  Magnetic behavior of the pseudo-binary alloy $Hf_{1-x}Ta_xFe_2$ has been
studied, for which the zero field ferromagnetic (FM) to antiferromagnetic (AFM)
transition temperature is tuned near to T=0 K. These alloys show anomalous
thermomagnetic irreversibility at low temperature due to kinetic arrest of the
first order AFM-FM transition. All the three studied compositions show
re-entrant transition in zero field cooled warming curve and anomalous
non-monotonic variation of upper critical field in isothermal magnetization.
The region in H-T space, where these features of kinetic arrest manifest
themselves, increases with increasing Ta concentration.
