Chiral order and electromagnetic dynamics in one-dimensional multiferroic cuprates

We show by unbiased numerical calculations that the ferromagnetic nearest-neighbor exchange interaction stabilizes a vector spin chiral order against the quantum fluctuation in a frustrated spin-1/2 chain relevant to multiferroic cuprates, LiCu2O2 and LiCuVO4. Our realistic semiclassical analyses for LiCu2O2 resolve controversies on the helical magnetic structure and unveil the pseudo-Nambu-Goldstone modes as the origin of experimentally observed electromagnons.     

On the Theory of Magnetoelectric Coupling in LiCu 2 O 2

A microscopic theory is proposed for coupling of copper spins with an external electric field in the magnetically ordered phase of LiCu2O2. The expressions are derived for the dipole moment components of exchange-coupled pairs of copper spins, as well as expressions for describing the macroscopic polarization in terms of the angles determining spatial orientations of spin rotation planes (helixes) in copper bichains. It is shown that zero electric polarization in isostructural compound NaCu2O2 can be explained by the difference in the spin structures in NaCu2O2 and LiCu2O2.     

Dynamical magnetoelectric coupling in helical magnets

We develop a theory of collective mode dynamics in the helical magnets coupled to electric polarization via spin-orbit interaction. The low-lying modes associated with the ferroelectricity are not the transverse optical phonons, but are the spin waves hybridized with the electric polarization. This hybridization leads to the Drude-like dielectric function epsilon(omega) in the limit of zero magnetic anisotropy. There are two additional low-lying modes: phason of the spiral and rotation of helical plane along the polarization axis. Role of these low-lying modes in the neutron scattering and antiferromagnetic resonance is revealed, and a novel experiment to detect the dynamical magnetoelectric coupling is discussed.     

Ferroelectricity generated by spin-orbit and spin-lattice couplings in multiferroic DyMnO3

While the ferroelectricity in type-II multiferroic rare-earth manganites is believed to be generated by the inverse Dzyaloshinskii-Moriya (DM) interaction (spin-orbit coupling) associated with the Mn spiral spin order, recent results revealed the strong spin-lattice coupling arising from the Dy-Mn spin interaction in DyMnO₃, which may also be an ingredient contributing to the ferroelectricity. In this work, we summarize our recent experiments on this issue by performing a series of rare-earth site nonmagnetic Y and magnetic Ho substitutions at Dy site for DyMnO₃. It is demonstrated that the Dy-Mn spin interaction contributes to the ferroelectric polarization through the symmetric exchange striction mechanism (spin-lattice coupling). A coexistence of the spin-orbit coupling and spin-lattice coupling in one compound is confirmed. At the same time, the independent Dy antiferromagnetic spin order at low temperature can be effectively suppressed by the substitutions, beneficial to the polarization enhancement.     

Magnetic ground state and transition of a quantum multiferroic LiCu2O2

Based on resonant soft x-ray magnetic scattering, we report that LiCu2O2 exhibits a large interchain coupling which suppresses quantum fluctuations along spin chains, and a quasi-2D short-range magnetic order prevails at temperatures above the magnetic transition. These observations unravel the fact that the ground state of LiCu2O2 possesses long-range 2D-like incommensurate magnetic order rather than being a gapped spin liquid as expected from the nature of quantum spin-1/2 chains. In addition, the spin coupling along the c axis is found to be essential for inducing electric polarization.     

Quantum theory of multiferroic helimagnets: collinear and helical phases

We study the quantum fluctuation in the cycloidal helical magnet in terms of the Schwinger boson approach. In sharp contrast to the classical fluctuation, the quantum fluctuation is collinear in nature which gives rise to the collinear spin density wave state slightly above the helical cycloidal state as the temperature is lowered. Physical properties such as the reduced elliptic ratio of the spiral, the neutron scattering and infrared absorption spectra are discussed from this viewpoint with the possible relevance to the quasi-one dimensional LiCu2O2 and LiCuVO4.     

Ferroelectricity in an s=1/2 chain cuprate

We report our discovery of ferroelectricity in the spiral-magnetic state in the quantum quasi-one-dimensional (1D) S=1/2 magnet of LiCu2O2. Electric polarization (P) emerges along the c direction below the spiral-magnetic order temperature, but changes from the c to a axis when magnetic fields (H) are applied along the b direction. We also found that P(c) increases with H(c), and P(a) appears with H(a). LiCu2O2 in zero field appears to be the first ferroelectric cuprate and also a prototypical example of the "1D spiral-magnetic ferroelectrics." However, the unexpected behavior in H may demonstrate the complexity of the ordered spin configuration, inherent in the 1D S=1/2 magnet of LiCu2O2.     

Correlation between spin helicity and an electric polarization vector in quantum-spin chain magnet LiCu2O2

Measurements of polarized neutron scattering were performed on a S=1/2 chain multiferroic LiCu2O2. In the ferroelectric ground state with the spontaneous polarization along the c axis, the existence of transverse spiral spin component in the bc plane was confirmed. When the direction of electric polarization is reversed, the vector spin chirality as defined by C_(ij)=S_(i)xS_(j) (i and j being the neighboring spin sites) is observed to be reversed, indicating that the spin-current model or the inverse Dzyaloshinskii-Moriya mechanism is applicable even to this e_(g)-electron quantum-spin system. Differential scattering intensity of polarized neutrons shows a large discrepancy from that expected for the classical-spin bc-cycloidal structure, implying the effect of large quantum fluctuation.     

Ferroelectricity driven by the noncentrosymmetric magnetic ordering in multiferroic TbMn(2)O(5): a first-principles study

The ground state structural, electronic, and magnetic properties of multiferroic TbMn(2)O(5) are investigated via first-principles calculations. We show that the ferroelectricity in TbMn(2)O(5) is driven by the noncentrosymmetric magnetic ordering, without invoking the spin-orbit coupling and noncollinear spins. The intrinsic electric polarization in this compound is calculated to be 1187 nC cm(-2), an order of magnitude larger than previously thought.     

Theory of magnetic switching of ferroelectricity in spiral magnets

We propose a microscopic theory for magnetic switching of electric polarization (P) in the spin-spiral multiferroics by taking TbMnO3 and DyMnO3 as examples. We reproduce their phase diagrams under a magnetic field Hex by Monte Carlo simulation of an accurate spin model and reveal that competition among the Dzyaloshinskii-Moriya interaction, spin anisotropy, and spin exchange is controlled by the applied Hex, resulting in magnetic transitions accompanied by reorientation or vanishing of P. We also discuss the relevance of the proposed mechanisms to many other multiferroics such as LiCu2O2, MnWO4, and Ni3V2O4.     

Coupling of magnetic and ferroelectric hysteresis by a multicomponent magnetic structure in Mn2GeO4

The olivine compound Mn(2)GeO(4) is shown to feature both a ferroelectric polarization and a ferromagnetic magnetization that are directly coupled and point along the same direction. We show that a spin spiral generates ferroelectricity, and a canted commensurate order leads to weak ferromagnetism. Symmetry suggests that the direct coupling between the ferromagnetism and ferroelectricity is mediated by Dzyaloshinskii-Moriya interactions that exist only in the ferroelectric phase, controlling both the sense of the spiral rotation and the canting of the commensurate structure. Our study demonstrates how multicomponent magnetic structures found in magnetically frustrated materials like Mn(2)GeO(4) provide a new route towards functional materials that exhibit coupled ferromagnetism and ferroelectricity.     

Magnetic field control of ferroelectric polarization and magnetization of LiCu_2O_2 compound

A spin model of LiCu2O2 compound with ground state of ellipsoidal helical structure is adopted. Taking into account the interchain coupling and exchange anisotropy, we investigate the magnetoelectric properties in a rotating magnetic field and perform the Monte Carlo simulation on a two-dimensional lattice. A prominent anisotropic response is observed in both the magnetization curve and the polarization curve, qualitatively coinciding with the behaviors that are detected in the experiment. In addition, the influences of the magnetic field with various magnitudes on polarization are also explored and analyzed in detail. As the magnetic field increases, a much smoother polarization of angle dependence is exhibited,indicating the strong correlation between the magnetic and ferroelectric orders.     

Consistency in formulation of spin current and torque associated with a variance of angular momentum

Based on the Noether's theorem, we develop systematically and rigorously the spin-dependent formulation of the conservation laws. The effect of the electronic polarization due to the spin-orbit coupling is included in the Maxwell equations. The polarization is related to the antisymmetric components of spin current, and it provides a possibility to measure the spin current directly. The variances of spin and orbit angular momentum currents imply a torque on the "electric dipole" associated with the moving electron. The dependencies of the torque on the polarization and the force on the motions of spin-polarized electrons in a two-dimensional electron gas with the Rashba spin-orbit coupling are discussed.     

Vertex correction of the anisotropic magnetic impurities to the spin polarization of 2D electron gas

In terms of Kubo's formula and Green's function method, for the two-dimensional electron gas (2DEG) with Rashba spin-orbit coupling (SOC), we study the spin polarization due to the effect from magnetic impurities with anisotropic spin dependent delta type coupling to electrons when an external dc electric field in plane is applied. The vertex correction of impurities in ladder approximation is carried out in the limit of EF?1/τ, Δ. We find that the strength of spin polarization can be significantly modified by vertex correction and the spin polarization is relevant to the anisotropy coefficient γ, but the direction of net spin polarization cannot be changed.     

Ferroelectricity in the magnetic E-phase of orthorhombic perovskites

We show that the symmetry of the spin zigzag chain E phase of the orthorhombic perovskite manganites and nickelates allows for the existence of a finite ferroelectric polarization. The proposed microscopic mechanism is independent of spin-orbit coupling. We predict that the polarization induced by the E-type magnetic order can potentially be enhanced by up to 2 orders of magnitude with respect to that in the spiral magnetic phases of TbMnO3 and similar multiferroic compounds.     

电子铁电体研究进展

电子铁电性是基于关联体系电荷有序态的一种新的物理现象。近期研究发现,这种新型铁电体通常表现出丰富的磁电性质和耦合效应,在发展可控性多功能微电子器件方面具有广阔的应用前景。本文重点介绍了电子型铁电体代表材料LuFe2O4的实验和理论研究进展,着重探讨了电荷序相变,极化机理,介电,铁电,磁电耦合等重要物理性能。随后,简要介绍了其它体系在相关问题研究中的进展情况,包括：钙钛矿体系Pr(Ca)MnO3,Fe3O4和有机材料(TMTTF)2X等。     

Spin transverse force on spin current in an electric field

As a relativistic quantum mechanical effect, it is shown that the electron field exerts a transverse force on an electron spin 1/2 only if the electron is moving. The spin force, analogue to the Lorentz for an electron charge in a magnetic field, is perpendicular to the electric field and the spin current whose spin polarization is projected along the electric field. This spin-dependent force can be used to understand the Zitterbewegung of the electron wave packet with spin-orbit coupling and is relevant to the generation of the charge Hall effect driven by the spin current in semiconductors.     

Ferroelectricity in an ising chain magnet

We report discovery of collinear-magnetism-driven ferroelectricity in the Ising chain magnet Ca3Co2-xMn(x)O6 (x approximately 0.96). Neutron diffraction shows that Co2+ and Mn4+ ions alternating along the chains exhibit an up-up-down-down ( upward arrow upward arrow downward arrow downward arrow) magnetic order. The ferroelectricity results from the inversion symmetry breaking in the upward arrow upward arrow downward arrow downward arrow spin chain with an alternating charge order. Unlike in spiral magnetoelectrics where antisymmetric exchange coupling is active, the symmetry breaking in Ca3(Co,Mn)2O6 occurs through exchange striction associated with symmetric superexchange.     

Rashba spin-orbit effect on dwell time of electrons tunneling through semiconductor barrier

A study on characteristics of electrons tunneling through semiconductor barrier is evaluated, in which we take into account the effects of Rashba spin-orbit interaction. Our numerical results show that Rashba spin-orbit effect originating from the inversion asymmetry can give rise to the spin polarization. The spin polarization does not increase linearly but shows obvious resonant features as the strength of Rashba spin-orbit coupling increases, and the amplitudes of spin polarization can reach the highest around the first resonant energy level. Furthermore, it is found that electrons with different spin orientations will spend quite different time through the same heterostructures. The difference of the dwell time between spin-up and spin-down electrons arise from the Rashba spin-orbit coupling. And it is also found that the dwell time will reach its maximum at the first resonant energy level. It can be concluded that, in the time domain, the tunneling processes of the spin-up and spin-down electrons can be separated by modulating the strength of Rashba spin-orbit coupling. Study results indicate that Rashba spin-orbit effect can cause a nature spin filter mechanism in the time domain.     

Spin-driven ferroelectricity in triangular lattice antiferromagnets ACrO2 (A=Cu, Ag, Li, or Na)

The correlation between the dielectric and magnetic properties is investigated on the triangular-lattice antiferromagnets ACrO2 (A=Cu, Ag, Li, or Na) with a 120-degree spiral structure. For the A=Cu and Ag compounds with a delafossite structure, the ferroelectric polarization emerges with a spiral-spin order, implying strong coupling between ferroelectricity and the spiral-spin structure. For the A=Li and Na compounds with an ordered rock salt structure, on the other hand, no spontaneous polarization is discerned, while the clear anomaly in the dielectric constant can be observed upon the transition to the spiral-spin ordered state. This feature can be ascribed to the possible antiferroelectric state induced by the alternate stacking of the Cr-spin sheet with opposite vector spin chirality.