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arXiv:cond-mat/0209074 · Journal of the Physical Society of Japan

Magnetization Plateaux in Random FrustratedS=1/2 Heisenberg Chains

Kazuo Hida

Published Apr 15, 2003• 3 citations
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Abstract

The $S=1/2$ frustrated Heisenberg chains with bond alternation is known to exhibit a magnetization plateau at half of the saturation magnetization $\Ms$ accompanied by the spontanuous translational symmetry breakdown. The effect of randomness on the magnetization process of this model is investigated. First we consider the mixture of the two kinds of chains both of which possess the $\Ms/2$-plateau in the common interval of the magnetization field. The plateau at $\Ms/2$ is found to vanish immediately if the randomness is switched on in agreement with Totsuka's prediction. The small plateau also appears near the saturation field due to the localization of inverted spins around the minority bond. On the other hand, if the stronger bond is replaced by the ferromagnetic bonds randomly, the randomness induced fractional plateau appears as in the nonfrustrated case. The plateau at $\Ms/2$ does not simply vanish but shifts and splits into two smaller plateaux. The magnetization on this plateau varies nonlinearly with $1-p$. The physical origin of this behavior is explained based on the strong coupling picture.

DOI
10.1143/jpsj.72.911

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The S=1/2S=1/2S=1/2 frustrated Heisenberg chains with bond alternation is known to exhibit a magnetization plateau at half of the saturation magnetization \Ms\Ms\Ms accompanied by the spontanuous translational symmetry breakdown. The effect of randomness on the magnetization process of this model is investigated. First we consider the mixture of the two kinds of chains both of which possess the \Ms/2\Ms/2\Ms/2-plateau in the common interval of the magnetization field. The plateau at \Ms/2\Ms/2\Ms/2 is found to vanish immediately if the randomness is switched on in agreement with Totsuka's prediction. The small plateau also appears near the saturation field due to the localization of inverted spins around the minority bond. On the other hand, if the stronger bond is replaced by the ferromagnetic bonds randomly, the randomness induced fractional plateau appears as in the nonfrustrated case. The plateau at \Ms/2\Ms/2\Ms/2 does not simply vanish but shifts and splits into two smaller plateaux. The magnetization on this plateau varies nonlinearly with 1−p1-p1−p. The physical origin of this behavior is explained based on the strong coupling picture.
The magnetization plateaux in two dimensionally coupled S=1/2 dimerized zigzag Heisenberg chains are investigated by means of the bond operator mean field approximation. In the absence of the interchain coupling, this model is known to have a plateau at half of the saturation magnetization accompanied by the spontanuous translational symmetry breakdown. The parameter regime in which the plateau appears is reproduced well within the present approximation. In the presence of the interchain coupling, this plateau is shown to be suppressed. This result is also supported by the numerical diagonalization calculation.
The S = 1/2 Heisenberg chains with bond alternation and randomness on the strong bonds are studied by the density matrix renormalization group method. It is assumed that the odd-th bond is antiferromagnetic with strength J and the even-th bond can take the values JA and JF (JA > J > 0 > JF) randomly. The ground state of this model interpolates between the Haldane and dimer phases via a randomness dominated intermediate phase. On the basis of the scaling of the low energy spectrum and mean field treatment of the interchain coupling, we find that the magnetic long range order is induced by randomness in the intermediate regime. In the magnetization curves, there appears a plateau at the fractional value of the saturated magnetization. The fine structures of the magnetization curves and low energy spectrum are understood using the cluster picture. The relation to the recent experiment for (CH3)2CHNH3Cu(ClxBr1-x)3 is discussed.
The S = 1/2 Heisenberg chains with bond alternation and randomness on the strong bonds are studied by the density matrix renormalization group method. It is assumed that the oddth bond is antiferromagnetic with strength J and even-th bond can take the values JA and JF (JA > J > 0 > JF) randomly. The ground state of this model interpolates between the Haldane and dimer phases via a randomness dominated intermediate phase. Based on the scaling of the low energy spectrum and mean field treatment of the interchain coupling, it is found that the magnetic long range order is induced by randomness in the intermediate regime. In the magnetization curves, there appears a plateau at the fractional value of thesaturated magnetization. The fine structures of the magnetization curves and low energy spectrum are understood based on the cluster picture. The relation with the recent experiment for (CH3)2CHNH3Cu(ClxBr1−x)3 is discussed.
The processes of magnetization of ferrimagnetic Heisenberg chains of alternating spins are studied theoretically. Size-scaling analysis with the exact diagonalization of finite systems for ( S , s ) = (3/2,1) and (2,1) indicates a multi-plateau structure in the ground-state magnetization curve for S and s >1/2. The first plateau in the spontaneous magnetization can be explained classically: as originating from the Ising gap. In contrast, the second and higher ones must be originating from the quantization of the magnetization. It is also found that all of the 2 s plateaux, both classical and quantum ones, appear even in the isotropic case with no bond alternation.
The competition between quantum and classical magnetization plateaus of S=1/2 frustrated Heisenberg chains with modified exchange couplings is investigated. The conventional S=1/2 frustrated Heisenberg chains is known to exhibit a 3-fold degenerate udu-type classical plateau at 1/3 of the saturation magnetization accompanied by the spontaneous Z_3 translational symmetry breakdown. The stability of this plateau phase against period 3 exchange modulation which favors the 00u-type quantum plateau state (00= singlet dimer) is studied by bosonization, renormalization group and numerical diagonalization methods. The ground state phase diagram and the spin configuration in each phase are numerically determined. The translationally invariant Valence Bond Solid-type model with 4-spin and third neighbor interactions, which has the exact 00u-type quantum plateau state, is also presented. The phase transition to the classical udu-type ground state is also observed by varying the strength of 4-spin and third neighbor interactions. The relation between these two types of models with quantum plateau states is discussed.
We report results of theoretical investigations on the effect of doping and quenched disorder on the occurrence of plateaux in the magnetization curve of 1D systems with periodic modulations in the couplings.For single q-merized Hubbard chains, doping is shown to affect the position at which plateaux appear, leading to the emergence of plateaux at irrational values of the magnetization.For random bond antiferromagnetic Heisenberg chains with periodically modulated bond distributions, disorder generically removes the plateau structure, except in the case of discrete probability distributions.In the latter case, wide plateaux emerge at values of the magnetization dependent on the strength of disorder.