Magnetic ordering and spin excitations in the frustrated magnet $\mathrm{Mn}{\mathrm{Sc}}_2{\mathrm{S}}_4$

The $A$-site spinel compound $\mathrm{Mn}{\mathrm{Sc}}_2{\mathrm{S}}_4$ exhibits strong frustration effects with a low ordering temperature $(T_N=2.3\mathrm{K})$. Detailed neutron-scattering investigations have been performed to study the magnetic ordering process and the associated magnetic excitations. The magnetic structure found at $T=1.5\mathrm{K}$ is a spiral within the $a\text{−}b$ plane characterized by a propagation vector of $\mathbf{q}=(3∕4,3∕4,0)$. The magnetic ordering process is spectroscopically reflected by a change from a purely quasielastic to an inelastic response. The quasielastic line width corresponds to a magnetic energy scale of $\approx 1\mathrm{meV}$ which is consistent with the spin wave stiffness as determined from the magnon dispersion at low temperatures.

Figure 1

(Color online) Coordination polyhedra of the spinel structure of $\mathrm{Mn}{\mathrm{Sc}}_2{\mathrm{S}}_4$. $A$-site Mn (red, dark grey) is embedded in a tetrahedral environment of sulphur (yellow, light grey), while $B$-site Sc has octahedral environment (left part). The $A$-site exchange is mediated via three different Mn-S-Sc-S-Mn interaction paths. The configuration containing nearest, next-nearest, and next-next-nearest neighbors of the $A$-site sublattice with corresponding exchange constants $J$, $J^{\prime }$, and $J^{″}$ is shown at the right. The right part corresponds to a projection of four neighboring $A$-site ions onto the [110]-[111] plane.

Figure 2

(Color online) Low-temperature part of the magnetic susceptibility of $\mathrm{Mn}{\mathrm{Sc}}_2{\mathrm{S}}_4$ and the corresponding Curie-Weiss fit as determined for temperatures between 50 and $400\mathrm{K}$ (full line). ${\theta }_{\mathrm{CW}}$ and the ordering temperatures $T_{N1}$ and $T_{N2}$ are indicated.

Figure 3

(Color online) Neutron powder diffraction pattern of $\mathrm{Mn}{\mathrm{Sc}}_2{\mathrm{S}}_4$ at $T=25\mathrm{K}$ measured on HRPT $(\lambda =1.154\mathrm{\AA })$. Shown are observed (open circles) and calculated (full line) intensities, as well as their difference (full line at the bottom) and the corresponding peak positions.

Figure 4

(Color online) Detailed neutron-powder-diffraction pattern of $\mathrm{Mn}{\mathrm{Sc}}_2{\mathrm{S}}_4$ at $T=1.6\mathrm{K}$ in the low-$Q$ range $(\lambda =2.45\mathrm{\AA })$ measured on D20. Shown are observed (open circles) and calculated intensities (full line), as well as their difference (bottom line). The vertical bars indicate the peak positions corresponding to the crystallographic (upper row) and magnetic (lower row) structure, respectively.

Figure 5

The magnetic structure of $\mathrm{Mn}{\mathrm{Sc}}_2{\mathrm{S}}_4$ within the $a\text{−}b$ plane showing a cycloidic spin arrangement.

Figure 6

Temperature dependence of the ordered magnetic moment of $\mathrm{Mn}{\mathrm{Sc}}_2{\mathrm{S}}_4$ compared to an $S=5∕2$ Brillouin function (full line). The dashed line is a guide to the eye according to two magnetic transitions occurring at $T_{N1}$ and $T_{N2}$, respectively, as indicated by the arrows.

Figure 7

(Color online) Upper frame: The temperature dependence of the first magnetic Bragg reflection of $\mathrm{Mn}{\mathrm{Sc}}_2{\mathrm{S}}_4$ around $0.62{\mathrm{\AA }}^{-1}$ measured on D20. The magnetic signal has two components: a sharp resolution limited and Gaussian shaped component and an additional broad Lorentzian shaped line. Lower frame: Temperature dependence of the corresponding two magnetic intensities based on fit results of HRPT data. Magnetic transition temperatures are indicated by arrows.

Figure 8

(Color online) Contour plot of $S(Q,\omega )$ of $\mathrm{Mn}{\mathrm{Sc}}_2{\mathrm{S}}_4$ at $T=75\mathrm{K}$ in the paramagnetic state (upper panel) and at $T=1.6\mathrm{K}$ in the afm magnetically ordered state (lower panel), respectively. Magnetic intensities are shown in a suitable color coding on a logarithmic scale.

Figure 9

$S\left(\omega \right)$ at constant $Q=0.4{\mathrm{\AA }}^{-1}$ of $\mathrm{Mn}{\mathrm{Sc}}_2{\mathrm{S}}_4$ at $T=75\mathrm{K}$ (lower panel), $T=10\mathrm{K}$ (middle), and at $T=1.6\mathrm{K}$ (upper panel) in the afm magnetically ordered state, respectively. The inset shows the temperature dependence of the quasielatic line width.

Figure 10

(Color online) Detailed part of $S(Q,\omega )$ around the first magnetic reflection. The full line corresponds to a fit of the magnetic excitations according to an antiferromagnetic spin wave dispersion.

Figure 11

(Color online) Upper part: Energy integrated structure factor $S\left(Q\right)$ for various energy width to illustrate the role of magnetic fluctuations onto the peak shape. Lower part: Pure elastic scattering of $\mathrm{Mn}{\mathrm{Sc}}_2{\mathrm{S}}_4$ for various temperatures.