https://doi.org/10.1140/epjb/e2011-20766-8
Regular Article
Magnetic order in spin-1 and
spin-
interpolating square-triangle Heisenberg antiferromagnets
School of Physics and Astronomy, The University of
Manchester, Schuster
Building, Manchester, M13
9PL, UK
a e-mail: peggyhyli@gmail.com
Received:
17
September
2011
Received in final form:
28
November
2011
Published online:
18
January
2012
Using the coupled cluster method we investigate
spin-sJ1-J'2
Heisenberg
antiferromagnets (HAFs) on an infinite, anisotropic, two-dimensional triangular lattice
for the two cases where the spin quantum number s = 1 and
s = . With
respect to an underlying square-lattice geometry the model has antiferromagnetic
(J1 > 0) bonds between nearest neighbours and
competing (J'2 > 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 J'2 ≡ κJ1
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-
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 =
cases is
analogous to that also observed in our previous work for the
s =
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 =
case it
appears to be weakly first-order in nature (although a second-order transition could not
be ruled out entirely).
Key words: Solid State and Materials
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2012