Reentrance, the return of a system from an ordered phase to a previously encountered less-ordered one as a controlled parameter is continuously varied, is a recurring theme found in disparate physical systems, from condensed matter to black holes. Wh
ile diverse in its many incarnations and generally unsuspected, the cause of reentrance at the microscopic level is often not investigated thoroughly. Here, through detailed characterization and theoretical modeling, we uncover the microscopic mechanism behind reentrance in the strongly frustrated pyrochlore antiferromagnet Er$_2$Sn$_2$O$_7$. Taking advantage of the recent advance in rare earth stannate single crystal synthesis, we use heat capacity measurements to expose that Er$_2$Sn$_2$O$_7$ exhibits multiple instances of reentrance in its magnetic field $B$ vs. temperature $T$ phase diagram for magnetic fields along three cubic high symmetry directions. Through classical Monte Carlo simulations, mean field theory and classical linear spin-wave expansions, we argue that the origins of the multiple occurrences of reentrance observed in Er$_2$Sn$_2$O$_7$ are linked to soft modes. Depending on the field direction, these arise either from a direct $T=0$ competition between the field-evolved ground states, or from a field-induced enhancement of the competition with a distinct zero-field antiferromagnetic phase. In both scenarios, the phase competition enhances thermal fluctuations which entropically stabilize a specific ordered phase. This results in an increased transition temperature for certain field values and thus the reentrant behavior. Our work represents a detailed examination into the mechanisms responsible for reentrance in a frustrated magnet and may serve as a template for the interpretation of reentrant phenomena in other physical systems.
Quantum spin ice materials, pyrochlore magnets with competing Ising and transverse exchange interactions, have been widely discussed as candidates for a quantum spin-liquid ground state. Here, motivated by quantum chemical calculations for Pr pyrochl
ores, we present the results of a study for frustrated transverse exchange. Using a combination of variational calculations, exact diagonalisation, numerical linked-cluster and series expansions, we find that the previously-studied U(1) quantum spin liquid, in its pi-flux phase, transforms into a nematic quantum spin liquid at a high-symmetry, SU(2) point.
We study the interplay between magnetic frustration and itinerant electrons. For example, how does the coupling to mobile charges modify the properties of a spin liquid, and does the underlying frustration favor insulating or conducting states? Suppo
rted by Monte Carlo simulations, our goal is in particular to provide an analytical picture of the mechanisms involved. The models under considerations exhibit Coulomb phases in two and three dimensions, where the itinerant electrons are coupled to the localized spins via double exchange interactions. Because of the Hund coupling, magnetic loops naturally emerge from the Coulomb phase and serve as conducting channels for the mobile electrons, leading to doping-dependent rearrangements of the loop ensemble in order to minimize the electronic kinetic energy. At low electron density rho, the double exchange coupling mainly tends to segment the very long loops winding around the system into smaller ones while it gradually lifts the extensive degeneracy of the Coulomb phase with increasing rho. For higher doping, the results are strongly lattice dependent, displaying loop crystals with a given loop length for some specific values of rho, which can melt into another loop crystal by varying rho. Finally, we contrast this to the qualitatively different behavior of analogous models on kagome or triangular lattices.
The Coulomb phase of spin ice, and indeed the Ic phase of water ice, naturally realise a fully-packed two-colour loop model in three dimensions. We present a detailed analysis of the statistics of these loops, which avoid themselves and other loops o
f the same colour, and contrast their behaviour to an analogous two-dimensional model. The properties of another extended degree of freedom are also addressed, flux lines of the emergent gauge field of the Coulomb phase, which appear as Dirac strings in spin ice. We mention implications of these results for related models, and experiments.
