Journal of Magnetism and Magnetic Materials 226}230 (2001) 1101}1102

Magnetic excitations at magnetization plateaux: ESR study onSrCu (BO )
H. Nojiri *, H. Kageyama, Y. Ueda, M. Motokawa
Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-ku Sendai 980-8577, Japan
Institute for Solid State Physics, University of Tokyo, Kashinoha 5-1-5, Kashiwa 277-8581, Japan

Abstract
Magnetic excitations of SrCu (BO ) have been studied in very high "elds including -plateau and -plateau phases by
means of electron spin resonance. Below the -plateau, a bending of the S "!1 branch of the lowest excited triplet isobserved, which is caused by the strong mixing between the ground state and the excited state. Besides the triplet,a strong main mode is observed which is apart from the resonance "eld expected for the conventional paramagneticresonance. At magnetization plateaux, the main mode appears around the paramagnetic resonance position and several
broad absorption peaks are observed at lower frequencies.  2001 Elsevier Science B.V. All rights reserved.
Keywords: ESR; High magnetic "eld; Magnetic excitation

1. Introduction
In a classical antiferromagnet, a magnetization plateau
appears mostly when there is an Ising-type anisotropy.
However, the mechanism is di!erent for the plateau appearing in quantum spin systems such as coupled dimer
systems. When there is an e!ective repulsive force acting
among triplets, a regular lattice made up of triplets isformed at a magnetization plateau. This new type ofplateau has been found in SrCu (BO ) [1] andNH CuCl [2]. The necessary condition for the plateauformation and the possible spatial arrangements of triplets such as stripe or checker have been discussed theoretically [3]. However, much less is known for the magnetic
excitation in these systems because neutron scatteringexperiments are di$cult in such high "elds. On the other
hand, ESR can be performed in very high "elds by using
pulsed magnetic "elds. Hence, ESR is considered asa unique and powerful tool to study the magnetic excitation at a magnetization plateau. In the present work,
ESR measurements have been performed up to 40 T for* Corresponding author. Tel.: #81-22-215-2019; fax: #8122-215-2016.
E-mail address: nojiri@imr.tohoku.ac.jp (H. Nojiri).

SrCu (BO ) . The characteristic features of the magnetic
excitation of the system are presented in the following.

2. Results and discussion
Submillimeter wave ESR measurements have been
performed up to 40 T. A far-infrared laser, backwardtravelling wave tubes and Gunn oscillators have been
employed as the radiation source. A single crystal isgrown by the travelling-solvent-#oating-zone method.
Fig. 1 shows the frequency-"eld diagram measured at
1.6 K for H#c. The magnetization curve taken from thereference is plotted together, where distinct magnetization plateaux are shown at  and  of the saturation
magnetization [4]. At zero "eld, the magnetization iszero for the existence of the spin gap. The transition
between the ground state and the lowest excited triplet
state is observed by ESR as indicated by the closed
circles. The small splitting of the lowest spin gap excitation may be caused by the inter-dimer coupling [5]. In
each triplet, the S "0 branch is not observed becauseESR absorption spectra are measured by scanning magnetic "elds at "xed frequencies. As the frequency is decreased, the S "!1 branches of the lowest tripletsX
show a bending above 17 T. This bending indicates the0304-8853/01/$ - see front matter  2001 Elsevier Science B.V. All rights reserved.
PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 0 6 3 6 - 3

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H. Nojiri et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1101}1102

Fig. 1. Frequency-"eld diagram for H#c. Closed circles, closeddiamonds and closed triangles indicate the lowest spin gapexcitation, the main mode and the low-frequency mode found at
plateau, respectively. The dashed line indicates the position ofparamagnetic resonance. The magnetization curve taken from
Ref. [4] is also plotted.

strong mixing between the ground state and the excitedstate. It is noticed that the magnetization becomes "niteabove 17 T. As the origin of this "nite magnetization, thetemperature e!ect is ruled out. It is because this behavior
appears even at 0.1 K [4]. Therefore, we speculate thatthe ground state of the system is changed although the"nite energy gap remains between the ground state andthe excited triplet state.
In a spin gap system, a disordered state or a threedimensional (3D) ordered state appears when the gap iscollapsed by a strong magnetic "eld. In a disorderedstate, the strong ESR absorption peak is observed at theresonance "eld identical with that of the conventionalparamagnetic resonance. In a 3D-ordered state, an antiferromagnetic resonance (AFMR) is observed. In Fig. 1,the strong ESR lines are indicated by closed diamonds. Itis noticed that these ESR lines show large deviation,
below the -plateau, from the positions expected for
a paramagnetic resonance, which is shown by the dashedline. Another interesting point is that the frequency of
ESR mode exhibits a jump at the jump of the magnetization just below the -plateau. As is well known, a single

ion-type anisotropy is not responsible for such a deviation in the case of S" Cu> ion. Hence, it is di$cult
to explain the origin of the signals as the ESR lines ofa disordered state. If a collective spin wave mode arises
due to the 3D-ordering, the deviation can be attributed
to the observation of AFMR. Therefore, we speculatethat a 3D-ordered state may exist just below the plateau. It should also be noted that the "nite energy gap
remains between the ground state and the excited tripletstate. Hence, the ordered state cannot be a simple Neelstate.

At the  and  plateaux, two types of magnetic excitations are found. The strongest main mode is locatedbeside the paramagnetic mode. A small deviation isfound between the main mode and the paramagnetic
resonance position and the deviation slightly changes
between these two plateaux. At -plateau, broad absorp
tion peaks are found at lower frequencies as depicted by
the closed triangles in Fig. 1. Such a low-energy mode
was also found in NH CuCl at magnetization plateauxand the mode was considered as the manifestation of theopening of the excitation gap at a magnetization plateau.
This gap is related to the energy required for the creationor annihilation of a new triplet in the lattice made up oftriplets. The energy needed for the creation of a new
triplet is roughly given by the sum of the one-triplet
excitation energy, the interaction energy with the surrounding triplets and the Zeeman energy. It is noticed
that the Zeeman energy is very large in the "eld range ofthe -plateau and it exceeds the one-triplet excitation
energy at zero "eld. Therefore, we can expect the excitation energy of a new triplet to be much lower than that of
the main mode. Hence, it is natural to attribute thelow-energy mode found in the present experiments to thecreation or annihilation of a new triplet. The estimate ofthe energy between a new triplet and the surrounding
triplets is a very di$cult task and thus the quantitative
analysis remains for future theoretical investigations.
As a conclusion, two types of ESR modes are found at
the magnetization plateaux in SrCu (BO ) . A gappedmode found in low frequency can be attributed to thecreation or annihilation of a new triplet. Below the plateau, several anomalies are found in ESR. It has beensuggested that the ground state of system is not a simple
singlet state above 17 T.

Acknowledgements
This work has been partly supported by a Grant-inAid from the Ministry of Education, Science, Sports andCulture, Japan and by the Sumitomo Foundation.

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