Spontaneous symmetry breaking and response functions

We study the quantum phase transition occurring in an infinite homogeneous system of spin 1/2 fermions in a non-relativistic context. As an example we consider neutrons interacting through a simple spin-spin Heisenberg force. The two critical values of the coupling strength—signaling the onset into the system of a finite magnetization and of the total magnetization, respectively—are found and their dependence upon the range of the interaction is explored. The spin response function of the system in the region where the spin-rotational symmetry is spontaneously broken is also studied. For a ferromagnetic interaction the spin response along the direction of the spontaneous magnetization occurs in the particle-hole continuum and displays, for not too large momentum transfers, two distinct peaks. The response along the direction orthogonal to the spontaneous magnetization displays instead, beyond a softened and depleted particle-hole continuum, a collective mode to be identified with a Goldstone boson of type II. Notably, the random phase approximation on a Hartree-Fock basis accounts for it, in particular for its quadratic—close to the origin—dispersion relation. It is shown that the Goldstone boson contributes to the saturation of the energy-weighted sum rule for ≈25% when the system becomes fully magnetized (that is in correspondence of the upper critical value of the interaction strength) and continues to grow as the interaction strength increases.     

Magnetoelectric Energy in Electrodynamics: Magnetoelectricity,Bi(an)isotropy,and Magnetoelectric Meta-Atoms

Magnetoelectricity denotes the relationship between electric polarization and magnetization. In materials with an intrinsic magnetoelectric (ME) effect, the energy density comprises the polarization, magnetization, and ME energy densities. These three components of energy define local (subwavelength) characteristics of electromagnetic (EM) responses in multiferroic materials. In a subwavelength domain, coupling between the electric and magnetic dipole oscillations forms the ME field structures that are characterized by the violation of both spatial and temporal symmetry. Unlike multiferroics, bi(an)isotropic metamaterials are associated with an EM response characterized only by spatial symmetry breaking. This also applies to chiral materials. Since no “intrinsic magnetoelectricity” is assumed in such structures, any concepts about the stored ME energy are not applicable. This clearly points to the effect of nonlocality. That is why the basic concepts of bi(an)isotropy can only be analyzed by the EM far-field characteristics. In this paper, it is argued that in the implementation of local (subwavelength) ME meta-atoms and systems for near-field probing of chirality, the concept on ME energy is crucial. Real ME energy can occur when ME fields in a singular subwavelength domain are characterized by a violation of both the symmetry of time reversal and spatial reflection.     

Symmetry theory of the flexomagnetoelectric effect in the magnetic domain walls

A local flexomagnetoelectric (A.P. Pyatakov, A.K. Zvezdin, 2009) effect in the magnetic domain walls (DWs) of the cubic hexoctahedral crystal has been investigated on the basis of a symmetry analysis. The strong connection between magnetic symmetry of the DW and the type of the distribution of the electric polarization was shown. Results were systemized in the scope of the DW chirality. It was shown, that new type of the local flexomagnetoelectric coupling corresponds to the presence of the coupled electric charge in the DW. It was found that all time-noninvariant chiral DWs have identical type of spatial distribution of the magnetization and polarization. There are coincidence between the symmetry predictions and results obtaining from the known term of the flexomagnetoelectric coupling for transverse polarization components.     

Analytic construction of magnetic multipoles from cylindric permanent magnets

We discuss an analytic method for the design of three-dimensional magnetic multipoles from permanent magnet materials. The concept is explicited with an idealized, continuously varying magnetization. The effect of segmentation for realistic implementations is discussed. As an example we present an open, experimentally accessible cylindric structure for a dipole and a quadrupole field with high purity. The fields are useful over several cm³.     

Scaling and infrared divergences in the replica field theory of the Ising spin glass

Replica field theory for the Ising spin glass in zero magnetic field is studied around the upper critical dimension d=6. A scaling theory of the spin glass phase, based on Parisi's ultrametrically organised order parameter, is proposed. We argue that this infinite step replica symmetry broken (RSB) phase is nonperturbative in the sense that amplitudes of scaling forms cannot be expanded in term of the coupling constant w². Infrared divergent integrals inevitably appear when we try to compute amplitudes perturbatively, nevertheless the -expansion of critical exponents seems to be well-behaved. The origin of these problems can be traced back to the unusual behaviour of the free propagator having two mass scales, the smaller one being proportional to the perturbation parameter w² and providing a natural infrared cutoff. Keeping the free propagator unexpanded makes it possible to avoid producing infrared divergent integrals. The role of Ward-identities and the problem of the lower critical dimension are also discussed. Received 23 December 1998 and Received in final form 23 March 1999     

Magnetic relaxation behavior in Tb-doped perovskite manganite

Tb-doped LaMnO₃ perovskite manganite has been synthesized by a conventional solid-state reaction method. The XRD patterns of the sample revealed that it has a single perovskite-type phase with orthorhombic symmetry at room temperature. The magnetic properties of the sample were investigated. The results of the static and dynamic magnetization measurements show that there is the magnetic relaxation behavior of the cluster (spin) glass in the Tb-doped LaMnO₃ sample. The outcomes of the ac nonlinear magnetization indicate that the magnetic relaxation behavior of the cluster (spin) glass was attributed to the coexistence and competition of a ferromagnetic double exchange between Mn³⁺ and Mn⁴⁺ and an antiferromagnetic superexchange coupling among Tb³⁺ and Tb³⁺ as well as Mn³⁺ and Mn³⁺.     

Many-body Green's function theory for the magnetic reorientation of thin ferromagnetic films

The field-induced reorientation of the magnetization of ferromagnetic films is treated within the framework of many-body Green's function theory by considering all components of the magnetization. We present a new method for the calculation of expectation values in terms of the eigenvalues and eigenvectors of the equations of motion matrix for the set of Green's functions. This formulation allows a straightforward extension of the monolayer case to thin films with many layers and for arbitrary spin and moreover provides a practicable procedure for numerical computation. The model Hamiltonian includes a Heisenberg term, an external magnetic field, a second-order uniaxial single-ion anisotropy, and the magnetic dipole-dipole coupling. We utilize the Tyablikov (RPA) decoupling for the exchange interaction terms and the Anderson-Callen decoupling for the anisotropy terms. The dipole coupling is treated in the mean-field approximation, a procedure which we demonstrate to be a sufficiently good approximation for realistic coupling strengths. We apply the new method to monolayers with spin and to multilayer systems with S=1. We compare some of our results to those where mean-field theory (MFT) is applied to all interactions, pointing out some significant differences. Received 19 June 2000 and Received in final form 2 August 2000     

Exact Solution of the Gauge Symmetric <Emphasis Type="Italic">p</Emphasis>-Spin Glass Model on a Complete Graph

We consider a gauge symmetric version of the p-spin glass model on a complete graph. The gauge symmetry guarantees the absence of replica symmetry breaking and allows to fully use the interpolation scheme of Guerra (Fields Inst. Commun. 30:161, 2001) to rigorously compute the free energy. In the case of pairwise interactions (p=2), where we have a gauge symmetric version of the Sherrington-Kirkpatrick model, we get the free energy and magnetization for all values of external parameters. Our analysis also works for even p≥4 except in a range of parameters surrounding the phase transition line, and for odd p≥3 in a more restricted region. We also obtain concentration estimates for the magnetization and overlap parameter that play a crucial role in the proofs for odd p and justify the absence of replica symmetry breaking. Our initial motivation for considering this model came from problems related to communication over a noisy channel, and is briefly explained.     

Effect of dipole–dipole interaction on self-control magnetization oscillation in double-domain nanomagnets

A double-domain model with long-range dipole–dipole interaction is proposed to investigate the self-oscillation of magnetization in nano-magnetic systems driven by self-controlled spin-polarized current. The dynamic behavior of magnetization oscillation is calculated by a modified Landau–Lifshitz–Gilbert equation in order to evaluate the effects of the long-range dipole–dipole interaction. While the self-oscillation of magnetization can be maintained substantially, several self-oscillation regions are experienced as the dipole–dipole interaction increases gradually.     

应变作用下EuTiO3材料磁性的格林函数理论研究

基于自旋波和格林函数理论,研究了低温下二维应变诱导的EuTiO3在铁电四方相下的磁性性质,主要讨论了在铁电四方相下Eu离子在铁磁性和反铁磁性有序时系统沿不同高对称性方向的自旋波散射和磁化。我们发现施加外加应变不仅可改变晶格结构的对称性,还可以通过改变电子自旋之间的交换耦合作用,进而改变该材料的磁性散射和磁化等。     

应变作用下EuTiO_3材料磁性的格林函数理论研究

基于自旋波和格林函数理论,研究了低温下二维应变诱导的EuTiO_3在铁电四方相下的磁性性质,主要讨论了在铁电四方相下Eu离子在铁磁性和反铁磁性有序时系统沿不同高对称性方向的自旋波散射和磁化.我们发现施加外加应变不仅可改变晶格结构的对称性,还可以通过改变电子自旋之间的交换耦合作用,进而改变该材料的磁性散射和磁化等.     

Symmetry theory of the flexomagnetoelectric interaction in the magnetic vortices and skyrmions

Symmetry classification of the magnetic vortices and skyrmions has been suggested. Relation between symmetry based predictions and direct calculation has been shown. It was shown that electric dipole moment of the vortex is located inside the small vortex core. The antivortices and antiskyrmions do not carry the total core electric dipole induced by the flexomagnetoelectric interaction in the hexoctahedral cubic crystal. The volumetric bound electric charge is distributed around the core. Switching of the core electric dipole direction produces the switching of the core magnetization or vortex chirality and vice versa. The vortices and skyrmions with time-invariant enantiomorphism have two degenerative states: clockwise and counterclockwise state.     

Magnetic properties of zig-zag ladders

We analyze the phase diagram of a system of spin-1/2 Heisenberg antiferromagnetic chains interacting through a zig-zag coupling, also called zig-zag ladders. Using bosonization techniques we study how a spin-gap or more generally plateaux in magnetization curves arise in different situations. While for coupled XXZchains, one has to deal with a recently discovered chiral perturbation, the coupling term which is present for normal ladders is restored by an external magnetic field, dimerization or the presence of charge carriers. We then proceed with a numerical investigation of the phase diagram of two coupled Heisenberg chains in the presence of a magnetic field. Unusual behaviour is found for ferromagnetic coupled antiferromagnetic chains. Finally, for three (and more) legs one can choose different inequivalent types of coupling between the chains. We find that the three-leg ladder can exhibit a spin-gap and/or non-trivial plateaux in the magnetization curve whose appearance strongly depends on the choice of coupling. Received 11 February 1999 and Received in final form 16 June 1999     

Best values for the CP-odd meson–nucleon couplings from supersymmetry

In the supersymmetric models, the dominant sources of the hadronic flavor-diagonal CP violation at low energy are the theta term and the chromoelectric dipole moments of quarks. Using QCD sum rules, we estimate the preferred range and the best values for the CP-odd meson–nucleon coupling constants induced by these operators. When the theta term is removed by the axion mechanism, the size of the most important isospin triplet pion–nucleon coupling is estimated to be , where chromoelectric dipole moments are given in units of 10⁻²⁶ cm.     

Kramers degeneracy in a magnetic field and Zeeman spin-orbit coupling in antiferromagnetic conductors

In this Letter, I study the magnetic response of electron wave functions in a commensurate collinear antiferromagnet. I show that, at a special set of momenta, hidden antiunitary symmetry protects Kramers degeneracy of Bloch eigenstates against a magnetic field, pointing transversely to staggered magnetization. Hence, a substantial momentum dependence of the transverse g-factor in the Zeeman term, turning the latter into a spin-orbit coupling that may be present in materials from chromium to borocarbides, cuprates, pnictides, as well as organic and heavy fermion conductors.     

Emergence of chiral magnetism in spinor Bose-Einstein condensates with Rashba coupling

Hydrodynamic theory of the spinor BEC condensate with Rashba spin-orbit coupling is presented. A close mathematical analogy of the Rashba-Bose-Einstein condensate model to the recently developed theory of chiral magnetism is found. Hydrodynamic equations for mass density, superfluid velocity, and the local magnetization are derived. The mass current is shown to contain an extra term proportional to the magnetization direction, as a result of the Rashba coupling. Elementary excitations around the two known ground states of the Rashba-Bose-Einstein condensate Hamiltonian, the plane-wave, and the stripe states, are worked out in the hydrodynamic framework, highlighting the cross coupling of spin and superflow velocity excitations due to the Rashba term.     

Dynamics of two interacting dipoles

We study the deterministic spin dynamic of two interacting magnetic moments with anisotropy and dipolar interaction under the presence of an applied magnetic field, by using the Landau–Lifshitz equation with and without a damping term. Due to different kinds of interactions, different time scales appear: a long time scale associated with the dipolar interaction and a short time scale associated with the Zeeman interaction. We found that the total magnetization is not conserved; furthermore, for the non-dissipative case it is a fluctuating function of time, with a strong dependence on the strength of the dipolar term. In the dissipative case there is a transient time before the total magnetization reaches its constant value. We examine this critical time as a function of the distance between the magnetic moments and the phenomenological damping coefficient, and found that it strongly depends on these control parameters.     

In situ imaging of field-induced hexagonal columns in magnetite ferrofluids

Field-induced structures in a ferrofluid with well-defined magnetite nanoparticles with a permanent magnetic dipole moment are analyzed on a single-particle level by in situ cryogenic transmission electron microscopy (2D). The field-induced columnar phase locally exhibits hexagonal symmetry and confirms the structures observed in simulations for ferromagnetic dipolar fluids in 2D. The columns are distorted by lens-shaped voids, due to the weak interchain attraction relative to field-directed dipole-dipole attraction. Both dipolar coupling and the dipole concentration determine the dimensions and the spatial arrangement of the columns. Their regular spacing manifests long-range end-pole repulsions that eventually dominate the fluctuation-induced attractions between dipole chains that initiate the columnar transition.     

Symmetries of the electrodynamic interactions between chiral molecules

A quantum electrodynamics calculation of the dynamic microscopic interactions between molecules beyond the electric dipole approximation is presented. The symmetry of the resulting terms is examined with respect to rotations, parity and index permutations. Their relative importance is also considered in the short-distance limit. A dominant term which exists only in chiral molecules and which involves the coupling of the anisotropic parts of the molecular optical activities is evidenced. Associated with the coupling of the anisotropic parts of the molecular polarisabilities which is usually invoked to account for the isotropic–nematic phase transition of liquid crystals, that term accounts for the possibility of the helical order which is observed in chiral nematics (cholesterics). Introducing in addition both the short-range correlations due to the exclusion principle driven repulsive forces and the thermally-induced effect of the static multipole interactions can explain the temperature dependence of the helical pitch. No assumption will be made on the shape of the molecules.     

Orbital magnetization in semiconductors

This paper theoretically investigates the orbital magnetization of electron-doped (n-type) semiconductor heterostructures and of hole-doped (p-type) bulk semiconductors, which are respectively described by a two-dimensional electron/hole Hamiltonian with both the included Rashba spin--orbit coupling and Zeeman splitting terms. It is the Zeeman splitting, rather than the Rashba spin--orbit coupling, that destroys the time-reversal symmetry of the semiconductor systems and results in nontrivial orbital magnetization. The results show that the magnitude of the orbital magnetization per hole and the Hall conductance in the p-type bulk semiconductors are about 10^-2--10^-1 effective Bohr magneton and 10^-1--1 e²/h, respectively. However, the orbital magnetization per electron and the Hall conductance in the n-type semiconductor heterostructures are too small to be easily observed in experiment.