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arXiv:cond-mat/0111521 · Progress of Theoretical Physics Supplement

Magnetic Properties ofS=1/2 Heisenberg Chains with Bond Alternation and Randomness on the Strong Bonds

Kazuo Hida

Published Jan 1, 2002• 6 citations
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Abstract

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.

DOI
10.1143/ptps.145.320

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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 multiple reentrant quantum phase transitions in the S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg chains with random bond alternation in the magnetic field are investigated by the density matrix renormalization group method combined with the interchain mean field approximation. It is assumed that the odd-th bond is antiferromagnetic with strength JJJ and even-th bond can take the values ${\JS}$ and ${\JW}$ $ ({\JS} > J > {\JW} > 0)$ randomly with probability ppp and 1−p1-p1−p, respectively. The pure version (p=0p=0p=0 and p=1p=1p=1) of this model has a spin gap but exhibits a field induced antiferromagnetism in the presence of interchain coupling if Zeeman energy due to the magnetic field exceeds the spin gap. For 0<p<10 < p < 10<p<1, the antiferromagnetism is induced by randomness at small field region where the ground state is disordered due to the spin gap in the pure case. At the same time, this model exhibits randomness induced plateaus at several values of magnetization. The antiferromagnetism is destroyed on the plateaus. As a consequence, we find a series of reentrant quantum phase transitions between the transverse antiferromagnetic phases and disordered plateau phases with the increase of the magnetic field for moderate strength of interchain coupling. Above the main plateaus, the magnetization curve consists of a series of small plateaus and the jumps between them, It is also found that the antiferromagnetism is induced by infinitesimal interchain coupling at the jumps between the small plateaus. We conclude that this antiferromagnetism is supported by the mixing of low lying excited states by the staggered interchain mean field even though the spin correlation function is short ranged in the ground state of each chain.
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.
The mixture of bond-alternating and uniform S=1/2 antiferromagnetic Heisenberg chains is investigated by the density matrix renormalization group method. The ground state magnetization curve is calculated and the exchange parameters are determined by fitting to the experimentally measured magnetization curve of \CuCl2x_{2x}2x​Br2(1−x)_{2(1-x)}2(1−x)​(γγγ-pic)2_22​. The low field behavior of the magnetization curve and low temperature behavior of the magnetic susceptibility are found to be sensitive to whether the bond-alternation pattern (parity) is fixed all over the sample or randomly distributed. The both quantities are compatible with the numerical results for the random parity model.
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=1/2S=1/2S=1/2 frustrated Heisenberg chains with bond alternation is known to exhibit a magnetization plateau at half of the saturation magnetization $\Ms$ 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−p1-p1−p. The physical origin of this behavior is explained based on the strong coupling picture.