N I S T Center for Neutron Research

Accomplishments and Opportunities 2001

Structure of Local Spin Excitations in a Geometrically Frustrated Antiferromagnet

For many crystalline magnetic materials, only a long range ordered spin configuration can satisfy all near neighbor spin interactions. Such systems generally display a finite temperature transition to a broken symmetry phase with long-range magnetic order. However, on certain lattices with weak connectivity and a triangular motif, short-range interactions can be satisfied without long-range order (Refer to Reference 1).

To explore this possibility we examined magnetic order and fluctuation
in Zn Cr_{2} O_{4}. The B-site of this spinel lattice is solely occupied
by spin -3 / 2 Cr^{3+}, and this leads to a magnet with dominant nearest neighbor
interactions on the lattice of corner-sharing tetrahedra shown in Figure 1.

Graphics Caption FIGURE 1. Lattice of corner-sharing tetrahedral formed by the octahedrally c
oordinated B sites of the spinel A B_{2} O_{4}. Black lines represent a
structural unit cell containing eight tetrahedra. Vertices are populated by antiferromagnetically
interacting spin -3 / 2 degrees of freedom in Zn Cr_{2} O_{4}. Yellow line and
six red spins represent a hexagonal loop of antiferromagnetically aligned spins.

Graphics Caption FIGURE 2. Constant-Q scans above and below T_{N} = 12.5 K. In the
cooperative
paramagnetic phase above T_{N} magnetic excitations form a continuum. Below T_{N}
the spectrum changes dramatically with a nearly dispersionless excitation near 4.5 meV
appearing abruptly. The red curves are to guide the eye.

Graphics Caption FIGURE 3. Color images of inelastic neutron scattering intensities in
the (h k 0) and (h k k) symmetry planes. From top to bottom are shown data from below and
above T_{N}, and the structure factor for the hexagon mode proposed by O.
Tchernyshyov. T = 1.7 K data were taken integrating over the energy range h ω from 3.0 meV to
6.7 meV. Data in the paramagnetic phase (T = 15 K) were taken at h ω = 1 meV.

Analysis of specific spin models on the B-site spinel (or pyrochlore) lattice indicates
that spin -1 / 2 and spin - ∞ models have short-range order down to T = 0 (Refer to Reference 2),
while long-range order is induced by quantum fluctuations for an unknown intermediate range of
spin values. Experiments indicate that spin -3 / 2 Zn Cr_{2} O_{4} is “close” to
the quantum critical point that separates the low spin quantum-disordered phase from the
intermediate spin long-range ordered phase. Specifically, the relaxation rate for magnetic
excitations, Γ , follows a power-law that extrapolates to zero as T approaches 0, indicating
quantum criticality (Refer to Reference 3). This state of affairs, however, does not persist
to the lowest temperatures. Instead, at T_{N} = 12.5 K a first order structural transition
from the cubic cooperative paramagnet to tetragonal Néel order intervenes.

Figure 2 shows that a gapless continuum of magnetic scattering above T_{N} is pushed
into a local spin resonance at h ω ≈ 4.5 meV ≈ J with remarkably little
dispersion throughout the Brillouin zone. The result is analogous to the spin-Peierls transition
of the uniform spin -1 / 2 chain, where quantum critical fluctuations are pushed into a finite
energy singlet-triplet transition through structural dimerization. Our recent synchrotron x-ray
and neutron powder experiments indicate that deformation of tetrahedra does indeed occur for
Zn Cr_{2} O_{4}. However, the structural changes push the system to long range
order rather than to quantum disorder, as indicated by the magnetic Bragg peaks and spin wave
excitations.

Our single crystal experiment (Refer to Reference 4) also enabled unique insight into the
local structure of spin-fluctuations in geometrically frustrated systems. Figure 3 shows the
Q-dependence of low energy magnetic scattering in two high symmetry planes above and below
T_{N}. While the spectrum for spin fluctuations changes dramatically at the first
order phase transition, the structure factor clearly does not. Also shown in the figure is
the structure factor for six spins of <111> type kagomé hexagons precessing with π phase shift
between neighbors. The proposal by O. Tchernyshyov et al., (Refer to Reference 5) that these
are the dominant low energy spin fluctuations for spins on the B-site spinel lattice is clearly
borne out by the data.

The present data for Zn Cr_{2} O_{4} show that geometrically frustrated
lattices have composite low energy degrees of freedom analogous to rigid unit modes in certain
open framework lattice structures. To better understand the unusual type of phase transition
that occurs in this system, it must be determined what defines the 4.5 meV energy scale for
hexagon excitation in the ordered phase. Do quantum fluctuations play a significant role or
does the broken symmetry between exchange interactions within tetrahedra induce the resonance?
The answer to this question is now being pursued through an accurate determination of the
complex low temperature lattice and magnetic structure.

References

[1] P. W. Anderson et al., Philos. Mag. 25, 1 (1972); J. Villain, Z. Phys. B 33, 31 (1979).

[2] R. Moessner et al., Phys. Rev. Lett. 80, 2929 (1998); B. Canals et al., Phys. Rev. Lett. 80, 2933 (1998).

[3] S.-H. Lee, C. Broholm, T.H. Kim, W. Ratcliff II, and S.-W. Cheong, Phys. Rev. Lett. 84, 3718 (2000).

[4] S.-H. Lee et al., unpublished (2002).

[5] O. Tchernyshyov et al., unpublished (2002).

Authors

S.-H. Lee

N I S T Center for Neutron Research

National Institute of Standards and Technology

Gaithersburg, MD 20899-8562

and

University of Maryland

College Park, MD 20742

C. Broholm and G. Gasparovic

Department of Physics and Astronomy

The Johns Hopkins University

Baltimore, MD 21218

T. H. Kim

Francis Bitter Magnet Laboratory

Massachusetts Institute of Technology

Cambridge, MA 02139

W. Ratcliff and S.-W. Cheong

Department of Physics and Astronomy

Rutgers University

Piscataway, NJ 08854