Biquadratic Coupling Research Articles

Biquadratic and ring exchange interactions in orthorhombic perovskite manganites

We use ab initio electronic structure calculations within the generalized gradient approximation (GGA+U) to density functional theory to determine the microscopic exchange interactions in the series of orthorhombic rare-earth manganites, o-$R{\mathrm{MnO}}_{3}$. Our motivation is to construct a model Hamiltonian (excluding effects due to spin-orbit coupling), which can provide an accurate description of the magnetism in these materials. First, we consider ${\mathrm{TbMnO}}_{3}$, which exhibits a spiral magnetic order at low temperatures. We map the exchange couplings in this compound onto a Heisenberg Hamiltonian and observe a clear deviation from the Heisenberg-like behavior. We consider first the coupling between magnetic and orbital degrees of freedom as a potential source of non-Heisenberg behavior in ${\mathrm{TbMnO}}_{3}$, but conclude that it does not explain the observed deviation. We find that higher order magnetic interactions (biquadratic and four-spin ring couplings) should be taken into account for a proper treatment of the magnetism in ${\mathrm{TbMnO}}_{3}$ as well as in the other representatives of the o-$R{\mathrm{MnO}}_{3}$ series with small radii of the $R$ cation.

The phase diagrams with influence of biquadratic exchange coupling on martensitic–austenitic transformations for core–surface nanoparticles

Recently, origin of the martensite–austenite transitions in core–surface type magnetic nanoparticles has been investigated theoretically and it has been indicated that repulsive biquadratic exchange coupling (K<0.0) causes the coexisting martensite and austenite phases. In the present paper, the phase diagrams of homogeneous and composite nanoparticles in the kBT/J0−D/J0 plane are studied for the presence and absence of attractive biquadratic exchange interaction in addition to repulsive biquadratic exchange interaction. Significant changes in the phase diagram points are discussed in the presence of martensitic and austenitic transformations. Four regions in the phase diagrams are found as second-order, martensitic–austenitic, TCid and first-order phase transition regimes.

Mechanism and Control of Antiferromagnetic Coupling in Fe/Fe3O4 Junctions

We analyzed the M-H loop observed for Fe3O4/bcc-Fe(001) junctions with thin insertion layers of Co or Mn by using several models that include bilinear and biquadratic coupling and twisting of magnetization near the interface. Both biquadratic and twisting of the magnetization are found to be important for explaining the M-H loop. To clarify the mechanism of antiparallel (AP) coupling in the Fe3O4/bcc-Fe junction, we performed first-principles calculations for junctions with and without extra Fe atoms on hollow sites of the spinel lattice at the interface. It was shown that parallel coupling is stable for junctions without extra Fe atoms whereas AP coupling becomes stable when the number of extra Fe atoms increases. The results suggest that magnetic frustration may occur when a nonuniform distribution of the extra Fe atoms exists at the interface.

Z3symmetry-protected topological phases in the SU(3) AKLT model

We study $\mathbb{Z}_3$ symmetry-protected topological (SPT) phases in one-dimensional spin systems with $Z_3 \times Z_3$ symmetry. We construct ground-state wave functions of the matrix product form for nontrivial $\mathbb{Z}_3$ phases and their parent Hamiltonian from a cocycle of the group cohomology $H^2(Z_3\times Z_3,U(1))$. The Hamiltonian is an SU(3) version of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, consisting of bilinear and biquadratic terms of su(3) generators in the adjoint representation. A generalization to the SU($N$) case, the SU($N$) AKLT Hamiltonian, is also presented which realizes nontrivial $\mathbb{Z}_N$ SPT phases. We use the infinite-size variant of the density matrix renormalization group (iDMRG) method to determine the ground-state phase diagram of the SU(3) bilinear-biquadratic model as a function of the parameter $\theta$ controlling the ratio of the bilinear and biquadratic coupling constants. The nontrivial $\mathbb{Z}_3$ SPT phase is found for a range of the parameter $\theta$ including the point of vanishing biquadratic term ($\theta=0$) as well as the SU(3) AKLT point [$\theta=\arctan(2/9)$]. A continuous phase transition to the SU(3) dimer phase takes place at $\theta \approx -0.027\pi$, with a central charge $c\approx3.2$. For SU(3) symmetric cases we define string order parameters for the $\mathbb{Z}_3$ SPT phases in a similar way to the conventional Haldane phase. We propose simple spin models that effectively realize the SU(3) and SU(4) AKLT models.

Interlayer coupling inNi80Fe20/Ru/Ni80Fe20multilayer films: Ferromagnetic resonance experiments and theory

We present a systematic study of the static and dynamic magnetization behavior of interlayer-coupled ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$(200 \AA{})/Ru(${t}_{\mathrm{Ru}}$)/${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$(100 \AA{}) trilayers as a function of the Ru spacer layer thickness ${t}_{\mathrm{Ru}}$. As ${t}_{\mathrm{Ru}}$ was varied in the range from 0 to 15.8 \AA{}, we observe a strong antiferromagnetic (AFM) exchange coupling between the two ferromagnetic (FM) layers for ${t}_{\mathrm{Ru}}$ = 5 \AA{}, which becomes weak for ${t}_{\mathrm{Ru}}$ = 10 \AA{}. For ${t}_{\mathrm{Ru}}$ = 14.1 \AA{}, the coupled magnetic system changes from AFM to FM ordering. Using broadband ferromagnetic resonance spectroscopy, we have probed the effects of the different coupling mechanisms on both the acoustic and optic magnetic modes. We found that the biquadratic exchange coupling has a negligible effect compared to Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange coupling, while the uniaxial anisotropy at the ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$/Ru interfaces also plays an important role in determining the behaviors of the modes. A mode anticrossing phenomenon is observed when the RKKY exchange interaction term is above a critical value. A theoretical framework developed is in very good agreement with our experimental results.

Ultrasonic and microwave investigation of the structural and magnetic transitions inCaFe2As2andBaFe2As2single crystals

Pulsed ultrasonic experiments performed on the parent compounds of FeAs based superconductors $A$Fe${}_{2}$${\mathrm{As}}_{2}$ ($A=\text{Ba}$, Ca) revealed elastic anomalies that agree with a two-step process for the structural/magnetic transitions. Upon cooling, a pronounced velocity softening of longitudinal phonons propagating along the $\mathbit{c}$ axis is observed at the structural transition ${T}_{\mathrm{s}}$ due to a distortion of the lattice. Below a slightly lower temperature ${T}_{\mathrm{N}}$, a biquadratic coupling between the distortion and an antiferromagnetic order parameter produces a steep velocity stiffening upon further cooling, the stiffening being five times larger in ${\mathrm{CaFe}}_{2}$${\mathrm{As}}_{2}$ than in ${\mathrm{BaFe}}_{2}$${\mathrm{As}}_{2}$. Microwave resistivity measurements at 16.5 GHz suggest that, upon cooling, the lattice distortion at ${T}_{\mathrm{s}}$ is driven by magnetic fluctuations in ${\mathrm{BaFe}}_{2}$${\mathrm{As}}_{2}$, while it is rather due to lattice fluctuations in ${\mathrm{CaFe}}_{2}$${\mathrm{As}}_{2}$. This suggestion appears consistent with a second-order character of the transitions in ${\mathrm{BaFe}}_{2}$${\mathrm{As}}_{2}$ and a first-order one in ${\mathrm{CaFe}}_{2}$${\mathrm{As}}_{2}$.

Thermodynamics of multicaloric effects in multiferroics

We provide a general thermodynamic framework to study multicaloric effects in multiferroic materials. This is applied to the case of a magnetoelectric multiferroic such as BiFeO, which is described by means of a Landau free energy with a biquadratic coupling between polarization and magnetization. We obtain a phase diagram, the isothermal entropy change and the adiabatic temperature change across different continuous and first-order phase transitions as the applied electric and magnetic fields are varied. The multicaloric effects are suitably decomposed into the corresponding electrocaloric and magnetocaloric contributions.

A Monte Carlo study of the spin-1 Blume–Emery–Griffiths phase diagrams within biquadratic exchange anisotropy

The effect of the bi-quadratic exchange coupling anisotropy on the phase diagram of the spin-1 Blume–Emery–Griffiths model on simple-cubic lattice is investigated using mean field theory (MFT) and Monte Carlo simulation (MC). It is found that the anisotropy of the biquadratic coupling favors the stability of the ferromagnetic phase. By decreasing the parallel and/or perpendicular bi-quadratic coupling, the ferrimagnetic and the antiquadrupolar phases broaden in contrast, the ferromagnetic and the disordered phases become narrow. The behavior of magnetization and quadrupolar moment as a function of temperature is also computed, especially in the ferrimagnetic phase.

Theoretical study of the multiferroic properties in M-doped (M=Co, Cr, Mg) ZnO thin films

Abstract The origin of multiferroism is still an open problem in ZnO. We propose a microscopic model to clarify the occurrence of multiferroism in this material. Using Green׳s function technique we study the influence of ion doping and size effects on the magnetization and polarization of ZnO thin films. The calculations for magnetic Co- and Cr-ions are based on the s–d model, the transverse Ising model in terms of pseudo-spins and a biquadratic magnetoelectric coupling, whereas in case of nonmagnetic Mg-ions the model takes into account the Coulomb interaction and an indirect coupling between the pseudo-spins via the conduction electrons. We show that the magnetization M exhibits a maximum for a fixed concentration of the doping ions. Furthermore M increases with decreasing film thickness N . The polarization increases with increasing concentration of the dopant and decreasing N . The results are in good agreement with the experimental data.

Thermotropic orientational order of discotic liquid crystals in nanochannels: an optical polarimetry study and a Landau-de Gennes analysis.

Optical polarimetry measurements of the orientational order of a discotic liquid crystal based on a pyrene derivative confined in parallelly aligned nanochannels of monolithic, mesoporous alumina, silica, and silicon as a function of temperature, channel radius (3-22 nm) and surface chemistry reveal a competition of radial and axial columnar orders. The evolution of the orientational order parameter of the confined systems is continuous, in contrast to the discontinuous transition in the bulk. For channel radii larger than 10 nm we suggest several, alternative defect structures, which are compatible both with the optical experiments on the collective molecular orientation presented here and with a translational, radial columnar order reported in previous diffraction studies. For smaller channel radii our observations can semi-quantitatively be described by a Landau-de Gennes model with a nematic shell of radially ordered columns (affected by elastic splay deformations) that coexists with an orientationally disordered, isotropic core. For these structures, the cylindrical phase boundaries are predicted to move from the channel walls to the channel centres upon cooling, and vice-versa upon heating, in accord with the pronounced cooling/heating hystereses observed and the scaling behavior of the transition temperatures with the channel diameter. The absence of experimental hints of a paranematic state is consistent with a biquadratic coupling of the splay deformations to the order parameter.

High-temperature noncollinear magnetism in a classical bilinear-biquadratic Heisenberg model

Motivated by the magnetically-driven high-temperature ferroelectric behavior of CuO and the subsequent theoretical efforts to understand this intriguing phenomenon, we study a spin model on a two-dimensional square lattice which possesses some of the key features of the models proposed for CuO. The model consists of Heisenberg couplings between nearest and next-nearest neighbor spins, and biquadratic couplings between nearest neighbors. We use a combination of variational calculations and classical Monte Carlo simulations to study this model at zero and finite temperatures. We show that even an arbitrarily weak biquadratic coupling plays a crucial role in selecting the magnetic ground state. More importantly, a non-collinear magnetic state, characterized by a finite spin current, is stable at finite temperatures. The interesting aspect is that the present model neither includes an inversion-symmetry-breaking term nor the effects of lattice distortions in the Hamiltonian. We conclude that non-collinear magnetism at high temperatures, as observed in CuO, can be explained via pure spin Hamiltonians. We find that the spiral phase is inhomogeneous, and is stabilized by entropic effects. Our study demonstrates that higher order interaction terms are of crucial importance if the stronger interactions together with the lattice geometry contemplate to generate a near degeneracy of magnetic states. The conclusions presented in this work are of particular relevance to the non-collinear magnetism and ferroelectricity observed at high temperatures in cupric oxide.

Biquadratic magnetic interaction in parent ferropnictides

We discuss an effective spin Hamiltonian with biquadratic interaction for ferropnictide superconductors from the point of view of band structure theory and available experimental data. This model is consistent with electronic structure calculations and captures many observed magnetic properties, including the anisotropy of the exchange coupling, thin domain walls, and the crossover from first to second-order phase transition under doping. The parameters of the model are analyzed as a function of the local spin moment using first-principles calculations. Calculations show the biquadratic coupling is negative in stoichiometric KFe2Se2, and the phase diagram is extended into this region. We also consider magnetic short-range order and discuss the limitations of this model in comparison with experiment.

Incommensurability and spin dynamics in the low-temperature phases of Ni3V2O8

Magnetic order and low-energy spin dynamics in the zero field ground state of Ni${}_{3}$V${}_{2}$O${}_{8}$ are revealed in elastic and inelastic neutron scattering experiments. Neutron diffraction shows that below $T=2.3$ K the Ni${}^{2+}$ moments (spin $S=1$) order in a cycloid pattern with incommensurate wave vector ${\mathbit{k}}_{\text{ICM}}=(0,1,\ensuremath{\tau})$, where $\ensuremath{\tau}=0.4030\ifmmode\pm\else\textpm\fi{}0.0004$, which is superimposed on a commensurate antiferromagnetic spin arrangement with ${\mathbit{k}}_{\text{CM}}=(0,0,0)$. Three spin wave modes are discerned below $E\ensuremath{\sim}3$ meV in inelastic measurements and qualitatively described by a model Hamiltonian that involves near neighbor exchange, local anisotropy, and a small biquadratic coupling between the spine and cross-tie sites. Results from both elastic and inelastic scattering experiments suggest that the two sublattices on spine and cross-tie sites are largely decoupled.

Spin-state crossover model for the magnetism of iron pnictides.

We propose a minimal model describing magnetic behavior of Fe-based superconductors. The key ingredient of the model is a dynamical mixing of quasidegenerate spin states of Fe(2+) ion by intersite electron hoppings, resulting in an effective local spin S(eff). The moments S(eff) tend to form singlet pairs and may condense into a spin nematic phase due to the emergent biquadratic exchange couplings. The long-range ordered part m of S(eff) varies widely, 0 ≤ m ≤ S(eff), but magnon spectra are universal and scale with S(eff), resolving the puzzle of large but fluctuating Fe moments. Unusual temperature dependences of a local moment and spin susceptibility are also explained.

Topology and Origin of Effective Spin Meron Pairs in Ferromagnetic Multilayer Elements

We report on pairs of converging-diverging spin vortices in Co/Rh/NiFe trilayer disks. The lateral magnetization distribution of these effective spin merons is directly imaged by means of element-selective x-ray microscopy. By this method, both the divergence and circulation states of the individual layers are identified to be antisymmetric. Reversal measurements on corresponding continuous films reveal that biquadratic interlayer exchange coupling is the cause for the effective meron pair formation. Moreover, their three-dimensional magnetization structure is determined by micromagnetic simulations. Interestingly, the magnetic induction aligns along a flux-closing torus. This toroidal topology enforces a symmetry break, which links the core polarities to the divergence configuration.

Intermixing and Magnetoelectric Coupling in Ferroelectric/Multiferroic Superlattices

We develop a simple model of superlattices consisting of alternate ferroelectric and multiferroic layers with interface intermixing based on the Landau-Ginzburg theory. Multiferroic system is described using a Landau-Ginzburg potential with a positive biquadratic coupling between magnetization and polarization. Intermixing at interfaces forms intermixed layers with electrical properties different from its constituent layers. Effects of intermixing and magnetoelectric coupling on multiferroic phase transitions in the ferroelectric/multiferroic superlattices is calculated and discussed.

Spin dynamics of aJ1-J2-Kmodel for the paramagnetic phase of iron pnictides

We study the finite-temperature spin dynamics of the paramagnetic phase of iron pnictides within an antiferromagnetic ${J}_{1}$-${J}_{2}$ Heisenberg model on a square lattice with a biquadratic coupling $\ensuremath{-}K{({\mathbf{S}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}_{j})}^{2}$ between the nearest-neighbor spins. Our focus is on the paramagnetic phase in the parameter regime of this ${J}_{1}$-${J}_{2}$-$K$ model where the ground state is a $(\ensuremath{\pi},0)$ collinear antiferromagnet. We treat the biquadratic interaction via a Hubbard-Stratonovich decomposition and study the resulting effective quadratic-coupling model using both modified spin wave and Schwinger boson mean-field theories; the results for the spin dynamics derived from the two methods are very similar. We show that the spectral weight of dynamical structure factor $\mathcal{S}(\mathbf{q},\ensuremath{\omega})$ is peaked at ellipses in the momentum space at low excitation energies. With increasing energy, the elliptic features expand towards the zone boundary and gradually split into two parts, forming a pattern around $(\ensuremath{\pi},\ensuremath{\pi})$. Finally, the spectral weight is anisotropic, being larger along the major axis of the ellipse than along its minor axis. These characteristics of the dynamical structure factor are consistent with the recent measurements of the inelastic neutron scattering spectra of BaFe${}_{2}$As${}_{2}$ and SrFe${}_{2}$As${}_{2}$.

Spin excitations in K2Fe4+xSe5: Linear response approach

Using ab initio linear response techniques we calculate spin-wave spectra in K${}_{2}$Fe${}_{4+x}$Se${}_{5}$, and find them to be in excellent agreement with a recent experiment. The spectrum can be described reasonably well by a localized spin Hamiltonian restricted to first and second nearest neighbor couplings. We confirm that exchange coupling between nearest neighbor Fe magnetic moments is strongly anisotropic, and show directly that in the ideal system this anisotropy has an itinerant nature which can be imitated by introducing higher order terms in the effective localized spin Hamiltonian (biquadratic coupling). In the real system, structural relaxation provides an additional source of the exchange anisotropy of approximately the same magnitude. The dependence of spin-wave spectra on the filling of Fe vacancy sites is also discussed.

Doping-induced metallicity and coexistence of magnetic subsystems in [formula omitted

Electronic structure calculations are used to analyze the electronic and magnetic properties in K2Fe4+xSe5. Fe atoms can be divided into two distinct groups. The x=0 (parent) compound forms an insulating, collinear, local moment phase with high Néel temperature. We show that large biquadratic exchange coupling and exchange-elastic interactions stabilize the magnetic order. For x>0 the additional Fe atoms fill vacancy sites. They form impurity bands for small x, which broaden as x increases. They determine the states at the Fermi level and may be viewed as a magnetic subsystem separate from the host. Spin fluctuations are prevalent because magnetic interactions between the ‘defect’ and the ‘parent’ atoms are relatively weak, while chemical fluctuations are prevalent for low x. Fluctuations of either type lead to the formation of a weakly metallic state. The unusual coexistence of the two magnetic subsystems offers a new perspective as to how superconductivity and strong antiferromagnetism can coexist. We argue that spin fluctuations of the impurity subsystem share common features with the Fe-pnictide superconductors.

Anomalous magnetoresistance in Fibonacci multilayers

We theoretically investigated magnetoresistance curves in quasiperiodic magnetic multilayers for two different growth directions, namely, [110] and [100]. We considered identical ferromagnetic layers separated by nonmagnetic layers with two different thicknesses chosen based on the Fibonacci sequence. Using parameters for Fe/Cr multilayers, four terms were included in our description of the magnetic energy: Zeeman, cubic anisotropy, bilinear coupling, and biquadratic coupling. The minimum energy was determined by the gradient method and the equilibrium magnetization directions found were used to calculate magnetoresistance curves. By choosing spacers with a thickness such that biquadratic coupling is stronger than bilinear coupling, unusual behaviors for the magnetoresistance were observed: (i) for the [110] case, there is a different behavior for structures based on even and odd Fibonacci generations, and, more interesting, (ii) for the [100] case, we found magnetic field ranges for which the magnetoresistance increases with magnetic field.