Unveiling the degeneracy of bound magnon crystals from magnetic and thermodynamic features of the spin-1/2 Heisenberg octahedral chain

TL;DR

This study tackles the problem of understanding a highly frustrated spin-1/2 Heisenberg octahedral chain in a magnetic field. It develops an extended localized-magnon framework by mapping bound magnon states to a five-component lattice-gas and validating it with exact diagonalization, enabling analytic access to magnetization plateaus and thermodynamics. The work identifies four bound-magnon crystal phases, TMP and TMD at low fields and OMP and OMD near saturation, which produce robust plateaus at $m=\frac{1}{5}$ and $m=\frac{3}{5}$. It also reveals strong magnetocaloric effects, including isoentropy-driven cooling and field-range pinning of temperature, with implications for magnetic refrigeration and experimental exploration of octahedral-chain geometries.

Abstract

Magnetic, thermodynamic, and magnetocaloric properties of a spin-1/2 Heisenberg octahedral chain with three distinct exchange interactions are investigated in an external magnetic field using the variational method, extended localized-magnon approach, and exact diagonalization. Variational arguments rigorously establish two distinct fragmented phases in the frustrated regime. In the former phase all four spins of each square plaquette form a collective plaquette singlet, whereas in the latter phase two dimer singlets are formed along diagonals of each square plaquette. These bound two-magnon states, supplemented with three localized one-magnon states, enable us to elaborate a generalized localized-magnon theory that is applicable in a frustrated regime across the entire field range as confirmed by comparison with exact diagonalization data. The concept of localized magnons provides a consistent description of low-temperature magnetization curves featuring intermediate one-fifth and three-fifths plateaus, which intersect each other at temperature-independent crossing points determined by the relative degeneracies of competing bound-magnon phases. Field variations of the specific heat reveal a pronounced double-peak structure near each field-driven transition with peak heights depending on the relative degeneracies of the respective bound-magnon states. Our results demonstrate that the system supports highly efficient cooling via adiabatic demagnetization, making it a promising candidate for magnetocaloric refrigeration.

Figures (6)

• Figure 1: A schematic illustration of the spin-$\frac{1}{2}$ Heisenberg octahedral chain. Red lines represent the monomer-plaquette coupling $J_1$, while green and blue lines correspond to nearest-neighbour and next-nearest-neighbour intra-plaquette couplings $J_2$ and $J_3$, respectively.
• Figure 2: (Color online) The one-magnon energy bands (\ref{['oms']}) of the spin-$\frac{1}{2}$ Heisenberg octahedral chain for four representative values of the interaction ratio: (a) $J_2/J_1 = 2$, $J_3/J_1 = 1$; (b) $J_2/J_1 = 4$, $J_3/J_1 = 2$; (c) $J_2/J_1 = 4$, $J_3/J_1 = 4$; (d) $J_2/J_1 = 4$, $J_3/J_1 = 8$.
• Figure 3: A few isothermal field variations of the magnetization (a), susceptibility (b), entropy (c), and specific heat (d) of the spin-$\frac{1}{2}$ Heisenberg octahedral chain with the interaction ratio $J_2/J_1 = 4$ and $J_3/J_1 = 2$. Symbols show ED data for the finite chain of 20 spins, while solid lines were derived from the analytical expression (\ref{['lmgfe']}) for the free energy of the effective lattice-gas model in the thermodynamic limit. The legend in the panel (a) applies also to panels (b)-(d).
• Figure 4: A few isothermal field variations of the magnetization (a), susceptibility (b), entropy (c), and specific heat (d) of the spin-$\frac{1}{2}$ Heisenberg octahedral chain with the interaction ratio $J_2/J_1 = 4$ and $J_3/J_1 = 4$. Symbols show ED data for the finite chain of 20 spins, while solid lines were derived from the analytical expression (\ref{['lmgfe']}) for the free energy of the effective lattice-gas model in the thermodynamic limit. The legend in the panel (a) applies also to panels (b)-(d).
• Figure 5: A few isothermal field variations of the magnetization (a), susceptibility (b), entropy (c), and specific heat (d) of the spin-$\frac{1}{2}$ Heisenberg octahedral chain with the interaction ratio $J_2/J_1 = 4$ and $J_3/J_1 = 8$. Symbols show ED data for the finite chain of 20 spins, while solid lines were derived from the analytical expression (\ref{['lmgfe']}) for the free energy of the effective lattice-gas model in the thermodynamic limit. The legend in the panel (a) applies also to panels (b)-(d).