Spin dynamics and magnetoelectric properties of the coupled-spin tetrahedral compound ${\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{O}}_5{\mathrm{Cl}}_2$

We report on the spin dynamics and discovery of magnetoelectricity in the coupled-spin tetrahedral compound ${\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{O}}_5{\mathrm{Cl}}_2$. ${}^{125}\mathrm{Te}$ NMR measurements show an anomalous resonance frequency shift and a signal wipe-out phenomenon around the Néel temperature $T_N$ = 18.2 K, which could be attributed to the anomalous critical slowing down of the Cu spin fluctuations on the NMR time scale ($\sim 10$–100 MHz). The critical exponent of ${\left(T_{1}T\right)}^{-1}\propto {(T-T_N)}^{-\alpha }$ is 0.40 ± 0.03, as compared to 0.5 for a three-dimensional mean-field model. This is in contrast to the Br compound [S.-H. Baek et al., Phys. Rev. B 86, 180405 (2012)], which exhibits pronounced singlet dynamics with a large spin gap. Electric polarization ($P_{\mathrm{c}}$) is observed along the $c$ axis for temperatures below $T_N$ under finite magnetic field but not sensitive to the electric poling. $P_{\mathrm{c}}$ increases sharply over zero to 2 T and then reaches saturation. Below $T_N{}_{,}$ $P_{\mathrm{c}}$ changes its sign depending on the applied magnetic field direction, positive for the $H\perp c$ axis and negative for $H$ ∥ $c$ axis. We discuss possible explanations for the observed magnetoelectric (ME) behavior in terms of linear ME effect, spin-driven multiferroicity, and an exchange striction of intertetrahedral exchange paths involving the ${\mathrm{Te}}^{4+}$ lone-pair ions. Our results suggest that ${\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{O}}_5{\mathrm{Cl}}_2$ is a type of ME material whose properties are tuned by intertetrahedral exchange interactions involving polarizable ${\mathrm{Te}}^{4+}$ ions.

Figure 1

Crystal structure of ${\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{O}}_5{\mathrm{Cl}}_2$ along the $c$ axis. The unlabeled atoms are the oxygen atoms.

Figure 2

Field-swept ${}^{125}\mathrm{Te}$ NMR spectra of a single crystal of ${\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{O}}_5{\mathrm{Cl}}_2$ obtained by integrating spin-echo intensity as a function of temperature. The upper inset shows two field-swept spectra obtained at $T$ = 30 K, one in an arbitrary field direction and one with H∥c, plotted against the Knight shift. The arrow indicates the peak used for the relaxation measurements (see main text). The lower inset shows the spectra for temperatures below $T_N$, obtained at ν = 111 MHz.

Figure 3

Wide-range ${}^{125}\mathrm{Te}$ NMR spectrum at $T$ = 4.2 K, i.e., below the magnetic transition. The double-horn line shapes are a signature of incommensurate magnetic ordering.

Figure 4

Temperature dependence of the magnetic shift $K$ of the ${}^{125}\mathrm{Te}$ nuclear spins measured in the field direction of $H$//$c$. The solid line is the SQUID (superconducting quantum interference device) susceptibility measurements. The inset shows a relative frequency shift of the NMR line versus dc susceptibility. The solid lines are the fits to Eq. (1).

Figure 5

${}^{125}\mathrm{Te}$ spin-lattice relaxation rate $1/T_1$ (circles) and spin-spin relaxation rate 1/$T_2$ (squares) on a logarithmic temperature scale at frequencies of ν = 111 MHz (open symbols) and ν = 94 MHz (filled symbols). The dashed vertical bar indicates the magnetic ordering temperature $T_N$.

Figure 6

${\left(T_{1}T\right)}^{-1}$ versus temperature at ν = 111 MHz. The lines are fits to Eq. (2). See the text for details.

Figure 7

Temperature dependence of dielectric constant (${\varepsilon }_c^{\prime }$) with the electric field parallel to the $c$ axis. The magnetic field is applied either parallel (solid line or solid symbol) or perpendicular (dotted line or open symbol) to the $c$ axis. Upper inset: expansion of ${\varepsilon }_c^{\prime }$ around the transition. Lower inset: magnetic field dependence of ${\varepsilon }_c^{\prime }$ for $H$//$c$.

Figure 8

Temperature dependence of electric polarization (a) for $H$⊥$c$ and (b) $H$//$c$.

Figure 9

(a) Pyroelectric current at $H$ = 7 T for different poling electric fields of +190 (blue open circles) and −190 kV/m (red solid line) for H⊥$c$ and +190 kV/m (full green circles) for $H$//$c$ configuration. The curves for $H$⊥$c$ are lying on top of each other. (b) Magnetic field dependence of the absolute value of polarization (|$P_c$|) measured at $T$ = 5 K. The dashed lines are linear fits to |$P_c$| for fields below 2 T.