Fig. 6: Magnetodielectric coupling of an ETO:MgO VAN film.

Magnetic field-dependent dielectric constant measured at 3.4 K (a) and 2 K (c). Comparison of the theoretical results with the experimental data of the magnetic field-dependent dielectric constant at 3.4 K (b) and 2 K (d). The open circles represent the experimental data, while the solid lines represent the theoretical results with different parameters. λ is the biquadratic spin–phonon coupling coefficient and α is the corresponding coefficient to scale the strength of the tuning effect of the magnetic field on the lattice parameters.