Intracluster interactions in butterfly $\left\{{\mathrm{Fe}}_3{\mathrm{LnO}}_2\right\}$ molecules with the non-Kramers ions Tb(III) and Ho(III)

The intracluster exchange interactions within the “butterfly” $\left[{\mathrm{Fe}}_3\mathrm{Ln}\right({\mu }_3-\mathrm{O}{)}_2\left({\mathrm{CCl}}_3\mathrm{COO}{)}_8\right({\mathrm{H}}_2\mathrm{O}\left)\right(\mathrm{THF}{)}_3]$ molecules, where Ln(III) represents a lanthanide cation, have been determined by a combination of x-ray magnetic circular dichroism (XMCD) and vibrating sample magnetometry (VSM) along with an interaction model. We have studied the compounds with $\mathrm{Ln}=\mathrm{Tb}$ and Ho, both non-Kramers lanthanides and with high uniaxial anisotropy, and $\mathrm{Ln}=\mathrm{Lu}$(III) and Y(III) as pseudolanthanides, which supply nonmagnetic Ln reference cases. At low temperature, the three Fe atoms can be considered as a self-unit with total spin $S_{{\mathrm{Fe}}_3}=5/2$. Using the element selectivity of the XMCD magnetometry, measured at the Ln $L_{2,3}$ edges, together with the VSM measurements, the local magnetization of the Ln ion and the ${\mathrm{Fe}}_3$ subcluster, as a function of the field and low temperature ($T\approx 2.5\mathrm{K}$), has been determined separately. These results are described quantitatively in the framework of a theoretical model based on an effective spin Hamiltonian, which considers the competing effects of intracluster interactions and the external applied magnetic field. The $\mathrm{Ln}-{\mathrm{Fe}}_3$ exchange interaction within the $\left\{{\mathrm{Fe}}_3{\mathrm{LnO}}_2\right\}$ cluster has been determined to be antiferromagnetic, in both Tb and Ho compounds, with ${\mathcal{J}}_{\mathrm{FeTb}}/{\mathrm{k}}_{\mathrm{B}}=-0.13\left(1\right)\mathrm{K}$ and ${\mathcal{J}}_{\mathrm{FeHo}}/{\mathrm{k}}_{\mathrm{B}}=-0.18\left(1\right)\mathrm{K}$, respectively. In both cases, a field-induced reorientation of the ${\mathrm{Fe}}_3$ and Ln spins from antiparallel to parallel orientation takes place at a threshold field ${\mu }_{0}H=1.1$ and 2 T, for the $\left\{{\mathrm{Fe}}_3{\mathrm{TbO}}_2\right\}$ and $\left\{{\mathrm{Fe}}_3{\mathrm{HoO}}_2\right\}$ compounds, respectively. By comparison with other compounds of the series with uniaxial anisotropy, it is concluded that the polarizability of the ${\mathrm{Fe}}_3$ subcluster magnetic moment decreases in the trend $\left\{{\mathrm{Fe}}_3{\mathrm{YO}}_2\right\}\to \left\{{\mathrm{Fe}}_3{\mathrm{TbO}}_2\right\}\to \left\{{\mathrm{Fe}}_3{\mathrm{HoO}}_2\right\}\to \left\{{\mathrm{Fe}}_3{\mathrm{DyO}}_2\right\}$, because of the increasing opposition of the exchange antiferromagnetic field caused by the Ln ion. In the $\mathrm{Ln}=\mathrm{Tb}$, Ho, and Dy, the magnetization of the whole molecule is dominated by the anisotropy of the Ln ion. The intracluster ${\mathrm{Fe}}_3-\mathrm{Ln}$ exchange interactions are very weak compared to the Ln ligand field and Fe-Fe exchange interactions.

Figure 1

Structure of the {${\mathrm{Fe}}_3{\mathrm{TbO}}_2$} complex. Easy axis of magnetization of the Tb ion (yellow arrow), obtained from the ab initio calculations of the ground state. Blue arrows indicate the magnetic moment direction of the three Fe atoms, taking into account that an exchange interaction is acting between the Tb and ${\mathrm{Fe}}_3$ spins. (Inset) Magnetic core of the {${\mathrm{Fe}}_3{\mathrm{TbO}}_2$} compound and definition of exchange parameters between the three Fe ions. The $Y$ axis points outwards from the figure. The $YZ$ plane forms the quasisymmetry plane.

Figure 2

(a) XAS spectra and (b) XMCD signal at the Ln $L_{2,3}$ edges in {${\mathrm{Fe}}_3{\mathrm{LnO}}_2$} compounds for $\mathrm{Ln}=\mathrm{Tb}$ (top) and Ho (bottom). Vertical lines indicate the chosen photon energy for the $I_{\mathrm{XMCD}}\left(H\right)$ measurements.

Figure 3

Collected magnetization curves as a function of applied field from XMCD experimental data at fixed energy in the {${\mathrm{Fe}}_3{\mathrm{LnO}}_2$} compounds: (a) for $\mathrm{Ln}=\mathrm{Tb}$, at $T=2.7$ K, $L_2$ edge at $E=8257$ eV; and (b) for $\mathrm{Ln}=\mathrm{Ho}$, at $T=2.2$ K, $L_3$ edge at $E=8078$ eV.

Figure 4

$M\left(H\right)$ curves of {${\mathrm{Fe}}_3{\mathrm{LnO}}_2$} compounds with Ln $=$ Tb (a) and Ho (b). Macroscopic $M_{\mathrm{tot}}\left(H\right)$ curve obtained from VSM measurements at $T=2.7$ and $2.2$ K, for Tb and Ho compounds, respectively ($•$). Microscopic magnetization curve obtained from XMCD at the $L_2$ and $L_3$ edges, respectively ($▴$). Magnetization of the total Fe present in the system obtained by subtraction of the two previous curves ($\blacksquare$). $M^{\mathrm{th}}\left(H\right)$ predictions for Tb (a) and Ho (b) (–), at $T=2.7$ and $2.2$ K, respectively.

Figure 5

Energy levels of the ground multiplet of (a) a single Tb(III) ion, provided by the ab initio calculations (Ref. [26]) and (b) the {${\mathrm{Fe}}_3{\mathrm{TbO}}_2$} cluster, calculated with the parameters shown in Table 1 and $H=0$.

Figure 6

(a) The {${\mathrm{Fe}}_3{\mathrm{TbO}}_2$} energy level Zeeman splitting scheme for applied field parallel to the $x$ direction. (b) The simulation of the $M_{\mathrm{th}}\left(H\right)$ curves of the {${\mathrm{Fe}}_3{\mathrm{TbO}}_2$} compound with $g_x^{*}=17.5, g_y^{*}=g_z^{*}=0, {\mathcal{J}}_{\mathrm{FeTb},x}^{*}/k_{\mathrm{B}}=-1.5$ K, and ${\mathrm{\Delta }}^{\exp }/k_{\mathrm{B}}=5.0$ K. Arrows indicate the average direction of the Tb (large $\uparrow$) and of ${\mathrm{Fe}}_3$ subcluster (small $\uparrow$) moments at points A (antiparallel) and C (parallel), point B indicates the crossover field. Note that the magnetic moments (arrows) and the third component of the spin are opposite in sign.

Figure 7

Energy levels of the ground multiplet of (a) a single Ho(III) ion, provided by the ab initio calculations (Ref. [26]) (only the eight lowest states are plotted) and (b) the {${\mathrm{Fe}}_3{\mathrm{HoO}}_2$} cluster, calculated with the parameters shown in Table 1 and $H=0$.

Figure 8

$M_{\mathrm{tot}}\left(H\right)\equiv M_{{\mathrm{Fe}}_3}\left(H\right)$ data of {${\mathrm{Fe}}_3{\mathrm{YO}}_2$} ($\square$) and $M_{{\mathrm{Fe}}_3}\left(H\right)$ curves of the uniaxial anisotropic clusters {${\mathrm{Fe}}_3{\mathrm{DyO}}_2$} ($▵$), {${\mathrm{Fe}}_3{\mathrm{TbO}}_2$} ($\circ$), and {${\mathrm{Fe}}_3{\mathrm{HoO}}_2$} ($\diamond$), and their correspondent simulated curves $M_{{\mathrm{Fe}}_3}^{\mathrm{th}}\left(H\right)$ (dashed lines).