Spin canting in a Dy-based single-chain magnet with dominant next-nearest-neighbor antiferromagnetic interactions

We investigate theoretically and experimentally the static magnetic properties of single crystals of the molecular-based single-chain magnet of formula ${\left[\text{Dy}{\left(\text{hfac}\right)}_3\text{NIT}\left({\text{C}}_6{\text{H}}_4\text{OPh}\right)\right]}_{\infty }$ comprising alternating ${\text{Dy}}^{3+}$ and organic radicals. The magnetic molar susceptibility ${\chi }_M$ displays a strong angular variation for sample rotations around two directions perpendicular to the chain axis. A peculiar inversion between maxima and minima in the angular dependence of ${\chi }_M$ occurs on increasing temperature. Using information regarding the monomeric building block as well as an ab initio estimation of the magnetic anisotropy of the ${\text{Dy}}^{3+}$ ion, this “anisotropy-inversion” phenomenon can be assigned to weak one-dimensional ferromagnetism along the chain axis. This indicates that antiferromagnetic next-nearest-neighbor interactions between ${\text{Dy}}^{3+}$ ions dominate, despite the large Dy-Dy separation, over the nearest-neighbor interactions between the radicals and the ${\text{Dy}}^{3+}$ ions. Measurements of the field dependence of the magnetization, both along and perpendicularly to the chain, and of the angular dependence of ${\chi }_M$ in a strong magnetic field confirm such an interpretation. Transfer-matrix simulations of the experimental measurements are performed using a classical one-dimensional spin model with antiferromagnetic Heisenberg exchange interaction and noncollinear uniaxial single-ion anisotropies favoring a canted antiferromagnetic spin arrangement, with a net magnetic moment along the chain axis. The fine agreement obtained with experimental data provides estimates of the Hamiltonian parameters, essential for further study of the dynamics of rare-earth-based molecular chains.

Figure 1

(Color online) (a) Representation of the Ising axes of the ${\text{Dy}}^{3+}$ ion, as gathered from ab initio calculations and superimposed on the chain in the $ab$ plane. Thin arrows correspond to the radical spins. The three different magnetic interactions along the magnetic chain have also been represented. (b) View along the $b$ crystallographic axis of the crystal packing, showing the two symmetry-related types of chains. The orientation of the $X$ and $Z$ axes in the $ac$ plane is also represented (the $Y$ axis coincides with $b$).

Figure 2

(Color online) Angular variation of the molar susceptibility, ${\chi }_M$, for three orthogonal rotations at 2.8 K, measured in a 1 kOe external field. Rotations were performed around $X$ (green circles), $b$ (blue triangles), and $Z$ (red squares).

Figure 3

(Color online) (Top) Angular variation of the molar susceptibility, ${\chi }_M=M/H$, for temperature $T$ ranging from 2.4 K (blue) to 51 K (red), measured in an external magnetic field of 1 kOe. Rotations were performed around the $X$ axis, with $0°$ and $180°$ corresponding to the field aligned perpendicularly to the chain along $-Z$ and $Z$, respectively, whereas, at $90°$, ${\chi }_M$ is measured along the chain. Temperature color mapping is described on the right part of the figure. Vertical dot lines are guides to the eyes. (Bottom) Transfer-matrix simulation of the angle dependence of ${\chi }_M=M/H$ (with $H=1\text{kOe}$) when rotating around $X$. The classical-spin Hamiltonian, Eq. (1), and the Hamiltonian parameters specified in Sec. 4 were used for the calculation. Lines of different colors refer to different temperatures.

Figure 4

(Color online) (Top) Field dependence of the magnetization along the chain (full squares) and perpendicular to the chain (along the $Z$ axis, open circles), for temperature $T$ ranging from 2.45 to 12.85 K. The temperature color mapping is depicted on the right. (Bottom) Transfer-matrix simulation of the field dependence of $M$ vs $H$ along the chain direction (dashed lines) and perpendicular to it (solid lines) obtained using the classical-spin Hamiltonian, Eq. (1), and the Hamiltonian parameters specified in Sec. 4. Lines of different colors refer to different temperatures.

Figure 5

(Color online) Influence of an applied magnetic field in the $ac$ plane on the orientation of the magnetic moments of neighboring Dy ions of the two types of chains (A and B).

Figure 6

(Color online) (Top) Angular variation of the molar susceptibility $\left({\chi }_M=M/H\right)$ for the rotations around the chain axis $b$ at 2.5 K, measured in a 30 kOe external field (blue triangles) or in a 1 kOe external field (black triangles). (Center) Transfer-matrix simulation of $M/H$ vs angle at 2.5 K in a field of 30 kOe, showing the contribution from each chain type (A and B), as well as their sum. The classical-spin Hamiltonian, Eq. (1), and the Hamiltonian parameters specified in Sec. 4 were used for the calculation. Perfect orthogonality $2\varphi =90°$ between the projections on the $ac$ plane of the easy axes of the two chain families $A$ and B was assumed. (Bottom) Schematic representation of the corresponding spin configurations.

Figure 7

(Color online) (Top) Angular variation of the susceptibility ${\chi }_M=M/H$ from 2.45 K (blue) to 20.45 K (red) measured in a 30 kOe external field. Rotations were performed around the chain axis $b$ as defined in the text. Color mapping is described on the right part of the figure. Solid lines are guides to the eyes. (Bottom) Transfer matrix simulation of ${\chi }_M=M/H$ vs angle, at selected temperatures in a field of 30 kOe. The classical-spin Hamiltonian, Eq. (1), and the Hamiltonian parameters specified in Sec. 4 were used for the calculation. Notice that, with respect to Fig. 6 (center), a slight deviation from perfect orthogonality between the two chain families was assumed, thus accounting for asymmetry in the height of the major peaks.

Figure 8

(Color online) Canted ground state of the spins of a single chain of type A, described by Hamiltonian (1). For each unit cell $l$, there are two spins (thick, green arrows, representing ${\text{Dy}}^{3+}$ ions) that belong to two different sublattices, I and II, with different local axes ${\mathbf{z}}_{\text{I}}^{\prime }$ and ${\mathbf{z}}_{\text{II}}^{\prime }$ (thin, dashed arrows).