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Journal of Applied Physics

Non-Heisenberg couplings and ferromagnetic instability in a random antiferromagnetic spin-1 chain

R. N. Bhatt, Kun Yang

Published Jun 1, 1998• 7 citations
Publisher

Abstract

A random antiferromagnetic spin-1 chain with both Heisenberg and biquadratic nearest neighbor couplings is found to exhibit a novel ferromagnetic-like instability at low energies, if there is competition between the Heisenberg and biquadratic couplings, even though each individual nearest neighbor coupling is such as to produce a singlet ground state for the isolated pair. This instability leads to the generation of ferromagnetic couplings, and thus to the formation of weakly coupled large moments at low temperatures. A perturbative calculation (up to 4th order) is performed to investigate whether such a situation is physically realizable in spin-1 systems.

DOI
10.1063/1.367612

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A random antiferromagnetic spin-1 chain with both Heisenberg and biquadratic nearest neighbor couplings is found to exhibit a novel ferromagnetic-like instability at low energies, if there is competition between the Heisenberg and biquadratic couplings, even though each individual nearest neighbor coupling is such as to produce a singlet ground state for the isolated pair. This instability leads to the generation of ferromagnetic couplings, and thus to the formation of weakly coupled large moments at low temperatures. A perturbative calculation (up to 4th order) is performed to investigate whether such a situation is physically realizable in spin-1 systems.
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The low energy properties of the spin-1/2 random Heisenberg chain with ferromagnetic and antiferromagnetic interactions are studied by means of the density matrix renormalization group (DMRG) and real space renormalization group (RSRG) method for finite chains. The results of the two methods are consistent with each other. The deviation of the gap distribution from that of the random singlet phase and the formation of the large-spin state is observed even for relatively small systems. For a small fraction of the ferromagnetic bond, the effect of the crossover to the random singlet phase on the low temperature susceptibility and specific heat is discussed. The crossover concentration of the ferromagnetic bond is estimated from the numerical data.
We study disordered antiferromagnetic spin-12\frac{1}{2}21​ chains with nearest- and further-neighbor interactions using the real-space renormalization-group method. We find that the system supports two different phases, depending on the ratio of the strength between nearest-neighbor and further-neighbor interactions as well the bond randomness strength. For weak further-neighbor coupling the system is in the familiar random singlet phase, while stronger further-neighbor coupling drives the system to a large spin phase similar to that found in the study of random antiferromagnetic-ferromagnetic spin chains. The appearance of the large spin phase in the absence of ferromagnetic coupling is due to the frustration introduced by further-neighboring couplings, and is unique to the disordered chains.
Low temperature properties of random antiferromagnetic Heisenberg spin-1/2 systems with a wide distribution of exchange couplings are examined using a scaling technique. The method iteratively discards the irrelevant high energy excitations of strongly coupled clusters, while retaining the low lying states which are reproduced by an equivalent smaller cluster. The method is applied to n-doped semiconductors, a spatially random three dimensional system of spin-1/2 donors with Heisenberg exchange varying exponentially with separation. It shows how the system does not order down to temperatures well below the median nearest neighbor exchange. Comparison is made with the corresponding system in two dimensions and the one-dimensional random antiferromagnetic chain (applicable to certain organic charge transfer salts), as well as with the case of Ising spins in three dimensions.
We study the 1D quantum Heisenberg chain with randomly ferromagnetic or antiferromagnetic couplings [a model previously studied by approximate strong-disorder renormalization group (RG)]. We find that, at least for sufficiently large spin S , the ground state has “spin glass” order. The spin waves on top of this state have the dynamical exponent z = 3 / 2 , intermediate between the values z = 1 of the antiferromagnet and z = 2 of the ferromagnet. Density matrix renormalization group (DMRG) simulations are in good agreement with the analytical results for spins S = 1 and S = 3 / 2 . The case S = 1 / 2 shows large finite size effects: We suggest that this case is also ordered, but with a small ordered moment.