Biquadratic Exchange Interaction Research Articles

Role of biquadratic exchange on thermodynamic quantities in anisotropic Heisenberg model

The magnetic and thermodynamic properties of the spin-1 anisotropic Heisenberg system are studied within Oguchi approximation. The system contains both the bilinear and biquadratic exchange interactions between the nearest neighboring spins located on a centered honeycomb lattice. For the positive biquadratic exchange interaction parameters, the phase transition in the Heisenberg case is of both second and first order where there is a discontinuity in the thermodynamic properties at this transition temperature. For some negative biquadratic exchange interaction parameters, in both the Heisenberg and Ising cases, the ferromagnetic state changes in favor of the antiferromagnetic state. The frustrated antiferromagnetic structure created by the biquadratic exchange parameter with negative sign was shown significantly influence the magnetization, quadrupolar moment, internal energy, heat capacity, entropy and free energy of the system, where the system has an oscillating chaotic phase regime. A double peak behavior was observed in the specific heat, with one at the critical temperature and another at a low temperature.

Electronic excitations and spin interactions in chromium trihalides from embedded many-body wavefunctions

Although chromium trihalides are widely regarded as a promising class of two-dimensional magnets for next-generation devices, an accurate description of their electronic structure and magnetic interactions has proven challenging to achieve. Here, we quantify electronic excitations and spin interactions in CrX3 (X = Cl, Br, I) using embedded many-body wavefunction calculations and fully generalized spin Hamiltonians. We find that the three trihalides feature comparable d-shell excitations, consisting of a high-spin 4A2(t2g3eg0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({t}_{2g}^{3}{e}_{g}^{0})$$\\end{document} ground state lying 1.5–1.7 eV below the first excited state 4T2 (t2g2eg1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${t}_{2g}^{2}{e}_{g}^{1}$$\\end{document}). CrCl3 exhibits a single-ion anisotropy Asia = − 0.02 meV, while the Cr spin-3/2 moments are ferromagnetically coupled through bilinear and biquadratic exchange interactions of J1 = − 0.97 meV and J2 = − 0.05 meV, respectively. The corresponding values for CrBr3 and CrI3 increase to Asia = −0.08 meV and Asia= − 0.12 meV for the single-ion anisotropy, J1 = −1.21 meV, J2 = −0.05 meV and J1 = −1.38 meV, J2 = −0.06 meV for the exchange couplings, respectively. We find that the overall magnetic anisotropy is defined by the interplay between Asia and Adip due to magnetic dipole–dipole interaction that favors in-plane orientation of magnetic moments in ferromagnetic monolayers and bulk layered magnets. The competition between the two contributions sets CrCl3 and CrI3 as the easy-plane (Asia + Adip >0) and easy-axis (Asia + Adip <0) ferromagnets, respectively. The differences between the magnets trace back to the atomic radii of the halogen ligands and the magnitude of spin–orbit coupling. Our findings are in excellent agreement with recent experiments, thus providing reference values for the fundamental interactions in chromium trihalides.

Spin wave resonance frequency in bilayer ferromagnetic films with the biquadratic exchange interaction

Abstract The dependences of spin wave resonance (SWR) frequency on the surface anisotropy field, interface exchange coupling, symmetry, biquadratic exchange (BQE) interaction, film thickness, and the external magnetic field in bilayer ferromagnetic films are theoretically analyzed by employing the linear spin wave approximation and Green’s function method. A remarkable increase of SWR frequency, except for energetically lower two modes, can be obtained in our model that takes the BQE interaction into account. Again, the effect of the external magnetic field on SWR frequency can be increased by increasing the biquadratic to interlayer exchange ratio. It has been identified that the BQE interaction is of utmost importance in improving the SWR frequency of the bilayer ferromagnetic films. In addition, for bilayer ferromagnetic films, the frequency gap between the energetically highest mode and lowest mode is found to increase by increasing the biquadratic to interlayer exchange ratio and film thickness and destroying the symmetry of the system. These results can be used to improve the understanding of magnetic properties in bilayer ferromagnetic films and thus may have prominent implications for future magnetic devices.

Thermal evolution of spin excitations in honeycomb Ising antiferromagnetic FePSe3

We use elastic and inelastic neutron scattering (INS) to study the antiferromagnetic (AF) phase transitions and spin excitations in the two-dimensional (2D) zig-zag antiferromagnet FePSe3. By determining the magnetic order parameter across the AF phase transition, we conclude that the AF phase transition in FePSe3 is first-order in nature. In addition, our INS measurements reveal that the spin waves in the AF ordered state have a large easy-axis magnetic anisotropy gap, consistent with an Ising Hamiltonian, and possible biquadratic magnetic exchange interactions. On warming across TN, we find that dispersive spin excitations associated with three-fold rotational symmetric AF fluctuations change into FM spin fluctuations above TN. These results suggest that the first-order AF phase transition in FePSe3 may arise from the competition between C3 symmetric AF and C1 symmetric FM spin fluctuations around TN, in place of a conventional second-order AF phase transition.

Magnetization process of antiferromagnetic quantum spin chains with the biquadratic exchange interaction

The magnetization processes of the S = 3/2 and S = 2 antiferromagnetic chains with the biquadratic interaction are investigated using the numerical diagonalization of the finite-size cluster. It is found that the system does not exhibit the spin nematic phase, which was predicted to occur for the S = 1 antiferromagnetic chain. Instead, the present analysis reveals that the quantum spin triatic and quatic liquid phases appear below the saturation magnetization for sufficiently large negative biquadratic interaction, for S = 3/2 and S = 2 chains, respectively. In addition it is also found that the magnetization jump up to the saturation magnetization appears for the small negative biquadratic interaction. The phase diagrams with respect to the negative biquadratic interaction and the magnetization are presented for the S = 3/2 and S = 2 antiferromagnetic chains.

Uniaxial Quadrupole Order in a Magnet With Strong Biquadratic Exchange

Abstract—It is shown that in a magnet with a sufficiently strong biquadratic exchange interaction (compared to bilinear exchange) and spin S 1, the temperature transition from a disordered paramagnetic state to the ground ferromagnetic state passes through an intermediate magnetically ordered phase—uniaxial quadrupole ordering. For a magnet with spin S = 3/2, a phase diagram of magnetic states was constructed in the region of large values of the biquadratic exchange and it was studied how the sequence of two phase transitions—“paramagnetic state–quadrupole state” and “quadrupole state–ferromagnetic state”—manifests itself in the temperature behavior of the magnetic heat capacity and the initial magnetic susceptibility.

Uniaxial Quadrupole Order in a Magnet with Strong Biquadratic Exchange

It is shown that the temperature transition from a disordered paramagnetic state to the ground ferromagnetic state in a magnet with sufficiently strong biquadratic exchange interaction (compared to bilinear exchange) and spin S > 1 passes through an intermediate magnetically ordered phase (uniaxial quadrupole ordering). For a magnet with spin S = 3/2, a phase diagram of magnetic states in the region of large values of the biquadratic exchange is constructed in the mean-field approximation and the influence of the sequence of two phase transitions (paramagnetic state−quadrupole state and quadrupole state–ferromagnetic state) on the temperature behavior of the magnetic heat capacity and the initial magnetic susceptibility is investigated.

Spin wave resonance frequency in ferromagnetic thin film with the biquadratic exchange interaction

Spin wave resonance (SWR) frequency in ferromagnetic thin film with the biquadratic exchange interaction, interlayer exchange coupling, film thickness, surface anisotropy field, and the external magnetic field has been investigated by using the linear spin-wave approximation and Green’s function techniques. In comparison to previous studies without considering the biquadratic exchange interaction, the SWR frequency behaviors of the energetically mid-higher modes were found to be highly sensitive to biquadratic exchange interaction. SWR frequencies of all modes are linearly proportional to external magnetic field. However, the SWR frequency has nonlinear dependence on the interlayer exchange coupling and surface anisotropy field. Moreover, the biquadratic exchange interaction enabled a considerable improvement in the effects of surface anisotropy field, interlayer exchange coupling, and external magnetic field on SWR frequency. Our results also reveal that a decrease in the SWR frequency of the corresponding mid-lower modes as the thickness of film is increased while the almost the same frequency gap between the energetically highest mode and lowest mode is obtained for the thicker film. These results could help improve the understanding of magnetic properties and promote magnetic materials applications in spintronic devices.

Bethe-Lattice Structure with Bilinear and Biquadratic Exchange Interactions: A Monte Carlo Study

Bethe-Lattice Structure with Bilinear and Biquadratic Exchange Interactions: A Monte Carlo Study

Reduced basis surrogates for quantum spin systems based on tensor networks.

Within the reduced basis methods approach, an effective low-dimensional subspace of a quantum many-body Hilbert space is constructed in order to investigate, e.g., the ground-state phase diagram. The basis of this subspace is built from solutions of snapshots, i.e., ground states corresponding to particular and well-chosen parameter values. Here, we show how a greedy strategy to assemble the reduced basis and thus to select the parameter points can be implemented based on matrix-product-state calculations. Once the reduced basis has been obtained, observables required for the computation of phase diagrams can be computed with a computational complexity independent of the underlying Hilbert space for any parameter value. We illustrate the efficiency and accuracy of this approach for different one-dimensional quantum spin-1 models, including anisotropic as well as biquadratic exchange interactions, leading to rich quantum phase diagrams.

Manifestation of spin nematic ordering in the spin-1 chain system

Spin-1 chain material is considered. Recently, it was predicted that the spin nematic ordered phase can be realized due to the spin-elastic coupling. In this study we show that the appearance of the spin nematic ordering and phase transitions to such ordered states can be studied using magneto-acoustic experiments. One can observe such phases and phase transitions considering relative changes of the velocity of sound (related to the changes of the elastic modulus of the crystal) as a function of temperature and the external magnetic field. It is shown that those relative changes are proportional to the spin quadrupole susceptibility of the system. The results are obtained using the exact Bethe ansatz solution and Quantum Monte Carlo simulations for several typical values of the biquadratic spin-spin exchange interaction and for various values of the spin-elastic coupling and elastic modules.

Effect of large single-ion anisotropy on the dynamic and static properties of a non-heisenberg ferrimagnet

The influence of a large single-ion anisotropy of the &amp;quot;easy plane&amp;quot; type on the phase states and spectra of elementary excitations of a ferrimagnet with sublattices S = 1 and sigma=1/2 and non-Heisenberg exchange interaction for a sublattice with S = 1 is studied. It is shown that for different ratios of the material parameters of the system, only one phase state is possible, characterized by both vector and tensor order parameters (quadrupole-ferrimagnetic). The condition for sublattice spin compensation is determined, as well as the behavior of the spectra of elementary excitations near the spin compensation line. In the vicinity of the spin compensation line, the magnon spectra are &amp;quot;antiferromagnetically similar&amp;quot;. Keywords: large single-ion anisotropy, biquadratic exchange interaction, ferrimagnet.

Same effect of biquadratic exchange interaction and Heisenberg linear interaction in a spin spiral.

Monolayer (ML) NiCl2 exhibits a strong biquadratic exchange interaction between the first neighboring magnetic atoms (B1), as demonstrated by the spin spiral model in J. Ni et al., Phys. Rev. Lett., 2021, 127, 247204. This interaction is crucial for stabilizing the ferromagnetic collinear order within the ML NiCl2. However, they neither point out the role of B1 nor discuss the dispersion relation from spin orbit coupling (SOC) in the spin spiral. As we have done in this work, these parameters might theoretically potentially be derived directly by fitting the calculated spin spiral dispersion relation. Here, we draw attention to the fact that B1 is equivalent to half of J3 in Heisenberg linear interactions and that the positive B1 partially counteracts the negative J3's impact on the spin spiral to make the ML NiCl2 ferromagnetic. The comparatively small J3 + 1/2B1 from the spin spiral led us to believe that J3 could be substituted by B1, yet it still exists and plays a crucial function in magnetic semiconductors or insulators. The dispersion relation, which we also obtain from SOC, displays weak antiferromagnetic behavior in the spin spiral.

S = 2 Quantum Spin Chain with the Biquadratic Exchange Interaction

The S = 2 quantum spin chain with the single-ion anisotropy D and the biquadratic exchange interaction JBQ is investigated using the numerical diagonalization of finite-size clusters and the level spectroscopy analysis. It is found that the intermediate-D phase corresponding to the symmetry protected topological (SPT) phase appears in a wide region of the ground state phase diagram. We also obtain the phase diagram at the half of the saturation magnetization which includes the SPT plateau phase.

Antiferromagnetic resonances in twinned EuFe2As2 single crystals

In this paper, we report the results of magnetic resonance spectroscopy of ${\mathrm{EuFe}}_{2}{\mathrm{As}}_{2}$ single crystals. We observe magnetic resonance responses, which are attributed to antiferromagnetic resonances of the Eu sublattice with orthorhombic crystal structure and with different orientations of twin domains relative to the external field. We confirm the validity of the recently proposed spin Hamiltonian with anisotropic Eu-Eu exchange interaction and biquadratic Eu-Fe exchange interaction.

Anticollinear order and degeneracy lifting in square lattice antiferromagnet LaSrCrO4

We report the static and dynamic magnetic properties of ${\mathrm{LaSrCrO}}_{4}$, a seemingly canonical spin-3/2 square-lattice antiferromagnet that exhibits frustration between magnetic layers---owing to their AB stacking---and offers a rare testbed to investigate accidental-degeneracy lifting in magnetism. Neutron diffraction experiments on single-crystal samples uncover a remarkable anticollinear magnetic order below ${T}_{N}$ = 170 K characterized by a N\'eel arrangement of the spins within each layer and an orthogonal arrangement between adjacent layers. To understand the origin of this unusual magnetic structure, we analyze the spin-wave excitation spectrum by means of inelastic neutron scattering and bulk measurements. A spectral gap of 0.5 meV, along with a spin-flop transition at 3.2 T, reflect the energy scale associated with the degeneracy-lifting. A minimal model to explain these observations requires both a positive biquadratic interlayer exchange and dipolar interactions, both of which are on the order of 10${}^{\ensuremath{-}4}$ meV, only a few parts per million of the dominant exchange interaction ${J}_{1}\ensuremath{\approx}11$ meV. These results provide direct evidence for the selection of a noncollinear magnetic structure by the combined effect of two distinct degeneracy lifting interactions.

Exact studies of the ground-state properties of the anisotropic Heisenberg dimer with spin [formula omitted

The extended Heisenberg Hamiltonian for the atomic dimer with spin S=1 is diagonalized exactly. The anisotropy of the exchange interaction, single-ion anisotropy and the biquadratic exchange interaction are taken into account. It has been assumed that the external magnetic field can be heterogeneous and different on both atoms of the dimer. Based on the rigorous analytical solutions, the ground state properties of the dimer are studied numerically in a wide range of Hamiltonian parameters. In particular, the energy spectrum, biquadratic moment, residual entropy, ground-state phase diagrams and magnetization curves are calculated. The results are presented in the figures and discussed.

Dome-shaped phase diagram in the spin-1 XY ferromagnet with biquadratic exchange and longitudinal easy-axis crystal field

We investigate the phase diagram of a spin-1 ferromagnetic XY model in the presence of a longitudinal easy-axis crystal field assuming bilinear (J) and biquadratic (I) exchange interactions between nearest neighbors spins and using the two-time Green Functions framework at the level of the Devlin strategy. Employing both analytical estimates and numerical calculations, we find that the structure of the crystal-field-induced phase boundary changes sensibly as the ratio alpha = I/J increases. In particular, when alpha overcomes a characteristic value alpha ^*, two quantum critical points appear which are connected by a dome-shaped critical line. Due to the paradigmatic nature of the anisotropic spin model here considered, we believe that our findings may provide useful insights into the physical origin of recent experimental results found for some innovative materials which exhibit two quantum critical points and dome-shaped phase diagrams induced by non-thermal control parameters driving a non-conventional quantum criticality.Graphic abstract

Non-Heisenberg ferrimagnet with single-ion anisotropy

We have investigated the effect of single-ion anisotropy of the &amp;quot;easy plane&amp;quot; type on the phase states of a ferrimagnet with S=1 and sigma=1/2 sublattices and non-Heisenberg (bilinear and biquadratic in spins) exchange interaction for the sublattice with S=1. It is shown that taking into account both the non-Heisenberg exchange interaction and the single-ion anisotropy of the sublattice with S=1 leads to the realization of a phase with vector order parameters (ferrimagnetic phase) and a phase characterized by both vector and tensor order parameters (quadrupole-ferrimagnetic). It is shown that taking into account single-ion anisotropy changes the type of phase transition in comparison with an isotropic non-Heisenberg ferrimagnet. A phase diagram is constructed, and the condition for the compensation of the sublattice spins is determined. Keywords: ferrimagnet, biquadratic exchange interaction, single-ion anisotropy &amp;quot;easy plane&amp;quot;, quadrupole-ferrimagnetic phase, phase transition.

Spin-hedgehog-derived electromagnetic effects in itinerant magnets.

In itinerant magnets, the indirect exchange coupling of Ruderman-Kittel-Kasuya-Yosida type is known to stabilize incommensurate spin spirals, whereas an account of higher order spin interactions favors the formation of a noncoplanar magnetic texture. This is manifested by the finite Berry phase the conduction electrons accumulate when their spins follow this texture, leading thus to the topological Hall effect. We herein utilize the effective spin model with bilinear-biquadratic exchange interactions for studying the formation of the magnetic hedgehog lattice, that represents a periodic array of magnetic anti- and monopoles and has been recently observed in the B20-type compounds, in a three-dimensional itinerant magnet. As opposed to widely used Monte Carlo simulations, we employ a neural-network-based approach for exploring the ground state spin configuration in a noncentrosymmetric crystal structure. Further, we address the topological Hall conductivity, associated with nonzero scalar spin chirality, in the itinerant magnet due to the coupling to the spin hedgehog lattice, and provide the evidence of a magneto-optic Kerr effect.