Supercooled spin liquid state in the frustrated pyrochlore Dy ₂ Ti ₂ O ₇

Abstract

A "supercooled" liquid develops when a fluid does not crystallize upon cooling below its ordering temperature. Instead, the microscopic relaxation times diverge so rapidly that, upon further cooling, equilibration eventually becomes impossible and glass formation occurs. Classic supercooled liquids exhibit specific identifiers including microscopic relaxation times diverging on a Vogel-TammannFulcher (VTF) trajectory, a Havriliak-Negami (HN) form for the dielectric function e(ω, T ), and a general Kohlrausch-Williams-Watts (KWW) form for time-domain relaxation. Recently, the pyrochlore Dy 2 Ti 2 O 7 has become of interest because its frustrated magnetic interactions may, in theory, lead to highly exotic magnetic fluids. However, its true magnetic state at low temperatures has proven very difficult to identify unambiguously. Here, we introduce highprecision, boundary-free magnetization transport techniques based upon toroidal geometries and gain an improved understanding of the time-and frequency-dependent magnetization dynamics of Dy 2 Ti 2 O 7 . We demonstrate a virtually universal HN form for the magnetic susceptibility χ (ω, T ), a general KWW form for the realtime magnetic relaxation, and a divergence of the microscopic magnetic relaxation rates with the VTF trajectory. Low-temperature Dy 2 Ti 2 O 7 therefore exhibits the characteristics of a supercooled magnetic liquid. One implication is that this translationally invariant lattice of strongly correlated spins may be evolving toward an unprecedented magnetic glass state, perhaps due to many-body localization of spin.spin liquid | supercooled liquids | magnetic dynamics | periodic boundaries C ooling a pure liquid usually results in crystallization via a first-order phase transition. However, in glass-forming liquids when the cooling is sufficiently rapid, a metastable "supercooled" state is achieved instead (1-3). Here, the microscopic relaxation times diverge until equilibration of the system is no longer possible at a given cooling rate. At this juncture there is generally a broad peak in the specific heat preceding the glass transition, at which no symmetry-breaking phase transition occurs (Fig. 1A). The antecedent fluid exhibits a set of phenomena characteristic of the supercooled liquid state (1-3). For example, the divergence of microscopic relaxation times τ 0 ðTÞ typically shows substantial departures from Arrhenius behavior [τ 0 ðTÞ = AexpðΔ=kTÞ and, instead, is described characteristically using the Vogel-Tammann-Fulcher (VTF) form (4)Here, T 0 is a temperature at which the relaxation time diverges to ∞ while D characterizes the extent of the super-Arrhenius behavior (Fig. 1B). One way to establish τ 0 ðTÞ is by measuring the characteristic frequency ω 0 ðTÞ = 1=τ 0 ðTÞ of peaks in the dissipative (imaginary) component of the dielectric function «ðω, TÞ.For classic supercooled liquids, «ðω, TÞ generally exhibits the Havriliak-Negami (HN) form (5, 6) «ðω,[2]Here, the exponents α and γ describe, respectively, the broadening and asymmetry of the rela...

Magnetic monopole noise

“…25,35 and thus correspond well with the -( ) derived from numerous susceptibility studies of this material (Refs. 22,23,24,25). However, the correspondence between -( ) and ( ) reported in this work remains to be understood within a quantitative microscopic theory.…”

“…These clearly follow a quantitatively equivalent trajectory to the ac susceptibility -( ) of Ref. 25,35 and thus correspond well with the -( ) derived from numerous susceptibility studies of this material (Refs. 22,23,24,25).…”

“…The superconducting pickup coil is wound around the SH and consists of 6 turns of thin Nb wire with inductance ≈ 0. 25 . The input inductance of the QD 550 SQUID is reported by the manufacturer (Quantum Design) to be =2.…”

“…It has been established empirically that the susceptibility-derived time constants -( ) representing the magnetization dynamics of Dy2Ti2O7 diverge with decreasing T (Refs 22,23,24) and are likely heterogeneous 25,35 . This type of ac susceptibility measurement has been made for Dy2Ti2O7 in different sample shapes ranging from polycrystalline samples 24 to toroidal single crystals 25,35 In E.D. Fig.…”

“…Additionally, evidence for a heterogeneous distribution of microscopic spin relaxation rates contributing to -( ) had been adduced from the stretched-exponential form for the time dependence of magnetization 25,35 in Dy2Ti2O7. From consideration of the related ac susceptibility studies [22][23][24][25]35 and the similarity between -( ) and ( ) , we estimate that any effects of such heterogeneity on the flux-noise spectrum S ¥ (ω, T) would first become visible at temperatures below T=1K. Therefore, they are unlikely to have been detected in these first SNS studies.…”