Emergence of novel magnetic order at finite temperature in overdoped pnictides

We examine the temperature dependence of the magnetic ordering in the frustrated Heisenberg $J_1-J_2$ model in presence of two different kind of dopants: vacancies or magnetic impurities. We demonstrate that, irrespective to their magnetic ratio, the introduction of impurities quenches the order by disorder selection mechanism associated with an Ising-like phase transition at low temperatures and gives way to a $90^\circ$ (anticollinear) order . The presence of dopants triggers a non trivial competition between entropically selected states (collinear) and energetically favoured ones (anticollinear) in dependence of both dilution and temperature. While in case of magnetic impurity, the interesting magnetic phases are observed for full range of temperature and doping, in case of nonmagnetic impurities every magnetic order is destroyed at all temperatures above $12\%$ dilution. At fixed low temperature and tuning the doping we show a first order phase transition leading to the re-entrance of the Ising-like order with percolation of islands of $90^\circ$ order. At fixed doping and varying the temperature we observe a transition from the anticollinear to the collinear phase assisted by a new emerging magnetic phase in the presence of magnetic impurities, whilst in case of vacancies this transition is characterised by a coexistent region of both. Furthermore, tuning the magnetic moment of the impurities, a complete collapse of the Ising-like order is attained. This is in agreement with observations of Ir dopant atoms in superconducting Ba(Fe$_{1-x}$Ir$_x$)$_2$As$_2$ with $x<0.047$.