Listening for magnetic monopoles: magnetic excitations in spin ice and the fluctuation-dissipation relation – ListenMonopoles

To achieve this project, a technological challenge has to be overcome: the development of a magnetic noise set-up, able to measure magnetic fluctuations down to very low temperature (typically 50 mK).
Such experimental development is challenging because any external disturbance (vibrations, electromagnetic disturbance) have to be controlled to be able to extract the signal. It becomes even more complicated when the system has to be cooled in a 3He-4He refrigerator to reach very low temperatures, which implies a pumping system, long cables, and efforts to ensure a good sample thermalisation. To succeed, we rely on our expertise in highly sensitive low temperature measurements, and on previous work of Ocio et al who developed at 4He temperatures (above 4.2 K) a set-up to measure magnetic noise in spin-glasses. This instrumental development imposes a careful methodology, and consciousness in all steps of the design: SQUID detection, sample holder, electromagnetic screening, implementation in the dilution fridge.
Concerning the numerical calculations, all the needed tools have been developed in the involved theoretical teams. The key of the project is to exploit these powerful codes to resolve the monopole dynamics in spin-ice at low temperature. A difficulty is that relaxation times become increasingly long at very low temperatures when the real dynamics is taken into account, the one of single spin flips. We have two classes of algorithms to challenge this issue. Kinetic monte carlo methods allow for simulating the very long time behavior through a time acceleration process without modifying the real monopole dynamics. On the other hand, we can accelerate the stochastic dynamics with loop like algorithms to access and characterize the ultimate thermodynamics of those systems.

The magnetic noise set-up is currently under development. Satisfactory results have been obtained concerning the noise level of the SQUID detectors. Pick-up coils are under construction. Thermometry for the dilution fridge has been calibrated. In parallel, conventional very low temperature SQUID measurements have been performed on a new spin ice candidate Ho2Ir2O7, where we have shown the existence of a new state, a «fragmented state«. Monopole dynamics should have different characteristics in this system, and we hope to measure it on our magnetic noise set-up when it will be operational.
Theoretically, a numerical study of the non equilibrium properties of spin ice in the context of the fluctuation dissipation theory and its violation has been completed by our partners in Lyon and Montpellier. The code has been developed, simulating the dumbbell model of spin ice to follow a complete set of thermodynamic quantities through a thermal quench for 1 to typically 0.1 K with parameters set for the spin ice material dysprosium titanate. Following such a quench, the magnetic monopole density evolves rapidly with time before hitting a plateau concentration whose lifetime scales exponentially with base temperature. The plateau has previously been identified by Castelnovo and collaborators as being due to trapped ''non-contractable pairs''. We have found linear fluctuation dissipation ratios indicating effective temperatures for energy, monopole concentration and magnetization. For the energy the effective temperature is negative, indicative of a constrained phase space for energy fluctuations. Such behaviour has previously been observed in kinetically constrained models for glass formation. For the other quantities the effective temperatures are higher than the base temperature.

Experimentally, we carry on the development of the very low temperature magnetic noise set-up. Next steps are i) the completion of the pick-up coils, their connection to the SQUID and the test of the noise level of this whole detection set-up ii) the implementation of the detection set-up in the dilution fridge iii) the measurements of the magnetic noise of the canonical spin ice sample Dy2Ti2O7. Further development will be the implementation of additional coils to perform the «avalanche quench« protocol which allows to freeze a large monopole density at low temperature.
Theoretically, we will pursue the work on the phase diagram of the dumbbell model in the presence of a staggered chemical potential which breaks the translational symmetry for monopole movement. The general phase diagram is a winged structure with 1st order transitions terminating on lines of critical end points. We plan to do simulations on Kibble-Zurek scaling of non-equilibrium fluctuations around these critical end points. This work has been motivated by experiments on Ho2Ir2O7 but is also relevant to experiments on spin ice in a [111] field.

Fragmentation in spin ice from magnetic charge injection
E. Lefrançois, V. Cathelin, E. Lhotel, J. Robert, P. Lejay, C. V. Colin, B. Canals, F. Damay, J. Ollivier, B. Fa°k, L. C. Chapon, R. Ballou, and V. Simonet, Nature Communications 8 (2017), 209.

Geometrical frustration in magnetism has become a central challenge in contemporary condensed matter physics. It is the source of many exotic ground states whose description remains challenging for both theoreticians and experimentalists. These unconventional magnetic states often originate from the strong degeneracy of the ground state manifold, which prevents the stabilization of standard magnetic phases and results in the emergence of novel excitations. In that context, the study of the frustrated spin-ice magnets has dramatically expanded during the last few years with the discovery of the existence of magnetic monopoles in these systems. These monopoles are magnetic excitations that behave as magnetic charges in that they can be driven apart by a magnetic field, in much the same way electricity is controlled by electric fields.

This project aims to probe non-equilibrium phenomena in spin-ice compounds through the direct measurement of magnetic "noise" (or magnetic fluctuations) due to magnetic monopole movement. It will allow the precise determination of deviations from the fluctuation-dissipation relation in spin ice for the first time, and thus to characterize quantitatively the out-of-equilibrium state and the monopole dynamics at very low temperature.

In that purpose, we will develop a unique experiment to measure magnetic noise down to very low temperature (50 mK), thanks to our expertise in very low temperature, highly sensitive, magnetic and noise measurements. To reach the expected sensitivity, we will use a SQUID as a detector, and a careful system of superconducting pick-up coils will enable to perform noise measurements and susceptibility measurements on the same set-up, thus allowing a direct comparison of the data. The great challenge is to protect this highly sensitive detection part from external disturbance, which will need the implementation of anti-vibrations, filtering and shielding systems. We will first apply this experimental set-up to the so-called 'canonical dipolar spin-ices' Dy2Ti2O7 and Ho2Ti2O7 for which the equilibrium properties are well undestood and characterized.

This project will be in strong collaboration with theoreticians who are specialists of both frustrated magnetism and out-of-equilibrium physics. They are developing local and loop kinetic Monte Carlo codes to probe the coupling between magnetic response and monopole dynamics. It is worth noting that spin-ice is a particularly good system to perform such out-of-equilibrium studies, since, although it exhibits glassy-like properties, the microscopic Hamiltonian is well defined and, contrary to spin-glass systems, the amount of disorder is scarce. Calculations will then allow a direct comparison between experimental results and microscopic models, thus opening up a new way of understanding out-of-equilibrium physics.

To achieve this project, we mainly ask funding for a PhD student who will work on the instrumental development and on the noise measurements, as well as funding for the building of the experimental set-up.

We expect that the study of out-of-equilibrium processes in the well controlled spin-ice system will give new insights into glassy physics and provide new and original probes of monopole quasi-particles. The project will enable the PI to develop new experimental expertise in her laboratory, magnetic noise measurements at very low temperature; a promising technique to probe magnetic fluctuations in other systems including quantum magnets and magnetic macro-molecules.