Pressure-Induced Mixed States Caused by Spin-Elastic Interactions during First-Order Spin Phase Transition in Spin Crossover Compounds.

Recently, the possibility of exploiting the phenomenon of spin transition (ST) has been intensively investigated; therefore, it is particularly important to study the behavior of ST under various stimuli. Here, the shape and content of the intermediate phase of ST in Hoffmann-like compounds [Fe(Fpz)2M(CN)4] (M = Pt, Pd) under external stimuli are studied. For this purpose, magnetic and Raman spectroscopy studies were carried out. In pressure-induced spin transition (PIST), a mixture of high-spin and low-spin states appears, while in temperature-induced spin transition (TIST), a homogeneous state occurs. The first-order ST induced by pressure has a hysteresis but is not abrupt. However, the temperature-induced spin transition at ambient pressure is hysteretic and abrupt. To investigate this difference, we discuss using a thermodynamic model that considers elastic interactions, showing that the slope of the hysteresis loop is related to the appearance of internal pressure, which is related to the difference in sample compressibility under high-spin and low-spin states.

Renormalization of the critical exponent for the shear modulus of magnetoactive elastomers.

It is shown that the critical exponent for the effective shear modulus of a composite medium where a compliant polymer matrix is filled with ferromagnetic particles may significantly depend on the external magnetic field. The physical consequence of this dependence is the critical behavior of the relative magnetorheological effect.

Effect of single-particle magnetostriction on the shear modulus of compliant magnetoactive elastomers.

The influence of an external magnetic field on the static shear strain and the effective shear modulus of a magnetoactive elastomer (MAE) is studied theoretically in the framework of a recently introduced approach to the single-particle magnetostriction mechanism [V. M. Kalita et al., Phys. Rev. E 93, 062503 (2016)10.1103/PhysRevE.93.062503]. The planar problem of magnetostriction in an MAE with magnetically soft inclusions in the form of a thin disk (platelet) having the magnetic anisotropy in the plane of this disk is solved analytically. An external magnetic field acts with torques on magnetic filler particles, creates mechanical stresses in the vicinity of inclusions, induces shear strain, and increases the effective shear modulus of these composite materials. It is shown that the largest effect of the magnetic field on the effective shear modulus should be expected in MAEs with soft elastomer matrices, where the shear modulus of the matrix is less than the magnetic anisotropy constant of inclusions. It is derived that the effective shear modulus is nonlinearly dependent on the external magnetic field and approaches the saturation value in magnetic fields exceeding the field of particle anisotropy. It is shown that model calculations of the effective shear modulus correspond to a phenomenological definition of effective elastic moduli and magnetoelastic coupling constants. The obtained theoretical results compare well with known experimental data. Determination of effective elastic coefficients in MAEs and their dependence on magnetic field is discussed. The concentration dependence of the effective shear modulus at higher filler concentrations has been estimated using the method of Padé approximants, which predicts that both the absolute and relative changes of the magnetic-field-dependent effective shear modulus will significantly increase with the growing concentration of filler particles.

Single-particle mechanism of magnetostriction in magnetoactive elastomers.

Magnetoactive elastomers (MAEs) are composite materials comprised of micrometer-sized ferromagnetic particles in a nonmagnetic elastomer matrix. A single-particle mechanism of magnetostriction in MAEs, assuming the rotation of a soft magnetic, mechanically rigid particle with uniaxial magnetic anisotropy in magnetic fields is identified and considered theoretically within the framework of an alternative model. In this mechanism, the total magnetic anisotropy energy of the filling particles in the matrix is the sum over single particles. Matrix displacements in the vicinity of the particle and the resulting direction of the magnetization vector are calculated. The effect of matrix deformation is pronounced well if the magnetic anisotropy coefficient K is much larger than the shear modulus µ of the elastic matrix. The feasibility of the proposed magnetostriction mechanism in soft magnetoactive elastomers and gels is elucidated. The magnetic-field-induced internal stresses in the matrix lead to effects of magnetodeformation and may increase the elastic moduli of these composite materials.