Quantum Strings in Quantum Spin Ice

Abstract

We study quantum spin ice in an external magnetic field applied along a 100 direction. When quantum spin fluctuations are weak, elementary excitations are quantum strings with monopoles at their ends manifested as multiple spin-wave branches in the dynamical structure factor. Strong quantum fluctuations make the string tension negative and give rise to the deconfinement of monopoles. We discuss our results in the light of recent neutron scattering experiments in Yb2Ti2O7.PACS numbers: 75.40.Gb, 75.40.Mg The quest for novel quantum phases and elementary excitations is one of the central themes in condensedmatter physics. The notion of an elementary excitation is conventionally associated with a point-like object, as the term quasiparticle implies. A natural question is whether elementary excitations in quantum materials could resemble strings, rather than particles. String excitations were recently found in spin ice Dy 2 Ti 2 O 7 [1, 2], a frustrated ferromagnet with fractionalized excitations known as magnetic monopoles [3,4]. In an applied magnetic field, excitations are strings of misaligned spins connecting two monopoles of opposite charge.Conventional spin ice is a classical magnet with Ising spins [5]. Therefore, magnetic monopoles and strings in it are classical objects whose dynamics are due to thermal fluctuations. In this letter, we propose that string excitations with inherent quantum dynamics may exist in quantum spin ice, a new family of spin-ice materials exemplified by Tb 2 Ti 2 O 7 and Yb 2 Ti 2 O 7 [6] [7]. In these compounds, spins exhibit substantial quantum fluctuations. We demonstrate that, in a certain regime of coupling constants, elementary excitations of quantum spin ice are strings with quantum dynamics. The calculated dynamical structure factor S(ω, k) reveals multiple branches of excitations that correspond, loosely speaking, to strings of different lengths. As the applied field increases, these branches gradually separate and the lowest one evolves into a magnon. We connect these findings to recent experiments on neutron scattering in Yb 2 Ti 2 O 7 [8,9].We begin with a toy model of quantum spin ice on the two-dimensional checkerboard lattice, Fig. 1. The point of departure is classical spin ice, in which spins have projections S z i = ±1/2 on local directionsẑ i shown in Fig. 1a. Magnetic charge on a crossed plaquette (planar tetrahedron) is defined as Q = − i∈ S z i , with = ±1 for sublattice A (B). The ground states of the classical spin-ice Hamiltonian,obey the Bernal-Fowler rule, Q = 0, on every tetrahedron [5]. Next we apply a weak magnetic field in the ac plane. In the local frames, the perturbation readsHere we chose the local y-axes to be orthogonal to the field and introduced cosines η i ≡ĉ ·ẑ i = (−1) ci / √ 2. The Zeeman term (2) has two effects. Its longitudinal component B breaks the degeneracy of ice states and favors arXiv:1201.5314v3 [cond-mat.str-el]

New physics in frustrated magnets: Spin ices, monopoles, etc. (Review Article)

“…That is why, there exists a possibility of spreading of a local spin flip to other places due to non-Ising components of the particle-particle interaction [222,223,224,225,226,227,228,229,230,231,232]. In general, such a possibility can yield magnetic ordering, hence, the level of magnetic frustration for quantum spin ices is lower than for usual ones (sometimes called classical).…”

Seeing the light: Experimental signatures of emergent electromagnetism in a quantum spin ice

“…In a charge ice we simply sum over m, n as in Eq. (74). In a spin ice we must account for the easy axes which lie along the vectorsê n [Eq.…”

“…The magnetic charges are the magnetic monopoles of the classical theory 12 , now quantised and endowed with dynamics 40,74,75 . They correspond to the "spinon" excitations of the spin liquid.…”

Crystal-field states of Pr3+in the candidate quantum spin ice Pr2Sn2

“…If the nature and strength of the exchange interactions between spins is favourable, the fluctuations can become correlated allowing quantum mechanical tunneling within the ice rules manifold of states. It has been predicted that this particular spin liquid state could realise a fully dynamical, lattice analogue of quantum electromagnetism with linearly dispersing magnetic excitations exactly analogous to photons 8,9 in addition to other exotic excitations 10,11 .…”