Magnetic Susceptibility Tensor Research Articles

Magnetic Anisotropy of Homo- and Heteronuclear Terbium(III) and Dysprosium(III) Trisphthalocyaninates Derived from Paramagnetic 1H-NMR Investigation.

1H-NMR spectroscopy of lanthanide complexes is a powerful tool for deriving spectral-structural correlations, which provide a clear link between the symmetry of the coordination environment of paramagnetic metal centers and their magnetic properties. In this work, we have first synthesized a series of homo- (M = M* = Dy) and heteronuclear (M ≠ M* = Dy/Y and Dy/Tb) triple-decker complexes [(BuO)8Pc]M[(BuO)8Pc]M*[(15C5)4Pc], where BuO- and 15C5- are, respectively, butoxy and 15-crown-5 substituents on phthalocyanine (Pc) ligands. We provide an algorithmic approach to assigning the 1H-NMR spectra of these complexes and extracting the axial component of the magnetic susceptibility tensor, χax. We show how this term is related to the nature of the lanthanide ion and the shape of its coordination polyhedron, providing an experimental basis for further theoretical interpretation of the revealed correlations.

Effect of Magnetic Anisotropy on the 1H NMR Paramagnetic Shifts and Relaxation Rates of Small Dysprosium(III) Complexes.

We present a detailed analysis of the 1H NMR chemical shifts and transverse relaxation rates of three small Dy(III) complexes having different symmetries (C3, D2 or C2). The complexes show sizeable emission in the visible region due to 4F9/2 → 6HJ transitions (J = 15/2 to 11/2). Additionally, NIR emission is observed at ca. 850 (4F9/2 → 6H7/2), 930 (4F9/2 → 6H5/2), 1010 (4F9/2 → 6F9/2), and 1175 nm (4F9/2 → 6F7/2). Emission quantum yields of 1-2% were determined in aqueous solutions. The emission lifetimes indicate that no water molecules are present in the inner coordination sphere of Dy(III), which in the case of [Dy(CB-TE2PA)]+ was confirmed through the X-ray crystal structure. The 1H NMR paramagnetic shifts induced by Dy(III) were found to be dominated by the pseudocontact mechanism, though, for some protons, contact shifts are not negligible. The analysis of the pseudocontact shifts provided the magnetic susceptibility tensors of the three complexes, which were also investigated using CASSCF calculations. The transverse 1H relaxation data follow a good linear correlation with 1/r6, where r is the distance between the Dy(III) ion and the observed proton. This indicates that magnetic anisotropy is not significantly affecting the relaxation of 1H nuclei in the family of complexes investigated here.

Solvation-Induced Conformational Switching of Trisphthalocyanates for Control of Their Magnetic Properties

Stabilization of different conformers of sandwich phthalocyaninates by changing the solvation environment has been demonstrated with the examples of new heteroleptic yttrium(III) and terbium(III) triple-decker complexes [(BuO)8Pc]M[(BuO)8Pc]M[(15C5)4Pc] (where M = Y or Tb, [(BuO)8Pc]2- = octa-n-butoxyphthalocyaninato ligand, and [(15C5)4Pc]2- = tetra-15-crown-5-phthalocyaninato ligand). To this end, we have performed a comprehensive crystallographic characterization of two solvates formed by the Y(III) complex with either toluene or dichloromethane. In the solvate with toluene, both pairs of Pc ligands are in staggered conformations, providing both metal cations with a square-antiprismatic environment. In contrast, in the solvate with dichloromethane, only one cation between the BuO- and 15C5-substituted ligands remains in a square-antiprismatic polyhedron, while the pair of BuO-substituted ligands switches to a gauche conformation. In both solvates, the staggered conformations are stabilized by weak interactions of peripheral substituents with solvent molecules. Detailed analysis of the 1H NMR spectra of the isostructural Tb(III) complex in aliphatic and aromatic solvents demonstrates that the stabilization of the corresponding conformations by solvation is also valid in the solution state, resulting in an increase in the axial component of the magnetic susceptibility tensor as the symmetry decreases from staggered to gauche. Thus, solvation-induced conformational switching of lanthanide trisphthalocyaninates can be used as a tool to control their magnetic properties.

Site-Selective Solvation-Induced Conformational Switching of Heteroleptic Heteronuclear Tb(III) and Y(III) Trisphthalocyaninates for the Control of Their Magnetic Anisotropy.

In the present work, we report the synthesis of isomeric heteronuclear terbium(III) and yttrium(III) triple-decker phthalocyaninates [(BuO)8Pc]M[(BuO)8Pc]M*[(15C5)4Pc] (M = Tb, M* = Y or M = Y, M* = Tb, [(BuO)8Pc]2--octa-n-butoxyphthalocyaninato-ligand, [(15C5)4Pc]2--tetra-15-crown-5-phthalocyaninato-ligand). We show that these complexes undergo solvation-induced switching: the conformers in which both metal centers are in square-antiprismatic environments are stabilized in toluene, whereas in dichloromethane, the metal centers M and M* are in distorted prismatic and antiprismatic environments, respectively. This conclusion follows from the detailed analysis of lanthanide-induced shifts in 1H NMR spectra, which makes it possible to extract the axial component of the magnetic susceptibility tensor χaxTb and to show that this term is particularly sensitive to conformational switching when terbium(III) ion is placed in the switchable "M" site. This result provides a new tool for controlling the magnetic properties of lanthanide complexes with phthalocyanine ligands.

Inertial rotational diffusion and magnetic relaxation of the spin system in a strong magnetic field

Analytical expressions for the longitudinal and transverse correlation functions pertaining to inertial magnetic relaxation are obtained by expanding the deterministic magnetization trajectories into a Fourier series and averaging the result over all possible initial conditions applying the stationary Boltzmann distribution function. The longitudinal and transverse components of the magnetic susceptibility tensor are calculated for a system of noninteracting macrospins in a strong uniform external field using Bloch's phenomenological approach, which postulates the exponential evolution of the spin system towards equilibrium, and the Lorentz model of rotational diffusion of the magnetization vector. It is shown that the strength of the external field and the magnitude of the inertia parameters noticeably affect the shape of the susceptibility in the THz (nutation resonance) spectrum region. It is also demonstrated that the simple analytical Lorentz-type expression describes the main features of the complex susceptibility in the ferromagnetic resonance and nutation resonance regions.

Determining Local Magnetic Susceptibility Tensors in Paramagnetic Lanthanide Crystalline Powders from Solid-State NMR Chemical Shift Anisotropies

Exploring magnetic properties at the molecular level is a challenge that has been met by developing many experimental and theoretical solutions, such as polarized neutron diffraction (PND), muon-spin rotation (μ-SR), electron paramagnetic resonance (EPR), SQUID-based magnetometry measurements, and advanced modeling on open-shell systems and relativistic calculations. These methods are powerful tools that shed light on the local magnetic response in specifically designed magnetic materials such as contrast agents, for MRI, molecular magnets, magnetic tags for biological NMR, etc. All of these methods have their advantages and disadvantages. In order to complement the possibilities offered by these methods, we propose a new tool that implements a new approach combining simulation and fitting for high-resolution solid-state NMR spectra of lanthanide-based paramagnetic species. This method relies on a rigorous acquisition thanks to short high-power adiabatic pulses (SHAP) of high-resolution solid-state NMR isotropic and anisotropic data on a powdered magnetic material. It is also based on an efficient modeling of this data thanks to a semiempirical model based on a parametrization of the local magnetism and the crystal structure provided by diffraction methods. The efficiency of the calculation relies on a thorough simplification of the electron-nucleus interactions (point-dipole interaction, no Fermi contact) which is validated by experimental analysis. By taking advantage of the efficient calculation possibilities offered by our method, we can compare a great number of simulated spectra to experimental data and find the best-matching local magnetic susceptibility tensor. This method was applied to a series of isostructural lanthanide oxalates which are used as a benchmark system for many analytical methods. We present the results of thorough solid-state NMR and extensive modeling of the hyperfine interaction (including up to 400 paramagnetic centers) that yield local magnetic susceptibility tensor measurements that are self-consistent as well as consistent with bulk susceptibility measurements.

Structure Determination of Binuclear Triple-Decker Phthalocyaninato Complexes by NMR via Paramagnetic Shifts Analysis Using Symmetry Peculiarities.

The detailed knowledge about the structure of multinuclear paramagnetic lanthanide complexes for the targeted design of these compounds with special magnetic, sensory, optical and electronic properties is a very important task. At the same time, establishing the structure of such multinuclear paramagnetic lanthanide complexes in solution, using NMR is a difficult task, since several paramagnetic centers act simultaneously on the resulting chemical shift of a particular nucleus. In this paper, we have demonstrated the possibility of molecular structure determination in solution on the example of binuclear triple-decker lanthanide(III) complexes with tetra-15-crown-5-phthalocyanine Ln2[(15C5)4Pc]3 {where Ln = Tb (1) and Dy (2)} by quantitative analysis of the pseudo-contact lanthanide-induced shifts (LIS). The symmetry of complexes was used for the simplification of the calculation of pseudo-contact shifts on the base of the expression for the magnetic susceptibility tensor in the arbitrary oriented magnetic axis system. Good agreement between the calculated and experimental shifts in the 1H NMR spectra indicates the similarity of the structure for the complexes 1 and 2 in solution of CDCl3 and the structure in the crystalline phase, found from the data of the X-ray structural study of the similar complex Lu2[(15C5)4Pc]3. The described approach can be useful for LIS analysis of other polynuclear symmetric lanthanide complexes.

Site-selective generation of lanthanoid binding sites on proteins using 4-fluoro-2,6-dicyanopyridine.

The paramagnetism of a lanthanoid tag site-specifically installed on a protein provides a rich source of structural information accessible by nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) spectroscopy. Here we report a lanthanoid tag for selective reaction with cysteine or selenocysteine with formation of a (seleno)thioether bond and a short tether between the lanthanoid ion and the protein backbone. The tag is assembled on the protein in three steps, comprising (i)reaction with 4-fluoro-2,6-dicyanopyridine (FDCP); (ii)reaction of the cyano groups with -cysteine, penicillamine or -cysteine to complete the lanthanoid chelating moiety; and (iii)titration with a lanthanoid ion. FDCP reacts much faster with selenocysteine than cysteine, opening a route for selective tagging in the presence of solvent-exposed cysteine residues. Loaded with and ions, pseudocontact shifts were observed in protein NMR spectra, confirming that the tag delivers good immobilisation of the lanthanoid ion relative to the protein, which was also manifested in residual dipolar couplings. Completion of the tag with different 1,2-aminothiol compounds resulted in different magnetic susceptibility tensors. In addition, the tag proved suitable for measuring distance distributions in double electron-electron resonance experiments after titration with ions.

Study of magnetoelastic interaction in MnF2 by the acoustoelectric transformation method

The mechanisms of magnetoelastic interaction in MnF2 are studied using the method of acoustoelectric transformation. The temperature dependence of the piezomagnetic coupling coefficient and its anisotropy were determined in the antiferromagnetic phase. We observe a new effect consisting in the appearance of a non-diagonal component of the magnetic susceptibility tensor, which is proportional to the square of the order parameter, under the action of the shear wave. A phenomenological interpretation of the effect, which takes into account a small-angle rotation of the crystal lattice, is presented. In the paramagnetic state, the effect of acoustic deformation is reduced to the modulation of the diagonal component of the susceptibility tensor.

Paramagnetic encoding of molecules.

Contactless digital tags are increasingly penetrating into many areas of human activities. Digitalization of our environment requires an ever growing number of objects to be identified and tracked with machine-readable labels. Molecules offer immense potential to serve for this purpose, but our ability to write, read, and communicate molecular code with current technology remains limited. Here we show that magnetic patterns can be synthetically encoded into stable molecular scaffolds with paramagnetic lanthanide ions to write digital code into molecules and their mixtures. Owing to the directional character of magnetic susceptibility tensors, each sequence of lanthanides built into one molecule produces a unique magnetic outcome. Multiplexing of the encoded molecules provides a high number of codes that grows double-exponentially with the number of available paramagnetic ions. The codes are readable by nuclear magnetic resonance in the radiofrequency (RF) spectrum, analogously to the macroscopic technology of RF identification. A prototype molecular system capable of 16-bit (65,535 codes) encoding is presented. Future optimized systems can conceivably provide 64-bit (~10^19 codes) or higher encoding to cover the labelling needs in drug discovery, anti-counterfeiting and other areas.

High-frequency magnetic susceptibility of a 2D electron gas with spin-orbit interaction in a parallel magnetic field under topological phase transition

We study theoretically spin transport in a two-dimensional electron system with an essential spin-orbit interaction under topological phase transition due to changing a parallel magnetic field. Analytical formulas for the high-frequency magnetic susceptibility tensor under conditions when both spin bands are filled have been obtained. A numerical analysis giving full enough representation of the dependence of the spin magnetic susceptibility on the frequency and magnetic field is presented. It has been established that the magnetic susceptibility experiences a jump for magnetic field values at which the connectivity of the Fermi contour is changed.

Incorporation of residual chemical shift anisotropy into the treatment of 15N pseudocontact shifts for structural refinement

Paramagnetic NMR experiments, including the pseudocontact shift experiment, have seen increasing use due to recently developed probes and labeling strategies. The pseudocontact shift experiment can provide valuable intra- or inter-molecular distance and orientation information. However, the use of 1H/13C or 1H/15N PCS data in structure calculations is currently complicated by the contribution of residual chemical shift anisotropy to the 13C or 15N datasets. Here, we present a corrected PCS energy term for the software package Xplor-NIH with the appropriate residual chemical shift anisotropy correction and show its suitability for model refinements of ubiquitin labeled at residue 57 with a Tm-M8-SPy tag. For data taken at 800 MHz, the improvement with the corrected energy term is sufficient to make the quality of the fit for the 15N dataset comparable to that of the 1H dataset, for which no correction is needed. The corrected energy term is expected to become more relevant with increased use of higher field instruments and as new paramagnetic probes with larger magnetic susceptibility tensors continue to be developed.

Ferromagnetic resonance of a magnetic particle using the Landau–Lifshitz–Bloch equation

In this work, we employ the Landau–Lifshitz–Bloch equation to study the ferromagnetic resonance of a magnetic nanoparticle assumed in a mono-domain with uniaxial anisotropy. We consider a constant magnetic field applied perpendicularly to the easy axis of anisotropy. We investigated the temperature effect on the resonance spectrum through the complex magnetic susceptibility tensor. We found a decrease in the resonance frequency as the temperature is incremented and a decrement in the resonance field range when the driven frequency increases.

Intrinsic anisotropy parameters of a series of lanthanoid complexes deliver new insights into the structure-magnetism relationship

Intrinsic anisotropy parameters of a series of lanthanoid complexes deliver new insights into the structure-magnetism relationship

Neogene Kinematics of the Potwar Plateau and the Salt Range, NW Himalayan Front: A Paleostress Inversion and AMS study

ABSTRACT We provide new kinematic data from the Potwar Plateau (Pakistan) to evaluate the tectonic evolution of the region during the Neogene. The plateau is bound by two major strike-slip faults in the west and the east, accommodating its southwards translation. We have recognized two Neogene deformation phases in the plateau, based on paleostress inversion and Anisotropy of Magnetic Susceptibility (AMS) tensors. The first phase lasted until the early Pliocene and was characterized by vertical minor stress and N-S compression, implying thrust tectonics. The second deformation phase is characterized by a near-vertical intermediate principal stress and near-horizontal major and minor stresses, interpreted to be associated with strike-slip tectonics since the late Pliocene. Kint vectors from 21 sites are relatively compatible with the major principal stress orientations (σ1) and indicate two distinct domains. This is possibly because Kmin orientations are related to compaction, whereas Kint orientations were always parallel to tectonic shortening and hence compression direction during both strike-slip (post-late Pliocene) and thrusting (pre-late Pliocene) phases. These phases are characterized by swapping of (σ2) and (σ3) orientations while (σ1) maintained its orientation. The most prominent change occurs at the western part of the Potwar Plateau, where major principal stress directions (σ1) and Kint axes fan out south-westwards. The eastern domain is dominated by NE-SW trending folds and thrust faults, which are absent in the western domain. These structural features are interpreted to be the result of the distribution of deposits of the Neoproterozoic Salt Range Formation as a substratum below the Potwar Plateau. The Salt Range Formation is very thick and widespread in the west area and almost absent in the east. This factor led to unconstrained southwards gliding of the Potwar Plateau over the salt deposits in the west as opposed to frictional sliding and substantial internal deformation in the east.

Heteroleptic Crown-Substituted Tris(phthalocyaninates) as Dynamic Supramolecular Scaffolds with Switchable Rotational States and Tunable Magnetic Properties.

Herein we report single-crystal X-ray diffraction characterization and complementary solution studies of supramolecular interaction between potassium salts and heteroleptic homo- and heteronuclear triple-decker crown phthalocyaninates [(15C5)4Pc]M*[(15C5)4Pc]M(Pc) or [M*,M], where M* and M = Y and/or Tb. Our results evidence that, in contrast to the previously studied crown-substituted phthalocyanines, the interaction of K+ cations with [M*,M] does not induce their intermolecular aggregation. Instead, the cations reversibly intercalate between the crown-substituted phthalocyanine ligands, resulting in switching of the coordination polyhedron of the metal center M* from square-antiprismatic to square-prismatic. In the case of terbium(III) complexes, such a switching alters their magnetic properties, which can be read-out by 1H NMR spectroscopy. For [Tb*,Y], such a switching causes an almost 25% increase in the axial component of the magnetic susceptibility tensor. Even though the polyhedron of the paramagnetic center in [Y*,Tb] is not switched, minor structural perturbations associated with the overall reorganization of the receptor also cause smaller, but nevertheless appreciable, growth of the axial anisotropy. The observed effects render the studied complexes as molecular switches with tunable magnetic properties.

Asymmetric susceptibility tensor imaging.

To investigate the symmetry constraint in susceptibility tensor imaging. The linear relationship between the MRI frequency shift and the magnetic susceptibility tensor is derived without constraining the tensor to be symmetric. In the asymmetric case, the system matrix is shown to be maximally rank 6. Nonetheless, relaxing the symmetry constraint may still improve tensor estimation because noise and image artifacts do not necessarily follow the constraint. Gradient echo phase data are obtained from postmortem mouse brain and kidney samples. Both symmetric and asymmetric tensor reconstructions are applied to the data. The reconstructions are then used for susceptibility tensor imaging fiber tracking. Simulations with ground truth and at various noise levels are also performed. The reconstruction methods are compared qualitatively and quantitatively. Compared to regularized and unregularized symmetric reconstructions, the asymmetric reconstruction shows reduced noise and streaking artifacts, better contrast, and more complete fiber tracking. In simulation, the asymmetric reconstruction achieves better mean squared error and better angular difference in the presence of noise. Decomposing the asymmetric tensor into its symmetric and antisymmetric components confirms that the underlying susceptibility tensor is symmetric and that the main sources of asymmetry are noise and streaking artifacts. Whereas the susceptibility tensor is symmetric, asymmetric reconstruction is more effective in suppressing noise and artifacts, resulting in more accurate estimation of the susceptibility tensor.

Temperature Dependence of 1 H Paramagnetic Chemical Shifts in Actinide Complexes, Beyond Bleaney's Theory: The AnVI O2 2+ -Dipicolinic Acid Complexes (An=Np, Pu) as an Example.

Actinide +VI complexes ( = , and ) with dipicolinic acid derivatives were synthesized and characterized by powder XRD, SQUID magnetometry and NMR spectroscopy. In addition, and complexes were described by first principles CAS based and two-component spin-restricted DFT methods. The analysis of the 1 H paramagnetic NMR chemical shifts for all protons of the ligands according to the X-rays structures shows that the Fermi contact contribution is negligible in agreement with spin density determined by unrestricted DFT. The magnetic susceptibility tensor is determined by combining SQUID, pNMR shifts and Evans' method. The SO-RASPT2 results fit well the experimental magnetic susceptibility and pNMR chemical shifts. The role of the counterions in the solid phase is pointed out; their presence impacts the magnetic properties of the complex. The temperature dependence of the pNMR chemical shifts has a strong contribution, contrarily to Bleaney's theory for lanthanide complexes. The fitting of the temperature dependence of the pNMR chemical shifts and SQUID magnetic susceptibility by a two-Kramers-doublet model for the complex and a non-Kramers-doublet model for the complex allows for the experimental evaluation of energy gaps and magnetic moments of the paramagnetic center.

High-resolution optical spectroscopy, magnetic properties, and single-crystal neutron diffraction of multiferroic HoFe3(BO3)4 : Magnetic structure

The magnetic structure is usually determined by the neutron diffraction measurements. However, in the case of complex multisublattice magnetics, this method fails to give an unambiguous result. Here, on the example of multiferroic ${\mathrm{HoFe}}_{3}{({\mathrm{BO}}_{3})}_{4}$, we show that in the case of rare-earth (RE) compounds the right magnetic structure can be determined by additionally using optical spectroscopy and a theoretical analysis based on spectroscopic data. ${\mathrm{HoFe}}_{3}{({\mathrm{BO}}_{3})}_{4}$ demonstrates a series of phase transitions and interesting magnetic and magnetoelectric properties. The available information on the magnetic structure of the compound, necessary for understanding and utilizing these properties, is contradictory. To resolve the existing ambiguities, we apply a combined approach. The high-resolution spectroscopy data deliver a set of the ${\mathrm{Ho}}^{3+}$ crystal-field (CF) levels in the paramagnetic and both easy-plane and easy-axis magnetic phases. These data are used to determine CF and ${\mathrm{Ho}}^{3+}\text{\ensuremath{-}}{\mathrm{Fe}}^{3+}$ exchange parameters and, then, to calculate the temperature dependencies of the magnetic susceptibility tensor of ${\mathrm{HoFe}}_{3}{({\mathrm{BO}}_{3})}_{4}$. Based on these calculations, we suggest an easy-plane antiferromagnetic structure with a collinear arrangement of the Fe spins along the $a$ axis and induced noncolinear moments of magnetically nonequivalent Ho ions. The suggested structure is further confirmed by single-crystal elastic neutron scattering experiments. We argue that specific features of the magnetic properties of RE iron borates isostructural to ${\mathrm{HoFe}}_{3}{({\mathrm{BO}}_{3})}_{4}$ are governed by the energy patterns and the symmetry properties of the wave functions of the lower CF levels of the RE ground multiplet in the crystal field of the ${C}_{2}$ symmetry.

Lanthanide(III) Complexes Based on an 18-Membered Macrocycle Containing Acetamide Pendants. Structural Characterization and paraCEST Properties.

We report a detailed investigation of the coordination properties of macrocyclic lanthanide complexes containing a 3,6,10,13-tetraaza-1,8(2,6)-dipyridinacyclotetradecaphane scaffold functionalized with four acetamide pendant arms. The X-ray structures of the complexes with the large Ln3+ ions (La and Sm) display 12- and 10-coordinated metal ions, where the coordination sphere is fulfilled by the six N atoms of the macrocycle, the four O atoms of the acetamide pendants, and a bidentate nitrate anion in the La3+ complex. The analogous Yb3+ complex presents, however, a 9-coordinated metal ion because one of the acetamide pendant arms remains uncoordinated. 1H NMR studies indicate that the 10-coordinated form is present in solution throughout the lanthanide series from La to Tb, while the smaller lanthanides form 9-coordinated species. 1H and 89Y NMR studies confirm the presence of this structural change because the two species are present in solution. Analysis of the 1H chemical shifts observed for the Tb3+ complex confirms its D2 symmetry in aqueous solution and evidences a highly rhombic magnetic susceptibility tensor. The acetamide resonances of the Pr3+ and Tb3+ complexes provided sizable paraCEST effects, as demonstrated by the corresponding Z-spectra recorded at different temperatures and studies on tube phantoms recorded at 22 °C.