  We analyze the biquadratic bilinear Heisenberg magnet on a honeycomb lattice
via Schwinger boson formalism. Due to their vulnerability to quantum
fluctuations, non conventional lattices (kagome, triangular and honeycomb for
example) have been cited as candidates to support spin liquid states. Such
states without long range order at zero temperature are known in
one-dimensional spin models but their existence in higher dimensional systems
is still under debate. Biquadratic interaction is responsible for various
possibilities and phases as it is well-founded for one-dimensional systems.
Here we have used a bosonic representation to study the properties at zero and
finite low temperatures of the biquadratic term in the two-dimensional
hexagonal honeycomb lattice. The results show a ordered state at zero
temperature but much more fragile than that of a square lattice; the behavior
at finite low temperatures is in accordance with expectations.
