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A new method is presented for measuring terms in the elastoresistivity tensor$m_{ij}$ of single crystal samples with tetragonal symmetry. The technique isapplied to a representative underdoped Fe-arsenide,Ba(Fe$_{0.975}$Co$_{0.025}$)$_2$As$_2$, revealing an anomalously large andanisotropic elastoresistance in comparison to simple metals. The $m_{66}$coefficient follows a Curie-Weiss temperature dependence, providing directevidence that the tetragonal-to-orthorhombic structural phase transition thatoccurs at $T_s$ = 97.5 K in this material is not the result of a true-properferro-elastic transition. Rather, the material suffers a pseudo-propertransition for which the lattice strain is not the primary order parameter.

Measurement of the elastoresistivity coefficients of the underdoped iron-arsenide Ba(Fe$_{0.975}$Co$_{0.025}$)$_2$As$_2$