Interplay between magnetic and vestigial nematic orders in the layered J1-J2 classical Heisenberg model

Abstract

We study the layered J1− J 2 classical Heisenberg model on the square lattice using a self-consistent bond theory. We derive the phase diagram for fixed J1 as a function of temperature T, J2, and interplane coupling Jz. Broad regions of (anti)ferromagnetic and stripe order are found, and are separated by a first-order transition near J2≈ 0.5 (in units of |J1|). Within the stripe phase the magnetic and vestigial nematic transitions occur simultaneously in first-order fashion for strong Jz. For weaker Jz, there is in addition, for J∗ 2 < J 2 < J * * 2 , an intermediate regime of split transitions implying a finite temperature region with nematic order but no long-range stripe magnetic order. In this split regime, the order of the transitions depends sensitively on the deviation from J∗ 2 and J**2, with split second-order transitions predominating for J∗ 2 ≪ J 2 ≪ J * * 2 . We find that the value of J∗ 2 depends weakly on the interplane coupling and is just slightly larger than 0.5 for |Jz|≲ 0.01 . In contrast, the value of J**2 increases quickly from J∗ 2 at |Jz|≲ 0.01 as the interplane coupling is further reduced. In addition, the magnetic correlation length is shown to directly depend on the nematic order parameter and thus exhibits a sharp increase (or jump) upon entering the nematic phase. Our results are broadly consistent with the predictions based on itinerant electron models of the iron-based superconductors in the normal state and, thus, help substantiate a classical spin framework for providing a phenomenological description of their magnetic properties.