Magnetization plateau in diamond chains with delocalized interstitial spins

M. S. S. Pereira, F. A. B. F. de Moura, and M. L. Lyra

Phys. Rev. B 77, 024402 – Published 2 January 2008

Abstract

Several low-dimensional magnetic compounds exhibit magnetization plateaus as a result of the interplay between frustration and quantum fluctuations. Here, we investigate the thermodynamic properties of diamond chains on which competing interactions emerge from the local quantum hopping of interstitial $S = 1 ∕ 2$ spins which are intercalated between nodal Ising spins. Using an exact diagonalization and the decoration-iteration transformation, we compute the temperature and external field dependences of the magnetization, specific heat, susceptibility, and the full ground state phase diagram. Magnetization plateaus of $1 ∕ 3$ are observed and related to field-driven transitions among four possible ground states: saturated paramagnetic, unsaturated paramagnetic, ferrimagnetic, and nodal antiferromagnetic. There is a range of hopping amplitudes and exchange mismatches for which the $1 ∕ 3$ magnetization plateau occurs between finite values of the external field. The specific heat and magnetic susceptibility also show signatures of the competition between the possible ground states.

Received 26 September 2007

DOI:https://doi.org/10.1103/PhysRevB.77.024402

Authors & Affiliations

M. S. S. Pereira, F. A. B. F. de Moura, and M. L. Lyra

Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió, Alagoas, Brazil

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Vol. 77, Iss. 2 — 1 January 2008

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Figure 1
Diagrammatic representation of the present diamond chain model. The corner (nodal) spins are Ising-like and localized. The exchange antiferromagnetic couplings are distinct along the nonparallel arms of the diamond units. Interstitial spins with antiparallel spins are allowed to hop within the inner sites of each diamond unit with hopping probability amplitude $t$ . When they have parallel spins (as shown in the third cell), they are not allowed to hop due to Pauli’s exclusion rule. The state vectors illustrate the notation used in the text.Reuse & Permissions
Figure 2
Representative phase diagrams in the magnetic field $H$ versus exchange mismatch $Δ J$ plane for distinct regimes of the hopping amplitude. (a) $t ∕ ∣ J_{1} ∣ ⩽ 1$ for which the phase diagram exhibits three possible phases: SPA, FRI, and NAF. (b) $1 < t ∕ ∣ J_{1} ∣ < 2$ for which the phase diagram also presents a region at which the UPA phase is stable. (c) $t ∕ ∣ J_{1} ∣ ⩾ 2$ for which the only possible ground states are the SPA, UPA, and NAF. The NAF state has null magnetization per site, while the FRI and UPA have $1 ∕ 3$ magnetization. The coexistence lines can be obtained by comparing the energies per unit cell of each phase as given by Eqs. (7, 8, 9, 10). The ground state becomes degenerated with the first-order phase transitions occurring on these lines. (d) At the bottom, we sketch the unit cell configuration for the four possible ground states.Reuse & Permissions
Figure 3
Field dependence of the magnetization per spin for two representative cases. (a) FRI is the zero-field ground state. In this case, two distinct regimes are seen at zero temperature: a $1 ∕ 3$ magnetization plateau below a critical field and the saturation plateau. For finite temperatures, thermal fluctuations round off the magnetization jump. (b) NAF is the zero-field ground state. Here, three regimes are seen: a zero magnetization plateau at low fields, a $1 ∕ 3$ magnetization plateau at intermediate fields, and the saturation plateau. At finite temperatures, the curves cross roughly at a single point signaling the upper critical field. The low field crossing is somewhat spread.Reuse & Permissions
Figure 4
Temperature dependence of the magnetization per site for two representative cases. (a) FRI is the zero-field ground state. In this case, two distinct regimes are seen, as in Fig. 3. At the critical field, the zero-temperature magnetization is $2 ∕ 3$ of the saturation value due to the degeneracy of the SPA and FRI states. (b) NAF is the zero-field ground state. At the lower and upper critical fields, the zero-temperature magnetization per site is $\sqrt{5} ∕ 15$ and $2 ∕ 3$ , respectively. These values correspond, respectively, to the degeneracy between the NFA and UPA states, and between the UPA and SPA states.Reuse & Permissions
Figure 5
Temperature dependence of the zero-field specific heat per site for two representative cases. (a) FRI is the ground state. (b) NAF is the zero-field ground state. A secondary peak appears in the vicinity of the critical mismatch separating these two possible ground states. Such peak appears at a temperature of the order of the difference between the energies of these competing ground states.Reuse & Permissions
Figure 6
Temperature dependence of the scaled zero-field susceptibility $k_{B} T χ$ per site for distinct exchange mismatches. The divergence at low temperatures is typical of a ferrimagnetic ground state. It vanishes as $T \to 0$ in the regime of nodal antiferromagnetic ground state, while it goes to a constant value at the degenerating exchange mismatch. The nonmonotonic behavior is the main signature of the presence of competing ground states. The inset is an amplification of the nonmonotonic behavior slightly inside the NAF phase.Reuse & Permissions

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