Elementary excitations in single-chain magnets

Single-chain magnets (SCMs) are one-dimensional coordination polymers or spin chains that display slow relaxation of the magnetization. Typically their static magnetic properties are described by the Heisenberg model, while the description of their dynamic magnetic properties is based on an Ising-like model. The types of excitations predicted by these models (collective vs localized) are quite different. Therefore we probed the nature of the elementary excitations for two SCMs abbreviated ${\mathrm{Mn}}_2\mathrm{Ni}$ and ${\mathrm{Mn}}_2\mathrm{Fe}$, as well as a mononuclear derivative of the ${\mathrm{Mn}}_2\mathrm{Fe}$ chain, by means of high-frequency electron paramagnetic resonance spectroscopy (HFEPR) and inelastic neutron scattering (INS). We find that the HFEPR spectra of the chains are clearly distinct from those of the monomer. The momentum transfer dependence of the INS intensity did not reveal significant dispersion, indicating an essentially localized nature of the excitations. At the lowest temperatures these are modified by the occurrence of short-range correlations.

Figure 1

Experimental (top) HFEPR and simulated (bottom) spectra of powder samples of ${\mathrm{Mn}}_2\mathrm{Fe}$ monomer at 5 K and different frequencies as indicated by the value on the ordinate axis. Spectra were normalized to their maximum intensities. The simulation parameters were $J_{xx}=-44.0$ K, $J_{yy}=-51.8$ K, $J_{zz}=57.8$ K, and $D_{\mathrm{Mn}}=-2.8$ K.

Figure 2

Top: Experimental HFEPR of a powder sample of ${\mathrm{Mn}}_2\mathrm{Fe}$ chain at 5 K and different frequencies as indicated by the value on the ordinate axis. Spectra were normalized to their maximum intensities. Bottom: Field-modulated frequency-domain magnetic resonance spectrum of the same compound at 5 K in the absence of a static applied field.

Figure 3

Experimental resonance positions of parallel (triangles) and perpendicular (circles) transitions observed for ${\mathrm{Mn}}_2\mathrm{Fe}$, as well as fits according to Eq. (3). The solid red line corresponds to the Heisenberg fit with $J_{\mathrm{MnMn}}=-0.3\left(3\right)$ K, $J_{\mathrm{MnFe}}=-13.1\left(10\right)$ K, and $D_{\mathrm{Mn}}=-5.7\left(1\right)$ K. The dashed black line corresponds to the Ising fit with $J_{\mathrm{MnMn},\mathrm{zz}}=-0.3\left(3\right)$ K, $J_{\mathrm{MnFe}}=-12.5\left(5\right)$ K, and $D_{\mathrm{Mn}}=-5.5\left(1\right)$ K.

Figure 4

Experimental resonance positions of parallel (triangles) and perpendicular (circles) transitions, observed for ${\mathrm{Mn}}_2\mathrm{Ni}$, as well as fits according to Eq. (3). The solid red line corresponds to the Heisenberg fit with $J_{\mathrm{MnMn}}=-1.2\left(4\right)$ K, $J_{\mathrm{MnNi}}=+37\left(2\right)$ K, and $D_{\mathrm{Mn}}=-5.0\left(1\right)$ K. The dashed black line corresponds to the Ising fit with $J_{\mathrm{MnMn},\mathrm{zz}}=-1.2\left(1\right)$ K, $J_{\mathrm{MnMn}}=+37\left(1\right)$ K, and $D_{\mathrm{Mn}}=-4.1\left(1\right)$ K.

Figure 5

Experimental scattering function as a function of the energy and momentum transfer, recorded on a powder sample of ${\mathrm{Mn}}_2\mathrm{Ni}$ at an incident neutron wavelength of 4.8 Å and $T=1.8$ K.

Figure 6

One-dimensional slices through the experimental scattering function reported in Fig. 5. Top: Scattering function as a function of the energy transfer integrated between $0.45{\AA }^{-1}<q<0.95{\AA }^{-1}$. Spectra were baseline corrected by subtracting a four-point spline curve to correct for the increase in the baseline with temperature due to the increase and broadening of the phonon lines at higher energies. Bottom: Scattering function as a function of the momentum transfer integrated between $1.2\mathrm{meV}<E<1.6$ meV. The dotted gray line is the expected dispersion for a spin-wave excitation, averaged over all angles between scattering vector and chain direction.