Magnetic neutron spectroscopy of a spin-transition ${\mathrm{Mn}}^{3+}$ molecular complex

We have investigated by inelastic neutron scattering (INS), neutron diffraction, and magnetometry the magnetic properties of the mononuclear complex $\left[{\mathrm{Mn}}^{3+}{\left(\mathrm{pyrol}\right)}_3\left(\mathrm{tren}\right)\right]$ in both high-spin (${}^{5}E$, HS, $S=2$) and low-spin (${}^3{T}_1$, LS, $S=1$) states. The system presents a spin transition (ST) around 47 K with a small hysteresis width ($T_{\text{ST},\uparrow }=47.5$ K and $T_{\text{ST},\downarrow }=46$ K) characteristic of an efficient collective transition process. In the HS state, the INS spectrum at 56 K and zero magnetic field is accounted for by a zero-field splitting with $D=-5.73\left(3\right)$ ${\mathrm{cm}}^{-1}$ and $\left|E\right|=+0.47\left(2\right)$ ${\mathrm{cm}}^{-1}$ which may be the result of a dynamic Jahn-Teller effect reported in the literature. In the LS state, a single magnetic peak at 4.87 meV is observed, still at zero field. Despite the existence of an unquenched orbital moment ($L=1$) in the ground ${}^3{T}_1$ state, we argue that it may be described by a genuine $S=1$ spin Hamiltonian owing to the existence of a strong trigonal distortion of the ${\mathrm{Mn}}^{3+}$ coordination octahedron. The observed peak corresponds to a transition $\Delta M=+1$ within the $S=1$ ground state split by a large single-ion anisotropy term $D=+39.3$ ${\mathrm{cm}}^{-1}$. A full spin-Hamiltonian model is proposed based on these first INS results obtained in a thermal ST molecular magnetic system.

Figure 1

(a) Full $Q$-range powder neutron diffraction ($\lambda =2.4226$ Å, G 4.1, LLB-Orphée, Saclay) across the ST at 46 and 48 K and representation of the molecular unit. N atoms are labeled $N_z$, $N_1$, and $N_2$ depending on their coordination type. The red arrow represents the threefold axis of the molecule which also corresponds to a remarkable compression direction of the coordination octahedron. Diffraction data were carried out while warming up from base temperature. (b) and (c) Diffraction patterns at 44, 46, 48, and 60 K on two selected $Q$ ranges ($Q=1.75$ and $2.1$ Å${}^{-1}$). The sudden shift around 47 K is a typical feature of the HS to LS transition.

Figure 2

Top panel: Susceptibility curve represented as $\chi T$ as a function of temperature obtained at 0.05 T during cooling and warming. Inset: Small hysteresis observed around the transition at $T\approx 47$ K. Bottom panel: Magnetization curves at different temperatures ($2–60$ K). In the LS state ($T\le 45$ K), $\chi T\left(T\right)$ and $M\left(H\right)$ have been fitted simultaneously (solid lines) using Eq. (1) with $S=1$ and $g_{\parallel }=2.12$, $g_{\perp }=2.30$, $D=39.3{\mathrm{cm}}^{-1}$, and $E=0$, $D$ being fixed from the INS data (vide infra). In the HS state ($T\ge 50$ K), the red line in the top panel is an attempt made to reproduce the susceptibility using Eq. (1) with $S=2$ and $g_x=g_y=g_z=2.00$, $D=-5.73{\mathrm{cm}}^{-1}$, and $\left|E\right|=0.475{\mathrm{cm}}^{-1}$, $D$ and $E$ being also fixed from the INS data. The magnetization curves (50 and 60 K) are reproduced using a Brillouin function with $S=2$ and $g=1.96$.

Figure 3

Top panel: INS spectra of $\left[{\mathrm{Mn}}^{3+}{\left(\mathrm{pyrol}\right)}_3\left(\mathrm{tren}\right)\right]$ ($k_f=1.55$ Å${}^{-1}$, 4F2, LLB-Orphée, Saclay) obtained at 5, 40, and 56 K and $q=1.35$ Å${}^{-1}$. The INS transitions are labeled A to E as discussed in the text. Bottom panel: Same set of data but corrected for incoherent background and the population factor $n(\omega ,T)$ to account for the contribution due to the phonons' density of states (DOS) $G\left(\omega \right)$ : $I_{\text{phonons}}(\omega ,T)\approx G\left(\omega \right)[1+n(\omega ,T)]$.

Figure 4

(a) INS spectra of $\left[{\mathrm{Mn}}^{3+}{\left(\mathrm{pyrol}\right)}_3\left(\mathrm{tren}\right)\right]$ obtained in the HS state ($S=2$) at 56 K. Best fits to the data are represented as solid lines with flat background $y_0=90$ and a Lorentzian elastic line shape centered at $E=0$. The resulting background is represented by the black solid line. (b) Energy diagram derived from the zero-field spin Hamiltonian $H=D{S}_z^2+E(S_x^2-S_y^2)$ with $S=2$ and $D<0$. The best agreement is obtained for $D=-0.711$ meV and $\left|E\right|=+0.059$ meV. Energy levels are $E_1=2D-2\Delta$ (an almost pure $M=\pm 2$ state for small rhombicity $E$ and lowest in energy for $D<0$), $E_2=4D$ (“$M=\pm 2$” as well), $E_3=D-3E$ ($M=\pm 1$), $E_4=D+3E$ ($M=\pm 1$), and $E_5=2D+2\Delta$ ($“M=0^{\prime \prime }$). In these expressions we have $\Delta ={(D^2+3E^2)}^{1/2}$. The five observed transitions are shown in the far right panel. The peak linewidths are FWHM $\approx 0.13$ meV for peaks I–III and FWHM $\approx 0.18$ meV for peaks IV and V.

Figure 5

(a) Field-dependence INS spectra in the LS state measured at 5 K under 0–9-T magnetic fields ($k_f=1.55$ Å${}^{-1}$). Inset: A zoom around the magnetic peak (C) of energy 4.87 meV at zero field. (b) Temperature evolution of magnetic peak (C)[5 and 40 K] at zero field and compared to HS signal at 56 K, with $k_f=1.55$ Å${}^{-1}$. (c) Peak (C) raw intensity as a function of temperature ($40–56$ K). (d) Raw intensity as a function of $Q$ of peak (C) at 5 K compared to the ${\mathrm{Mn}}^{3+}$ magnetic form factor squared.

Figure 6

Magnetic states energy diagram in the LS state ($S=1$, $L=1$) as a function of the trigonal distortion parameter $\Delta$ with orbital reduction factor $\kappa =1$ and the SO coupling parameter $\lambda =-180{\mathrm{cm}}^{-1}$ (see text for details). The states are labeled in the basis $(J,M_J)$ where $\vec{J}=\vec{L}+\vec{S}$. The three lowest states in energy are, in this basis, $E(0,0)=(1/2)[-(\Delta /3)+\kappa \lambda -\sqrt{{(\Delta +\kappa \lambda )}^2+8{\left(\kappa \lambda \right)}^2}]$, $E(1,0)=(\Delta /3)+\kappa \lambda$, and $E(1,\pm 1)=(1/2)[-(\Delta /3)-\sqrt{{\Delta }^2+{\left(2\kappa \lambda \right)}^2}]$. For $\Delta =0$ the energy spectrum consists of three levels—$E(J=0)=2\kappa \lambda$, $E(J=1)=\kappa \lambda$, and $E(J=2)=-\kappa \lambda$—whose degeneracy is partially lifted by the axial distortion. Arrows represent the two possible $\Delta$ values for which the energy of the first excitation matches the energy of the observed magnetic peak (C) at 4.87 meV (39 ${\mathrm{cm}}^{-1}$), namely, $\Delta \approx +800{\mathrm{cm}}^{-1}$ in one situation [first excited state equals $E(1,\pm 1)$] or $\Delta \approx -1100{\mathrm{cm}}^{-1}$ in the other situation [first excited state equals $E(1,0)$].