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Nearly a century of research has established the Born–Oppenheimer approximation as a cornerstone of condensed-matter systems, stating that the motion of the atomic nuclei and electrons may be treated separately. Interactions beyond the Born–Oppenheimer approximation are at the heart of magneto-elastic functionalities and instabilities. We report comprehensive neutron spectroscopy and ab initio phonon calculations of the coupling between phonons, CEF-split localized 4 f electron states, and conduction electrons in the paramagnetic regime of C e A u A l 3 , an archetypal Kondo lattice compound. We identify two distinct magneto-elastic hybrid excitations that form even though all coupling constants are small. First, we find a CEF–phonon bound state reminiscent of the vibronic bound state (VBS) observed in other materials. However, in contrast to an abundance of optical phonons, so far believed to be essential for a VBS, the VBS in C e A u A l 3 arises from a comparatively low density of states of acoustic phonons. Second, we find a pronounced anticrossing of the CEF excitations with acoustic phonons at zero magnetic field not observed before. Remarkably, both magneto-elastic excitations are well developed despite considerable damping of the CEFs that arises dominantly by the conduction electrons. Taking together the weak coupling with the simultaneous existence of a distinct VBS and anticrossing in the same material in the presence of damping suggests strongly that similarly well-developed magneto-elastic hybrid excitations must be abundant in a wide range of materials. In turn, our study of the excitation spectra of C e A u A l 3 identifies a tractable point of reference in the search for magneto-elastic functionalities and instabilities.

SignificanceUnderstanding the relationship between entangled degrees of freedom (DOF) is a central problem in correlated materials and the possibility to influence their balance is promising toward realizing novel functionalities. In Sr2IrO4, the interaction between spin–orbit coupling and electron correlations induces an exotic ground state with magnetotransport properties promising for antiferromagnetic spintronics applications. Moreover, the coupling between orbital and spin DOF renders the magnetic structure sensitive to the Ir–O bond environment. To date, a detailed understanding of the microscopic spin-lattice and electron–phonon interactions is still lacking. Here, we use strain engineering to perturb the local lattice environment and, by tracking the response of the low-energy elementary excitations, we unveil the response of the microscopic spin and charge interactions. In the high spin–orbit-coupled Sr2IrO4, the high sensitivity of the ground state to the details of the local lattice structure shows a large potential for the manipulation of the functional properties by inducing local lattice distortions. We use epitaxial strain to modify the Ir–O bond geometry in Sr2IrO4 and perform momentum-dependent resonant inelastic X-ray scattering (RIXS) at the metal and at the ligand sites to unveil the response of the low-energy elementary excitations. We observe that the pseudospin-wave dispersion for tensile-strained Sr2IrO4 films displays large softening along the [h,0] direction, while along the [h,h] direction it shows hardening. This evolution reveals a renormalization of the magnetic interactions caused by a strain-driven cross-over from anisotropic to isotropic interactions between the magnetic moments. Moreover, we detect dispersive electron–hole pair excitations which shift to lower (higher) energies upon compressive (tensile) strain, manifesting a reduction (increase) in the size of the charge gap. This behavior shows an intimate coupling between charge excitations and lattice distortions in Sr2IrO4, originating from the modified hopping elements between the t2g orbitals. Our work highlights the central role played by the lattice degrees of freedom in determining both the pseudospin and charge excitations of Sr2IrO4 and provides valuable information toward the control of the ground state of complex oxides in the presence of high spin–orbit coupling.

Fe-based amorphous and nanocrystalline alloys, such as FINEMET and its improved variants, are highly valued as green energy-saving materials due to their unique magnetic properties, including high permeability, low coercivity, and near-zero saturation magnetostriction. These characteristics have enabled their extensive use in power electronics and information technology. However, the full potential of these alloys remains unfulfilled due to insufficient understanding of their stress sensitivity. This study focuses on the development history, heat treatment, annealing processes, chemical composition, and underlying mechanisms of Fe-based amorphous and nanocrystalline alloys, aiming to provide insights into stress-induced magnetic anisotropy and guide the development of greener and more efficient soft magnetic materials.

This paper presents analytical solutions for full-field radiation in magnetoelectric (ME) antennas, considering a fully magneto-elastic coupled constitutive relation. A nonlinear converse ME coupling model is established, incorporating mechanical, electric, and magnetic variables with generalized Maxwell equations. This model emphasizes the essence of ME antennas, where radiation is achieved through strain/stress-mediated coupling between different phases. The magnetic flux density and electric displacement obtained from the model are used as sources to solve the full-field radiations of ME antennas. The proposed model is validated through existing experiments and simulations, demonstrating that the radiation performance of ME antennas is strongly influenced by nonlinear magneto-elastic coupling. The material parameters and magnetic bias significantly impact the magnetic flux density and far-field radiation due to the nonlinear magnetization process. The study reveals the mechanisms behind enhanced working bandwidth and frequency tuning by examining the frequency response of the radiation impedance with material parameters. By adjusting the initial magnetization rate, saturation magnetostriction, and saturation magnetization, the radiation efficiency/gain can be increased by 340%, 108%, and 112% respectively. This model enhances our understanding of the full-field radiation of ME antennas and provides a foundation for designing tunable ME antennas.

This paper presents an analytical model for the near-field radiation of acoustically actuated magnetoelectric (ME) antennas considering a fully magneto-elastic coupled magnetostrictive constitutive relation. The nonlinearity of the magnetostrictive phase is introduced into the governing equation of the ME antennas using the equivalent parameter method, resulting in analytical expressions of the near-field radiation. The strain distribution in the ME antenna is calculated first and then extracted as a source for solving the magnetic flux density, energies, average radiated power, and radiation impedance. The predictions for the admittance and impedance show good agreement with simulation and experimental data, respectively. The effects of the external stimuli on the radiation performance are investigated, to theoretically evaluate the ME antennas operated in complex magnetic and stress conditions. The required magnetic bias corresponding to the maximum radiation of the ME antennas is determined, which is changed with the pre-stress. In addition, the radiation power can be improved by tensile stress before the required magnetic bias or by compressive stress after the required magnetic bias. The present model may provide a basis for the evaluation and regulation of acoustically actuated ME antenna.

Co 3 Sn 2 S 2 is a recently identified magnetic Weyl semimetal in Shandite compounds. Upon cooling, Co 3 Sn 2 S 2 undergoes a ferromagnetic transition with c -axis polarized moments (∼0.3 µ B /Co) around T C = 175 K, followed by another magnetic anomaly around T A ≈ 140 K. A large intrinsic anomalous Hall effect is observed in the magnetic state below T C with a maximum of anomalous Hall angle near T A . Here, we report an elastic neutron scattering on the crystalline lattice of Co 3 Sn 2 S 2 in a magnetic field up to 10 T. A strongly anisotropic magnetoelastic response is observed-while only a slight enhancement of the Bragg peaks is observed when B // c . The in-plane magnetic field (B // ab ) dramatically suppresses the Bragg peak intensity probably by tilting the moments and lattice toward the external field direction. The in-plane magnetoelastic response commences from T C , and as it is further strengthened below T A , it becomes nonmonotonic against the field between T A and T C because of the competition from another in-plane magnetic order. These results suggest that a magnetic field can be employed to tune the Co 3 Sn 2 S 2 lattice and its related topological states.

This work shows a three-dimensional (3D) layerwise model for static and free vibration analyses of functionally graded piezomagnetic materials (FGPM) spherical shell structures where magnetic and elastic fields are completely coupled. The 3D magneto-elastic governing equations for spherical shells are made of the three equations of equilibrium in three-dimensional form and the three-dimensional divergence equation for the magnetic induction. Governing equations are written in the orthogonal mixed curvilinear reference system (α, β, z) allowing the analysis of several curved and flat geometries (plates, cylindrical shells and spherical shells) thanks to proper considerations of the radii of curvature. The static cases, actuator and sensor configurations and free vibration investigations are proposed. The resolution method uses the imposition of the Navier’s harmonic forms in the two in-plane directions and the exponential matrix methodology in the transverse normal direction. Single-layered and multilayered simply-supported FGPM structures have been investigated. In order to understand the behavior of FGPM structures, numerical values and trends along the thickness direction for displacements, stresses, magnetic potential, magnetic induction and free vibration modes are proposed. In the results section, a first assessment phase is proposed to demonstrate the validity of the formulation and to fix proper values for the convergence of results. Therefore, a new benchmark section is presented. Different cases are proposed for several material configurations, load boundary conditions and geometries. The possible effects involved in this problem (magneto-elastic coupling and effects related to embedded materials and thickness values of the layers) are discussed in depth for each thickness ratio. The innovative feature proposed in the present paper is the exact 3D study of magneto-elastic coupling effects in FGPM plates and shells for static and free vibration analyses by means of a unique and general formulation.

A continuum micromorphic approach to nematic liquid crystals is exploited in order to describe electro-magneto-elastic coupling effects. Nematic microdeformation is modeled by relating microinertia, electric dipole and quadrupole densities to microrotation. Accordingly, polarization and magnetization are obtained together with a constitutive law for magnetic induction. The coupled system of balance laws for linear and angular momentum and Maxwell’s equations is employed to model equilibrium for an homeotropic structure of a nematic layer subject to electric and magnetic fields, assuming strong anchoring on the layer’s boundaries. It is shown that the trivial solution of null deformation allows for a not uniform magnetic field in the presence of a not null applied electric potential. The magnetic field induced Freedericksz transition is derived obtaining a threshold value of magnetic field which depends on the electric potential. Numerical results show an hysteresis behavior of the deformation solution just behind the threshold field, which is compatible with a first order, magnetic induced transition.

Purpose Due to the increasing amount of high power density high-speed electrical machines, a detailed understanding of the consequences for the machine’s operational behaviour and efficiency is necessary. Magnetic materials are prone to mechanical stress. Therefore, this paper aims to study the relation between the local mechanical stress distribution and magnetic properties such as magnetic flux density and iron losses. Design/methodology/approach In this paper, different approaches for equivalent mechanical stress criteria are analysed with focus on their applicability in electrical machines. Resulting machine characteristics such as magnetic flux density distribution or iron are compared. Findings The study shows a strong influence on the magnetic flux density distribution when considering the magneto-elastic effect for all analysed models. The influence on the iron loss is smaller due to a high amount of stress-independent eddy current loss component. Originality/value The understanding of the influence of mechanical stress on dimensions of electrical machines is important to obtain an accurate machine design. In this paper, the discussion on different equivalent stress approaches allows a new perspective for considering the magneto-elastic effect.

Considering the complex strongly nonlinear coupling characteristic of the magnetostrictive strain and magnetization under the excitation of the bias magnetic field and the pre-stress in the giant magnetostrictive material, this paper adopts the nonlinear magnetostrictive constitutive model and the equivalent circuit method to establish a strongly nonlinear resonant magnetoelectric (ME) effect theoretical model for the ME laminate composites compounding by the giant magnetostrictive material and the piezoelectric material. For the L-T mode magnetostrictive/piezoelectric/magnetostrictive (MPM) ME laminate, the predicted results coincide well with the experiment results of the resonant frequency and the resonant ME field coefficient varying with the external magnetic field when the pre-stress degenerates to zero in our model. The agreement indicates the proposed theoretical model validity. On the basis, we use the theoretical model to forecast the varying characteristic of the resonant ME field coefficient and the resonant frequency effect under the influence of the different bias magnetic field and the pre-stress in ME laminate composites. And we also predict that the resonant ME coefficient and the resonant frequency appear \"reversal\" with the pre-stress increasing. After that, the influence of the different volume ratio on the ME effect and resonant frequency is analyzed. Particularly, a resonant frequency value not influenced by the volume ratio with increasing bias magnetic or pre-stress occurs. This research can provide theory basis for improving the resonant ME conversion performance and for controlling the resonant frequency under the excitation of the bias conditions (i.e. the bias magnetic field and the pre-stress) for the ME devices (i.e. sensor, transducer, microwave device and so on).