Magnetic phase transition in coupled spin-lattice systems: A replica-exchange Wang-Landau study

Coupled, dynamical spin-lattice models provide a unique test ground for simulations investigating the finite-temperature magnetic properties of materials under the direct influence of the lattice vibrations. These models are constructed by combining a coordinate-dependent interatomic potential with a Heisenberg-like spin Hamiltonian, facilitating the treatment of both the atomic coordinates and the spins as explicit phase variables. Using a model parameterized for bcc iron, we study the magnetic phase transition in these complex systems via the recently introduced, massively parallel replica-exchange Wang-Landau Monte Carlo method. Comparison with the results obtained from rigid lattice (spin-only) simulations shows that the transition temperature as well as the amplitude of the peak in the specific heat curve is marginally affected by the lattice vibrations. Moreover, the results were found to be sensitive to the particular choice of interatomic potential.

Figure 1

Partitioning the global energy range into seven windows with overlap $o=75\%$. Arrows indicate the communication pathways between neighboring windows for replica-exchange attempts.

Figure 2

Comparison of the temperature dependence of the internal energy for coupled spin-lattice systems of size $L=20$ using the Dudarev-Derlet [spin + lattice (DD)] and Finnis-Sinclair [spin + lattice (FS)] potentials. Error bars are smaller than the symbols.

Figure 3

Specific heat as a function of temperature for $L=20$ with [spin + lattice (DD) and spin + lattice (FS)] and without (spin only) the influence of lattice vibrations: (a) expanded temperature range $[500\text{K},1200\text{K}]$ including the experimental results for $C_P$ obtained from Ref. [37] and the corresponding $C_V$ values calculated from the $C_P$ data; (b) closeup view in the vicinity of the peak positions. Vertical arrows in both (a) and (b) mark the Curie temperature $T_C^{\text{exp}}\approx 1043$ K as predicted by the peak position of the experimental $C_P$ curve.