Inelastic neutron scattering and frequency-domain magnetic resonance studies of $S=4$ and $S=12$ ${\text{Mn}}_6$ single-molecule magnets

We investigate the magnetic properties of three ${\text{Mn}}_6$ single-molecule magnets by means of inelastic neutron scattering and frequency domain magnetic resonance spectroscopy. The experimental data reveal that small structural distortions of the molecular geometry produce a significant effect on the energy-level diagram and therefore on the magnetic properties of the molecule. We show that the giant spin model completely fails to describe the spin-level structure of the ground spin multiplets. We analyze theoretically the spin Hamiltonian for the low-spin ${\text{Mn}}_6$ molecule $\left(S=4\right)$ and we show that the excited $S$ multiplets play a key role in determining the effective energy barrier for the magnetization reversal, in analogy to what was previously found for the two high spin ${\text{Mn}}_6$ $\left(S=12\right)$ molecules [S. Carretta et al., Phys. Rev. Lett. 100, 157203 (2008)].

Figure 1

(Color online) Core of molecules (1) (left) and (3) (right) showing at the bottom the difference in torsion angles (${\alpha }_1$, ${\alpha }_2$, and ${\alpha }_3$). Color scheme: Mn, large orange circles; O, dark red circles; and N, small light blue circles. H and C ions are omitted for clarity.

Figure 2

(Color online) Structure of the ${\text{Mn}}_6$ (1) molecular core. The ${\text{Mn}}^{3+}$ ions are located at the vertices of two oxocentered triangles. Ions Mn1, Mn2, $\text{Mn}{1}^{\prime }$, and $\text{Mn}{2}^{\prime }$ are in octahedral geometry and ions Mn3 and $\text{Mn}{3}^{\prime }$ in square pyramidal geometry, as highlighted in filled and striped orange (left figure). Color scheme: Mn, large orange circles; O, dark red circles; and N, small light blue circles. H and C ions are omitted for clarity.

Figure 3

(Color online) (a) FDMR spectra of unpressed polycrystalline powder of (1) recorded at various temperatures. The intensity of the higher-frequency resonance line decreases with temperature while that of the lower-frequency lines increases up to 30 K, beyond which it decreases again. Dotted lines indicate resonance lines due to impurities. (b) Expanded view of the low-frequency part of the 30 K spectrum. (c) Experimental and fitted spectrum at $T=30\text{K}$ using the GSH approximation. Note the logarithmic scale in (a) and (c).

Figure 4

(Color online) (a) INS spectra of (1) with an incident wavelength of $\lambda =4.6\text{Å}$ (NEAT) for $T=2\text{K}$ (blue circles) and $T=20\text{K}$ (red squares). The continuous lines represent the spectra calculated assuming a dimer model for the spin Hamiltonian [Eq. (3)]. (b) $Q$ dependence of first intramultiplet (green circles) and intermultiplet (black squares) transitions measured on IN6 for $\lambda =4.1\text{Å}$ and $T=2\text{K}$. Continuous lines represent the calculated $Q$ dependence using the dimer spin Hamiltonian, Eq. (3), (assuming a dimer distance of $R=5.17\text{Å}$, which corresponds to the distance between the center of the two triangles).

Figure 5

(Color online) Calculated energy-level diagram for molecule (1). The level scheme on the left side is calculated using the dimer model spin Hamiltonian in Eq. (3). The color maps $S_{\text{eff}}$, where $⟨S^2⟩≔S_{\text{eff}}\left(S_{\text{eff}}+1\right)$. The black dashed line corresponds to the observed value of $U_{\text{eff}}=28\text{K}$. The black arrows indicate transitions which contribute to the observed peak in the INS and FDMR spectra at $E\approx 1.33\text{meV}$ (see text for details). The level diagram on the right has been calculated using the GSH approximation [Eq. (1)].

Figure 6

(Color online) Structure of the ${\text{Mn}}_6$ (2) molecular core. The ${\text{Mn}}^{3+}$ ions are located at the vertices of two oxocentered triangles. All Mn ions are in octahedral geometry and the octahedra are highlighted in orange (left figure). Color scheme: Mn, large orange circles; O, dark red circles; and N, small light blue circles. H and C ions are omitted for clarity. On the right, a schematic representation is given, together with the exchange coupling scheme adopted for the spin Hamiltonian calculations.

Figure 7

(Color online) (a) FDMR spectra recorded on a pressed powder pellet of 2 at different temperatures. At the lowest temperature, the highest-frequency line has highest intensity. The other transitions are indicated by vertical lines. (b) 10 K FDMR spectrum (symbols) and best fit using the GSH [Eq. (1)] with $D=-0.368{\text{cm}}^{-1}$ and $B_4^0=-4.0\times {10}^{-6}{\text{cm}}^{-1}$.

Figure 8

(Color online) (a) FDMR spectra of unpressed polycrystalline powder of (3) recorded at various temperatures. (b) Experimental and fitted spectrum at $T=10\text{K}$.

Figure 9

(Color online) INS spectra collected on IN5 with incident wavelength of $6.7\text{Å}$ at $T=2\text{K}$ (blue circles) and $T=12\text{K}$ (red squares). (a) for sample (2) and (b) for sample (3). The spectra calculated with the parameters listed in Table are shown as continuous lines.

Figure 10

(Color online) INS spectra collected on IN5 with incident wavelength of $3.4\text{Å}$ at $T=2\text{K}$ (blue circles) and 16 K (red squares). (a) for sample (2) and (b) for sample (3). The observed transitions are labeled with the corresponding transition energies in meV.

Figure 11

(Color online) High-resolution INS spectra of molecule (3) collected on IN5 with incident wavelength $10.5\text{Å}$ at 24 K. The energy gain spectra is displayed. Continuous lines are the calculations using the spin Hamiltonian of Eq. (2).

Figure 12

(Color online) (a) Energy-wave vector color map of sample (3) collected on IN5 with incident wavelength of $5.0\text{Å}$. (b) $Q$ dependence of two transitions from the ground state. The black squares correspond to the $|S=12,M_s=\pm 12⟩\to |S=12,M_s=\pm 11⟩$ intramultiplet transition and the green circles display the $|S=12,M_s=\pm 12⟩\to \mid S=11,M_s=\pm 11⟩$.

Figure 13

(Color online) Calculated energy-level diagram for molecule (2) (top) and molecule (3) (bottom). The level scheme on the left side is calculated using the microscopic spin Hamiltonian in Eq. (2) while the level diagram on the right has been calculated in the GSH approximation [Eq. (1)]. The dashed lines correspond to the observed value of $U_{\text{eff}}$.