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

Abstract

We investigate the spin S = 1/2 Heisenberg model on the body centered cubic lattice in the presence of ferromagnetic and antiferromagnetic nearest-neighbor J1, second-neighbor J2, and third-neighbor J3 exchange interactions. The classical ground state phase diagram obtained by a Luttinger-Tisza analysis is shown to host six different (noncollinear) helimagnetic orders in addition to ferromagnetic, Néel, stripe and planar antiferromagnetic orders. Employing the pseudofermion functional renormalization group (PFFRG) method for quantum spins (S = 1/2) we find an extended nonmagnetic region, and significant shifts to the classical phase boundaries and helimagnetic pitch vectors caused by quantum fluctuations while no new long-range dipolar magnetic orders are stabilized. The nonmagnetic phase is found to disappear for S = 1. We calculate the magnetic ordering temperatures from PFFRG and quantum Monte Carlo methods, and make comparisons to available data. arXiv:1902.01179v1 [cond-mat.str-el]

Size- and temperature-dependent magnetization of iron nanoclusters

“…These fluctuations may result in values of J (r i j ) (see parametrization of J (r i j ) in Ref. [37]), that could drive the systems into an antiferromagnetic phase for the smallest clusters at 600 K, as it is shown in Ghosh et al [82].…”

“…14 for T = 600 K, show that there are non-negligible fluctuations on the first and second-neighbor separation distance as the size of the system is reduced. These fluctuations may result in values of J(r ij ) (see parametrization of J(r ij ) in [37]), that could drive the systems into an antiferromagnetic phase for the smallest clusters at 600 K, as it is shown in Ghosh et al [79].…”

“…This is because solving the Heisenberg model in 3D is not trivial, even for periodic boundary conditions. Recent work shows the "phase diagram" for different values of J at first, sec- ond and third nearest neighbors (J 1 , J 2 , J 3 ) [79]. The frontier for the (π, π, π) antiferromagnetic phase appears at J 2 /J 1 = 2/3 ∼ 0.67.…”

Degenerate manifolds, helimagnets, and multi-$\mathbf{Q}$ chiral phases in the classical Heisenberg antiferromagnet on the face-centered-cubic lattice

“…In particular, the triple points and phase boundaries which are host to a subextensively degenerate manifold of ground states would provide for a promising route towards potentially realizing classical as well as quantum (for S = 1/2, 1) spin liquids on a three-dimensional lattice, in the scenario when order-by-disorder fails to lift the degeneracy as is known to occur for the pyrochlore [40][41][42] and hyper-hyperkagome lattices [61]. The triple points occurring in the J 1 -J 2 -J 3 Heisenberg model on the simple cubic and body-centered-cubic lattices are known to give way to a quantum paramagnetic phase for S = 1/2 [62][63][64][65]. Given the fact that three of the degenerate manifolds involve a ferromagnetic phase implies that in the scenario that long-range dipolar magnetic orders are absent, multipole orders such as quadrupolar [66][67][68][69][70][71][72][73][74][75][76], and octupolar [37] orders could be stabilized in both classical and quantum models.…”

Frustrated Quantum Spins at finite Temperature: Pseudo-Majorana functional RG approach

“…Within the last decade the PFFRG has been successfully applied to a wide range of spin systems [22, and has constantly been extended and generalized. Today, the PFFRG is, hence, remarkably flexible with a scope of applicability comprising two [22, 24-35, 37, 38, 40, 41, 44-46, 48, 49, 51, 54, 55, 57, 59-61, 63] and three dimensional [36,39,42,43,47,50,52,53,55,56,58,62] quantum spin systems on arbitrary lattices, including complex frustrated and longer-range coupled networks [48,49] with general isotropic or anisotropic [54] two-body spin interactions. Further recent developments concern the generalization to arbitrary spin magnitudes S [41] or higher spin symmetry groups SU (N ) [44,45,60] and, on a more technical level, the implementation of multi-loop schemes [46,62,63].…”