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

Concentration dependence in kinetic arrest of first order magnetic transition in Ta doped $HfFe_2$