Order induced by dipolar interactions in a geometrically frustrated antiferromagnet

Abstract

We study the classical Heisenberg model for spins on a pyrochlore lattice interacting via long range dipole-dipole forces and nearest neighbor exchange. Antiferromagnetic exchange alone is known not to induce ordering in this system. We analyze low temperature order resulting from the combined interactions, both by using a mean-field approach and by examining the energy cost of fluctuations about an ordered state. We discuss behavior as a function of the ratio of the dipolar and exchange interaction strengths and find two types of ordered phase. We relate our results to the recent experimental work and reproduce and extend the theoretical calculations on the pyrochlore compound, Gd${}_2$Ti${}_2$O${}_7$, by Raju \textit{et al.}, Phys. Rev. B {\bf 59}, 14489 (1999).

5 pages, 5 figures, AMSLaTeX

References in corpus (5)

• Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet
• Low-temperature properties of classical, geometrically frustrated antiferromagnets
• Ising pyrochlore magnets: Low temperature properties, ice rules and beyond
• Transition to Long Range Magnetic Order in the Highly Frustrated Insulating Pyrochlore Antiferromagnet Gd_2Ti_2O_7
• Magnetic susceptibility of diluted pyrochlore and SCGO antiferromagnets

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