Magnetic excitations from the singlet dimerized state in Na
2
Co
2
„C
2
O
4
…
3
„H
2
O…
2
M. Matsuda, S. Wakimoto, and K. Kakurai
Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan
Z. Honda and K. Yamada
Faculty of Engineering, Saitama University, Urawa, Saitama 338-8570, Japan
Received 21 June 2006; revised manuscript received 25 October 2006; published 19 January 2007
Na
2
Co
2
C
2
O
4
3
H
2
O
2
consists of two-leg ladders of Co
2+
ions. It was reported that this is a candidate
compound to show a magnetic state in the vicinity of the gapped and the Néel ordered state, where the quantum
phase transition occurs Z. Honda et al., Phys. Rev. Lett. 95, 087204 2005. Neutron scattering experiments
were performed to study the magnetic ground state of this compound. It is found that the system is well
described by an almost isolated dimer model, in which dimers are formed between spins along the rung
direction and the interaction along the rung direction is much larger than that along the leg direction. The
intradimer coupling constant is determined to be 5.2 meV. Other interactions were found to be very small.
DOI: 10.1103/PhysRevB.75.012405 PACS numbers: 75.10.Jm, 75.25.+z, 75.50.Ee
Low-dimensional spin system exhibits various interesting
phenomena originating from quantum fluctuations. Magne-
tism of spin-ladder has attracted much attention because the
spin-ladder is a system between one and two dimensions.
1
Interestingly, the ground state depends on the number of
legs. The antiferromagnetic ladder with an even number of
legs shows a singlet ground state with a spin gap. On the
other hand, the antiferromagnetic ladder with an odd number
of legs shows a gapless ground state.
2–4
Recently, macroscopic magnetic properties have been
measured in Na
2
Co
2
C
2
O
4
3
H
2
O
2
abbreviated to SCO,
hereafter, which consists of two-leg ladders of Co
2+
ions.
5
It
was reported that SCO can be well described as the fictitious
1/2 system with anisotropic g values and exchange interac-
tions at low temperatures. Therefore, SCO is a model com-
pound for the two-leg ladder with an Ising anisotropy. Sus-
ceptibility measurements show a broad maximum around
20 K and show an exponential decay down to 5 K. Below
5 K, the susceptibility is almost independent of tempera-
ture. No anomaly was observed in heat capacity measure-
ments. In Ref. 5 the results were discussed in the context of
the quantum phase transition.
7
It was suggested that a mag-
netic ordering occurs because the interladder coupling is
slightly larger than the critical value in SCO.
In order to clarify the ground state in SCO, it is important
to measure the magnetic properties from a microscopic point
of view. We carried out neutron scattering experiments using
polycrystalline sample to study the magnetic correlations and
the energy level scheme of the Co
2+
moments. Since the
excited states were found to be almost dispersionless, we
could obtain useful information on the magnetic excitations
even with the polycrystalline sample. We found that the sys-
tem is well described by an almost isolated dimer model, in
which dimers are formed between Co
2+
moments along the
rung direction.
A polycrystalline sample of undeuterated SCO was syn-
thesized following the procedure described in Ref. 6. About
1 g of the sample was used in the measurements.
The elastic and inelastic neutron-scattering experiments
were carried out on the thermal neutron three-axis spectrom-
eter TAS2 and on the cold neutron three-axis spectrometer
LTAS installed at JRR-3 at the Japan Atomic Energy Agency.
The fixed final neutron energies were 14.7 meV and
3.5 meV on TAS2 and LTAS, respectively. Contamination
from higher-order beams was effectively eliminated using
PG and Be filters on TAS2 and LTAS, respectively. The hori-
zontal collimator sequence for elastic measurements was
guide-80'-S-80'-80' on TAS2. The horizontal collimator se-
quences for inelastic measurements were guide-80'-S-40'-
40' and guide-80'-S-80'-80' on TAS2 and LTAS, respec-
tively. The samples were mounted in a
4
He closed cycle
refrigerator.
We first performed neutron elastic measurements in SCO
in order to check whether a long-range magnetic order oc-
curs or not. Although we performed neutron powder diffrac-
tion measurements down to 3.8 K, no distinct magnetic sig-
nal was observed. This result does not necessarily exclude
the possibility of the Néel ordering because the ordered mo-
ment can be very small due to the quantum fluctuations.
However, as will be describe below, the ground state was
found to be singlet, which is consistent with the absence of
elastic magnetic signals.
Figure 1 shows the typical magnetic excitation spectra in
SCO measured with an energy resolution E of 1 meV
in full width at half maximum. Two sharp peaks, which are
almost resolution limited, are observed around 1.8 and
3.4 meV. It is found that the two excitations are almost in-
dependent of Q. The scattering intensity shows a maximum
around Q =0.9 Å
-1
and gradually decreases with increasing
Q, as shown in Fig. 1a. The scattering intensity decreases
with increasing temperature, as shown in Fig. 1b. These
results indicate that the two peaks are magnetic in origin.
Figure 2 shows the typical magnetic excitation spectra in
SCO measured with E 0.2 meV. The high-energy resolu-
tion experiments indicate that the single peaks around 1.8
and 3.4 meV shown in Fig. 1 consist of two peaks. It is also
confirmed that the excitations are almost dispersionless. The
excitation energies are estimated from the fits to the two
Gaussians. The energies are 1.651, 1.811, 3.261, and
3.591 meV at Q =2.0 Å
-1
. The peak width in energy is
PHYSICAL REVIEW B 75, 012405 2007
1098-0121/2007/751/0124054 ©2007 The American Physical Society 012405-1