Thermodynamic observables of ${\mathrm{Mn}}_{12}$-acetate calculated for the full spin Hamiltonian

Thirty-five years after its synthesis, magnetic observables are calculated for the molecular nanomagnet ${\mathrm{Mn}}_{12}$-acetate using a spin Hamiltonian that contains all spins. Starting from a very advanced density functional theory parametrization [V. V. Mazurenko et al., Phys. Rev. B 89, 214422 (2014)], we evaluate magnetization and specific heat for this anisotropic system of 12 manganese ions with a staggering Hilbert space dimension of 100 000 000 using the finite-temperature Lanczos method. We compare the results with those obtained from other parametrizations. Our investigations demonstrate that it is now possible to assess the quality of parametrizations of effective spin Hamiltonians for rather large magnetic molecules.

Figure 1

Schematic structure of Mn12; same labeling as in Ref. [16]. ${\mathrm{Mn}}^{\text{(IV)}}$ ions (1–4) are shown as red circles, and ${\mathrm{Mn}}^{\text{(III)}}$ ions (5–12) as blue ones. An $S_4$ symmetry is assumed.

Figure 2

Effective magnetic moment of ${\mathrm{Mn}}_{12}$-acetate at $B=0.1$ T. Data of Sessoli [27] and Murrie [60] are given by symbols. Observables employing the Heisenberg part of parametrizations only are displayed by curves. The parametrizations correspond to those given in Table 1 from top to bottom.

Figure 3

Effective magnetic moment of ${\mathrm{Mn}}_{12}$-acetate at $B=0.1$ T; same as Fig. 2. The dashed curve shows the result of a calculation employing the full Hamiltonian of Ref. [16]. The powder average is performed over a regular grid of 20 directions on the unit sphere [65].

Figure 4

Magnetization of ${\mathrm{Mn}}_{12}$-acetate at $T=2$ K. Color code of curves as above. The dashed curve is evaluated for two field values per 1 T field interval only.

Figure 5

Magnetization of ${\mathrm{Mn}}_{12}$-acetate at $T=2$ K. The dashed curves are evaluated for two field values per 1 T field interval only. Direction $t=(0.0,-0.35682,0.93417)$, direction $p=(-0.35682,0.93417,0.0)$.

Figure 6

High-field magnetization of ${\mathrm{Mn}}_{12}$-acetate at $T=2$ K.

Figure 7

Specific heat of ${\mathrm{Mn}}_{12}$-acetate at $B=0$ (top) and $B=0.3$ T (bottom). Data taken from Ref. [25]. Color code of curves as above. For $B=0.3$ T the calculation for the anisotropic spin model was averaged over 20 directions.