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Quantitative relationship between structural orthorhombicity, shear modulus and heat capacity anomaly of the nematic transition in iron-based superconductors

Electronic nematicity in iron pnictide materials has been extensively studied by various experimental techniques, yet its heat capacity anomaly at the phase transition has not been examined quantitatively. In this work we review the thermodynamic description of nematicity in $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$ using the Landau free energy, which defines the behavior of three thermodynamic quantities: the structural orthorhombicity that develops below the nematic transition, the softening shear modulus above the transition, and the discontinuous heat capacity at the transition. We derive a quantitative relationship between these three quantities, which is found to hold for a range of dopings. This result shows that the nematic transition is exceedingly well described by a mean-field model in the underdoped regime of the phase diagram.