Sampling the two-dimensional density of states $g(E,M)$ of a giant magnetic molecule using the Wang-Landau method

The Wang-Landau method is used to study the magnetic properties of the giant paramagnetic molecule $\left\{{\mathrm{Mo}}_{72}{\mathrm{Fe}}_{30}\right\}$ in which 30 ${\mathrm{Fe}}^{3+}$ ions are coupled via antiferromagnetic exchange. The two-dimensional density of states $g(E,M)$ in energy and magnetization space is calculated using a self-adaptive version of the Wang-Landau method. From $g(E,M)$ the magnetization and magnetic susceptibility can be calculated for any temperature and external field.

Figure 1

Geometrical structure of an icosidodecahedron. For the molecule $\left\{{\mathrm{Mo}}_{72}{\mathrm{Fe}}_{30}\right\}$ the vertices represent spin sites and the edges represent nearest-neighbor interactions.

Figure 2

Low-energy part of the two-dimensional map for the reference histogram with $\mathrm{RH}(E,M)\ne 0$ for the molecule $\left\{{\mathrm{Mo}}_{72}{\mathrm{Fe}}_{30}\right\}$. $\mathrm{RH}(E,M)\ne 0$ defines the accessible energy and magnetization space. The grid shows the bins in energy and magnetization space.

Figure 3

(Color online) Joint DOS $\ln \left[g(E,M)\right]$ for the magnetic molecule $\left\{{\mathrm{Mo}}_{72}{\mathrm{Fe}}_{30}\right\}$.

Figure 4

(Color online) Magnetization $M$ as a function of temperature $T$ and external magnetic field $B$.

Figure 5

(Color online) Comparison of the magnetization $M$ as a function of external magnetic field calculated from $g(E,M)$ (solid lines) with computed data using the Metropolis algorithm at $T=2\mathrm{K}$ (open circles) and $4\mathrm{K}$ (open squares), respectively. Statistical sampling errors are smaller than the used symbols and linewidths.

Figure 6

(Color online) Magnetic susceptibility $\chi$ as a function of temperature $T$ and external magnetic field $B$.

Figure 7

(Color online) Comparison of the magnetic susceptibility $\chi$ as a function of external magnetic field calculated from $g(E,M)$ (solid lines) with computed data using the Metropolis algorithm at $T=2\mathrm{K}$ (open circles) and $4\mathrm{K}$ (open squares), respectively.

Figure 8

(Color online) Specific heat $C$ as a function of temperature $T$ and external magnetic field $B$.