Giant anisotropic magnetostriction in Pr$_{0.5}$Sr$_{0.5}$MnO$_3$

Magnetic, linear thermal expansion (LTE), anisotropic ($\lambda_t$) and volume ($\omega $) magnetostriction properties of Pr$_{0.5}$Sr$_{0.5}$MnO$_3$ were investigated. The LTE decreases smoothly from 300 K without a clear anomaly either around the Curie (T$_C$ = 270 K) or the Neel temperature (T$_N$ = 100 K) and it exhibits hysteresis over a wide temperature range (60 K-270 K) upon warming. Isothermal magnetization study suggests that 13 % of the ferromagnetic phase coexists with 87 % of the antiferromagnetic phase at 25 K. The parallel and perpendicular magnetostrictions undergo rapid changes during the metamagnetic transition. Contrary to the isotropic giant volume magnetostriction reported in manganites so far, this compound exhibits a giant anisotropic magnetostriction ($\lambda_t \approx 10^{-3}$) and smaller volume ($\omega \approx 10^{-4}$) magnetostrictions below T$_N$. We suggest that the field induced antiferromagnetic to ferromagnetic transition is accompanied by a structural transition from the d$_{x^2-y^2}$ orbital ordered antiferromagnetic (orthorhombic) to the orbital disordered ferromagnetic (tetragonal) phase. The metamagnetic transition proceeds through nucleation and growth of the ferromagnetic domains at the expense of the antiferromagnetic phase. The preferential orientation of the ferromagnetic (tetragonal) domains along the field direction increases the linear dimension of the sample in the field direction and decreases in the orthogonal direction leading to the observed giant anisotropic magnetostriction effect. Our study also suggests that nanodomains of the low temperature antiferromagnetic phase possibly exist in the temperature region T$_N$ < T < T$_C$.