Two-Dimensional Monopole Dynamics in the Dipolar Spin Ice Dy₂Ti₂O₇

Abstract

The spin dynamics of the dipolar spin-ice Dy 2 Ti 2 O 7 under a dc magnetic field (B dc ) along the [111] direction has been investigated using ac susceptibility ( ac ), which enables us to study two-dimensional monopole motion in an ac magnetic field perpendicular to B dc . We have observed the slowing down of monopole dynamics in the kagomé spinice regime (B dc $ 0:4 T) and the extreme speeding up under B dc close to the critical point (B dc $ 0:93 T). An analysis using a Monte Carlo simulation suggests that the dynamics changes from a random walk of monopoles to a collective motion as B dc increases.

Critical speeding-up in the magnetoelectric response of spin-ice near its monopole liquid–gas transition

“…2a. The loss peak in the imaginary part w 00 (n) at a temperature of 2 K is located at n w p % 350 Hz, and the resulting relaxation time, t ¼ 1/(2pn p ), is in nice agreement with previously reported results [9][10][11][12][13] . Although our spectral range for w(n) is also experimentally limited to nr1 kHz, it is already apparent that the real part w 0 (n) levels off at a finite value at higher frequencies.…”

“…The critical speeding-up close to the critical end point in spin-ice might be a generic property of monopole dynamics that is not only reflected in the dielectric but might be also detectable in the magnetic response. In fact, recent results for the dynamical susceptibility by Takatsu et al 13 obtained down to 0.5 K provide first evidence that the relaxation of the magnetization also exhibits a pronounced speeding-up. The corresponding inverse relaxation time 1/t at low T was found to increase sharply as a function of magnetic field, similarly as our results for n p in Fig.…”

“…Nevertheless, for the limited frequency range considered in ref. 13, it was argued that single spin-flip Monte Carlo dynamics already accounts for the speeding-up, hinting at a critical enhancement of monopole diffusion.…”

“…We confirmed this magnetoelectricity in Dy 2 Ti 2 O 7 and, in addition, demonstrated that the dielectric dynamics gets dramatically modified close to the monopole liquid-gas transition resulting in a critical speeding-up. In order to confirm its precise link to monopoles, detailed measurements of the critical magnetic dynamics at frequencies extending 1 kHz are now called for 13 . Besides elucidating a peculiar aspect of the dynamical critical behaviour of monopole condensation, our findings provide a proof of principle for dielectric spectroscopy of monopoles in spin-ice.…”

“…2a,b. The spin dynamics up to kHz frequencies was already intensively explored by magnetic a.c.-susceptibility w(n) measurements [8][9][10][11][12][13] . In zero magnetic field the corresponding spin relaxation time is found to be temperature-independent between 3 and 12 K but increases exponentially at lower temperatures as the ice rules start to establish themselves.…”