Evidence for the confinement of magnetic monopoles in quantum spin ice

Abstract

Magnetic monopoles are hypothesised elementary particles connected by Dirac strings that behave like infinitely thin solenoids [Dirac 1931 Proc. Roy. Soc. A 133 60]. Despite decades of searches, free magnetic monopoles and their Dirac strings have eluded experimental detection, although there is substantial evidence for deconfined magnetic monopole quasiparticles in spin ice materials [Castelnovo, Moessner & Sondhi 2008 Nature 326 411]. Here we report the detection of a hierarchy of unequally-spaced magnetic excitations via high resolution inelastic neutron spectroscopic measurements on the quantum spin ice candidate Pr<sub>2</sub>Sn<sub>2</sub>O<sub>7</sub>. These excitations are well-described by a simple model of monopole pairs bound by a linear potential [Coldea et al. Science 327 177] with an effective tension of 0.7(1) K/Angstrom. The success of the linear potential model suggests that these low energy magnetic excitations are direct spectroscopic evidence for the confinement of magnetic monopole quasiparticles in the quantum spin ice candidate Pr<sub>2</sub>Sn<sub>2</sub>O<sub>7</sub>.

Absence of moment fragmentation in the mixed B -site pyrochlore Nd2GaSbO7

“…Corresponding to a canonical frustrated lattice geometry, the pyrochlore oxides (A 2 B 2 O 7 ) consist of two interpenetrating networks of corner-sharing tetrahedra, composed of the A and B-site cations, respectively [1]. In the cases when A and/or B are magnetic, the pyrochlore lattice has played a key role in the realization of a diverse array of exotic magnetic ground states and phenomena that include unconventional long-range order [2,3], magnetic monopole quasiparticles [4,5], classical [6,7] and quantum [8][9][10] spin ices, and other spin-liquid states [11,12].…”

Ultrasound detection of emergent photons in generic quantum spin ice

“…Furthermore, we demonstrated how the speed of the emergent photon can be extracted from the renormalized spectrum without requiring knowledge of the precise effective coupling parameters. This protocol may help shed some light on the lowest energy excitations of QSI candidates such as Ce 2 (Sn, Zr) 2 O 7 [30][31][32][33] or Pr 2 (Zr, Sn, Hf) 2 O 7 [43][44][45][46][47][48][49][50]. Previous estimates from inelastic neutron scattering have suggested the speed of photons v ≈ 3.6 m/s for Pr 2 Hf 2 O 7 [50], while thermal conductivity measurements on Pr 2 Zr 2 O 7 yield an estimate of v ≈ 90 m/s and a speed of sound s ≈ 3700 m/s [12].…”

“…The non-trivial symmetry nature of the octupolar moment provides a daunting task for inelastic neutron scattering, due to the lack of standard linear coupling with the neutron's dipolar moment. Other promising QSI candidates, including Pr 2 (Zr, Sn, Hf) 2 O 7 , feature a non-Kramers doublet crystal-field ground state, which is only protected by the crystalline symmetries [43][44][45][46][47][48][49][50]. The Ising component transforms like a dipole moment whereas the transversal components transform like parts of a quadrupole.…”

Electric Model for Electromagnetic Wave Fields

“…Therefore, efforts have been made to modify Maxwell's equations to include terms for magnetic charges. But no natural magnetic charges have ever been identified to prove their existence [56,57,58,59,60,61,62]. However, this assumption has not been ignored since there is no theoretical framework that is available to deny it, and there is no apparent source for magnetic fields.…”