Minimum energy for electric-field reversal of magnetization
In plain words
A magnetoelectric memory bit would compete with transistors only if an electric field can flip its magnetization with very little energy. How small that energy can be in principle, given that the bit must stay stable against heat, is not known.
Precise statement
For a single-domain magnetoelectric element of volume $V$ that must remain thermally stable (anisotropy energy $K_u V \ge 40 k_B T$ at $T = 300\,\mathrm{K}$), derive a lower bound $W_{\min}$ on the energy supplied by the electric field to reverse the magnetization deterministically, in terms of the spontaneous polarization $P_s$, coercive field $E_c$, magnetoelectric coupling and $V$, and determine whether $W_{\min}$ can lie below about $10^{-11}\,\mathrm{erg}$ with a bias below about $3 \times 10^{-4}\,\mathrm{statvolt}$. An answer is the bound with its derivation and the material parameters that reach it.
What would settle it
A thermodynamic derivation of $W_{min}$ checked against measured switching energies in scaled magnetoelectric stacks.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
A target of about $10^{-11}$ erg per bit at about $3 \times 10^{-4}$ statvolt was set for magnetoelectric spin-orbit logic (Manipatruni et al., Nature 2019).
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