Spin-1/2 One-Dimensional Heisenberg Ferromagnet at Low-Temperature

Takahashi, Minoru; Yamada, M.

doi:10.1143/jpsj.54.2808

Cited by 106 publications

(74 citation statements)

References 11 publications

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“…Apart from the coefficient of t 3/2 in the expansion for C v , the above expressions reproduce precisely the thermodynamic Bethe-ansatz calculations for the spin-1/2 FM Heisenberg chain [45,46]. It is interesting to note that without the factor const in the expression for C v , both expansions fulfill the general hypothesis according to which in 1D Heisenberg ferromagnets all observables should be universal functions of the bare couplings M 0 , s , and h, realizing a no-scale-factor universality [47,48].…”

Section: Thermodynamicssupporting

confidence: 58%

Spin models of quasi-1D quantum ferrimagnets with competing interactions

Ivanov¹

2009

Condens. Matter Phys.

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We present a brief survey of the recent theoretical work related to generic Heisenberg spin models describing quasi-one-dimensional quantum ferrimagnets. The emphasis is on quantum chains and ladders with strong competing interactions, such as the frustrated J 1 − J 2 chain with alternating (1, 1/2) spins, the spin-1/2 diamond chain with four-spin cyclic couplings, and some generic types of mixed-spin ladders with geometric frustration. As a rule, the discussed models exhibit rich quantum phase diagrams and provide some interesting examples of one-dimensional magnetic-paramagnetic quantum phase transitions. A number of open problems in the reviewed research area are discussed.

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Section: Thermodynamicssupporting

confidence: 58%

Spin models of quasi-1D quantum ferrimagnets with competing interactions

Ivanov¹

2009

Condens. Matter Phys.

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“…Equation (11) was shown to precisely agree with the thermodynamic Bethe-ansatz calculation [24] in the case of S = 1/2. On the other hand, the author and Fukui [17] have recently developed the scheme for quantum ferrimagnets.…”

supporting

confidence: 57%

Magnetic properties of quantum ferrimagnetic spin chains

Yamamoto

1999

Phys. Rev. B

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Magnetic susceptibilities of spin-(S, s) ferrimagnetic Heisenberg chains are numerically investigated. It is argued how the ferromagnetic and antiferromagnetic features of quantum ferrimagnets are exhibited as functions of (S, s). Spin-(S, s) ferrimagnetic chains behave like combinations of spin-(S − s) ferromagnetic and spin-(2s) antiferromagnetic chains provided S = 2s.PACS numbers: 75.10. Jm, 75.40.Mg, 65.50.+m Quantum behavior of mixed-spin systems is one of the hot topics and a recent progress in the theoretical understanding of it deserves special mention. In contrast with pioneering calculations [1] in the 1980s, the current vigorous argument might more or less be motivated by the Haldane conjecture [2] in that it covers not only ferrimagnetism but also mixed-spin antiferromagnetism. As coexistent spins of different kinds do not necessarily result in magnetic ground states, it remains a stimulative problem there whether the system is massive or massless. Actually various mixed-spin chains [3,4] and ladders [5] with singlet ground states have also been discussed extensively via the nonlinear-σ-model technique with particular emphasis on the competition between massive and massless phases. On the other hand, an arbitrary alignment of alternating spins S and s, which is described by the Hamiltonianshows ferrimagnetism instead of antiferromagnetism and thus has gapless excitations from the ground state. Chemical explorations into ferrimagnetic chain compounds have vigorously been reported so far. In an attempt to obtain bimetallic complexes including onedimensional systems, CuMn(S 2 C 2 O 2 ) 2 (H 2 O) 3 ·4.5H 2 O [6] was first synthesized. Since then numerous bimetallic chain compounds [7] were systematically synthesized and measured. In the series of investigations, the smaller spin s was fixed to 1/2 and the larger spin S was changed from 1/2 to 5/2 featuring several important concepts. One of their main interests was the achievement of a ferromagnetic interaction between nearest-neighbor metal ions, namely, the design of molecular-based ferromagnets. Therefore quantum ferrimagnetism was not necessarily the main subject there. Though there also appeared theoretical investigations [1,8] in close contact with experiments, the argument was restricted to the spin combinations (S, 1/2) and the larger spin S was sometimes treated as classical.In such circumstances, several renewed interests [9][10][11][12][13][14][15][16][17][18][19], have recently been introduced into the field. Alcaraz and Malvezzi [9] predicted the universal low-energy physics of anisotropic ferrimagnetic chains and the distinct behavior of isotropic ones. Kuramoto [16] discussed critical properties of the model in a field showing its magnetization curve with a plateau. Maisinger et al. [19] revealed the field-induced double-peak structure of the specific heat. Another noteworthy subject, which is the main interest here, is the coexistence of the ferromagnetic and antiferromagnetic features in quantum ferrimagnets. The author et al. pointe...

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“…(18) is indeed the correct asymptotic lowtemperature behavior of the susceptibility for arbitrary S. For S = 1/2 the nearest-neighbor Heisenberg chain is exactly solvable via Bethe ansatz, 24 so that in this case one can obtain an independent check of Eq. (18).…”

Section: B One-dimensional Ferromagnetmentioning

confidence: 85%

“…(18). Indeed, from a numerical analysis of the Bethe-ansatz integral equations 24 Takahashi with Eq. (18) for S = 1/2, which is remarkable because a priori linear spin-wave theory is only expected to be accurate in the ordered state and for large S. We shall further comment on this agreement below.…”

Section: B One-dimensional Ferromagnetmentioning

confidence: 99%

Spin-wave theory at constant order parameter

2003

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We derive the low-temperature properties of spin-S quantum Heisenberg magnets from the Gibbs free energy G(M ) for fixed order parameter M . Assuming that the low-lying elementary excitations of the system are renormalized spin waves, we show that a straightforward 1/S expansion of G(M ) yields qualitatively correct results for the low-temperature thermodynamics, even in the absence of long-range magnetic order. We explicitly calculate the two-loop correction to the susceptibility of the ferromagnetic Heisenberg chain and show that it quantitatively modifies the mean-field result.

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Spin-1/2 One-Dimensional Heisenberg Ferromagnet at Low-Temperature

Cited by 106 publications

References 11 publications

Spin models of quasi-1D quantum ferrimagnets with competing interactions

Spin models of quasi-1D quantum ferrimagnets with competing interactions

Magnetic properties of quantum ferrimagnetic spin chains

Spin-wave theory at constant order parameter

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