Magnetic Field Induced Ordering in Quasi-One-Dimensional Quantum Magnets

Three-dimensional magnetic ordering transitions are studied theoretically in strongly anisotropic quantum magnets. An external magnetic field can drive quasi-one-dimensional subsystems with a spin gap into a gapless regime, thus inducing long-range three-dimensional magnetic ordering due to weak residual magnetic coupling between the subsystems. Compounds with higher spin degrees of freedom, such as N-leg spin-1/2 ladders, are shown to have cascades of ordering transitions. At high magnetic fields, zero-point fluctuations within the quasi-1D subsystems are suppressed, causing quantum corrections to the ordering temperature to be reduced. Compounds with strongly anisotropic crystal structures typically exhibit low-dimensional behavior at high temperatures. At low temperatures, the specific nature of their quantum fluctuations determines whether three-dimensional (3D) ordering [1] or other instabilities [2] occur, or whether there is no transition at all [3]. In particular, weakly coupled Heisenberg spin-1/2 chains are known to have a 3D magnetic ordering transition [1] or a spin-Peierls (SP) instability at low temperatures [2], if there is sufficiently strong coupling with low-lying phonon modes. On the other hand, compounds with an intrinsic spin gap, like e.g. weakly coupled integer-spin chains [4] or even-leg spin-1/2 Heisenberg ladders in a spin-liquid state, retain their one-dimensionality down to zero temperature [5]. The pure RVB nature of their 1 groundstate renders them inert to weak residual magnetic couplings between the quasi-1D subsystems. Thus 3D magnetic ordering and SP transitions are suppressed. In this second class of materials, an applied magnetic field, h, can decrease the singlettriplet excitation gap of the quasi-1D subsystem, and eventually drive it into a gapless regime if the field exceeds a critical strength, hc1. A transition to a low-temperature ordered phase due to residual magnetic couplings becomes again possible in this partially polarized regime [6,7]. In this paper, we propose that 3D ordering as a result of the deconfinement of pairs of bound spinons by an external magnetic field can actually be realized in a wide variety of quasi-1D physical systems, including anisotropic spin chains, ladders, and SP compounds. Furthermore, a unified phenomenology for the magnetic phase diagram of these materials is presented, starting from an analysis of weakly coupled antiferromagnetic Heisenberg spin-1/2 chains (AFHC) with an easy-axis anisotropy. Interestingly, we observe that for compounds such as N-leg spin ladders with plateaus in their magnetization curves, m(h), [8] a cascade of N/2 ordering transitions for N even and (N+1)/2 transitions for N odd occurs at high magnetic fields. We are especially interested in the application of this magnetic field induced ordering transition to the material Cu2(C2H12N2)2Cl4 (CuHpCl) [9]. Typically, the spin gap in most of the ladder compounds known to date is too large to be overcome by presently available magnetic fields. However, this particular material has only a small spin gap of ≈ 10.5 Kelvin which makes the interesting gapless regime experimentally accessible. It has recently been pointed out that CuHpCl may better be modeled by an ensemble of weakly coupled dimers than as an antiferromagnetic 2-leg ladder [10]. Whatever the precise magnetic structure may turn out to be, a magnetic field induced ordering transition can occur in all quasi-1D spin systems with a singlet-triplet excitation gap, including Ising-like chains, spin-Peierls chains, and ensembles of spin dimers. Other possible candidate materials with (relatively small) spin gaps include KCuCl3 [11], CuGeO3 [2], α ′ −NaV2O5 [12], and the homologous series of cuprates Srn−1Cun+1O2n [5]. Let us first consider a crystal of weakly coupled anisotropic antiferromagnetic spin-1/2 2