The magnetocapacitance and magnetoresistance properties near room temperature of partially disordered double perovskite $\mathrm{L}{\mathrm{a}}_2\mathrm{NiMn}{\mathrm{O}}_6$ are related, at least in part, to coupled ferroelastic and magnetic instabilities that are responsible for a ferromagnetic phase transition near 280 K. A systematic analysis of this coupling from the perspectives of strain and elasticity has revealed a system with biquadratic coupling among three order parameters belonging to irreducible representations of $X_3^{+}, {\mathrm{\Gamma }}_{\text{4}}^{\text{+}}$ and $\text{m}{\mathrm{\Gamma }}_{\text{4}}^{\text{+}}$ of the parent space group $Fm\overline{3}m$. Classical octahedral tilting drives the structural transitions at high temperatures and strong acoustic attenuation through the temperature interval ∼300–500 K, observed by resonant ultrasound spectroscopy from a polycrystalline sample, is consistent with pinning of ferroelastic twin walls by point defects. Below room temperature, stiffening of the shear modulus by up to ∼40% can be understood in terms of biquadratic coupling of the ferromagnetic order parameter with strain. Acoustic attenuation with Debye-like patterns of loss in the temperature interval ∼150–280 K yielded activation energies and relaxation times which match up with AC magnetic and dielectric spectroscopy data reported previously in the literature. The dynamic loss mechanism, perhaps related to hopping of electrons between $\mathrm{N}{\mathrm{i}}^{2+}$ and $\mathrm{M}{\mathrm{n}}^{4+}$, is potentially multiferroic, therefore. In addition to the possibilities for tailoring the intrinsic properties of $\mathrm{L}{\mathrm{a}}_2\mathrm{NiMn}{\mathrm{O}}_6$ by controlling oxygen content, $B$-site order or by choice of substrate for imposing a strain on thin films, it should be possible also to engineer extrinsic properties which would respond to applied electric, magnetic, and stress fields.

• Received 19 March 2019
• Revised 21 May 2019

DOI:https://doi.org/10.1103/PhysRevB.100.014304