Transverse Magnetic Susceptibility Research Articles

Simultaneous MR quantification of hepatic fat content, fatty acid composition, transverse relaxation time and magnetic susceptibility for the diagnosis of non-alcoholic steatohepatitis.

Non-alcoholic steatohepatitis (NASH) is characterized at histology by steatosis, hepatocyte ballooning and inflammatory infiltrates, with or without fibrosis. Although diamagnetic material in fibrosis and inflammation can be detected with quantitative susceptibility imaging, fatty acid composition changes in NASH relative to simple steatosis have also been reported. Therefore, our aim was to develop a single magnetic resonance (MR) acquisition and post-processing scheme for the diagnosis of steatohepatitis by the simultaneous quantification of hepatic fat content, fatty acid composition, T2 * transverse relaxation time and magnetic susceptibility in patients with non-alcoholic fatty liver disease. MR acquisition was performed at 3.0T using a three-dimensional, multi-echo, spoiled gradient echo sequence. Phase images were unwrapped to compute the B0 field inhomogeneity (ΔB0 ) map. The ΔB0 -demodulated real part images were used for fat-water separation, T2 * and fatty acid composition quantification. The external and internal fields were separated with the projection onto dipole field method. Susceptibility maps were obtained after dipole inversion from the internal field map with single-orientation Bayesian regularization including spatial priors. Method validation was performed in 32 patients with biopsy-proven, non-alcoholic fatty liver disease from which 12 had simple steatosis and 20 NASH. Liver fat fraction and T2 * did not change significantly between patients with simple steatosis and NASH. In contrast, the saturated fatty acid fraction increased in patients with NASH relative to patients with simple steatosis (48±2% versus 44±4%; p<0.05) and the magnetic susceptibility decreased (-0.30±0.27ppm versus 0.10±0.14ppm; p<0.001). The area under the receiver operating characteristic curve for magnetic susceptibility as NASH marker was 0.91 (95% CI: 0.79-1.0). Simultaneous MR quantification of fat content, fatty acid composition, T2 * and magnetic susceptibility is feasible in the liver. Our preliminary results suggest that quantitative susceptibility imaging has a high diagnostic performance for the diagnosis of NASH.

The spin-half XXZ antiferromagnet on the square lattice revisited: A high-order coupled cluster treatment

We use the coupled cluster method (CCM) to study the ground-state properties and lowest-lying triplet excited state of the spin-half XXZ antiferromagnet on the square lattice. The CCM is applied to it to high orders of approximation by using an efficient computer code that has been written by us and which has been implemented to run on massively parallelized computer platforms. We are able therefore to present precise data for the basic quantities of this model over a wide range of values for the anisotropy parameter Δ in the range −1≤Δ<∞ of interest, including both the easy-plane (−1<Δ<1) and easy-axis (Δ>1) regimes, where Δ→∞ represents the Ising limit. We present results for the ground-state energy, the sublattice magnetization, the zero-field transverse magnetic susceptibility, the spin stiffness, and the triplet spin gap. Our results provide a useful yardstick against which other approximate methods and/or experimental studies of relevant antiferromagnetic square-lattice compounds may now compare their own results. We also focus particular attention on the behaviour of these parameters for the easy-axis system in the vicinity of the isotropic Heisenberg point (Δ=1), where the model undergoes a phase transition from a gapped state (for Δ>1) to a gapless state (for Δ≤1), and compare our results there with those from spin-wave theory (SWT). Interestingly, the nature of the criticality at Δ=1 for the present model with spins of spin quantum number s=12 that is revealed by our CCM results seems to differ qualitatively from that predicted by SWT, which becomes exact only for its near-classical large-s counterpart.

Effect of magnetic nanoparticle shape on flux amplification in inductive coil magnetic resonance detection

We model and analyze the effect of particle shape on the signal amplification in inductive coil magnetic resonance detection using the reversible transverse magnetic susceptibility of oriented magnetic nanostructures. Utilizing the single magnetic domain Stoner-Wohlfarth model of uniform magnetization rotation, we reveal that different ellipsoidal particle shapes can have a pronounced effect on the magnetic flux enhancement in detection configurations typical of magnetic resonance settings. We compare and contrast the prolate ellipsoids, oblate ellipsoids, and exchange-biased spheres and show that the oblate ellipsoids and exchange-biased spheres have a significantly higher flux amplification effect than the prolate ellipsoids considered previously. In addition, oblate ellipsoids have a much broader polarizing magnetic field range over which their transverse flux amplification is significant. We show the dependence of transverse flux amplification on magnetic resonance bias field and discuss the resulting signal-to-noise ratio of inductive magnetic resonance detection due to the magnetic nanoparticle-filled core of the magnetic resonance detection coil.

Nonequilibrium itinerant-electron magnetism: A time-dependent mean-field theory

We study the dynamical magnetic susceptibility of a strongly correlated electronic system in the presence of a time-dependent hopping field, deriving a generalized Bethe-Salpeter equation which is valid also out of equilibrium. Focusing on the single-orbital Hubbard model within the time-dependent Hartree-Fock approximation, we solve the equation in the non-equilibrium adiabatic regime, obtaining a closed expression for the transverse magnetic susceptibility. From this, we provide a rigorous definition of non-equilibrium (time-dependent) magnon frequencies and exchange parameters, expressed in terms of non-equilibrium single-electron Green functions and self-energies. In the particular case of equilibrium, we recover previously known results.

Acoustic magnons in the long-wavelength limit: Investigating the Goldstone violation in many-body perturbation theory

Collective spin excitations in magnetic materials arise from the correlated motion of electron-hole pairs with opposite spins. The pair propagation is described by the transverse magnetic susceptibility, which we calculate within many-body perturbation theory from first principles employing the full-potential linearized augmented-plane-wave formalism. Ferromagnetic materials exhibit a spontaneously broken global rotation symmetry in spin space leading to the appearance of acoustic magnons (zero gap) in the long-wavelength limit. However, due to approximations used in the numerical scheme, the acoustic magnon dispersion exhibits a small but finite gap at $\mathrm{\ensuremath{\Gamma}}$. We analyze this violation of the Goldstone mode and present an approach that implements the magnetic susceptibility using a renormalized Green function instead of the Kohn-Sham one. This much more expensive approach shows substantial improvement of the Goldstone-mode condition. In addition, we discuss a possible correction scheme, which involves an adjustment of the Kohn-Sham exchange splitting, which is motivated by the spin-wave solution of the one-band Hubbard model. The new exchange splittings turn out to be closer to experiment. We present corrected magnon spectra for the elementary ferromagnets Fe, Co, and Ni.

Neuromelanin Imaging and Dopaminergic Loss in Parkinson's Disease.

Parkinson's disease (PD) is a progressive neurodegenerative disorder in which the major pathologic substrate is a loss of dopaminergic neurons from the substantia nigra. Our main objective was to determine the correspondence between changes in the substantia nigra, evident in neuromelanin and iron sensitive magnetic resonance imaging (MRI), and dopaminergic striatal innervation loss in patients with PD. Eighteen patients and 18 healthy control subjects were included in the study. Using neuromelanin-MRI, we measured the volume of the substantia nigra and the contrast-to-noise-ratio between substantia nigra and a background region. The apparent transverse relaxation rate and magnetic susceptibility of the substantia nigra were calculated from dual-echo MRI. Striatal dopaminergic innervation was measured as density of dopamine transporter (DAT) by means of single-photon emission computed tomography and [123I] N-ω-fluoropropyl-2b-carbomethoxy-3b-(4-iodophenyl) tropane. Patients showed a reduced volume of the substantia nigra and contrast-to-noise-ratio and both positively correlated with the corresponding striatal DAT density. The apparent transverse relaxation rate and magnetic susceptibility values of the substantia nigra did not differ between patients and healthy controls. The best predictor of DAT reduction was the volume of the substantia nigra. Clinical and imaging correlations were also investigated for the locus coeruleus. Our results suggest that neuromelanin-MRI can be used for quantifying substantia nigra pathology in PD where it closely correlates with dopaminergic striatal innervation loss. Longitudinal studies should further explore the role of Neuromelanin-MRI as an imaging biomarker of PD, especially for subjects at risk of developing the disease.

Ground-state phases of the spin-1J1−J2Heisenberg antiferromagnet on the honeycomb lattice

We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange coupling $J_{1}>0$ and frustrating next-nearest-neighbor coupling $J_{2} \equiv \kappa J_{1} > 0$, using the coupled cluster method implemented to high orders of approximation, and based on model states with different forms of classical magnetic order. For each we calculate directly in the bulk thermodynamic limit both ground-state low-energy parameters (including the energy per spin, magnetic order parameter, spin stiffness coefficient, and zero-field uniform transverse magnetic susceptibility) and their generalized susceptibilities to various forms of valence-bond crystalline (VBC) order, as well as the energy gap to the lowest-lying spin-triplet excitation. In the range $0 < \kappa < 1$ we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with 2-sublattice N\'{e}el order for $\kappa < \kappa_{c_{1}} = 0.250(5)$, and another with 4-sublattice N\'{e}el-II order for $\kappa > \kappa_{c_{2}} = 0.340(5)$. Two different paramagnetic phases are found to exist in the intermediate region. Over the range $\kappa_{c_{1}} < \kappa < \kappa^{i}_{c} = 0.305(5)$ we find a gapless phase with no discernible magnetic order, which is a strong candidate for being a quantum spin liquid, while over the range $\kappa^{i}_{c} < \kappa < \kappa_{c_{2}}$ we find a gapped phase, which is most likely a lattice nematic with staggered dimer VBC order that breaks the lattice rotational symmetry.

Quantitative Susceptibility Mapping Indicates a Disturbed Brain Iron Homeostasis in Neuromyelitis Optica - A Pilot Study.

Dysregulation of brain iron homeostasis is a hallmark of many neurodegenerative diseases and can be associated with oxidative stress. The objective of this study was to investigate brain iron in patients with Neuromyelitis Optica (NMO) using quantitative susceptibility mapping (QSM), a quantitative iron-sensitive MRI technique. 12 clinically confirmed NMO patients (6 female and 6 male; age 35.4y±14.2y) and 12 age- and sex-matched healthy controls (7 female and 5 male; age 33.9±11.3y) underwent MRI of the brain at 3 Tesla. Quantitative maps of the effective transverse relaxation rate (R2*) and magnetic susceptibility were calculated and a blinded ROI-based group comparison analysis was performed. Normality of the data and differences between patients and controls were tested by Kolmogorov-Smirnov and t-test, respectively. Correlation with age was studied using Spearman’s rank correlation and an ANCOVA-like analysis. Magnetic susceptibility values were decreased in the red nucleus (p<0.01; d>0.95; between -15 and -22 ppb depending on reference region) with a trend toward increasing differences with age. R2* revealed significantly decreased relaxation in the optic radiations of five of the 12 patients (p<0.0001; -3.136±0.567 s-1). Decreased relaxation in the optic radiation is indicative for demyelination, which is in line with previous findings. Decreased magnetic susceptibility in the red nucleus is indicative for a lower brain iron concentration, a chemical redistribution of iron into less magnetic forms, or both. Further investigations are necessary to elucidate the pathological cause or consequence of this finding.

Large-s expansions for the low-energy parameters of the honeycomb-lattice Heisenberg antiferromagnet with spin quantum number s

The coupled cluster method (CCM) is employed to very high orders of approximation to study the ground-state (GS) properties of the spin-s Heisenberg antiferromagnet (with isotropic interactions, all of equal strength, between nearest-neighbour pairs only) on the honeycomb lattice. We calculate with high accuracy the complete set of GS parameters that fully describes the low-energy behaviour of the system, in terms of an effective magnon field theory, viz., the energy per spin, the magnetic order parameter (i.e., the sublattice magnetization), the spin stiffness and the zero-field (uniform, transverse) magnetic susceptibility, for all values of the spin quantum numbers in the range 12≤s≤92. The CCM data points are used to calculate the leading quantum corrections to the classical (s→∞) values of these low-energy parameters, considered as large-s asymptotic expansions.

Transverse dynamical magnetic susceptibilities from regular static density functional theory: Evaluation of damping andgshifts of spin excitations

The dynamical transverse magnetic Kohn-Sham susceptibility calculated within time-dependent density functional theory shows a fairly linear behavior for a finite energy window. This observation is used to propose a scheme where the computation of this quantity is greatly simplified. Regular simulations based on static density functional theory can be used to extract the dynamical behavior of the magnetic response function. Besides the ability to calculate elegantly damping of magnetic excitations, we derive along the way useful equations giving the main characteristics of these excitations: effective $g$-factors and the resonance frequencies that can be accessed experimentally using inelastic scanning tunneling spectroscopy or spin-polarized electron energy loss spectroscopy.

In-Plane Transverse Susceptibility of (111)-Oriented Iron Garnet Films

Iron garnet films with various compositions Y3Fe5O12 (YIG), (LuPr)3Fe5O12 (LuPrIG), and Tm3(FeSc)5 O 12 (TmScIG) were grown by liquid phase epitaxy on gadolinium gallium garnet substrates. The angular dependences of in-plane transverse magnetic susceptibility $\chi ^\prime $ ( $\varphi $ ) were investigated to estimate their applicability as a fluxgate core. The $\chi ^\prime $ ( $\varphi $ ) dependence permitted the determination of the anisotropy field ${H}_{C}$ in the film plane. Experimentally obtained values of ${H}_{C}$ show good agreement with theoretical values and correspond to 2.5, 0.92, and 0.03 Oe for YIG, LuPrIG, and TmScIG epitaxial films, respectively. The influence of garnet composition on mechanisms of decreasing of induced in-plane anisotropy field was determined. TmScIG films exhibit about 100-fold reduction in the anisotropy in the plane of the film as compared with films of pure YIG.

Anisotropic Magnetic Response in Kondo Lattice with Antiferromagnetic Order

Magnetic properties are investigated for the Kondo lattice by using the continuous time quantum Monte Colro (CT-QMC) and the dynamical mean field theory (DMFT). The DMFT+CT-QMC approach is extended so as to derive the anisotropic magnetic response in the antiferromagnetic phase. The longitudinal and transverse magnetic susceptibilities are numerically derived in the antiferromagnetic phase. For the RKKY regime with a small Kondo coupling, the transverse susceptibility does not decrease below the transition temperature while the longitudinal susceptibility decreases as expected from the mean field picture. In the competing region between the RKKY interaction and the Kondo effect, however, both longitudinal and transverse susceptibilities decrease below the transition temperature. The results obtained naturally explain the temperature dependence of the magnetic susceptibility observed in CeT$_2$Al$_{10}$ ($T$=Ru,Os,Fe) family.

Parimagnetism in HoCo2 and TmCo2

X-ray magnetic circular dichroism (XMCD), longitudinal and transverse (TS) ac magnetic susceptibility have been measured in the RCo2 series (R = Ho, and Tm) as a function of temperature and applied magnetic field. We show that parimagnetism is a general behavior among the RCo2 ferrimagnetic series (R being a heavy rare-earth ion). XMCD results supply evidence of the presence of two compensation temperatures above Tc, defining two different parimagnetic configurations, which is a fully unexpected result. The inverse χ′ac curve exhibits a small anomaly which vanishes under low applied magnetic fields. The combination of TS and XMCD measurements allows one to depict new magnetic phase diagrams for these compounds of the RCo2 series. A new scenario allowing one to understand the observed phenomenology as a Griffiths phase-like behavior is proposed, where the amorphous RCo2 represents the undiluted system case.

Invariance of the magnetization axis under spin reorientation transitions in polycrystalline magnets of Nd2Fe14B

A great number of useful and practical devices benefit from the use of Nd2Fe14B magnets because of their good magnetic properties and relatively low cost. However, Nd2Fe14B presents a spin-reorientation transition (SRT) at cryogenic temperature that constitutes a challenge for engineers aiming to design devices for use in this environment. Although the spin reorientation transition is well-known for single crystals, there are very few papers describing experiments with polycrystalline samples. In this paper we show the effects of the SRT in macroscopic commercial samples, providing useful experimental data for designers. It has been proven that the macroscopic axis of magnetization in polycrystalline magnets of Nd2Fe14B remains invariant under spin reorientation transition whenever it occurs at H = 0 T. However, the transverse magnetic susceptibility slightly increases after the spin reorientation transition. This makes Nd2Fe14B suitable for cryogenic applications in which permanent magnets with defined axis of magnetization are required.

New Magnetoresistance Results in GdB&lt;sub&gt;6&lt;/sub&gt;

Detailed study of transverse magnetoresistance (MR) and magnetic susceptibility have been done on the high quality single crystals of antiferromagnet GdB6 (TN15.5K) in the wide range of temperatures 2-40K in magnetic fields up to 8T. The data obtained allow to establish the low temperature antiferromagnetic (AFMII) phase below T*~4.7K with the complex behavior of MR including the field hysteresis of the magnetoresistance. It was shown that MR behavior depends on the cooling-warming prehistory in AFM state of GdB6. The analysis of experimental data allowed us to deduce three contributions to MR in AFM(I), (T*) and paramagnetic (PM) phases of GdB6. In addition to the main negative component Δρ˿ρ~ H2 interpreted in terms of Yosida model both the linear and nonlinear magnetic contributions were also established. The anomalies of MR found in AFM(I) state seem to be associated with the local spin polarization of 5d-electron states of Gd3+ ion.

Efficient computation of magnon dispersions within time-dependent density functional theory using maximally localized Wannier functions

An efficient scheme is presented to compute the transverse magnetic susceptibility within time-dependent density functional theory from which magnon dispersions can be extracted. The scheme makes use of maximally localized Wannier functions in order to interpolate the band structure onto a fine $\mathbf{k}$ mesh in order to converge sums on the first Brillouin zone. The gap error in the magnon dispersion at $\ensuremath{\Gamma}$, numerically violating Goldstone's theorem, is analyzed and a correction scheme is devised that can be generalized to systems where Goldstone's theorem does not apply. The method is applied to the computation of the magnon dispersion of bulk bcc iron and fcc nickel.

Transverse susceptibilities of ferromagnetic spin wave interacting with phonon reservoir, II: Temperature dependence of line shapes

A form of the transverse magnetic susceptibility of a ferromagnetic spin system with a uniaxial anisotropy energy and an anisotropic exchange interaction, interacting with a phonon reservoir, is derived in the spin-wave approximation using the TCLE method, where the phonon reservoir interacts with not only the x and y components of each spin but also its z component. The transverse magnetic susceptibility is numerically and analytically studied for the system of one-dimensional infinite spins in the lowest spin-wave approximation, by assuming a damped oscillator model of the phonon reservoir. The temperature dependence and wave number dependence of the susceptibility are numerically investigated for the half-widths and peak-heights of the line shapes in the resonance region. It is shown that as the temperature increases, the half-widths of the line shapes increase and the peak heights decrease in the resonance region, and that as the wave number increases, the half-widths of the line shapes decrease and the peak heights increase in the resonance region. It is also shown that as the uniaxial anisotropy energy of the z direction increases or as the exchange interaction between the z components of spins increases, the half-widths of the line shapes decrease and the peak heights increase in the resonance region. It is besides shown that as the characteristic frequency of the phonon increases, the line shapes show ‘motional broadening’ at the low temperature and show ‘motional narrowing’ at the high temperature. Furthermore, the resonance frequency is shown to increase as the wave number increases or as the temperature increases. The numerical results are examined analytically.

Quantum phase transitions in bosonic heteronuclear pairing Hamiltonians

We explore the phase diagram of two-component bosons with Feshbach resonant pairing interactions in an optical lattice. It has been shown in previous work to exhibit a rich variety of phases and phase transitions, including a paradigmatic Ising quantum phase transition within the second Mott lobe. We discuss the evolution of the phase diagram with system parameters and relate this to the predictions of Landau theory. We extend our exact diagonalization studies of the one-dimensional bosonic Hamiltonian and confirm additional Ising critical exponents for the longitudinal and transverse magnetic susceptibilities within the second Mott lobe. The numerical results for the ground-state energy and transverse magnetization are in good agreement with exact solutions of the Ising model in the thermodynamic limit. We also provide details of the low-energy spectrum, as well as density fluctuations and superfluid fractions in the grand canonical ensemble.

Transverse Susceptibilities of Ferromagnetic Spin Wave Interacting with Phonon Reservoir

A form of the transverse magnetic susceptibility of a ferromagnetic system interacting with a phonon reservoir is derived in the spin-wave approximation using the TCLE method in which the admittance of the system is directly calculated from time-convolutionless equations with external driving terms, and is investigated numerically and analytically for the system of one-dimensional infinite spins. It is confirmed that the effects of the initial correlation and memory for the spin system and phonon reservoir, which are represented by the interference terms in the TCLE method, increase the peak heights of the power spectra in the resonance region and cause the power spectra to decrease in the low-frequency region. It is shown that as the damping of the phonon reservoir becomes rapid, the half-widths of the line shapes in the resonance region decrease and the peak heights increase for small wave numbers, and thus the line shapes show ‘motional narrowing’ for small wave numbers but not for large wave numbers. For the case of an acoustic phonon reservoir, it is shown that as the wave number increases, the half-widths decrease and the peak heights increase, except in the vicinity of 0 and π. For a damped oscillator model of the phonon reservoir, it is shown that as the characteristic frequency of the phonon increases, the half-widths increase and the peak heights decrease, and thus the line shapes show ‘motional broadening’. It is also shown that as the magnitude of the spin becomes large, the peak heights increase and the half-widths increase for small wave numbers but decrease for large wave numbers. Furthermore, the resonance frequency is shown to increase as the wave number increases or as the magnitude of the spin becomes large. The numerical results are examined analytically.

Measurements of the transverse susceptibility and magnetization of magnetic fluids

A new method for calculating the magnetization of magnetic fluids and a setup for measuring the transverse magnetic susceptibility as a function of an external bias field are described. The results obtained via the new method and a known sweep method are compared. The presented results of a magnetogranulometric analysis of five samples of a magnetic fluid with different concentrations of the magnetic phase confirm the high accuracy of the new technique.