Quantum & Classical Spin Liquids
Discovery of Dynamical Heterogeneity in a Supercooled Magnetic Monopole Fluid
Essence: Dynamical heterogeneity is fundamental to the theory of all supercooled liquids transitioning into the glass state. But its spatiotemporal phenomenology has remained unobservable for virtually all molecular glass-forming liquids.Now, for the first time we directly detect and quantify dynamical heterogeneity by experimentally measuring the temperature dependence of its four-point dynamical susceptibility χ4(T,t) of supercooled monopole fluids.
Left: Schematic snapshot of theorists anticipation of dynamic heterogeneity in all glass forming fluids. Right: First experimental measurement of four-point dynamical susceptibility χ4(T,t) of supercooled liquid, in this case a monopole fluid, show that theoretically classic signature of dynamical heterogeneity diverging with length scales coincident with slowing time scales.
Dynamical heterogeneity, in which transitory local fluctuations occur in the conformation and dynamics of constituent particles, is widely hypothesized to be essential to evolution of general supercooled liquids into the glass state. Yet its microscopic spatiotemporal phenomenology has remained unobservable in virtually all molecular glass forming liquids. Because recent theoretical advances predict that corresponding dynamical heterogeneity could occur in supercooled magnetic monopole fluids (which we had previously identified PNAS 112, 8549-8554 (2015)), we searched for such phenomena in Dy2Ti2O7.
By measuring its microsecond-resolved spontaneous magnetization fluctuations M(t,T) we discovered a sharp bifurcation in monopole noise characteristics below T≈1500 mK, with the appearance of powerful spontaneous monopole current bursts. This intense dynamics emerges entering the supercooled monopole fluid regime, reaches maximum strength near T≈500 mK and then terminates along with coincident loss of ergodicity near T≲250 mK. Moreover, the four-point dynamical susceptibility χ4(T,t) can now be observed experimentally for the first time. χ4 evolves as predicted when dynamical heterogeneity is present, clearly revealing its diverging length scales ξ(T). This overall phenomenology greatly expands our empirical knowledge of supercooled monopole fluids and, perhaps more generally, demonstrates direct detection of the time sequence, magnitude, statistics and correlations of dynamical heterogeneity in supercooled quantum matter, access to which may greatly accelerate fundamental vitrification studies.
Spiral Spin Liquid Noise
Essence: By comparing the temperature and frequency dependence of spin noise generated by Ca10Cr7O28, with Monte-Carlo simulations of a 2D spiral spin liquid state - parametrized for the same material - we find quantitative correspondence with the spin noise power spectral density SM(ω,T), its correlation function CM(t,T), and its total power σ2M(T), thus identifying it as a classical spiral spin liquid.
Top row: Snapshot configurations of in-plane spin polarization in the dynamic of a spiral spin liquid temperature falling from left to right. Bottom row: two presentative of the measured power spectral density of spin noise in Ca10Cr7O28, highly consist with the Monte-Carlo simulation of spin noise spectra in a spiral spin liquid.
An emerging concept for identification of different types of spin liquids is through the use of spontaneous spin noise. We developed spin noise spectroscopy for spin liquid studies by considering Ca10Cr7O28, a material hypothesized to be either a quantum or a spiral spin liquid. We measured the time and temperature dependence of spontaneous flux Φ(t,T) and thus magnetization M(t,T) of Ca10Cr7O28 samples. The resulting power spectral density of magnetization noise SM(ω,T) reveals intense spin fluctuations with SM(ω,T) ∝ω−α(T) and 0.84 < α(T) < 1.04 . Both the variance σ2M(T) and the correlation function CM(t,T) of this spin noise undergo crossovers at a temperature T∗≈ 450 mK. While predictions for quantum spin liquids are inconsistent with this phenomenology, those from Monte-Carlo simulations of a 2D spiral spin liquid state in Ca10Cr7O28 yield overall quantitative correspondence with the measured frequency and temperature dependences of SM(ω,T),CM(t,T) and σ2M(T), thus indicating that Ca10Cr7O28 is a classical spin liquid.
Dichotomous Dynamics of Magnetic Monopole Fluids
Essence: By developing an ammeter for magnetic monopole currents, we reveal a sharp dichotomy of field-driven monopole currents, separated by distinct relaxation time-constants before and after t≈600μs from monopole transport imitation. This is consistent with recent fractal-network transport theory for magnetic monopole transport in spin ice.
Schematic of our monopole current ammeter setup which use a DC-SQUID to measure monopole currentsJ(t)= (dΦ/dt)1/μ0 with microsecond time resolution and with sensitivity J<100 monopole per second .
A recent advance in the study of emergent magnetic monopoles was the discovery that monopole motion is restricted to dynamical fractal trajectories (Science 378, 1218 (2022)). We explored the dynamics of field-driven monopole currents, finding them comprised of two quite distinct transport processes: initially swift fractal rearrangements of local monopole configurations followed by conventional monopole diffusion. The theory also predicts a characteristic frequency dependence of the dissipative loss-angle for AC-field-driven currents. To explore these novel perspectives we introduce simultaneous monopole current control and measurement techniques using SQUID-based monopole current sensors. For the canonical material Dy2Ti2O7, we measure Φ(t), the time-dependence of magnetic flux threading the sample when a net monopole current J(t)= (dΦ/dt)1/μ0 is generated by applying an external magnetic field B0(t). These experiments find a sharp dichotomy of monopole currents, separated by their distinct relaxation time-constants before and after t≈600μs from monopole current initiation. Application of sinusoidal magnetic fields B0(t)=Bcos(ωt) generates oscillating monopole currents whose loss angle θ(f) exhibits a characteristic transition at frequency f≈1.8 kHz over the same temperature range. This complex phenomenology represents a new form of heterogeneous dynamics generated by the interplay of fractionalization and local spin configurational symmetry.
Magnetic Monopole Noise
Essence: By developing and introducing spin noise spectroscopy for study of spin liquids we discovered the existence of spontaneous magnetization noise generated by a fluid of emergent magnetic monopoles in Dy2Ti2O7 crystals. Virtually all the elements of spin noise power spectral density S(ω,T) predicted for a magnetic monopole plasma were revealed for the firs time & confirmed consistent with theory.
Top left: Schematic of DC-SQUID based monopole noise spectrometer. Top right: Typical Dy2Ti2O7 sample studied. Bottom row: Comparison of measured magnetic monopole noise power spectral density to that predicted by Monte-Carlo simulations from accurate Dy2Ti2O7 spin-ice Hamiltonian.
Magnetic monopoles are hypothetical elementary particles exhibiting quantized magnetic charge m0=±(h/μ0e) and quantized magnetic flux Φ0=±h/e. A classic proposal for detecting such magnetic charges is to measure the quantized jump in magnetic flux Φ threading the loop of a superconducting quantum interference device (SQUID) when a monopole passes through it. Naturally, with the theoretical discovery that a plasma of emergent magnetic charges should exist in several lanthanide-pyrochlore magnetic insulators, including Dy2Ti2O7, this SQUID technique was proposed for their direct detection. Experimentally, this has proven extremely challenging because of the high number density, and the generation-recombination (GR) fluctuations, of the monopole plasma. Recently, however, theoretical advances have allowed the spectral density of magnetic-flux noise SΦ(ω,T) due to GR fluctuations of ±m* magnetic charge pairs to be determined. These theories present a sequence of strikingly clear predictions for the magnetic-flux noise signature of emergent magnetic monopoles. Here we report development of a high-sensitivity, SQUID based flux-noise spectrometer, and consequent measurements of the frequency and temperature dependence of SΦ(ω,T) for Dy2Ti2O7 samples. Virtually all the elements of SΦ(ω,T) predicted for a magnetic monopole plasma, including the existence of intense magnetization noise and its characteristic frequency and temperature dependence, are detected directly. Moreover, comparisons of simulated and measured correlation functions CΦ(t) of the magnetic-flux noise Φ(t) imply that the motion of magnetic charges is strongly correlated because traversal of the same trajectory by two magnetic charges of same sign is forbidden.
Supercooled Spin Liquid in Dy2Ti2O7
Essence: We demonstrate a virtually universal Havriliak-Negami form for the magnetic susceptibility, an equivalently universal Kohlrausch-Williams-Watts form for the real-time magnetic relaxation dynamics, and the corresponding divergence of the microscopic relaxation rates with the Vogel-Tammann-Fulcher trajectory for low temperature magnetization of Dy2Ti2O7. Therefore the magnetic state of this material exhibits all the characteristics of a supercooled spin liquid.
The frequency (HN) and time (KWW) dependence of the susceptibility along with the VTF temperature dependence of relaxation times, together reveal that the monopole fluid is a supercooled spin liquid.
In general, 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-Tammann-Fulcher (VTF) trajectory, a Havriliak-Negami (HN) form for the dielectric function, and a general Kohlrausch-Williams-Watts (KWW) form for time-domain relaxation.
We introduced high-precision, boundary-free magnetization transport techniques to achieve a fundamentally new understanding of the time- and frequency-dependent magnetization dynamics of Dy2Ti2O7. We demonstrated a virtually universal HN form for both the magnetic susceptibility, an equivalently universal KWW form for the real-time magnetic relaxation, and a divergence of the microscopic magnetic relaxation rates with precisely the VTF trajectory. Low temperature Dy2Ti2O7 therefore exhibits the characteristics of a supercooled spin liquid the first of its kind.