Quantum Spin Ice: A Search for Gapless Quantum Spin Liquids in Pyrochlore Magnets (1311.1817v1)

Abstract: The spin ice materials, including Ho2Ti2O7 and Dy2Ti2O7, are rare earth pyrochlore magnets which, at low temperatures, enter a constrained paramagnetic state with an emergent gauge freedom. Remarkably, the spin ices provide one of very few experimentally realised examples of fractionalization because their elementary excitations can be regarded as magnetic monopoles and, over some temperature range, the spin ice materials are best described as liquids of these emergent charges. In the presence of quantum fluctuations, one can obtain, in principle, a quantum spin liquid descended from the classical spin ice state characterised by emergent photon-like excitations. Whereas in classical spin ices the excitations are akin to electrostatic charges, in the quantum spin liquid these charges interact through a dynamic and emergent electromagnetic field. In this review, we describe the latest developments in the study of such a quantum spin ice, focussing on the spin liquid phenomenology and the kinds of materials where such a phase might be found.

• The paper demonstrates how quantum fluctuations in spin ice systems generate emergent, gapless photon-like excitations.
• It uses ring-exchange Hamiltonians and U(1) gauge theory mappings to derive effective models for quantum spin liquids.
• Experimental evaluations of rare-earth pyrochlores reveal challenges and prospects for realizing stable quantum spin ice states.

Quantum Spin Ice: An In-Depth Analysis of Gapless Quantum Spin Liquids in Pyrochlore Magnets

The paper "Quantum Spin Ice: A Search for Gapless Quantum Spin Liquids in Pyrochlore Magnets" by M. J. P. Gingras and P. A. McClarty provides a comprehensive exploration into the properties and experimental aspects of quantum spin ice (QSI), a theoretical model for realizing quantum spin liquids with emergent gapless excitations resembling photons. Quantum spin ice state is a manifestation of quantum fluctuations acting on the classical spin ice (CSI) systems. This analysis encompasses perturbative mechanisms, effects of interactions, and prospects for experimental realizations.

Overview of Classical Spin Ice

Classical spin ice (CSI) systems, such as Ho$_2$Ti$_2$O$_7$ and Dy$_2$Ti$_2$O$_7$, are characterized by their spin ice behavior facilitated by a "2-in, 2-out" rule on each tetrahedron in the pyrochlore lattice. This rule results in a macroscopically degenerate ground state analogous to the proton disorder in water ice. The frustration induced by the combination of these Ising interactions with long-range dipolar interactions leads to an effective magnetic Coulomb phase, characterized by emergent monopolar excitations.

Quantum Spin Ice and the Emergent U(1) Spin Liquid

The crux of quantum spin ice (QSI) is the involvement of quantum fluctuations within these degenerate CSI states, enabled by anisotropic interactions in a spin-1/2 model. The QSI phase is characterized by three key components: an emergent gapless photon-like excitation, magnetic monopoles analogous to classical excitations, and visons, which are gapped topological defects. The emergent U(1) spin liquid arises due to a ring-exchange Hamiltonian and manifests as a deconfined phase in a compact U(1) gauge theory, with the gauge structure furnishing robustness against local perturbations.

Modeling QSI: From Spin Models to Gauge Theories

The essential steps in modeling QSI involve the perturbative treatment of transverse couplings in an Ising x-y-z model, deriving effective Hamiltonians dominated by ring-exchange processes on hexagonal plaquettes. Through series of mappings, the effective Hamiltonian connects to an emergent gauge theory, supporting a stable deconfined photon phase. Quantum Monte Carlo simulations and field-theoretical approaches suggest a stable gapless photon-like mode, making distinct experimental predictions.

Experimental Perspectives and Candidate Materials

Despite the theoretical elegance, experimental realization of QSI phases remains challenging. The paper reviews potential QSI candidates within rare-earth pyrochlores, focusing on materials like Tb$_2$Ti$_2$O$_7$, Pr$_2$Sn$_2$O$_7$, Pr$_2$Zr$_2$O$_7$, and Yb$_2$Ti$_2$O$_7$. Each material presents unique attributes and pitfalls, from disorder effects to competing ground states. For instance, while Tb$_2$Ti$_2$O$_7$ and Pr$_2$(Sn,Zr)$_2$O$_7$ display dynamic ground states and some principles of spin ice phenomenology, clarity about reaching a true QSI state remains elusive. Alternatively, Yb$_2$Ti$_2$O$_7$ demonstrates strong XY anisotropy and exhibits ferrimagnetic ordering, further complicating its identification as a QSI.

Theoretical Implications and Future Directions

The exploration of QSI phases is pivotal for advancing our understanding of quantum phases with emergent gauge structures. The paper of QSI informs not only the theory of spin liquids but also extends to correlated systems with fractionalized excitations. Future research hinges on synthesizing new materials with tailored interactions that can stabilize QSI-like phases and refining theoretical models that incorporate further neighbor interactions and dipolar effects. Experimental breakthroughs in isolating the fractionalized excitations and photon-like modes could confirm QSI phases, providing insights into emergent phenomena in condensed matter systems.

In conclusion, the paper underscores a promising but challenging arena in condensed matter physics—realizing and understanding quantum spin liquids via quantum spin ice models. As the search for robust QSI systems unfolds, the confluence of theoretical innovation and experimental exploration will be crucial for observing these elusive quantum states of matter.