Quantum fluctuations in antiferromagnetic spin configurations

We consider fluctuations in magnetic systems around the classically-ordered ground state. We use a Holstein-Primakoff transformation to calculate the zero-point energy fluctuations in antiferromagnetic lattice configurations using the Heisenberg exchange Hamiltonian. We show that these quantum fluctuations lower the classically expected ground state. Furthermore we provide a numerical method to calculate dispersion relations for magnetic systems and specifically show that our analytical results can be produced. Also, we investigate the spin-flop transition in a one dimensional antiferromagnetic system with anisotropy. Our calculations show that the transition occurs at B/K ≈ -14, where B is the external field and K the anisotropy constant. Furthermore, we show that quantum fluctuations decrease the energy of both the antiferromagnetic and the spin-flop state by calculating the dispersion relation. Our results imply a shift of the transition point between the two states. Our results are a first step towards incorporating the effects of quantum fluctuations in inhomogeneous antiferromagnets.