The Geometric Frustration Effects in Nanostructured Magnetic Systems

We numerically investigate the geometric frustration effects in finite ring-shaped antiferromagnetic S = 1/2 Heisenberg model,, with an odd number spins in a ring. It is shown that., in a single ring, the lattices always display heterogeneous distortions for an arbitrarily large spring constant. However for any nonzero antiferromagnetic interring coupling in a finite two-leg spin ladder structure, a second order magnetoelastic transition (not the thermodynamic transition) takes place from the heterogeneous lattice distortion phase to the uniform phase (without lattice distortion) when the spring constant is increased. For ferromagnetic inter-ring coupling, there exists a critical coupling strength J(perpendicular to)(c) for J(perpendicular to) > J(perpendicular to)(c) first order magnetoelastic transition is present.