Tunnel magnetodielectric effect: Theory and experiment

The recently discovered tunnel magnetodielectric (TMD) effect - the magnetic field-induced increase in the dielectric permittivity (ϵ′) of nanogranular composites caused by the spin-dependent quantum mechanical charge tunneling - is of interest for both the scientific value that combines the fields of magnetoelectric and spintronics and multifunctional device applications. However, little is known about how large the maximum dielectric change Δϵ′/ϵ′ can achieve and why the Δϵ′/ϵ′ variations obey the dependence of square of normalized magnetization (m2), which are critically important for searching and designing materials with higher Δϵ′/ϵ′. Here, we perform approximate theoretical derivation and reveal that the maximum Δϵ′/ϵ′ can be estimated using intrinsic tunneling spin polarization (PT) and extrinsic normalized magnetization (m), that is, Δϵ′/ϵ′ = 2PT2m2. This formulation allows predicting over 200% of theoretical limit for m = 1 and accounts for the observed m2 dependence of Δϵ′/ϵ′ for a given PT. We experimentally demonstrate that x-dependence of Δϵ′/ϵ′ in (CoxFe100-x)-MgF2 films is phenomenologically consistent with this formulation. This work is pivotal to the design of ultra-highly tunable magnetoelectric applications of the TMD effect at room temperature.