# Emergence and out-of-equilibrium phenomena in frustrated magnets on pyrochlore lattices

Lead Research Organisation: University of Cambridge
Department Name: Physics

### Abstract

Emergence -- the ability of a large ensemble of interacting particles to give rise to properties and behaviours that transcend those of the microscopic constituents -- and far from equilibrium phenomena are some of the grand challenges of modern day physics.

Frustration in magnetic systems has been fertile ground for novel emergent and out of equilibrium phenomena. The term frustration'' indicates the inability of a system to reach its lowest energy state where all interaction terms are simultaneously minimised. The quintessential example is the triangular Ising antiferromagnet. In magnetism, frustration prevents the formation of ferro- or antiferromagnetically ordered phases at low temperature. This allows the emergence of new phases that often escape a conventional description in terms of local order parameters. Frustration is also at the core of paradigmatic non-equilibrium systems such as spin glasses.

The variety of new phenomena that emerge in frustrated magnetism, combined with the many experimental probes that have been developed for magnetic systems, continue to produce new and exciting physics both concerning thermodynamic as well as far from equilibrium behaviours. Examples include extensively degenerate ground states with emergent gauge symmetries (e.g., systems with dimer and vertex constraints), and topological order (e.g., spin liquids).

A lattice structure that has been demonstrated to be particularly conducive to frustration and novel emergent phenomena is the one that is obtained from tiling a volume with corner-sharing tetrahedra, dubbed the pyrochlore lattice. A notable example are spin ice materials, which received much attention of late thanks to the theoretical proposal and experimental discovery of magnetic monopole excitations. This is a rare experimental instance of fractionalisation in three dimensions and the first context where we can access and manipulate free magnetic charges. The existence of these emergent excitations has been demonstrated to have a direct effect on the thermodynamic properties of these systems (with the observation of unprecedented phenomena such as a liquid-gas transition in a localised magnetic system) as well as on their response, relaxation, and far from equilibrium behaviour. In 2012, this research effort was recognised internationally by the Condensed Matter Division of the Europen Science Foundation with the award of the Europhysics Prize \emph{to S.Bramwell, C.Castelnovo, S.Grigera, R.Moessner, S.Sondhi and A.Tennant for the prediction and experimental observation of magnetic monopoles in spin ice}''.

The overall aim of the proposal is to investigate emergent phenomena, in particular the physics of magnetic monopoles in spin ice. A central focus is the theme of non-equilibrium dynamics and equilibration. Recent experiments on these materials highlighted interesting controversies in their behaviour out of equilibrium and many of the results await theoretical understanding. The setting of the proposal is provided by frustrated magnetic systems on pyrochlore lattices, which allow a close interaction with numerous experimental studies currently undertaken on a broad range of materials, enabling us not only to provide theoretical support in interpreting results but also to shape the future experimental agenda. Specific objectives of the proposal include: developing a consistent understanding of spin ice materials in and out of equilibrium (e.g., to study spin and monopole dynamics in relation to AC susceptibility, magnetisation, and $\mu$SR measurements, and to develop new ways to detect and manipulate the monopole excitations); studying the role of impurities and chemical substitutions in spin ice and related compounds; modelling and understanding quantum effects in systems with less anisotropic spins; investigating the effects of conduction electrons in frustrated magnetic systems on the pyrochlore lattice.

### Planned Impact

One of the most direct non-academic beneficiaries of this proposal is the industry of scientific instruments. Through collaboration with experimental groups who are developing novel cutting-edge measurement techniques (e.g., with S.Grigera on low-temperature, high-precision magnetisation measurements; and with P.Schiffer on low-temperature, high-frequency magnetic susceptibility measurements), the proposal will help test the results in known and new experimental settings, and it will provide feedback for further technological improvements. The theoretical effort in this proposal will also contribute to the design of analytical / numerical tool kits to interpret the data. These new techniques will feed directly into the next generation of commercial scientific instruments .

Indirect economic and societal impact will also be produced by the training of young scientists (graduate students and PDRA). In particular, the proposal will give them the valuable opportunity to work in a context of close collaboration between theory and experiment. Some will remain in academia, forming the next generation of scientist in the UK and overseas, and some will seek other jobs, thus effectively transferring knowledge and expertise to the industry.

A potential long-term beneficiary is the IT industry, although naming specific beneficiaries in this context would be premature. It has been speculated that spin ice monopoles may be used to develop new magnetic memories and magnetic circuits [O.Tchernyshyov, Nature N&V 451, 22 (2008)]. The research in this proposal will directly address several issues that are crucial to test whether this speculation can ever become reality, such as understanding spin dynamics in spin ice, modelling monopole motion, and investigating how they can be experimentally controlled and manipulated. Moreover, the phenomenon by which magnetically charged point-like excitations emerge in spin ice is not dissimilar from the better known fractional anyonic excitations in quantum topologically ordered phases [see e.g., our recent review: C.Castelnovo, R.Moessner, and S.L.Sondhi, Annu. Rev. Condens. Matter Phys. 3, 35 (2012)]. Therefore, studying how monopole motion in spin ice can be modelled and how they can be manipulated may be of help to understanding how to control fractional excitations in general. This is a key aspect in topological quantum information storage and processing. Of course, the transition from the classical context of spin ice to quantum topologically ordered systems is highly non-trivial and it remains to be seen how much of the knowledge and techniques developed in the former carry through (at least in part) to the latter.

### Publications

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Bovo L (2014) Restoration of the third law in spin ice thin films. in Nature communications

Castelnovo C (2018) Dephasing with strings attached in Physical Review B

Castelnovo C (2019) Rod motifs in neutron scattering in spin ice in Physical Review B

Castelnovo C (2013) Negativity and topological order in the toric code in Physical Review A

Castelnovo C (2015) The monopole movement in Nature Physics

Description progress in undertstanding emergent properties and dynamics of frustrated spin systems on the pyrocholore lattice, including transport properties in iridate materials; investigation of emergent phases and phase transitions in layered kagome systems. Study of the dynamics and correlatoins of quasiparticle excitations in quantum spin ilquids. Investigation of the band structure and role of intercalated transition metal ions in pyrochlore oxides. Further progress in understanding quantum spin liquid dynamics. Two new research directions recently opened: configurational disorder and localisation in the motion of emergent quasiparticle excitations; disorder and glassiness in defect fluorites.
Exploitation Route general interest from frustrated magnetism community; dynamics of constrained systems; topological order; magnetic refrigeration; underrstanding of thermodynamics and dynamics of fractionalised excitations
Sectors Other

Description informed outreach and public seminars and discussions; public lectures
Sector Education,Other

Title Research data supporting "Color-dependent interactions in the three coloring model"
Description Included in this archive is the software to generate the numerical values for the central charge, the data obtained from it for the cases studied and plotted in the paper, and the scripts to generate those plots from the data.
Type Of Material Database/Collection of data
Year Produced 2018
Provided To Others? Yes

Title Research data supporting "Color-dependent interactions in the three coloring model"
Description Included in this archive is the software to generate the numerical values for the central charge, the data obtained from it for the cases studied and plotted in the paper, and the scripts to generate those plots from the data.
Type Of Material Database/Collection of data
Year Produced 2018
Provided To Others? Yes