Dynamically Induced Frustration as a Route to a Quantum Spin Ice State in ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ via Virtual Crystal Field Excitations and Quantum Many-Body Effects

The ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ pyrochlore magnetic material is attracting much attention for its spin liquid state, failing to develop long-range order down to 50 mK despite a Curie-Weiss temperature ${\theta }_{\mathrm{CW}}\sim -14\mathrm{K}$. In this Letter we reinvestigate the theoretical description of this material by considering a quantum model of independent tetrahedra to describe its low-temperature properties. The naturally tuned proximity of this system near a Néel to spin ice phase boundary allows for a resurgence of quantum fluctuation effects that lead to an important renormalization of its effective low-energy spin Hamiltonian. As a result, ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ is argued to be a quantum spin ice. We put forward an experimental test of this proposal using neutron scattering on a single crystal.

Figure 1

$\mathcal{J}-\Delta$ phase diagram of a single tetrahedron. TTO has $\mathcal{J}=0.167\mathrm{K}$ and $\Delta =18.7\mathrm{K}$ (cross symbol). Main panel: The boundary ${\mathcal{J}}_c(1/\Delta )$ (filled circles) separates a ground state singlet ($\mathcal{J}<{\mathcal{J}}_c$) from a ground state doublet ($\mathcal{J}>{\mathcal{J}}_c$). The open circles show the same boundary, but as predicted by exact diagonalization of $H_{\mathrm{eff}}$. Inset: neglecting transverse terms in $H_{\mathrm{eff}}$ ($\lambda =0$), the filled squares show the renormalized classical sextet-doublet boundary set by the condition $J_{ij}^{zz}(\mathcal{J},1/\Delta )=0$. The open squares show the incorrect sextet-doublet boundary predicted when $J_{ij}^{zz}$ for pair $⟨i,j⟩$ in $H_{\mathrm{eff}}$ is obtained by ignoring contributions in PHRHP coming from (intermediate) excited states $|{\Psi }_{\mathrm{e}}^{\pm }⟩$ that belong to the two other ${\mathrm{Tb}}^{3+}$ ions ($k$ and $l$) on the tetrahedron.

Figure 2

Theoretical diffuse neutron scattering intensity $I(\mathit{q})/|F(\mathit{q}){|}^2$ for a single tetrahedron with four CF states per ${\mathrm{Tb}}^{3+}$ in (hhl) plane at 9 K.

Figure 3

Theoretical diffuse neutron scattering intensity $I(\mathit{q})/|F(\mathit{q}){|}^2$ along $\mathit{q}=(\mathrm{hh}2)]$ at 400 mK (left panel) and 40 mK (right panel) as a function of the nearest-neighbor antiferromagnetic exchange $\mathcal{J}$ for a single tetrahedron with four CF states per ${\mathrm{Tb}}^{3+}$.