TY - JOUR
T1 - Magnetic order in spin-1 and spin-3/2 interpolating square-triangle Heisenberg antiferromagnets
AU - Li, P. H Y
AU - Bishop, R. F.
PY - 2012
Y1 - 2012
N2 - Using the coupled cluster method we investigate spin-s J1-J2' Heisenberg antiferromagnets (HAFs) on an infinite, anisotropic, two-dimensional triangular lattice for the two cases where the spin quantum number s = 1 and s = 3/2 . With respect to an underlying square-lattice geometry the model has antiferromagnetic (J1 > 0) bonds between nearest neighbours and competing (J2' > 0) bonds between next-nearest neighbours across only one of the diagonals of each square plaquette, the same diagonal in each square. In a topologically equivalent triangular-lattice geometry, the model has two types of nearest-neighbour bonds: namely the J2' ≡ κ J1 bonds along parallel chains and the J1 bonds producing an interchain coupling. The model thus interpolates between an isotropic HAF on the square lattice at one limit (κ = 0) and a set of decoupled chains at the other limit (κ → ∞), with the isotropic HAF on the triangular lattice in between at κ = 1. For both the spin-1 model and the spin- 3/2 model we find a second-order type of quantum phase transition at κc = 0.615 ± 0.010 and κc = 0.575 ± 0.005 respectively, between a Néel antiferromagnetic state and a helically ordered state. In both cases the ground-state energy E and its first derivative dE/dκ are continuous at κ = κc, while the order parameter for the transition (viz., the average ground-state on-site magnetization) does not go to zero there on either side of the transition. The phase transition at κ = κc between the Néel antiferromagnetic phase and the helical phase for both the s = 1 and s = 3/2 cases is analogous to that also observed in our previous work for the s = 1/2 case at a value κc = 0.80 ± 0.01. However, for the higher spin values the transition appears to be of continuous (second-order) type, exactly as in the classical case, whereas for the s = 1/2 case it appears to be weakly first-order in nature (although a second-order transition could not be ruled out entirely).
AB - Using the coupled cluster method we investigate spin-s J1-J2' Heisenberg antiferromagnets (HAFs) on an infinite, anisotropic, two-dimensional triangular lattice for the two cases where the spin quantum number s = 1 and s = 3/2 . With respect to an underlying square-lattice geometry the model has antiferromagnetic (J1 > 0) bonds between nearest neighbours and competing (J2' > 0) bonds between next-nearest neighbours across only one of the diagonals of each square plaquette, the same diagonal in each square. In a topologically equivalent triangular-lattice geometry, the model has two types of nearest-neighbour bonds: namely the J2' ≡ κ J1 bonds along parallel chains and the J1 bonds producing an interchain coupling. The model thus interpolates between an isotropic HAF on the square lattice at one limit (κ = 0) and a set of decoupled chains at the other limit (κ → ∞), with the isotropic HAF on the triangular lattice in between at κ = 1. For both the spin-1 model and the spin- 3/2 model we find a second-order type of quantum phase transition at κc = 0.615 ± 0.010 and κc = 0.575 ± 0.005 respectively, between a Néel antiferromagnetic state and a helically ordered state. In both cases the ground-state energy E and its first derivative dE/dκ are continuous at κ = κc, while the order parameter for the transition (viz., the average ground-state on-site magnetization) does not go to zero there on either side of the transition. The phase transition at κ = κc between the Néel antiferromagnetic phase and the helical phase for both the s = 1 and s = 3/2 cases is analogous to that also observed in our previous work for the s = 1/2 case at a value κc = 0.80 ± 0.01. However, for the higher spin values the transition appears to be of continuous (second-order) type, exactly as in the classical case, whereas for the s = 1/2 case it appears to be weakly first-order in nature (although a second-order transition could not be ruled out entirely).
KW - Solid State and Materials
U2 - 10.1140/epjb/e2011-20766-8
DO - 10.1140/epjb/e2011-20766-8
M3 - Article
SN - 1434-6036
VL - 85
JO - European Physical Journal B
JF - European Physical Journal B
M1 - 25 (15pp)
ER -