Defect propagation in one-, two-, and three-dimensional compounds doped by magnetic atoms

Inelastic neutron scattering experiments were performed to study manganese(II) dimer excitations in the diluted one-, two-, and three-dimensional compounds $\mathrm{CsM}{\mathrm{n}}_x\mathrm{M}{\mathrm{g}}_{1-x}\mathrm{B}{\mathrm{r}}_3$, ${\mathrm{K}}_2\mathrm{M}{\mathrm{n}}_x\mathrm{Z}{\mathrm{n}}_{1-x}{\mathrm{F}}_4$, and $\mathrm{KM}{\mathrm{n}}_x\mathrm{Z}{\mathrm{n}}_{1-x}{\mathrm{F}}_3$ ($x\le 0.10$), respectively. The transitions from the ground-state singlet to the excited triplet, split into a doublet and a singlet due to the single-ion anisotropy, exhibit remarkable fine structures. These unusual features are attributed to local structural inhomogeneities induced by the dopant Mn atoms, which act like lattice defects. Statistical models support the theoretically predicted decay of atomic displacements according to $1/r^2$, $1/r$, and constant (for three-, two-, and one-dimensional compounds, respectively) where $r$ denotes the distance of the displaced atoms from the defect. The observed fine structures allow a direct determination of the local exchange interactions $J$, and the local intradimer distances $R$ can be derived through the linear law $dJ/dR$.

Figure 1

Diagram of neighboring atoms around an isolated Mn dimer marked by spheres. (a) One-dimensional case studied for $\mathrm{CsM}{\mathrm{n}}_x\mathrm{M}{\mathrm{g}}_{1-x}\mathrm{B}{\mathrm{r}}_3$ (only the Mn and Mg positions are shown). (b) Two-dimensional case studied for ${\mathrm{K}}_2\mathrm{M}{\mathrm{n}}_x\mathrm{Z}{\mathrm{n}}_{1-x}{\mathrm{F}}_4$ (only the Mn and Zn positions are shown). The full and open triangles denote the 10 nearest-neighbor and 14 next-nearest-neighbor positions, respectively. (c) Three-dimensional case studied for $\mathrm{KM}{\mathrm{n}}_x\mathrm{Z}{\mathrm{n}}_{1-x}{\mathrm{F}}_3$ (only the Mn and Zn positions are shown). The triangles denote the 26 nearest-neighbor positions.

Figure 2

Energy level scheme of a Mn(II) dimer for antiferromagnetic exchange coupling ($J<0$) according to Eq. (1). The higher lying dimer states with $3\le S\le 5$ are not shown.

Figure 3

Energy spectra of neutrons scattered from $\mathrm{CsM}{\mathrm{n}}_{0.10}\mathrm{M}{\mathrm{g}}_{0.90}\mathrm{B}{\mathrm{r}}_3$ at $T=2\mathrm{K}$ corresponding to the Mn dimer ground-state transitions $|0,0\rangle \to |1,\pm 1\rangle$ (a) and $|0,0\rangle \to |1,0\rangle$ (b). The incoming neutron energy was 2.5 meV. The lines are the result of least-squares fitting procedures as explained in the text. The vertical bars correspond to the probabilities $p_m\left(x\right)$ predicted by Eq. (2).

Figure 4

Energy spectra of neutrons scattered from ${\mathrm{K}}_2\mathrm{M}{\mathrm{n}}_x\mathrm{Z}{\mathrm{n}}_{1-x}{\mathrm{F}}_4$ at $T=2\mathrm{K}$ with incoming neutron energy of 1.55 meV. (a) New data for $x=0.02$. (b) Data taken from Ref. [2]. The lines in (a) and (b) are the result of least-squares fitting procedures as explained in the text. The vertical bars in (b) correspond to the probabilities $p_m\left(x\right)$ predicted by Eq. (3).

Figure 5

Energy spectra of neutrons scattered from $\mathrm{KM}{\mathrm{n}}_x\mathrm{Z}{\mathrm{n}}_{1-x}{\mathrm{F}}_3$ at $T=2\mathrm{K}$ with incoming neutron energy of 1.55 meV. (a) New data for $x=0.01$. (b) Data taken from Ref. [2]. The lines in (a) and (b) are the result of least-squares fitting procedures as explained in the text. The vertical bars correspond to the probabilities $p_m\left(x\right)$ predicted by Eq. (3).