Cr₂O₃ is a magnetoelectric antiferromagnet, and its antiferromagnetic domain state is controllable by the simultaneous application of magnetic and electric fields. In the 2000s, that is, more than 50 years since the discovery of the magnetoelectirc effect in Cr₂O₃, efforts were initiated apply this effect to engineering applications. In this article, we review the recent progress of the magnetoelectric control of the antiferromagnetic domain state and the related phenomena of Cr₂O₃, in particular, in an all-thin film system, an essential step to the application.

  We improve our model calculation for heat-assisted magnetic recording (HAMR) considering the temperature dependence of the attempt frequency. Then, the signal-to-noise ratio dependence on writing field is calculated for various calculation parameters by employing both our model calculation and the conventionally used micromagnetic calculation. The tendencies of the results of our model calculation and of the micromagnetic calculation are almost the same by this improvement. Therefore, our model calculation can be used for HAMR design. The writing process can be described using the temperature dependences of the grain magnetization reversal probability and the attempt number. If the Gilbert damping constant is small, writing is difficult since the attempt number is small. Write-error can be reduced by reducing the linear velocity, and erasure-after-write can be reduced by increasing the thermal gradient and/or the grain column number.