Dielectric Relaxation by Quantum Critical Magnons

We report the experimental observation of dielectric relaxation by quantum critical magnons. Complex capacitance measurements reveal a dissipative feature with a temperature-dependent amplitude due to low-energy lattice excitations and an activation behavior of the relaxation time. The activation energy softens close to a field-tuned magnetic quantum critical point at $H=H_c$ and follows single-magnon energy for $H>H_c$, showing its magnetic origin. Our study demonstrates the electrical activity of coupled low-energy spin and lattice excitations, an example of quantum multiferroic behavior.

Figure 1

False color plots of complex capacitance $\mathrm{\Delta }C=\mathrm{\Delta }{C}^{\prime }+i\mathrm{\Delta }{C}^{\prime \prime }$. The electric field is applied parallel to the ${\mathit{c}}^{*}$ axis. The magnetic field is applied along two orthogonal crystallographic directions: (a),(b) $\mathit{H}\parallel \mathit{a}$ and (c),(d) $\mathit{H}\parallel {\mathit{c}}^{*}$. The color scale is shared across (a) and (c), and (b) and (d), respectively. It has been chosen to highlight the novel low temperature anomalies (arrows). As a result some stronger peaks at the magnetic phase boundary (dashed line, Ref. [26]) are blown out.

Figure 2

Constant-field measurements of complex capacitance. (a) Regardless of the applied field, all capacitance curves collapse on a single line (solid black line) at elevated temperatures. The data shown in (b), real part, and (c), imaginary part, were normalized by the thus determined “background.” The geometry corresponds to that of Figs. 1 and 1 $\mathit{E}\parallel {\mathit{c}}^{*}$ and $\mathit{H}\parallel \mathit{a}$. In all panels, same colors correspond to same magnetic field values. An offset of 0.4 units has been added between sets for visibility. Black solid lines show the best fit to the Cole-Cole model of Eq. (1). Note that both panels show the same scale and units. Shaded triangles denote the position of $T^{*}$.

Figure 3

Frequency dependence of complex capacitance at zero magnetic field: (a) real and (b) imaginary parts. The excitation frequency is consistently color-coded in the two panels. An offset of 0.5 units has been added for clarity. Black lines show the best fit to Eq. (1) with parameters fixed from Fig. 2.

Figure 4

Characteristic energy barrier extracted from Cole-Cole model (circles). Above the QCP, it follows the Zeeman energy of a single magnon, given by a pink dashed line. Triangles represent the position of $T^{*}$, at which the relaxing dissipative anomaly is observed. For completeness, the phase boundary is depicted, showing the PM-PE (paramagnetic-paraelectric) and AF-FE phases (shadowed) [26].