Brownian motion and quantum dynamics of magnetic monopoles in spin ice

Abstract

Spin ice illustrates many unusual magnetic properties, including zero point entropy, emergent monopoles and a quasi liquid–gas transition. To reveal the quantum spin dynamics that underpin these phenomena is an experimental challenge. Here we show how crucial information is contained in the frequency dependence of the magnetic susceptibility and in its high frequency or adiabatic limit. The typical response of Dy2Ti2O7 spin ice indicates that monopole diffusion is Brownian but is underpinned by spin tunnelling and is influenced by collective monopole interactions. The adiabatic response reveals evidence of driven monopole plasma oscillations in weak applied field, and unconventional critical behaviour in strong applied field. Our results clarify the origin of the relatively high frequency response in spin ice. They disclose unexpected physics and establish adiabatic susceptibility as a revealing characteristic of exotic spin systems.

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.…”

“…Interestingly, the resulting crossover appears to be markedly different from the one extracted from the full-width at half-maximum of n p ; however, it is reminiscent of the one observed in the adiabatic susceptibility in ref. 12, see Supplementary Fig. 5 and the Supplementary Discussion for further information.…”

“…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. One expects that a second relaxation process, which has not been detected yet, eventually leads to a vanishing of w 0 (n) at even larger n. The first, slow relaxation process has been associated with the Brownian diffusion of monopole excitations 5,12 .…”

“…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.…”

Far-from-equilibrium monopole dynamics in spin ice

“…This has been discussed in terms of intrinsic kinetic effects 22 , slowing down of the monopole hop rate 18,23,24 , and the trapping of monopoles on extrinsic defects 23 , and it is likely that all such factors play a role. However, the degree of non-equilibration has not hitherto been brought under experimental control.…”