monovalent charge compensators for both and , replaced at the sites Ti(1) and Ti(2). Possible charge-compensation models related to ions for providing an explanation of the origins of the two different centres arising from the and at crystallographically equivalent Ti sites are also suggested.

Electron paramagnetic resonance study of a new centre and eight new sites of ions in

Careful reanalysis of EPR spectra of ions in (KTP) has been carried out in order to resolve the weaker lines not considered in our previous study. Eight additional sets of fine-structure (FS) lines, (Y = 3, 4 and j = a, b, c, d), have now been identified and their respective spin-Hamiltonian parameters have been determined. These sets are classified into two groups denoted as centres C3 and C4, each of which yields identical principal values of the tensor and second-order zero-field splitting tensor but different orientations of the principal axes. For four sets of FSs belonging to each centre, the direction cosines of the principal axes are found to be , and , consistently with the crystal symmetry of KTP. The FS C4a agrees well with that denoted as the centre ST4 by other investigators, whereas the others are newly identified. The eight magnetically inequivalent sites are assigned to two titanium sites: Ti(1) and Ti(2). Two different centres, C1 and C3 as well as C2 and C4, arising from ions at the respective Ti(1) and Ti(2) sites, are explained by differing charge compensation. It is also suggested that a vacancy of the first-neighbour oxygen OT(1), denoted as , plays the role of a divalent positive charge compensator simultaneously for two ions at the adjacent Ti(1) and Ti(2) sites.

Determination of new sites for two Fe3+ EPR centres in KTiOPO4

EPR spectra of Fe3+ ions in single crystals of KTiOPO4 (KTP), synthesized by the flux method, have been investigated at room temperature by employing a Bruker Q-band spectrometer. From the angular dependence of the EPR spectra, two Fe3+ centres denoted as C1 and C2 have been identified, in agreement with the previous analysis by other investigators. In this study, for the first time we have fully identified two groups of four magnetically inequivalent Fe3+ sites each belonging to the centres C1 and C2. Two sets of triclinic spin-Hamiltonian parameters, which simultaneously fitted EPR data for the four sites belonging to the centres C1 and C2, were determined. The direction cosines of the principal axes of the g-tensor as well as the second-order zero-field splitting (ZFS) tensor are found to be given by the relations: lmn, lmn, lmn and lmn for each four Fe3+ sites of C1 as well as C2, respectively, consistent with the crystallographic point group mm2 of KTP.

Superposition model analysis of zero-field splitting for Mn 2+IN La 2Mg 3(NO 3) 12 · 24H 2O single crystals

The Newman superposition model has been applied to the second-order zero-field splitting parameter b 2 0 for Mn 2+ in La 2 Mg 3 (NO 3 ) 123 · 24H 2 O single crystals at both the sites. It is shown that calculated values of b 2 0 are in agreement with the experimental values if local relaxation effects are taken into account.

Superposition model analysis of zero-field splitting for Mn 2+ in some hosts

Abstract The Newman superposition model has been applied to the second-order zero-field splitting parameter b 0 2 taken from the literature for Mn 2+ in scheelite, Ca 5 (PO 4 ) 3 F, Mg(OMPA) 3 (ClO 4 ) 2 , metal hexakisantipyrine perchlorate and A 2 CdCl 4 (A = Cs, Rb). In the calculations, the local lattice relaxation has been taken into account. It is shown that nearly the same value as the intrinsic parameter b 2 is obtained in the case of scheelite and the Mg host. In the other hosts, where Mn 2+ substitutes for the same cation, different values of b 2 are obtained. It appears that drastic local lattice relaxation occurs in Pb hexakisantipyrine perchlorate.

Correlation of Zero-Field Splittings and Site Distortions. IX. Fe3+ and Cr3+ in β -Ga2O3

EPR of Fe3+ in distorted tetrahedral sites in single crystals of β-Ga2O3 has been measured for the first time, and the second-order zero-field splitting (ZFS) parameters and principal axes directions were determined. The data for the sixfold coordinated Fe3+ are in good agreement with results from the literature. Comparison of the ZFS patterns with those calculated from the crystal structure data using the superposition model (SPM) shows reasonable agreement in the orientations of the principal axes, but only for the tetrahedral site is a reasonable value of the intrinsic ZFS parameter obtained. Besides large uncertainties in the sizes of the distortions the crystal structure data also appear to be systematically wrong. For Cr3+ in sixfold coordinated sites the discrepancies are even larger, but for this ion a reduced validity of the SPM may also be involved.

Local relaxations around Fe3+ and Cr3+ in Al sites in minerals

Second-order zero-field splitting (ZFS) parameters from the literature for Fe3+ in twelve and for Cr3+ in seven minerals substituting for Al were evaluated by application of the superposition model. For Fe3+ in monoclinic site symmetries a fair agreement of the observed splitting patterns with those calculated from the crystal structure data was observed in most cases, but the distortions for Fe3+ appear to be usually larger than those of the unrelaxed Al sites. In cases of not too large local relaxation the unknown sign of the axialZFS parameterb02could be predicted, in two cases a different sign than that reported was postulated. In cordierite and scolecite the reportedEPR spectra could thus be assigned to the sites with larger average bond distances. For Fe3+ in beryl the relaxation of the axial site can be deduced within narrow limits.