Langevin dynamics in crossed magnetic and electric fields: Hall and diamagnetic fluctuations

Based on the classical Langevin equation, we have re-visited the problem of orbital motion of a charged particle in two dimensions for a normal magnetic field crossed with or without an in-plane electric bias. We are led to two interesting fluctuation effects: First, we obtain not only a longitudinal "work-fluctuation" relation as expected for a barotropic type system, but also a transverse work-fluctuation relation perpendicular to the electric bias. This "Hall fluctuation" involves the product of the electric and the magnetic fields. And second, for the case of harmonic confinement without bias, the calculated probability density for the orbital magnetic moment gives non-zero even moments, not derivable as field derivatives of the classical free energy.Comment: 4 pages, 2 figures, revised versio

Spin-State Transition and Metal-Insulator Transition in La1−x_{1-x}Eux_xCoO3_3}

We present a study of the structure, the electric resistivity, the magnetic susceptibility, and the thermal expansion of La$_{1-x}$Eu$_x$CoO$_3$. LaCoO$_3$ shows a temperature-induced spin-state transition around 100 K and a metal-insulator transition around 500 K. Partial substitution of La$^{3+}$ by the smaller Eu$^{3+}$ causes chemical pressure and leads to a drastic increase of the spin gap from about 190 K in LaCoO$_3$ to about 2000 K in EuCoO$_3$, so that the spin-state transition is shifted to much higher temperatures. A combined analysis of thermal expansion and susceptibility gives evidence that the spin-state transition has to be attributed to a population of an intermediate-spin state with orbital order for $x<0.5$ and without orbital order for larger $x$. In contrast to the spin-state transition, the metal-insulator transition is shifted only moderately to higher temperatures with increasing Eu content, showing that the metal-insulator transition occurs independently from the spin-state distribution of the Co$^{3+}$ ions. Around the metal-insulator transition the magnetic susceptibility shows a similar increase for all $x$ and approaches a doping-independent value around 1000 K indicating that well above the metal-insulator transition the same spin state is approached for all $x$.Comment: 10 pages, 6 figure

Interplay of Spin-Orbit Interaction and Electron Correlation on the Van Vleck Susceptibility in Transition Metal Compounds

We have studied the effects of electron correlation on Van Vleck susceptibility ($\chi_{\rm{VV}}$) in transition metal compounds. A typical crossover behavior is found for the correlation effect on $\chi_{\rm{VV}}$ as sweeping spin-orbit interaction, $\lambda$. For a small $\lambda$, orbital fluctuation plays a dominant role in the correlation enhancement of $\chi_{\rm{VV}}$; however, the enhancement rate is rather small. In contrast, for an intermediate $\lambda$, $\chi_{\rm{VV}}$ shows a substantial increase, accompanied by the development of spin fluctuation. We will discuss the behavior of $\chi_{\rm{VV}}$ in association with the results of Knight-shift experiments on Sr$_2$RuO$_4$ and an anomalously large magnetic susceptibility observed for $5d$ Ir compounds.Comment: 5 pages, 3 figures, to appear in J. Phys. Soc. Jp

Direct perturbation theory on the shift of Electron Spin Resonance

We formulate a direct and systematic perturbation theory on the shift of the main paramagnetic peak in Electron Spin Resonance, and derive a general expression up to second order. It is applied to one-dimensional XXZ and transverse Ising models in the high field limit, to obtain explicit results including the polarization dependence for arbitrary temperature.Comment: 5 pages (no figures) in REVTE

Landau-Drude Diamagnetism: Fluctuation, Dissipation and Decoherence

Starting from a quantum Langevin equation (QLE) of a charged particle coupled to a heat bath in the presence of an external magnetic field, we present a fully dynamical calculation of the susceptibility tensor. We further evaluate the position autocorrelation function by using the Gibbs ensemble approach. This quantity is shown to be related to the imaginary part of the dynamical susceptibility, thereby validating the fluctuation-dissipation theorem in the context of dissipative diamagnetism. Finally we present an overview of coherence-to-decoherence transition in the realm of dissipative diamagnetism at zero temperature. The analysis underscores the importance of the details of the relevant physical quantity, as far as coherence to decoherence transition is concerned.Comment: 8 pages and 5 figure

Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise

It is generally known that the orbital diamagnetism of a classical system of charged particles in thermal equilibrium is identically zero -- the Bohr-van Leeuwen theorem. Physically, this null result derives from the exact cancellation of the orbital diamagnetic moment associated with the complete cyclotron orbits of the charged particles by the paramagnetic moment subtended by the incomplete orbits skipping the boundary in the opposite sense. Motivated by this crucial, but subtle role of the boundary, we have simulated here the case of a finite but \emph{unbounded} system, namely that of a charged particle moving on the surface of a sphere in the presence of an externally applied uniform magnetic field. Following a real space-time approach based on the classical Langevin equation, we have computed the orbital magnetic moment which now indeed turns out to be non-zero, and has the diamagnetic sign. To the best of our knowledge, this is the first report of the possibility of finite classical diamagnetism in principle, and it is due to the avoided cancellation.Comment: Accepted for publication in EP

Theoretical Analysis of the "Double-q" Magnetic Structure of CeAl2

A model involving competing short-range isotropic Heisenberg interactions is developed to explain the "double-q" magnetic structure of CeAl$_2$. For suitably chosen interactions, terms in the Landau expansion quadratic in the order parameters explain the condensation of incommensurate order at wavevectors in the star of (1/2 $-\delta$, 1/2 $+\delta$, 1/2)$(2\pi/a)$, where $a$ is the cubic lattice constant. We show that the fourth order terms in the Landau expansion lead to the formation of the so-called "double-q" magnetic structure in which long-range order develops simultaneously at two symmetry-related wavevectors, in striking agreement with the magnetic structure determinations. Based on the value of the ordering temperature and of the Curie-Weiss $\Theta$ of the susceptibility, we estimate that the nearest neighbor interaction $K_0$ is ferromagnetic, with $K_0/k=-11\pm 1$K and the next-nearest neighbor interaction $J$ is antiferromagnetic with $J/k=6 \pm 1$K. We also briefly comment on the analogous phenomenon seen in the similar system TmS.Comment: 22 pages, 6 figure

When are Antiaromatic Molecules Paramagnetic?

Magnetizabilities and magnetically induced current densities have been calculated and analyzed for a series of antiaromatic cyclo[4k]carbons (k = 2-11), iso[n]phlorins (n = 4-8), expanded porphyrinoids, and meso-meso, beta-beta,beta-beta triple-linked porphyrin and isophlorin arrays. The cyclo[4k]carbons with k = 2-6 are predicted to be closed-shell paramagnetic molecules due to the very strong paratropic ring current combined with its large radius. Larger cyclo[4k]carbons with k = 6-11 are diamagnetic because they sustain a paratropic ring current whose strength is weaker than -20 nA T-1, which seems to be the lower threshold value for closed-shell paramagnetism. This holds not only for cyclo[4k]carbons but also for other organic molecules like expanded porphyrinoids and oligomers of porphyrinoids. The present study shows that meso-meso, beta-beta, beta-beta triple-linked linear porphyrin and isophlorin arrays have a domainlike distribution of alternating diatropic and paratropic ring currents. The strength of their local paratropic ring currents is weaker than -20 nA T-1 in each domain. Therefore, linear porphyrin and isophlorin arrays become more diamagnetic with increasing length of the ribbon. For the same reason, square-shaped meso-meso, beta-beta, beta-beta triple-linked free-base porphyrin and isophlorin tetramers as well as the Zn(II) complex of the porphyrin tetramer are diamagnetic. We show that closed-shell molecules with large positive magnetizabilities can be designed by following the principle that a strong paratropic current ring combined with a large ring-current radius leads to closed-shell paramagnetism.Peer reviewe

Metallic ferromagnetism: Progress in our understanding of an old strong-coupling problem

Metallic ferromagnetism is in general an intermediate to strong coupling phenomenon. Since there do not exist systematic analytic methods to investigate such types of problems, the microscopic origin of metallic ferromagnetism is still not sufficiently understood. However, during the last two or three years remarkable progress was made in this field: It is now certain that even in the one-band Hubbard model metallic ferromagnetism is stable in dimensions $d=1,$ 2, and $\infty$ on regular lattices and at intermediate values of the interaction $U$ and density $n$. In this paper the basic questions and recent insights regarding the microscopic conditions favoring metallic ferromagnetism in this model are reviewed. These findings are contrasted with the results for the orbitally degenerate case.Comment: 16 pages, 13 figures, latex using vieweg.sty (enclosed); typos corrected; to appear in "Advances in Solid State Physics", Vol. 3

On Which Length Scales Can Temperature Exist in Quantum Systems?

We consider a regular chain of elementary quantum systems with nearest neighbor interactions and assume that the total system is in a canonical state with temperature $T$. We analyze under what condition the state factors into a product of canonical density matrices with respect to groups of $n$ subsystems each, and when these groups have the same temperature $T$. While in classical mechanics the validity of this procedure only depends on the size of the groups $n$, in quantum mechanics the minimum group size $n_{\text{min}}$ also depends on the temperature $T$! As examples, we apply our analysis to different types of Heisenberg spin chains.Comment: To appear in: Proceedings of the SPQS conference, J. Phys. Soc. Jpn. 74 (2005) Supp