Non-linear spin wave theory results for the frustrated S=\frac {1}{2} Heisenberg antiferromagnet on a body-centered cubic lattice

Abstract

At zero temperature the sublattice magnetization of the quantum spin-1/2 Heisenberg antiferromagnet on a body-centered cubic lattice with competing first and second neighbor exchange (J1 and J2) is investigated using the non-linear spin wave theory. The zero temperature phases of the model consist of a two sublattice Néel phase for small J2 (AF1) and a collinear phase at large J2 (AF2). We show that quartic corrections due to spin-wave interactions enhance the sublattice magnetization in both the AF1 and the AF2 phase. The magnetization corrections are prominent near the classical transition point of the model and in the J2 > J1 regime. The ground state energy with quartic interactions is also calculated. It is found that up to quartic corrections the first order phase transition (previously observed in this model) between the AF1 and the AF2 phase survives.

High-temperature Expansion for Frustrated Magnets: Application to the J1-J2 Model on the BCC Lattice

“…This increase of S Q C with growing J 2 is a precursor of the so-called collinear AFM phase present for J 2 > J c 2 . From previous studies [17,18,19,21] it is known that for T = 0 the critical J c 2 for s = 1/2 is close its classical value J c,clas 2 = 2/3, i.e. the maximum frustration J 2 = 0.5 used in Fig.…”

Ground-state ordering of theJ1−J2model on the simple cubic and body-centered cubic lattices

“…The few investigations of the 3D BCC spin-half J 1 -J 2 model include exact diagonalization (ED) [39], series expansions around the Ising limit [40], spin-wave theory [39,41], and the random phase approximation [42]. Thus, all methods (except ED) start from the symmetrybroken classical antiferromagnetic states and then quantum corrections are subsequently taken into account.…”

Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice

“…This is because the transition point depends only on the coordination number at nearest-neighbor z 1 (= 8) and second-neighbor z 2 (= 6) distances, with the critical (J 2 /|J 1 |) c = z 1 /2z 2 , hence (J 2 /|J 1 |) c = 2/3 [24,25]. For the corresponding S = 1/2 BCC J 1 -J 2 model, all previous studies suggest a single direct phase transition from the FM or Néel state to the stripe ordered state [24,[29][30][31][32][33][34]. Thus, in contrast to the square lattice S = 1/2 J 1 -J 2 Heisenberg model [22,[35][36][37], there is an absence of an intermediate quantum paramagnetic phase, a manifestation of the weakening of quantum fluctuations in 3D.…”

“…J1-Ferromagnetic (0, 0, 0) (π, π, π) PFFRG * 0.56(2) Exact Diagonalization * 0.568 Coupled Cluster Method * 0.579 Rotation-invariant Green's function method [30] 0.68 Random phase approximation [29] 0.6799 J1-Antiferromagnetic (2π, 0, 0) (π, π, π) PFFRG * 0.70(2) Coupled Cluster Method [34] 0.704 Exact Diagonalization [24] 0.7 Non-linear spin-wave theory [32] 0.705 Random phase approximation [33] 0.72 Linked Cluster Series expansions [31] 0.705 (5) TABLE III. The critical value J c 2 /|J1| of the transition between the FM/Néel and the stripe order obtained from PFFRG and compared to different methods for the S = 1/2 J1-J2 Heisenberg model on the BCC lattice with J3 = 0.…”