Biquadratic Coupling Research Articles

Temperature dependence of the order parameters (spontaneous polarisation and the tilt angle) at various concentrations for a mixture of SCE9+SCE10

The smectic A- smectic C* (AC*) transition in a binary mixture of SCE9+SCE10 is studied at various concentrations of SCE9 near (x c = 0.12) and above x c (tricritical concentration). The temperature dependences of the spontaneous polarisation and the tilt angle (order parameters) are calculated using our mean field model with the bilinear and biquadratic couplings between these two order parameters. The expressions derived from the mean field model are fitted to the experimental data from the literature and the coefficients given in the free energy are determined. It is demonstrated that our mean field model explains the observed mean field to tricritical behaviour in SCE9+SCE10.

Critical behaviour of the dielectric constant for the smectic AC* transition under the electric field in ferroelectric liquid crystals

The temperature dependencies of the dielectric constant and the tilt angle (order parameter) are calculated under the electric field for the smectic A–smectic C* (AC*) transition in 4-(3-methyl-2-chlorobutanoyloxy)-4′-heptyloxybiphenyl (A7). The dielectric constant is fitted to the experimental data by using our mean field model with the biquadratic coupling between the spontaneous polarisation P and the tilt angle . Our results show that the mean field model with the coupling describes satisfactorily the observed behaviour of the AC* transition in A7. It is indicated here that a first-order AC* transition occurring at low electric fields changes its character towards a second order as the electric field increases in A7.

Theory of the magnetoeletric effect in a lightly doped high-Tccuprate

In a recent study Viskadourakis et al. discovered that extremely underdoped La_2CuO_(4+x) is a relaxor ferroelectric and a magnetoelectric material at low temperatures. It is further observed that the magnetoelectric response is anisotropic for different directions of electric polarization and applied magnetic field. By constructing an appropriate Landau theory, we show that a bi-quadratic magnetoelectric coupling can explain the experimentally observed polarization dependence on magnetic field. This coupling leads to several novel low-temperature effects including a feedback enhancement of the magnetization below the ferroelectric transition, and a predicted magnetocapacitive effect.

Control of vortex pair states by post-deposition interlayer exchange coupling modification

We report on both the global and micromagnetic properties of interlayer exchange coupled spin systems. Irradiation with Ne ions is employed to achieve a phase transition from antiferromagnetic to ferromagnetic coupling. For extended trilayer films a full quantitative analysis of the bilinear and biquadratic coupling constants is performed. With increasing ion fluence we observe a steady increase of the bilinear coupling constant at an almost negligible decrease in saturation magnetization. The mixing of atoms at the layer interfaces is identified as the origin for this. The effects of ion modification on the magnetic microstructure are studied for the model system of layered vortex pairs. X-ray microscopy is used to directly image the individual magnetization circulations in trilayer disks. The circulation configuration is found to be determined by the film coupling for both coupling orientations with a homogenous coupling angle throughout the structure. For the vortex cores, however, micromagnetic simulations indicate that due to the significant local demagnetization fields, parallel states are always energetically preferred. Nevertheless antiparallel configurations are metastable, having their signature in reduced core diameters. Our study provides new results on spin structures in interlayer exchange coupled trilayers and it demonstrates a promising way to control the local interlayer coupling post-deposition.

Interface biquadratic coupling and magnon scattering in exchange-biased ferromagnetic thin films grown on epitaxial FeF2

The magnetic anisotropy of ferromagnetic (FM) Ni, Co, and Fe polycrystalline thin films grown on antiferromagnetic (AF) FeF2(110) epitaxial layers was studied, as a function of temperature, using ferromagnetic resonance. In addition to an in-plane anisotropy in the FM induced by fluctuations in the AF short-range order, a perpendicular (biquadratic) magnetic anisotropy, with an out-of-plane component, was found which increased with decreasing temperature above the AF Neél temperature (TN = 78.4 K). This is a surprising result given that the AF’s uniaxial anisotropy axis was in the plane of the sample, but is consistent with prior experimental and theoretical work. The resonance linewidth had a strong dependence on the direction of the external magnetic field with respect to in-plane FeF2 crystallographic directions, consistent with interface magnon scattering due to defect-induced demagnetizing fields. Below TN, the exchange bias field HE measured via FMR for the Ni sample was in good agreement with HE determined from magnetization measurements if the perpendicular out-of-plane anisotropy was taken into account. A low field resonance line normally observed at H ≈ 0, associated with domain formation during magnetization in ferromagnets, coincided with the exchange bias field for T < TN, indicating domain formation with the in-plane FM magnetization perpendicular to the AF easy axis. Thus, biquadratic FM–AF coupling is important at temperatures below and above TN.

The magnetoelectric effect and double‐perovskite structure

AbstractBased on a microscopic model with a biquadratic magnetoelectric coupling the properties of Bi2NiMnO6 thin films are investigated. Using Green's functions the phonon spectrum is calculated which is determined by the polarization and the magnetization. The phonon energy and its damping offer a kink at the magnetic phase transition temperature. The phonon energy is enhanced if an external magnetic field is increased, whereas, the damping of the phonons decreases. The observed behavior is a strong evidence for a magnetoelectric coupling. The relevance of our approach for other multiferroics is discussed.

Multicritical Dynamic Phase Diagrams and Dynamic Hysteresis Loops in a Mixed Spin-2 and Spin-5/2 Ising Ferrimagnetic System with Repulsive Biquadratic Coupling: Glauber Dynamic Approach

The stationary states of the kinetic mixed spin-2 and spin-5/2 Ising ferrimagnetic system with repulsive biquadratic coupling are examined within a mean-field approach under the presence of a time varying (sinusoidal) magnetic field. We employ Glauber-type stochastic dynamics to construct a set of coupled mean-field dynamic equations, and we solve these equations to find the phases in the system. We also investigate the thermal behavior of the dynamic order parameters to characterize the nature (continuous or discontinuous) of the dynamic phase transitions (DPTs) and obtain the DPT points. The phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane, and a comparison is made with the results of other kinetic mixed spin systems. We also study the behavior of the dynamic magnetic hysteresis and investigate the effects of the frequency on hysteresis properties, and we find the results are in good agreement with some previous theoretical and experimental works.

Specular and off-specular polarized neutron reflectometry of canted magnetic domains in loose spin coupled CuMn/Co multilayers

Specular and off-specular polarized neutron reflectometry of strong biquadratic coupling in a Cu${}_{0.94}$Mn${}_{0.06}$/Co multilayer is presented. Detailed analysis of the reflectivity via the distorted-wave Born approximation reveals a formation of on average $\ensuremath{\langle}\ifmmode\pm\else\textpm\fi{}$30${}^{\ensuremath{\circ}}\ensuremath{\rangle}$ canted lateral magnetic domains. Domains with mean width of 0.43 $\ensuremath{\mu}$m extend throughout the multilayer structure and magnetization alternates in the sign of the canting with subsequent layers. Temperature and field dependence of the magnetic structure are evaluated and included in the magnetic model, which is used to deduce bilinear and biquadratic interlayer exchange coupling energies.

Magnetoelectric Coupling in Disordered Multiferroics

Higher order magnetoelectric effects dominate in disordered multiferroics with broken translational symmetry such as multiglassy Sr0.98Mn0.02TiO3, antiferromagnetic quantum paraelectric EuTiO3, relaxor ferroelectric antiferromagnetic Pb(Fe0.5Nb0.5)O3, and antiferroelectric antiferromagnetic CuCr1-xInxP2S6. The E 2 H 2 effect is allowed in all symmetries. In EuTiO3 it is due to biquadratic coupling between spins and soft phonon pseudospins and yields ‘giant’ values at critical magnetic fields. Weak magnetoelectric coupling is due to spin or dipole glass phases in Pb(Fe0.5Nb0.5)O3 and CuCr1-xInxP2S6, respectively. EH effects are observed after field-induced ordering, e.g. in EuTiO3 or in the spin glass phase of Pb(Fe0.5Nb0.5)O3.

Flexoelectric Polarization, Interactions of Longer Range and Multilayer Structures

Flexoelectric interactions in antiferroelectric liquid crystals are a reason for effective interactions to more distant layers in systems where the polarizations in neighboring layers directly interact. In a presence of strong biquadratic coupling which favors uniplanar tilts, the system locks to commensurate structure. The commensurate period of the structure is related to the range of indirect interlayer interactions which are the strongest on average. Systems with strong interaction to nearest neighboring layers favor period one i.e. synclinic tilts for negative sign of the coefficient giving corresponding interaction and period two i.e. anticlinic tilts. As in antiferroelectric liquid crystals the effective interactions to next nearest neighboring layers always favor antiparallel tilts due to the flexoelectric effect, the period four, i. e. two times two, is stabilized when interactions to nearest layers are negligible. As interactions to third nearest neighbors favor either parallel or antiparallel tilts, structures with periods three and six layers are possible. Structures with other periods are highly unlikely to appear in antiferroelectric liquid crystals as stable states.

Thickness-dependent magnetic structure of ultrathin Fe/Ir(001) films: From spin-spiral states toward ferromagnetic order

We present a detailed study of the ground-state magnetic structure of ultrathin Fe films on the surface of fcc Ir(001). We use the spin-cluster expansion technique in combination with the relativistic disordered local moment scheme to obtain parameters of spin models and then determine the favored magnetic structure of the system by means of a mean-field approach and atomistic spin dynamics simulations. For the case of a single monolayer of Fe, we find that layer relaxations very strongly influence the ground-state spin configurations, whereas Dzyaloshinskii-Moriya (DM) interactions and biquadratic couplings also have remarkable effects. To characterize the latter effect, we introduce and analyze spin collinearity maps of the system. While for two monolayers of Fe we find a single-$q$ spin spiral as ground state due to DM interactions, for the case of four monolayers, the system shows a noncollinear spin structure with nonzero net magnetization. These findings are consistent with experimental measurements indicating ferromagnetic order in films of four monolayers and thicker.

Bi-quadratic interlayer exchange coupling in Co2MnSi/Ag/Co2MnSi pseudo spin-valve

Bi-quadratic interlayer exchange coupling is found below 100 K in a Co2MnSi/Ag/Co2MnSi current-perpendicular-to-plane pseudo spin valves. The bi-quadratic coupling constant J2 was estimated to be ∼−0.30 erg/cm2 at 5 K and the strong temperature dependence of the coupling strength points its likely origin to the “loose spin” model. Application of current of ∼2 × 107 A/cm2 below 100 K leads to an increase in the magnetoresistance (MR), indicating current induced antiparallel alignment of the two magnetic layers. These results strongly suggest that the presence of the bi-quadratic interlayer exchange coupling causes the reduction of the magnetoresistance at low temperature and illustrates the importance of understanding the influence of interlayer exchange coupling on magnetization configuration in magnetic nanostructures.

Theory of inelastic light scattering in spin-1 systems: Resonant regimes and detection of quadrupolar order

Motivated by the lack of an obvious spectroscopic probe to investigate non-conventional order such as quadrupolar orders in spin S>1/2 systems, we present a theoretical approach to inelastic light scattering for spin-1 quantum magnets in the context of a two-band Hubbard model. In contrast to the S=1/2 case, where the only type of local excited state is a doubly occupied state of energy $U$, several local excited states with occupation up to 4 electrons are present. As a consequence, we show that two distinct resonating scattering regimes can be accessed depending on the incident photon energy. For $\hbar\omega_{in}\lesssim U$, the standard Loudon-Fleury operator remains the leading term of the expansion as in the spin-1/2 case. For $\hbar\omega_{in}\lesssim4U$, a second resonant regime is found with a leading term that takes the form of a biquadratic coupling $\sim({\bf S}_{i}\cdot{\bf S}_{j)^{2}$. Consequences for the Raman spectra of S=1 magnets with magnetic or quadrupolar order are discussed. Raman scattering appears to be a powerful probe of quadrupolar order.

Ferroelectricity and ferromagnetism in EuTiO3nanowires

We predicted the ferroelectric-ferromagnetic multiferroic properties of EuTiO3 nanowires and generated the phase diagrams in coordinates of temperature and wire radii. The calculations were performed within the Landau-Ginzburg-Devonshire theory with phenomenological parameters extracted from tabulated experimental data and first principles calculations. Since bulk EuTiO3 is antiferromagnetic at temperatures lower than 5.5 K and paraelectric at all temperatures, our goal was to investigate the possibility of inducing the ferroelectric and ferromagnetic properties of EuTiO3 by reducing the bulk to nanosystems. Our results indicate that ferroelectric spontaneous polarization of ~0.1-0.5C/m2 is induced in EuTiO3 nanowires due to the intrinsic surface stress, which is inversely proportional to the nanowire radius. The spontaneous polarization exists at temperatures lower than 300 K, for the wire radius less than 1 nm and typical surface stress coefficients ~ 15 N/m. Due to the strong biquadratic magnetoelectric coupling, the spontaneous polarization in turn induces the ferromagnetic phase at temperatures lower than 30 K for 2 nm nanowire, and at temperatures lower than 10 K for 4 nm nanowire in EuTiO3. Thus we predicted that the EuTiO3 nanowires can be the new ferroelectric-ferromagnetic multiferroic.

Origin of the multiferroicity in Eu0.5Ba0.5TiO3

AbstractWe have proposed a microscopic model with a biquadratic magnetoelectric coupling between the two ordered parameters taking into account the spin–phonon coupling in order to study different properties of multiferroic Eu0.5Ba0.5TiO3. This magnetoelectric coupling is due to an epitaxial strain which occurs by the replacing of the Eu‐ions with the larger Ba‐ions and vice versa. A Green's function technique allows the calculation of magnetic, electric, and phonon properties which are discussed in dependence of temperature and external fields. The magnetization increases with increasing of the electric field, whereas the phonon energy with the magnetic field. This is an evidence for the magnetoelectric coupling.

Inter-Layer Exchange Coupling in $\hbox{Fe}_{2}\hbox{CrSi/Fe}_{2}\hbox{VSi}$ Multilayers Fabricated on $\hbox{MgAl}_{2}\hbox{O}_{4}$ Substrates

In this study, we have fabricated Heusler alloy Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> CrSi/Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> VSi superlattice on MgAl <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> substrate and have investigated inter-layer exchange coupling among Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> CrSi layers. Biquadratic coupling is dominated below the Neel temperature of Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> VSi. By comparing magnetic coupling energy at 77 K and room temperature, it is suggested that the inter-layer exchange coupling is dominated by the proximity effect, i.e. the antiferromagnetic alignment of magnetic moments in Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> VSi spacer layer.

Spatial Fluctuations of Loose Spin Coupling inCuMn/CoMultilayers

A detailed investigation of magnetic impurity-mediated interlayer exchange coupling observed in Cu(0.94)Mn(0.06)/Co multilayers using polarized neutron reflectometry and magnetic x-ray techniques is reported. Excellent descriptions of temperature and magnetic field dependent biquadratic coupling are obtained using a variant of the loose spin model that takes into account the distribution of the impurity Mn ions in three dimensions. Positional disorder of the magnetic impurities is shown to enhance biquadratic coupling via a new contribution J(2)(fluct), leading to a temperature dependent canting of magnetic domains in the multilayer. These results provide measurable effects on RKKY coupling associated with the distribution of impurities within planes parallel to the interfaces.

What the Theory Says about the Six Layer Periodic Structures in Antiferroelectric Liquid Crystals?

We discuss the prerequisites for the formation of the structure with a period of six layers in antiferroelectric liquid crystals. We find that such a structure can appear in the region where the incommensurate helical pitch in the phase approaches six layers, if biquadratic coupling favoring uniplanar tilts in neighboring layers is already significant and if electrostatic dipolar interactions favor parallel ordering of dipoles in neighboring layers.

Magnetoelastic coupling in the phase diagram of Ba1−xKxFe2As2as seen via neutron diffraction

We report a high resolution neutron diffraction investigation of the coupling of structural and magnetic transitions in Ba1xKxFe2As2. The tetragonal-orthorhombic and antiferromagnetic transitions are suppressed with potassium-doping, falling to zero at x <~ 0.3. However, unlike Ba(Fe1xCox)2As2, the two transitions are first-order and coincident over the entire phase diagram, with a biquadratic coupling of the two order parameters. The phase diagram is refined showing that the onset of superconductivity is at x = 0.133 with all three phases coexisting until x >~ 0.24.

TILT ANGLE AND THE TEMPERATURE SHIFTS CALCULATED AS A FUNCTION OF CONCENTRATION FOR THE AC* PHASE TRANSITION IN A BINARY MIXTURE OF LIQUID CRYSTALS

We study here the tilt angle and the temperature shifts as a function of concentration for the AC* phase transition in a binary mixture, using our mean field model with the biquadratic P2θ2 coupling — and also with the bilinear Pθ and P2θ2 couplings. By expanding the free energy in terms of the tilt angle and polarization, the tilt angle and the temperature shift are evaluated by using the coefficients given in the free energy expansion. By employing a concentration-dependent coefficient, the tilt angle and the temperature shift are calculated as a function of concentration of 10.O.4 for the SmAC* transition in a binary mixture of C7 and 10.O.4. Our calculated values of the tilt angle and the temperature shifts decrease as the concentration of 10.O.4 increases, as confirmed experimentally for the AC* transition in this binary mixture. This indicates that our mean field models studied here are satisfactory to explain the observed behavior of the AC* transition of the binary mixture of C7 and 10.O.4.