Diamagnetic Term Research Articles

Reentrant canonical spin-glass dynamics and tunable field-induced transitions in (GeMn)Co2O4 Kagomé lattice

We report on the reentrant canonical semi spin-glass characteristics and controllable field-induced transitions in distorted Kagomé symmetry of (GeMn)Co2O4. This B-site spinel exhibits complicated, yet interesting magnetic behaviour in which the longitudinal ferrimagnetic (FiM) order sets in below the Néel temperature T FN ∼ 77 K due to uneven moments of divalent Co (↑ 5.33 μ B) and tetravalent Mn (↓ 3.87 μ B) which coexists with transverse spin-glass state below 72.85 K. Such complicated magnetic behaviour is suggested to result from the competing anisotropic superexchange interactions (J AB/k B ∼ 4.3 K, J AA/k B ∼ −6.2 K and J BB/k B ∼ −3.3 K) between the cations, which is extracted following the Néel’s expression for the two-sublattice model of FiM. Dynamical susceptibility (χ ac (f, T)) and relaxation of thermoremanent magnetization, M TRM (t) data have been analysed by means of the empirical scaling-laws such as Vogel–Fulcher law and Power law of critical slowing down. Both of which reveal the reentrant spin-glass like character which evolves through a number of intermediate metastable states. The magnitude of Mydosh parameter (Ω ∼ 0.002), critical exponent zυ = (6.7 ± 0.07), spin relaxation time τ 0 = (2.33 ± 0.1) × 10−18 s, activation energy E a/k B = (69.8 ± 0.95) K and interparticle interaction strength (T 0 = 71.6 K) provide the experimental evidences for canonical spin-glass state below the spin freezing temperature T F = 72.85 K. The field dependence of T F obtained from χ ac (T) follows the irreversibility in terms of de Almeida–Thouless mean-field instability in which the magnitude of crossover scaling exponent Φ turns out to be ∼2.9 for the (Ge0.8Mn0.2)Co2O4. Isothermal magnetization plots reveal two field-induced transitions across 9.52 kOe (H SF1) and 45.6 kOe (H SF2) associated with the FiM domains and spin-flip transition, respectively. Analysis of the inverse paramagnetic susceptibility after subtracting the temperature independent diamagnetic term (=−3 × 10−3 emu mol−1 Oe−1) results in the effective magnetic moment = 7.654 μ B/f.u. This agrees well with the theoretically obtained = 7.58 μ B/f.u. resulting the cation distribution in support of the Hund’s ground state spin configuration and of Mn4+ and Co2+, respectively. The H–T phase diagram has been established by analysing all the parameters (T F(H), T FN(H), H SF1(T) and H SF2(T)) extracted from various magnetization measurements. This diagram enables clear differentiation among the different phases of the (GeMn)Co2O4 and also illustrates the demarcation between short-range and long-range ordered regions.

Polaritonic linewidth asymmetry in the strong and ultrastrong coupling regime.

The intriguing properties of polaritons resulting from strong and ultrastrong light-matter coupling have been extensively investigated. However, most research has focused on spectroscopic characteristics of polaritons, such as their eigenfrequencies and Rabi splitting. Here, we study the decay rates of a plasmon-microcavity system in the strong and ultrastrong coupling regimes experimentally and numerically. We use a classical scattering matrix approach, approximating our plasmonic system with an effective Lorentz model, to obtain the decay rates through the imaginary part of the complex quasinormal mode eigenfrequencies. Our classical model automatically includes all the interaction terms necessary to account for ultrastrong coupling without dealing with the rotating-wave approximation and the diamagnetic term. We find an asymmetry in polaritonic decay rates, which deviate from the expected average of the uncoupled system's decay rates at zero detuning. Although this phenomenon has been previously observed in exciton-polaritons and attributed to their disorder, we observe it even in our homogeneous system. As the coupling strength of the plasmon-microcavity system increases, the asymmetry also increases and can become so significant that the lower (upper) polariton decay rate reduction (increase) goes beyond the uncoupled decay rates, γ - < γ 0,c < γ +. Furthermore, our findings demonstrate that polaritonic linewidth asymmetry is a generic phenomenon that persists even in the case of bulk polaritons.

Synthesis of possible room temperature superconductor LK-99: Pb9Cu(PO4)6O

The quest for room temperature superconductors has been teasing scientists and physicists, since its inception in 1911 itself. Several assertions have already been made about room temperature superconductivity, but have never been verified or reproduced across the labs. The cuprates were the earliest high transition temperature (T c) superconductors, and it seems that copper has done the magic once again. In July 2023, a Korean group synthesized a lead apatite based compound LK-99, showing a T c of above 400 K (Lee et al 2023 arXiv: 2307.12008; 2023 arXiv: 2307.12037; Lee et al 2023 J. Korean Cryst. Growth Cryst. 33 61). The signatures of superconductivity in the compound are very promising, in terms of resistivity (ρ = 0) and diamagnetism at T c. Although, the heat capacity (C p) did not show the obvious transition at T c. Inspired by the interesting claims of the above room temperature superconductivity in LK-99, in this article, we report the synthesis of polycrystalline samples of LK-99, by following the same heat treatment as reported in Lee et al (2023 arXiv: 2307.12008; 2023 arXiv: 2307.12037) using a two-step precursor method. The phase is confirmed through x-ray diffraction measurements, performed after each heat treatment. The room temperature diamagnetism is not evidenced by the levitation of a permanent magnet over the sample or vice versa. The isothermal magnetization measurement at 280 K shows that as synthesized sample of LK-99 is paramagnetic. Further measurements for the confirmation of bulk superconductivity in variously synthesized samples are underway. Our results on the present LK-99 sample, synthesized at 925 °C, as of now do not confirm the appearance of bulk superconductivity at room temperature. Further studies with different heat treatments are underway.

Effect of erbium concentration on the Verdet constant dispersion of LiY1.0-xErxF4 single crystal

The dispersion of the Verdet constant of LiY1.0-xErxF4 crystals was evaluated from 190 nm to 500 nm for different doping concentrations of Er ions. A 15% doping concentration yielded a high Verdet constant of 54.5 rad/(T·m) at 193 nm. This value can be explained by the contribution of the diamagnetic term associated with LiYF4 and the paramagnetic term of the Er ions. Although the LiYF4 crystal yielded a lower value of −36.6 rad/(T·m) at 193 nm from Er-doped LiYF4, it can be used in the vacuum–ultraviolet region because of its high transmittance at wavelengths longer than 120 nm.

Stark broadening of low-[formula omitted] hydrogen lines in strongly magnetized hydrogen plasmas: Influence of [formula omitted]-degeneracy removal due to the quadratic Zeeman effect

The Stark broadening of hydrogen lines with a low upper principal quantum number n is reexamined in the case of plasmas subject to a large (≳1 kT) external magnetic field. This investigation has been motivated by the observation of strong Zeeman splitting in a significant number of white dwarf spectra. The diamagnetic Zeeman effect term present in the Hamiltonian removes the degeneracy of the energy levels in orbital quantum number l, which results in an alteration of the Stark perturbation due to the microfield. In this work, we investigate this effect by applying a computer simulation method designed for Stark broadening modeling. A focus is put on the Lyman α and H-α lines. Based on line shape calculations, we show that the width of the Zeeman components is strongly dependent on the magnetic field.

Structure of the JET edge radial electric field in He and D plasmas

Perpendicular velocity, v ⊥, measurements have been obtained in JET experiments designed to investigate the underlying mechanisms influencing the L–H power threshold. L–H transitions were induced by using both NBI and ICRH in deuterium and helium plasmas. The v ⊥ profile in the low density branch of the L–H transition has a modest or even no well and a marked peak near the separatrix in NBI heated discharges for both D and He plasmas, with a sharper SOL peak for He plasmas. As the line-averaged density increases, the SOL v ⊥ peak decreases, in agreement with the modifications in the electron temperature profile at the divertor target, while the v ⊥ well becomes deeper. Nevertheless, even in the high density branch, a shallow v ⊥ well is found at the L–H transition, v ⊥ ∼ 1–2 km s−1, which is lower by a factor of about two than the contribution from the diamagnetic term. No evidence for the existence of a critical value in v ⊥ is found at JET, particularly for helium plasmas. This may be explained by the existence of an edge toroidal flow relevant mainly at low density where the power threshold is high. In addition, no significant change in the edge v ⊥ is measured preceding the L–H transition.

I-mode in non-deuterium plasmas in ASDEX Upgrade

The I-mode confinement regime in non-deuterium plasmas has been investigated in the ASDEX Upgrade tokamak. We report the first experimental observations on the existence and the main characteristics of this regime in hydrogen and helium plasmas and compare them with deuterium I-modes. Hydrogen features a higher power threshold to enter I-mode and a higher electron edge pressure at the L- to I-mode transition with respect to deuterium. Furthermore, all the hydrogen I-modes obtained exhibit pedestal relaxation events (PRE). The I-mode power window in hydrogen is found to be 2–3 times larger than in deuterium. This property allows a better characterization of PRE and to differentiate them from type-III ELMs. Helium I-modes feature properties which are similar to those of deuterium I-modes. The analysis on the minimum of the edge radial electric field E r shows a correlation between the E r minimum, the net input power and the ion diamagnetic term in the ion radial force balance. Indications of the dominant role of the edge ion temperature in the evolution of the radial electric field with increasing input power are also reported.

On the spatial and temporal non-locality of dynamo mean-field effects in supersonic interstellar turbulence

ABSTRACT The interstellar medium (ISM) of the Milky Way and nearby disc galaxies harbour large-scale coherent magnetic fields of microgauss strength, that can be explained via the action of a mean-field dynamo. As in our previous work, we aim to quantify dynamo effects that are self-consistently emerging in realistic direct magnetohydrodynamic simulations, but we generalize our approach to the case of a non-local (non-instantaneous) closure relation, described by a convolution integral in space (time). To this end, we leverage our comprehensive simulation framework for the supernova-regulated turbulent multiphase ISM. By introducing spatially (temporally) modulated mean fields, we extend the previously used test-field method to the spectral realm – providing the Fourier representation of the convolution kernels. The resulting spectra of the dynamo mean-field coefficients that we obtain broadly match expectations and allow to rigorously constrain the degree of scale separation in the Galactic dynamo. A surprising result is found for the diamagnetic pumping term, which increases in amplitude when going to smaller scales. Our results amount to the most comprehensive description of dynamo mean-field effects in the Galactic context to date. Surveying the relevant parameter space and quenching behaviour, this will ultimately enable the development of assumption-free subgrid prescriptions for otherwise unresolved global galaxy simulations.

Relevance of the Quadratic Diamagnetic and Self-Polarization Terms in Cavity Quantum Electrodynamics.

Experiments at the interface of quantum optics and chemistry have revealed that strong coupling between light and matter can substantially modify the chemical and physical properties of molecules and solids. While the theoretical description of such situations is usually based on nonrelativistic quantum electrodynamics, which contains quadratic light–matter coupling terms, it is commonplace to disregard these terms and restrict the treatment to purely bilinear couplings. In this work, we clarify the physical origin and the substantial impact of the most common quadratic terms, the diamagnetic and self-polarization terms, and highlight why neglecting them can lead to rather unphysical results. Specifically, we demonstrate their relevance by showing that neglecting these terms leads to the loss of gauge invariance, basis set dependence, disintegration (loss of bound states) of any system in the basis set limit, unphysical radiation of the ground state, and an artificial dependence on the static dipole. Besides providing important guidance for modeling of strongly coupled light–matter systems, the presented results also indicate conditions under which those effects might become accessible.

Turbulence regulation with radial wavenumber spectral shift caused by externally driven E × B velocity shear during edge-localized mode mitigation

Mitigation of edge-localized modes by lower hybrid current drive (LHCD) has been observed in H-mode plasmas of the HL-2A tokamak. It has been found that this mitigation is strongly desynchronized with the LHCD pulse but synchronized with the pedestal turbulence enhancement. This turbulence is enhanced by LHCD induced pedestal velocity shear resulting from the ion diamagnetic term . This velocity shear modifies the turbulence radial wavenumber (kr) spectrum by varying the averaged radial wavenumber from large negative value to zero, reducing the turbulence dissipation . A modified turbulence spectral shift model has been used to simulate the experimental results. A critical growth rate for the turbulence regulation is identified in this model and experimentally determined. The criterion for triggering the spectral shift and turbulence enhancement is established. It has been found that there exists a threshold Uc of the LHCD induced velocity shear rate,which determines the desynchronization time delay. This threshold value is directly related to , for the pedestal turbulence enhancement. Good agreement has been found between experiment and theory for the regulation of the turbulence intensity calculated with a selected poloidal wavenumber by its averaged radial wavenumber.

Overview of physics studies on ASDEX Upgrade

The ASDEX Upgrade (AUG) programme, jointly run with the EUROfusion MST1 task force, continues to significantly enhance the physics base of ITER and DEMO. Here, the full tungsten wall is a key asset for extrapolating to future devices. The high overall heating power, flexible heating mix and comprehensive diagnostic set allows studies ranging from mimicking the scrape-off-layer and divertor conditions of ITER and DEMO at high density to fully non-inductive operation (q95 = 5.5, ) at low density. Higher installed electron cyclotron resonance heating power 6 MW, new diagnostics and improved analysis techniques have further enhanced the capabilities of AUG.Stable high-density H-modes with MW m−1 with fully detached strike-points have been demonstrated. The ballooning instability close to the separatrix has been identified as a potential cause leading to the H-mode density limit and is also found to play an important role for the access to small edge-localized modes (ELMs). Density limit disruptions have been successfully avoided using a path-oriented approach to disruption handling and progress has been made in understanding the dissipation and avoidance of runaway electron beams. ELM suppression with resonant magnetic perturbations is now routinely achieved reaching transiently . This gives new insight into the field penetration physics, in particular with respect to plasma flows. Modelling agrees well with plasma response measurements and a helically localised ballooning structure observed prior to the ELM is evidence for the changed edge stability due to the magnetic perturbations. The impact of 3D perturbations on heat load patterns and fast-ion losses have been further elaborated.Progress has also been made in understanding the ELM cycle itself. Here, new fast measurements of and Er allow for inter ELM transport analysis confirming that Er is dominated by the diamagnetic term even for fast timescales. New analysis techniques allow detailed comparison of the ELM crash and are in good agreement with nonlinear MHD modelling. The observation of accelerated ions during the ELM crash can be seen as evidence for the reconnection during the ELM. As type-I ELMs (even mitigated) are likely not a viable operational regime in DEMO studies of ‘natural’ no ELM regimes have been extended. Stable I-modes up to have been characterised using -feedback.Core physics has been advanced by more detailed characterisation of the turbulence with new measurements such as the eddy tilt angle—measured for the first time—or the cross-phase angle of and fluctuations. These new data put strong constraints on gyro-kinetic turbulence modelling. In addition, carefully executed studies in different main species (H, D and He) and with different heating mixes highlight the importance of the collisional energy exchange for interpreting energy confinement. A new regime with a hollow profile now gives access to regimes mimicking aspects of burning plasma conditions and lead to nonlinear interactions of energetic particle modes despite the sub-Alfvénic beam energy. This will help to validate the fast-ion codes for predicting ITER and DEMO.

Quantum Phase Properties in Collective Three-Level V-Type System with Diamagnetic Term

In this paper, we present a rigorous investigation of the quantum phase transitions (QPTs) for a model which describes the degenerate collective regime of a three-level V-configuration atoms Bose-Einstein condensate (BEC). We consider that the three-level atoms of a BEC coupled to an optical resonator (cavity) with high finesse in the presence of a diamagnetic term, i. e., a system of N-identical three-level atoms interacting with a one-mode quantized electromagnetic cavity field. Also, the different components of this system are labeled by the different phase factors. By using the Glauber’s coherent states for the field, we calculate the free energy and study the finite-temperature phase transition for this model in the thermodynamic limit (N → ∞). Also, the potential energy surfaces constructed by taking the expectation value with respect to the direct product for a test state a direct product of coherent Heisenberg-Weyl HW(1)-states (for the electromagnetic field ), and U(3) (for the atomic field, i. e., matter contribution) coherent states. Moreover, the scaled ground-state energy is obtained by taking the expectation value of an effective Hamiltonian in the framework of the mean-field approach. In the thermodynamic limit, the energy surface takes a simple form for a direct description of the phase transitions. The relation between the QPTs and the symmetry physics are established and the QPTs for this model are investigated numerically. The properties of both stability and the equilibrium are calculated using the catastrophe theory. We notice that the second-order phase transitions (superradiant (SR)) with multi-level systems might be achievable in a wide range of physical systems, especially those where it is possible to engineer the spec-tra and oscillator strengths.

Sublinear scaling quantum chemical methods for magnetic shieldings in large molecules.

It is shown that quantum chemical calculations of the nuclear magnetic shieldings of a group of vicinal nuclei in a large molecule can be made sublinear scaling [i.e., O(1)] with respect to the molecular size. This is achieved by making both the diamagnetic and paramagnetic terms translation invariant [following the work of Ochsenfeld et al. J. Chem. Phys. 134, 074102 (2011)] and by making use of a local representation that is independent of the molecular size. Although only Hartree-Fock results are reported here, the idea can readily be extended to correlated wave function methods as well as the relativistic domain.

Nuclear spin-lattice relaxation time in TaP and the Knight shift of Weyl semimetals

We first analyze the recent experimental data on the nuclear spin-lattice relaxation rate of the Weyl semimetal TaP. We argue that its non-monotonic temperature dependence is explained by the temperature dependent chemical potential of Weyl fermions. We also develop the theory of the Knight shift in Weyl semimetals, which contains two counteracting terms. The diamagnetic term follows $-\ln[W/\max(|\mu|,k_BT)]$ with $W$, $\mu$ and $T$ being the high energy cutoff, chemical potential and temperature, respectively, and is always negative. The paramagnetic term scales with $\mu$ and changes sign depending on the doping level. Altogether, the Knight shift is predicted to vanish or even change sign upon changing the doping or the temperature, making it a sensitive tool to identify Weyl points. We also calculate the Korringa relation for Weyl semimetals which shows an unusual energy dependence rather than being constant as expected for a non-interacting Fermi system.

Effect of the Diamagnetic term in the ultra-strong coupling regime

We consider a set of two level atoms interacting with a single quantized bosonic mode governed by the Dicke model. In this model it is well known that under a critical value of the light-matter coupling a spontaneous radiation process takes place. In the present work, we investigate the dynamics of the system and we study the Wigner distribution function to visualize the effect of the minimal coupling on the ground state wavefunction from the normal phase to the superradiant one. We show also that the entanglement of Bi-partite model is limited by the presence of the diamagnetic term.

Generalized Hartree-Fock with Nonperturbative Treatment of Strong Magnetic Fields: Application to Molecular Spin Phase Transitions.

In this work, we present a framework of an ab initio variational approach to effectively explore electronic spin phase transitions in molecular systems inside of a homogeneous magnetic field. In order to capture this phenomenon, the complex generalized Hartree-Fock ([Formula: see text]) method is used in the spinor formalism with London orbitals. Recursive algorithms for computing the one- and two-electron integrals of London orbitals are also provided. A Pauli matrix representation of the [Formula: see text] method is introduced to separate spin contributions from the scalar part of the Fock matrix. Next, spin phase transitions in two different molecular systems are investigated in the presence of a strong magnetic field. Noncollinear spin configurations are observed during the spin phase transitions in H2 and a dichromium complex, [(H3N)4Cr(OH)2Cr(NH3)4]4+, with an increase in magnetic field strength. The competing driving forces of exchange coupling and the spin Zeeman effect have been shown to govern the spin phase transition and its transition rate. Additionally, the energetic contributions of the spin Zeeman, orbital Zeeman, and diamagnetic terms to the potential energy surface are also analyzed.

Anisotropy dependence of the fluctuation spectroscopy in the critical and gaussian regimes in superconducting NaFe1\u2212xCoxAs single crystals

We investigate thermal fluctuations in terms of diamagnetism and magnetotransport in superconducting NaFe1−xCoxAs single crystals with different doping levels. Results show that in the case of optimal doped and lightly overdoped (x = 0.03, 0.05) crystals the analysis in the critical as well as in the Gaussian fluctuation regions is consistent with the Ginzburg-Landau 3D fluctuation theory. However, in the case of strongly overdoped samples (x ≥ 0.07) the Ullah-Dorsey scaling of the fluctuation induced magnetoconductivity in the critical region confirms that thermal fluctuations exhibit a 3D anisotropic nature only in a narrow temperature region around Tc(H). This is consistent with the fact that in these samples the fluctuation effects in the Gaussian region above Tc may be described by the Lawrence-Doniach approach. Our results indicate that the anisotropy of these materials increases significantly with the doping level.

Numerical linear analysis of the effects of diamagnetic and shear flow on ballooning modes

The linear analysis of the influence of diamagnetic effect and toroidal rotation at the edge of tokamak plasmas with BOUT++ is discussed in this paper. This analysis is done by solving the dispersion relation, which is calculated through the numerical integration of the terms with different physics. This method is able to reveal the contributions of the different terms to the total growth rate. The diamagnetic effect stabilizes the ideal ballooning modes through inhibiting the contribution of curvature. The toroidal rotation effect is also able to suppress the curvature-driving term, and the stronger shearing rate leads to a stronger stabilization effect. In addition, through linear analysis using the energy form, the curvature-driving term provides the free energy absorbed by the line-bending term, diamagnetic term and convective term.

Quasiclassical Theory on Third-Harmonic Generation in Conventional Superconductors with Paramagnetic Impurities

We investigate the third-harmonic generation (THG) of s-wave superconductors under microwave pulse irradiation. We consider the effect of paramagnetic impurities on the THG intensity of dirty superconductors. The nonlinear response function is calculated using the method of the quasiclassical Green function. It is shown that the amplitude mode is included as the vertex correction and makes a predominant contribution to the THG intensity. When the effect of paramagnetic impurities is weak, the THG intensity shows a peak at the temperature at which the superconducting gap is about the same as the frequency of the incident pulse, similarly to in experiments. As the effect of paramagnetic impurities is strengthened, the peak of the THG intensity disappears. This indicates that time-reversal symmetry breaking due to paramagnetic impurities eliminates the well-defined amplitude mode. The result of our calculation shows that the existence of the amplitude mode can be confirmed through the THG intensity. The result of a semiquantitative calculation is in good agreement with the experimental result, and it also shows that the diamagnetic term is negligible.

Ionization of atomic hydrogen by an intense x-ray laser pulse: An ab initio study of the breakdown of the dipole approximation

Solving the time-dependent Schr\odinger equation numerically within the framework of an ab initio model, the breakdown of the dipole approximation in modeling the ionization and excitation dynamics of a hydrogen atom exposed to an intense 1.36-keV x-ray laser pulse is investigated in some detail. The relative importance of the ${\mathbit{A}}^{2}$ diamagnetic term in comparison with the $\mathbit{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ contribution to the resulting beyond-dipole (nondipole) light-matter interaction is studied for laser pulse intensities ranging from the weak perturbative to the strong-field regime. It is found that the diamagnetic interaction represents by far the most important correction to the dipole approximation at higher field strengths, while nondipole corrections induced by the $\mathbit{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ operator are generally small and largely independent of the laser intensity. The most profound finding of the present study was the discovery of a forward-backward asymmetry in the underlying electron ejection dynamics: Depending on the electron's kinetic energy in the final state, the photoelectron tends to be emitted in the laser propagation (forward) and/or counterpropagation (backward) directions, for energies corresponding to the low-energy and/or high-energy side of the multiphoton resonances, respectively.