Evidence for unidimensional low-energy excitations as the origin of persistent spin dynamics in geometrically frustrated magnets

We report specific heat, magnetic, and muon spin relaxation measurements performed on a polycrystalline sample of the normal spinel ${\mathrm{CdHo}}_2{\mathrm{S}}_4$. The rare-earth ions sit on a lattice of corner-sharing regular tetrahedra as in pyrochlore compounds. Magnetic ordering is detected at $T_{\mathrm{c}}\simeq 0.87$ K. From spin-lattice relaxation rate measurements on both sides of $T_{\mathrm{c}}$ we uncover similar magnetic excitation modes driving the so-called persistent spin dynamics at $T<T_{\mathrm{c}}$. Unidimensional excitations are argued to be at its origin. Often observed spin loop structures are suggested to support these excitations. The possibility of a generic mechanism for their existence is discussed.

Figure 1

(a) Rare-earth ions lattice in the pyrochlore $R_2{M}_2{\mathrm{O}}_7$ and normal spinel $\mathrm{Cd}{R}_2{X}_4$ compounds. The thicker light blue (thinner dark blue) bold line represents a 6 (10)-site loop. (b) Low-temperature heat capacity of ${\mathrm{CdHo}}_2{\mathrm{S}}_4$.

Figure 2

Inverse of the magnetic susceptibility versus temperature. The data have been measured in a magnetic field of 1.1 mT. The solid line results from a fit of the Curie-Weiss law to the data measured above 150 K. The susceptibility is dimensionless since we use SI units.

Figure 3

Magnetic measurements for a ${\mathrm{CdHo}}_2{\mathrm{S}}_4$ powder sample. The data for the magnetic susceptibility $\chi$ versus temperature were recorded with external fields $B_{\mathrm{ext}}$ ranging from 0.5 to 50 mT and were found to match one another. The field was applied in the plane of the sample pellet so that the demagnetization field is small. The solid line at low temperature together with the dotted line extension above $T_{\mathrm{c}}$ represents a fit of the function $C_{\mathrm{fs}}/(T-{\theta }_{\mathrm{CW},\mathrm{fs}})+a+bT$ to the data recorded below $T_{\mathrm{c}}$. The former term represents the contribution of weakly interacting ${\mathrm{Ho}}^{3+}$ spins, while the remaining terms describe the majority spin state; see main text. The quantity $K_{\exp }$, defined in the main text and measured for different $B_{\mathrm{ext}}$ as indicated in the figure, is shown for comparison.

Figure 4

$\mu \mathrm{SR}$ spectra recorded in a transverse of 50 mT at 0.2 and 1.2 K. The full lines are the results of fits to the data. The model consists of a sum of two exponentially damped cosine functions, the former and latter accounting for muons stopped in the sample and its surroundings, respectively. The amplitudes extracted from the fits are temperature independent for the two components. The precession frequency ${\nu }_{\mu }$ of the former provides a measure of the mean field $\langle B_{\mu }\rangle$ = $2\pi {\nu }_{\mu }/{\gamma }_{\mu }$ at the muon site in the sample; see main text for details. ${\gamma }_{\mu }=851.615\mathrm{Mrad}{\mathrm{s}}^{-1}{\mathrm{T}}^{-1}$ is the muon gyromagnetic ratio.

Figure 5

Magnetic moment per holmium ion of a ${\mathrm{CdHo}}_2{\mathrm{S}}_4$ powder versus field measured for different temperatures as indicated in the figure.

Figure 6

External field derivative of the ${\mathrm{Ho}}^{3+}$ magnetic moment of a ${\mathrm{CdHo}}_2{\mathrm{S}}_4$ powder for different temperatures as indicated in the figure.

Figure 7

Four $\mu \mathrm{SR}$ spectra recorded for a ${\mathrm{CdHo}}_2{\mathrm{S}}_4$ powder sample, two zero-field spectra taken on both sides of the magnetic phase transition temperature $T_{\mathrm{c}}$, and two longitudinal field spectra recorded at $T=0.12$ K, i.e., $T\ll T_{\mathrm{c}}$. The early time details are shown in the insert. The solid lines result from fits as explained in the main text.

Figure 8

Spin-lattice relaxation rate ${\lambda }_Z$ versus longitudinal field intensity $B_{\mathrm{ext}}$ and temperature $T$ for a ${\mathrm{CdHo}}_2{\mathrm{S}}_4$ powder. In the main frame is displayed ${\lambda }_Z\left(B_{\mathrm{ext}}\right)$ for two temperatures below and above $T_{\mathrm{c}}$. The ${\lambda }_Z(T=0.12\mathrm{K})$ maximum occurs at 20 mT. The solid lines are explained in the main text. The dashed line at small $B_{\mathrm{ext}}$ and $T=0.12$ K is a guide to the eyes. In the insert is displayed ${\lambda }_Z\left(T\right)$ measured from 0.019 to 55 K under zero field or $B_{\mathrm{ext}}=5$ mT. The temperature $T_{\mathrm{c}}$ at which the compound exhibits a magnetic phase transition is specified by an arrow.