[Paper Review] Towards an Effective Spin Hamiltonian of the Pyrochlore Spin Liquid Tb2Ti2O7

Hamid R. Molavian, Paul McClarty+1 more|ArXiv.org|Dec 15, 2009

Advanced Condensed Matter Physics4 references3 citations

TL;DR

This paper develops an effective spin-1/2 Hamiltonian for the pyrochlore spin liquid Tb2Ti2O7 by incorporating virtual crystal field excitations (VCFEs), revealing that quantum corrections from VCFEs stabilize a q=0 ordered ice phase and induce ferromagnetic correlations despite antiferromagnetic nearest-neighbor exchange. The VCFE-induced three-body interactions and Ising couplings lead to frustration beyond dipolar interactions, explaining the absence of long-range order down to 50 mK.

ABSTRACT

Tb2Ti2O7 is a pyrochlore antiferromagnet that has dynamical spins and only short-range correlations even at 50 mK; the lowest temperature explored so far, which is much smaller than the scale set by the Curie-Weiss temperature T_{CW}~14 K. The absence of long-range order in this material is not understood. Recently, virtual crystal field excitations (VCFEs) have been shown to be significant in Tb2Ti2O7. While previous work found that VCFEs-induced renormalization of the nearest neighbor Ising exchange leads to spin ice correlations on a single tetrahedron, their effect on spin correlations has not been fully explored. In this paper, we construct an effective spin-1/2 low-energy theory for Tb2Ti2O7 on the pyrochlore lattice. We determine semiclassical ground states on a lattice that allow us to see how the physics of spin ice is connected to the possible physics of Tb2Ti2O7. We observe a shift in the phase boundaries with respect to those of the dipolar spin ice model as the quantum corrections become more significant. In addition to the familiar classical dipolar spin ice model phases, we see a stabilization of a q = 0 ordered ice phase over a large part of the phase diagram; ferromagnetic correlations being preferred by quantum corrections in spite of an antiferromagnetic nearest neighbor exchange in the microscopic model. Frustration is hence seen to arise from virtual crystal field excitations over and above the effect of dipolar interactions in spin ice in inducing ice-like correlations.

Motivation & Objective

• To construct a low-energy effective spin-1/2 Hamiltonian for Tb2Ti2O7 that incorporates virtual crystal field excitations (VCFEs).
• To understand how VCFEs contribute to frustration and suppress long-range magnetic order in this pyrochlore spin liquid.
• To determine the role of quantum corrections in stabilizing unconventional spin correlations, including a q=0 ordered ice phase.
• To connect the physics of spin ice with that of Tb2Ti2O7 by analyzing the interplay between dipolar interactions and VCFE-induced terms.

Proposed method

• Derives an effective spin Hamiltonian using second-order perturbation theory to account for virtual crystal field excitations (VCFEs) in Tb2Ti2O7.
• Maps the microscopic spin-1/2 Hamiltonian onto a low-energy effective theory on the pyrochlore lattice using Pauli matrix algebra.
• Computes VCFE-induced interactions via summation over excited crystal field states, yielding Ising and three-body spin interactions.
• Uses numerical evaluation of matrix elements and trace decomposition to extract coupling constants for the effective Hamiltonian.
• Analyzes semiclassical ground states to map phase boundaries and identify stabilized phases.
• Compares results with the classical dipolar spin ice model to isolate the effects of quantum corrections from VCFEs.

Experimental results

Research questions

• RQ1 How do virtual crystal field excitations (VCFEs) modify the effective spin Hamiltonian in Tb2Ti2O7 beyond standard dipolar interactions?
• RQ2 What is the role of quantum corrections from VCFEs in stabilizing a q=0 ordered ice phase in the absence of long-range order?
• RQ3 To what extent do VCFE-induced three-body and Ising interactions contribute to frustration in Tb2Ti2O7?
• RQ4 How does the phase diagram of Tb2Ti2O7 differ from the classical dipolar spin ice model due to VCFE effects?
• RQ5 Can VCFEs explain the persistence of short-range spin correlations down to 50 mK in Tb2Ti2O7?

Key findings

• Virtual crystal field excitations (VCFEs) induce effective Ising and three-body spin interactions in Tb2Ti2O7, modifying the low-energy Hamiltonian beyond dipolar terms.
• Quantum corrections from VCFEs stabilize a q=0 ordered ice phase, which is not present in the classical dipolar spin ice model.
• Despite an antiferromagnetic nearest-neighbor exchange in the microscopic model, VCFEs favor ferromagnetic correlations in the effective theory.
• The phase boundaries shift significantly with increasing quantum corrections, indicating that VCFEs are a dominant source of frustration beyond geometric and dipolar effects.
• The stabilization of a q=0 ordered phase suggests that quantum effects from VCFEs can be significant in any pyrochlore material with a crystal field gap of order 100 K or smaller.