  We report on a theoretical study on the tunneling anomalous Hall effect
(TAHE) in a ferroelectric tunnel junction (FTJ), resulting from spin-orbit
coupling (SOC) in the ferroelectric barrier. For ferroelectric barriers with
large SOC, such as orthorhombic HfO2 and BiInO3, we predict values of the
tunneling anomalous Hall conductivity (TAHC) measurable experimentally. We
demonstrate strong anisotropy in TAHC depending on the type of SOC. For the SOC
with equal Rashba and Dresselhaus parameters, we predict the perfect anisotropy
with zero TAHC for certain magnetization orientations. The TAHC changes sign
with ferroelectric polarization reversal providing a new functionality of FTJs.
Conversely, measuring the TAHC as a function of magnetization orientation
offers an efficient way to quantify the type of SOC in the insulating barrier.
Our results provide a new insight into the TAHE and open avenues for potential
device applications.
