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arXiv:cond-mat/0402402 · Physical Review B

Criticality of the uniform magnetic order in a ferromagnetic-antiferromagnetic random alternating quantum spin chain

Tota Nakamura

Published Apr 1, 2005• 19 citations
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Abstract

An $S=1∕2$ ferromagnetic (F) and antiferromagnetic (AF) random alternating Heisenberg quantum spin chain model is investigated in connection to its realization compound ${(\mathrm{C}{\mathrm{H}}_{3})}_{2}\mathrm{C}\mathrm{H}\mathrm{N}{\mathrm{H}}_{3}\mathrm{Cu}{({\mathrm{Cl}}_{x}{\mathrm{Br}}_{1\ensuremath{-}x})}_{3}$. The exchange interaction bonds consist of alternating strong F-AF random bonds and weak uniform AF bonds. Using the quantum Monte Carlo method we have found that the excitation energy gap closes and the uniform AF order becomes critical in the intermediate-concentration region. This finding explains the experimental observation of the magnetic transition by considering weak interchain interactions. The present results suggest that uniform AF order survives even in the presence of randomly located ferromagnetic bonds. This may be an exotic quantum effect.

DOI
10.1103/physrevb.71.144401

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A possibility of the uniform antiferromagnetic order is pointed out in an S=1/2 ferromagnetic (F) - antiferromagnetic (AF) random alternating Heisenberg quantum spin chain compound: (CH_3)_2 CHNH_3 Cu(Cl_x Br_{1-x})_3. The system possesses the bond alternation of strong random bonds that take +/- 2J and weak uniform AF bonds of -J. In the pure concentration limits, the model reduces to the AF-AF alternation chain at x=0 and to the F-AF alternation chain at x=1. The nonequilibrium relaxation of large-scale quantum Monte Carlo simulations exhibits critical behaviors of the uniform AF order in the intermediate concentration region, which explains the experimental observation of the magnetic phase transition. The present results suggest that the uniform AF order may survive even in the presence of the randomly located ferromagnetic bonds.
The S=1/2 ferromagnetic (F) - antiferromagnetic (AF) random alternating Heisenberg quantum spin chain is investigated by the quantum Monte Carlo method. The randomness is only present on the strong bonds taking values of ±2J randomly, and the weak bonds are uniformly antiferromagnetic with J. The model corresponds to the quasi one-dimensional compound, (CH3)2CHNH3Cu(Clx, Br1-x)3, whose ground state interpolates the Haldane state of the F-AF alternating spin chain at x=1 and the singlet-dimer state of the AF-AF alternating spin chain at x=0. The nonequilibrium relaxation function of the staggered magnetic susceptibility exhibits algebraic divergence in the intermediate region of 0.44 ≪ x ≪ 0.87, which explains the experimental observation of the magnetic phase transition. The results suggest that the antiferromagnetic order becomes critical by the randomness of the bond distributions even in the presence of the rich ferromagnetic bonds.
We study the one-dimensional Heisenberg spin-1∕21∕21∕2 alternating bond chain in which the nearest neighbor exchange couplings are ferromagnetic (FM) and antiferromagnetic (AF) alternatively. By using exact diagonalization and the density matrix renormalization group method, we discuss how the system approaches the AF uniform spin-1 chain under certain conditions. When the ratio of AF to FM coupling strengths, $\ensuremath{\alpha}$ $(\ensuremath{\alpha}={J}_{AF}∕{J}_{F})$, is very small, physical properties of the alternating bond chain such as spin-spin correlation, the string correlation function, and the spin density coincide with those of the AF uniform spin-1 chain. The edge state problem is discussed in the present model with the small $\ensuremath{\alpha}$ limit. In addition, the Haldane gap of the AF uniform spin-1 chain is four times the gap of the system considered.
Bond-dilution effects on the ground state of the square-lattice antiferromagnetic Heisenberg model, consisting of coupled bond-alternating chains, are investigated by means of the quantum Monte Carlo simulation. It is found that, when the ground state of the non-diluted system is a non-magnetic state with a finite spin gap, a sufficiently weak bond dilution induces a disordered state with a mid gap in the original spin gap, and under a further stronger bond dilution an antiferromagnetic long-range order emerges. While the site-dilution-induced long-range order is induced by an infinitesimal concentration of dilution, there exists a finite critical concentration in the case of bond dilution. We argue that this essential difference is due to the occurrence of two types of effective interactions between induced magnetic moments in the case of bond dilution, and that the antiferromagnetic long-range-ordered phase does not appear until the magnitudes of the two interactions become comparable.
At T = 0 and in a sufficiently large field, the nearest-neighbor antiferromagnetic Ising chain undergoes a first-order spin-flop transition into the ferromagnetic phase. We consider its smearing under the random-bond disorder such that all independent random bonds are antiferromagnetic (AF). It is shown that the ground-state thermodynamics of this random AF chain can be described exactly for an arbitrary distribution P(J) of AF bonds. Moreover, the site magnetizations of finite chains can be found analytically in this model. We consider a continuous P(J) that is zero above some −J 1 and behaves near it as (−J 1−J)λ, λ > −1. In this case, the ferromagnetic phase emerges continuously in a field H > H c = 2J 1. At 0 > λ > −1, it has the usual second-order anomalies near H c with the critical indices obeying the scaling relation and depending on λ. At λ > 0, higher-order transitions occur (third, fourth, etc.), marked by a divergence of the corresponding nonlinear susceptibilities. In the chains with an even number of spins, the intermediate “bow-tie” phase with linearly modulated AF order exists between the AF and ferromagnetic phases at J 1 < H < H c . Its origin can be traced to the infinite correlation length of the degenerate AF phase from which it emerges. This implies the existence of similar inhomogeneous phases with size- and form-dependent order in a number of other systems with infinite correlation length. The possibility to observe the signs of the “bow-tie” phase in low-T neutron diffraction experiments is discussed.
The effect of bond randomness on the spin-gapped ground state of the spin-1 bond-alternating antiferromagnetic Heisenberg chain is discussed. By using the loop cluster quantum Monte Carlo method, we investigate the stability of topological order in terms of the recently proposed twist order parameter [M. Nakamura and S. Todo: Phys. Rev. Lett. 89 (2002) 077204]. It is observed that the dimer phases as well as the Haldane phase of the spin-1 Heisenberg chain are robust against a weak randomness, though the valence-bond-solid-like topological order in the latter phase is destroyed by introducing a disorder stronger than the critical value.