[Paper Review] Soft dipolar spin ice physics and the ordered phase of the frustrated Tb2Sn2O7 pyrochlore magnet

Paul McClarty, Pawel Stasiak+1 more|arXiv (Cornell University)|Nov 29, 2010

Advanced Condensed Matter Physics2 references3 citations

TL;DR

This paper derives an effective pseudospin-1/2 Hamiltonian for Tb2Sn2O7 that incorporates virtual crystal field excitations, showing that soft dipolar interactions lead to a two-in/two-out spin ice ground state with q=0 order and spin canting—matching experimental observations. Monte Carlo simulations of a soft dipolar spin ice model confirm a phase with long-range order resembling Tb2Sn2O7 and a competing spin ice-like freezing phase.

ABSTRACT

From a microscopic model for the pyrochlore antiferromagnet Tb2Sn2O7, including the crystal field Hamiltonian and interactions between the angular momenta, we compute an effective pseudospin-1/2 Hamiltonian Heff$ that incorporates perturbatively in the effective interactions the effect of excited crystal field levels. We obtain the semiclassical ground states of Heff and find a region of parameter space with a two-in/two-out spin ice configuration on each tetrahedron with ordering wavevector q=0 and with spins canted away from the local Ising axes as found in Tb2Sn2O7. This ground state can also be obtained from a dipolar spin ice model in which the Ising constraint is softened. Monte Carlo simulations on the latter model reveal a region of the phase diagram with spin ice-like freezing and another with a transition into Tb2Sn2O7-type long range order. We comment on the differences between Tb2Sn2O7 and the perplexing spin liquid Tb2Ti2O7.

Motivation & Objective

• To derive a low-energy effective Hamiltonian for Tb2Sn2O7 that captures the effects of virtual crystal field excitations.
• To explain the experimentally observed q=0 long-range ordered phase with canted spins in Tb2Sn2O7 using a microscopic model.
• To investigate whether the observed order in Tb2Sn2O7 arises from dipolar interactions and single-ion anisotropy, independent of spin-lattice coupling.
• To explore the phase diagram of a soft dipolar spin ice model and compare its behavior to Tb2Sn2O7 and the spin liquid Tb2Ti2O7.
• To determine the conditions under which spin ice-like freezing and long-range order coexist or compete in rare earth pyrochlores.

Proposed method

• Derive an effective pseudospin-1/2 Hamiltonian $H_{\rm eff}$ from a microscopic model including crystal field, exchange, and dipolar interactions.
• Use perturbation theory to incorporate virtual crystal field excitations into $H_{\rm eff}$, accounting for excited crystal field levels.
• Compute semiclassical ground states of $H_{\rm eff}$ to identify phases with two-in/two-out ice rules and q=0 order.
• Introduce a toy model $H_{\rm m}$, a soft dipolar spin ice model (SDSIM), with tunable single-ion anisotropy to explore phase competition.
• Perform Monte Carlo simulations on $H_{\rm m}$ to map the phase diagram, including transitions to long-range order and spin ice-like freezing.
• Analyze order parameters ($Y_{\mathbf{q}=0}$), specific heat, and transition temperatures across system sizes to identify phase boundaries and crossovers.

Experimental results

Research questions

• RQ1 What is the microscopic origin of the q=0 long-range ordered phase with canted spins in Tb2Sn2O7?
• RQ2 Can the observed magnetic order in Tb2Sn2O7 be explained by dipolar interactions and single-ion anisotropy without requiring spin-lattice coupling?
• RQ3 How do competing interactions—exchange, dipolar, and single-ion anisotropy—determine the phase diagram of rare earth pyrochlore oxides?
• RQ4 Is the spin liquid behavior in Tb2Ti2O7 related to the freezing transition observed in Tb2Sn2O7, or are they distinct phenomena?
• RQ5 What is the role of softening the Ising constraint in stabilizing long-range order in a dipolar spin ice model?

Key findings

• The effective Hamiltonian $H_{\rm eff}$ derived from a microscopic model reproduces the two-in/two-out spin ice ground state with q=0 order and spin canting observed in Tb2Sn2O7.
• A soft dipolar spin ice model (SDSIM) with tunable anisotropy reproduces the long-range ordered phase of Tb2Sn2O7 over a wide parameter range.
• Monte Carlo simulations of the SDSIM reveal a finite-temperature transition into the Tb2Sn2O7-type long-range ordered phase, with a crossover at $X^* \approx 0.35$ from freezing to true long-range order.
• The phase diagram of the SDSIM shows a fanning out of multiple phases upon tuning away from the classical Heisenberg antiferromagnet spin liquid point.
• The study identifies a regime with spin ice-like freezing and another with finite-temperature long-range order, suggesting that spin-lattice coupling is not required to explain the ordered phase in Tb2Sn2O7.
• The model provides a plausible explanation for persistent low-temperature spin dynamics in both Tb2Sn2O7 and Tb2Ti2O7, suggesting that such dynamics may coexist with spin ice-like freezing in materials with similar anisotropy.