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arXiv:0907.0723 · Physical Review B

Magnetization of planar four-fermion systems

Heron Caldas, Rudnei O. Ramos

Published Sep 24, 2009• 45 citations
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Abstract

We consider a planar system of fermions, at finite temperature and density under a static magnetic field parallel to the two-dimensional plane. This magnetic field generates a Zeeman effect and then a spin polarization of the system. The critical properties are studied from the Landau's free energy. The possible observable consequences of the magnetization of planar systems such as polymer films and graphene are discussed.

DOI
10.1103/physrevb.80.115428

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We consider a planar system of fermions, at finite temperature and density under a static magnetic field parallel to the two-dimensional plane. This magnetic field generates a Zeeman effect and then a spin polarization of the system. The critical properties are studied from the Landau's free energy. The possible observable consequences of the magnetization of planar systems such as polymer films and graphene are discussed.
Magnetic properties of two-dimensional (2D) spin-polarized Fermi gas with dipole-dipole interaction are studied in the presence of external magnetic field at zero temperature. Within perturbation theory and the second quantization formalism, the total energy is explicitly obtained as a function of three dimensionless parameters: the spin polarization, dipolar coupling, and Zeeman parameters. We examine the effects of these agents on the magnetic properties of 2D Fermi gas. The results show that an induced ferromagnetic phase transition is observed only for adequately large values of magnetic field. This paper offers two controllable factors to change the spin polarization of the system.
The magnetic properties of a two-dimensional interacting electron system in a strong magnetic field are considered in the quantum Hall regime, where the motion of the electrons is restricted to the lowest Landau level. We apply an approach based on the many-particle quantum-field theory which we developed recently for the spin-polarized system in the fractional quantum Hall regime, and which treats the problem of the degeneracy of a partially filled Landau level properly. Via a gauge transformation of the fermion Green's function, we achieve a dressing of the propagator with multiple collective excitations. Our theory allows a calculation of the magnetic polarization M(T)M(T)M(T) for higher temperatures TTT, where $M(T)\ensuremath{\lesssim}0.4$ is not too large. For filling factor $\ensuremath{\nu}=1$ we obtain a magnetic polarization M(T)M(T)M(T) which agrees quite well with the data of a NMR experiment by Barrett [Phys. Rev. Lett. 74, 5112 (1995)].
Novel controlled nonperturbative techniques are a must in the study of strongly correlated systems, especially near quantum criticality. One of these techniques, bosonization, has been extensively used to understand one-dimensional, as well as higher-dimensional electronic systems at finite density. In this paper, we generalize the theory of two-dimensional bosonization of Fermi liquids, in the presence of a homogeneous weak magnetic field perpendicular to the plane. Here, we extend the formalism of bosonization to treat free spinless fermions at finite density in a uniform magnetic field. We show that particle-hole fluctuations of a Fermi surface satisfy a covariant Schwinger algebra, allowing to express a fermionic theory with forward scattering interactions as a quadratic bosonic theory representing the quantum fluctuations of the Fermi surface. By means of a coherent-state path integral formalism, we compute the fermion propagator as well as particle-hole bosonic correlations functions. We analyze the presence of de Haas-van Alphen oscillations and show how the quantum oscillations of the orbital magnetization, the Lifshitz-Kosevich theory, are obtained by means of the bosonized theory. We also study the effects of forward scattering interactions. In particular, we obtain oscillatory corrections to the Landau zero sound collective mode.
We investigate the combined influence of a magnetic field and a harmonic interparticle interaction on the thermodynamic properties of a finite number of spin-polarized fermions in a confinement potential. This study is an extension using our path integral approach of symmetrized density matrices for identical particles. The thermodynamical properties are calculated for a three-dimensional model of N harmonically interacting spin-polarized fermions in a parabolic potential well in the presence of a magnetic field. The free energy and the internal energy are obtained for a limited number of particles. Deviations from the thermodynamical limit become negligible for about 100 or more particles, but even for a smaller number of fermions present in the well, scaling relations similar to those of the continuum approximation to the density of states are already satisfied.
A system of a finite number of harmonically trapped fermions in one dimension, in the presence of a static magnetic field, is studied within the framework of the static fluctuation approximation, for different repulsive and attractive potential strengths. Specifically, the thermodynamic properties of the system (the chemical potential, total energy, heat capacity, and entropy), as well as its magnetic properties (the magnetization and susceptibility), are calculated. It is observed that the system remains in an ordered phase for a small number of particles N, even at high temperatures T. Disorder sets in for large N, even at low T. The effect of the potential strength on the heat capacity is particularly tangible in the region bordering the quantum and classical regimes. The effect of the temperature (representing disorder) is directly opposite to that of the magnetic field (representing order), as expected on basic physical grounds. These features are consistent with experimental results.
The low-temperature critical properties and crossovers of a spin-12\frac{1}{2}21​ planar ferromagnet in a longitudinal magnetic field are explored in $4\ensuremath{-}\ensuremath{\epsilon}$ dimensions in terms of an anisotropic bosonic action, suitable to describe the spin model in the low-temperature regime. This is performed adopting a procedure, which combines a preliminary averaging over dynamic degrees of freedom and a next static Wilson renormalization group transformation. We work to one-loop level to obtain results which are exact to first order in $\ensuremath{\epsilon}$ and believed to be qualitatively correct for 2<d<42<d<42<d<4. Within this static framework, we get the phase boundary, ending in a quantum critical point, and the general expressions for the correlation length and susceptibility as functions of the temperature and the applied magnetic field within the disordered phase. With these basic ingredients, the critical properties and a rich crossover scenario in the influence domain of the quantum critical point are derived in a simple and transparent way. Remarkably, one can speculate that the crossovers, found to occur decreasing the temperature with the magnetic field fixed at its quantum critical point value, might be actually observable in complex magnetic compounds, as suggested by recent experiments.