J. S. Gardner, S.R. Dunsiger, B.D. Gaulin, M.J.P. Gingras, J.E. Greedan,
R.F. Kiefl, M.D. Lumsden, W.A. MacFarlane, N.P. Raju, J.E. Sonier, I. Swainson,
and Z. Tun
Physical Review Letters, Vol. 82 No. 5, 1 February 1999
Gardner1999.htm
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Journal
Abstract
Introduction
Notes by Dr. Zin Tun
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Contents of this page
The combination of antiferromagnetism and certain lattice symmetries based on triangles results in phenomena known broadly as geometrical frustration [1]. These local symmetries preclude the occurrence of two-sublattice Néel ordering, as it is not possible to satisfy the antiferromagnetic (AF) coupling with mutually antiparralel near-neighbor spins on such lattices. Antiferromagnetically coupled spins residing on a network of corner sharing tetrahedra can occur in cubic pyrochlores which are often constituted by the chemical formula A2B2O7, where the A site is occupied by a trivalent rare-earth ion with eightfold oxygen coordination and the B site by a tetravalent transition metal ion with sixfold oxygen coordination [2]. The A and B sites individually form infinite interpenetrating sublattices of corner-sharing tetrahedra, and if either the A or B site is occupied by a magnetic atom with an AF nearest-neighbor interaction, then a high degree of frustration must be present. (Gardner1999intro01.gif)
Theoretical arguments have been made which lead to large ground
state dengeneracies for both discrete [3] and continuous spin symmetries [4,5]
on the pyrochlore lattice. For near-neighbor AF interactions, long-range order
is suppressed, with incoherent, local ordering of the spin configurations on a
tetrahedron subject to the constraint
, where
the sum is over those spins on a single tetrahedra. Villain [5] coined the term
"cooperative paramagnetism" to describe such a state at low temperatures.
(Gardner1999intro02.gif)
Experimentally, however, it has been found that such systems do not typically remain paramagnetic, but either order into a noncollinear antiferromagnetic state, as in the case of FeFe3 [6], or enter a spin-glass-like state. This latter possibility is more common, occurring in the chemically ordered pyrochlores Y2Mo2O7 [7], Tb2Mo2O7 [8], and Y2Mn2O7 [9], as well as the disordered pyrochlore CsNiCrF6 [10] and the well-studied disordered kagomé system SrCr9pGa12-9pO19 [11]. In this Letter we report on elastic and inelastic neutron scattering (INS), muon spin relaxation (µSR), and susceptibility studies of the chemically ordered pyrochlore Tb2Ti2O7. These results show that despite the onset of AF short-range order at ~50 K, this material remains paramagnetic at least to temperatures ~0.07 K. In addition, INS shows incomplete soft mode behavior in the low-lying magnetic excitation spectrum below about 30 K. (Gardner1999intro03.gif)
Other related low temperature states have recently been studied in the pyrochlore rare-earth titanates. Counter-intuitively, ferromagnetic exchange and strong anisotropy lead to a geometrically frustrated state referred to as "spin-ice" in Ho2Ti2O7 [12]. A nonmagnetic (i.e., singlet) ground state is also possible, and has been shown to exist in Tm2Ti2O7 [13]. (Gardner1999intro04.gif)
Tb2Ti2O7 is an insulator
which crystallizes in the cubic, face centered space group Fd3m
with lattice parameter a = 10.15(1) Å at 300 K, and only the Tb3+
ions on the A site possess a magnetic moment. Polycrystalline sample of
Tb2Ti2O7 were prepared by firing, in air at
1350°C, stoichiometric amounts of Tb2O3 and TiO2
for several days with intermittent grindings to ensure a complete reaction.
There are more in the introduction.
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