PHYSICAL REVIEW B

VOLUME 61, NUMBER 21

1 JUNE 2000-I

Far-infrared study of the two-dimensional dimer spin system SrCu2 „BO3 … 2T. Rõõm, U. Nagel, and E. Lippmaa
National Institute of Chemical Physics and Biophysics, Akadeemia tee 23, 12618 Tallinn, Estonia

H. Kageyama, K. Onizuka, and Y. Ueda
Institute for Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo 106-8666, Japan
共Received 13 September 1999; revised manuscript received 10 March 2000兲
Using far-infrared spectroscopy in magnetic fields up to 12 T we have studied a two-dimensional dimer spin
gap system SrCu2 (BO3 ) 2 . We found several infrared-active modes in the dimerized state 共below 10 K兲 in thefrequency range from 3 to 100 cm⫺1 . The measured splitting from the ground state to the excited triplet M S⫽0 sublevel is ⌬ 1 ⫽24.2 cm⫺1 and the other two triplet state sublevels in zero magnetic field are 1.4 cm⫺1below and above the M S ⫽0 sublevel. Another multiplet is at ⌬ 2 ⫽37.6 cm⫺1 from the ground state. A strong
electric dipole active transition polarized in the (ab) plane is activated in the dimer spin system below 15 K
at 52 cm⫺1 .

The discovery of high-temperature superconductivity inlightly doped antiferromagnets has renewed interest in lowdimensional spin systems with specific spatial structures. Recently a two-dimensional spin gap system SrCu2 (BO3 ) 2 wasfound.1 The SrCu2 (BO3 ) 2 is interesting, first, because theground state is known. SrCu2 (BO3 ) 2 has a tetragonal structure where structural dimers of Cu2⫹ ions form an orthogonal network in the CuBO3 planes, separated by Sr atoms.2 It
is topologically equivalent to a system where the singlet
dimer state is an exact eigenstate of the spin Hamiltonian.3,4Second, among two-dimensional spin systems the quantizedmagnetization plateaus were observed.1 Third, SrCu2 (BO3 ) 2
is close to the quantum critical transition point J ⬘ /J⫽0.7
from the gapful magnetic dimer state to the antiferromagnetically ordered gapless state.4–6 A fit of magnetic susceptibility
data gives J⫽100 K and J ⬘ ⫽68 K for the nearest-neighborand next-nearest-neighbor antiferromagnetic coupling constants between copper S⫽1/2 spins.
Despite the well-defined ground state, little is known
about the excited states. The distance from the ground singlet
state to the excited triplet state estimated from copper
nuclear magnetic relaxation rate in a powdered sample is⌬ R ⫽30 K. A submillimeter wave electron spin resonance
共ESR兲 study7 on monocrystals shows that the excited triplet
state splits into two triplet modes and the averaged value forthe spin gap is 34.7 K. According to the same ESR study
there must be another spin excitation above the triplet mode.
Infrared spectroscopy is a good method for studying excitations in a magnetic system because it is sensitive to spin,charge, and lattice degrees of freedom. We present here theresults of a low-temperature 共4–45 K兲 far-infrared study ofSrCu2 (BO3 ) 2 in magnetic fields from 0 to 12 T and at frequencies in the 3 –100 cm⫺1 range. We have determined thezero-field splitting of the excited triplet state and have founda strong infrared-active resonance at 52 cm⫺1 .
We studied two single crystals of SrCu2 (BO3 ) 2 . The firstsample was 0.17 mm thick in the c direction and had an areaof 10 mm2 in the (ab) plane (CuBO3 plane兲. This sample
was used in measurements where the light k vector was perpendicular to the (ab) plane and electric field E1 polarized
0163-1829/2000/61共21兲/14342共4兲/$15.00

PRB 61in the (ab) plane. The second sample consisted of twopieces 0.65 mm thick in the a direction and with a total areaof 11.5 mm2 in the (ac) plane. This sample was used formeasurements where the light k vector was in the (ab) planeand E1 either parallel to the c axis or to the (ab) plane.
Far-infrared measurements were done with a polarizing
Martin-Pupplett Fourier transform spectrometer8 and asample cryostat equipped with a 12 T Oxford Instruments
magnet and two 3 He-cooled silicon bolometers from Infrared Laboratories. Spectra were recorded at 0.4 cm⫺1 resolution. The magnetic field was applied parallel to the directionof light propagation. Absolute absorption spectra ␣ ( ␻ ,T)were calculated from the transmission taking into accounttwo backreflections from sample to vacuum interface:␣ ( ␻ ,T)⫽⫺d ⫺1 ln关I(␻,T)/I0(␻)(1⫺R)2兴, where I 0 ( ␻ ) is theintensity of the incident and I( ␻ ,T) the intensity of thetransmitted infrared radiation at frequency ␻ ; d is the thickness of the crystal. The reflection coefficient R⫽0.33 wascalculated from the refraction index n⫽3.7 determined fromthe fringe pattern of the 0.17-mm-thick sample transmission
spectrum.
Below 10 K several lines appear between 3 and 100 cm⫺1in the far-infrared transmission spectrum which is rather featureless for the paramagnetic 共20 K兲 state 关Fig. 1共a兲兴. Strongfeatures seen below 30 cm⫺1 are due to light interference inthe sample. Therefore, to see finer details we present in Fig.
1共b兲 spectra where the 20 K spectrum has been subtracted
from the 4.4 K spectrum. The transmission does not change
by more than a few percent between 20 and 45 K. For„k储 (ab),E1 储 (ab)… there are absorption lines at 24.2, 37.6,43.0, 52, 69, and 84 cm⫺1 . The spectrum in „k储 c,E1 储 (ab)…
geometry is similar and is not plotted. When the electric field
is perpendicular to the planes „k储 (ab),E1 储 c… only one line at25.4 cm⫺1 is present.
The temperature dependence of the spectra is shown inFigs. 2 and 3. We have plotted the spectral weight 共area
under the line兲, full width at half maximum 共FWHM兲, andpeak positions of the 24.2 and 52 cm⫺1 lines. For the24.2 cm⫺1 line a better fit was obtained with a Gaussian,
14 342©2000 The American Physical Society

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14 343

FIG. 1. Infrared absorption spectra of SrCu2 (BO3 ) 2 for different
light polarizations. 共a兲 Absolute spectra in the dimerized state 共4.4K兲 and in the paramagnetic state 共20 K兲. 共b兲 Difference of 4.4 K and
20 K spectra. The spectrum in k储 (ab), E1 储 c geometry has been
lowered in the vertical direction by 5 cm⫺1 .

while a Lorentzian was used for the 52 cm⫺1 line. Analysisof the 52 cm⫺1 line is complicated by a side peak at
53.5 cm⫺1 and rapid broadening above 8 K. Therefore below
8 K we plot the spectral weight of the 52 cm⫺1 line as a sumof spectral weights of two Lorentzians located at 52 and53.3 cm⫺1 . Above 8 K we use a single Lorentzian fit.
Only the 24.2 and 37.6 cm⫺1 lines split in a magnetic
field 共Fig. 4兲. The 24.2 cm⫺1 line corresponds to the transition from the ground singlet state 兩 S 典 to the excited triplet
state sublevel 兩 T 0 典 . This is obvious from the magnetic fielddependence of the resonance frequency 关Figs. 4共a兲 and 4共c兲兴.

FIG. 2. Temperature dependence of absorption spectra in zeromagnetic field. Inset 共a兲 is a detailed view of the T dependence ofthe singlet to triplet transition 兩 S 典 → 兩 T 0 典 . Side peaks at 22.7 and25.4 cm⫺1 are the 兩 S 典 → 兩 T ⫺1 典 and 兩 S 典 → 兩 T ⫹1 典 transitions.

FIG. 3. Temperature dependencies of the 24, 52, and 53.5 cm⫺1lines. 共a兲 The spectral weight 共area under the line兲. Below 8 K thespectral weight of the 52 cm⫺1 line is shown as the sum of two
Lorentzian lines, one at 52 and the other at 53.5 cm⫺1 . 共b兲 The linepositions. 共c兲 The full width at half maximum 共FWHM兲.

The line at 25.4 cm⫺1 seen in Fig. 1共b兲 for E1 perpendicular
to the planes is the 兩 S 典 → 兩 T ⫹1 典 transition because its resonace frequency increases with magnetic field 关Figs. 4共a兲 and4共c兲兴. The third component of the triplet resonance, the 兩 S 典 to兩 T ⫺1 典 transition, is seen when the magnetic field is applied,B0 储 (ab) and E1 储 (ab) 关Fig. 4共c兲兴. There is an additional
splitting of the triplet-state field-dependent components
关open and solid triangles in Figs. 4共a兲 and 4共c兲兴 caused byanisotropic inter dimer exchange interaction.7 Line positionsof the triplet were fitted with E⫽⌬⫾ 冑E 2 ⫹(g i ␤ B 0 ) 2 , where⌬⫽24.15⫾0.05 cm⫺1 , E⫽1.4⫾0.1 cm⫺1 , and, in planeelectron g factor, g a ⫽2.06⫾0.06; the Bohr magneton ␤⫽0.4669 cm⫺1 T⫺1 . Within the error margins for both geometries E1 储 c 关Fig. 4共a兲兴 and E1 储 (ab) 关Fig. 4共c兲兴 the parameters are the same.
The resonance line at 37.6 cm⫺1 splits in the magnetic
field into two components. From the magnetic field dependence of its resonance frequency we can identify these twotransitions as transitions from the ground singlet state to them S ⫽⫺1 and m S ⫽⫹1 sublevels of the S⭓1 multiplet. The
fit for this multiplet gives slightly different g factors for theupper spin level, g u ⫽2.08⫾0.04, and for the lower spinlevel, g l ⫽2.02⫾0.01, with ⌬⫽37.6 cm⫺1 and E⫽0.
From the magnetic field dependence of the S⫽1/2 Cu2⫹ spin signal in the paramagnetic state at 20 K we

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FIG. 4. Magnetic field B0 储 k dependences of line positions andspectral weights for two light polarizations at 4.4 K. Diamonds are
the sums of spectral weights of the 兩 S 典 → 兩 T ⫺1 典 and 兩 S 典 → 兩 T ⫹1 典
transitions shown by open and solid triangles in panels 共a兲 and 共c兲.
Solid lines in panels 共a兲 and 共c兲 are the fits described in the text. Thedashed line in panel 共c兲 is the fit of Nojiri et al. of their ESR data
共Ref. 7兲. Lines in panels 共b兲 and 共d兲 are drawn to guide the eye.

determined the electron g factor parallel to the planes, g 储⫽2.04⫾0.04, and perpendicular to the planes, g⬜ ⫽2.33⫾0.04. These are typical values for the Cu2⫹ spin in a tetragonal crystal field.9 If we normalize the paramagnetic
Cu2⫹ signal to the temperature and energy splitting of the24.2 cm⫺1 singlet-triplet transition in zero magnetic field at
4.4 K, we get that the spectral weight of the singlet to triplet
transition is 3 times smaller than that of the paramagnetic
signal. Magnetic dipole transitions between singlet 共antisymmetric兲 and triplet 共symmetric兲 states are forbidden. The antisymmetric Dzialoshinski-Moriya interaction10 mixes thesinglet and triplet states and therefore makes the singlettriplet transition possible. The local symmetry of a dimer isC 2 v and consequently the Dzialoshinski-Moriya interaction(J DM ) does not vanish. The magnitude of J DM is J DM⬇(⌬g/g)J 0 where ⌬g is the deviation of the electron g factor from the free electron value, g⬇2, and J 0 is the isotropic
exchange interaction. If we use g c ⫽2.28 共Ref. 7兲 and J 0⫽24 cm⫺1 , we get J DM ⫽2.9 cm⫺1 . The zero-field splittingof the triplet resonance is 2E⫽2.8 cm⫺1 , close to the estimate of J DM .
Variation of line intensities with magnetic field for thetriplet state is observed. In k储 (ab), E1 储 c 关Fig. 4共b兲兴 the兩 S 典 → 兩 T 0 典 resonance intensity increases from zero to0.5 cm⫺2 with increasing magnetic field while the 兩 S 典→ 兩 T ⫹1 典 loses its intensity. The 兩 S 典 → 兩 T ⫺1 典 resonance intensity is below noise level. In k储 (ab), E1 储 (ab) geometry 关Fig.
4共d兲兴 the 24.2 cm⫺1 line loses its intensity whereas transitions to 兩 T ⫺1 典 and 兩 T ⫹1 典 levels gain intensity. The intensityof the 37.6 cm⫺1 multiplet decreases nearly linearly withincreasing field 共not plotted兲. When the magnetic field is perpendicular to the planes the intensity of the 兩 S 典 → 兩 T 0 典 transition (24.2 cm⫺1 ) does not change with magnetic field. ThePRB 61

FIG. 5. Magnetic field effect on the 24 cm⫺1 共inset兲 and52 cm⫺1 lines at 4.4 K.

other two components of the singlet to triplet transition, 兩 S 典→ 兩 T ⫺1 典 and 兩 S 典 → 兩 T ⫹1 典 , are too weak to be detected in thefar-infrared in this field orientation but were observed by
ESR.7 The effect of the magnetic field on the singlet to triplet
transition described so far is in changing the oscillator
strength of the singlet to triplet transitions. The magnetic
field, besides changing the oscillator strength, has anothereffect as shown in Fig. 5. Above 8 T lines start to broaden
and to lose their intensity.
The 52 cm⫺1 resonance is active when the electric field isparallel to the (ab) plane independent of the direction oflight propagation 关Fig. 1共b兲兴. Because the light k, E1 , and H1
are orthogonal, we come to the conclusion that the 52 cm⫺1resonance is an electric dipole transition. This is also supported by the fact that the oscillator strength of the 52 cm⫺1resonance is considerably larger than the oscillator strengthof the high-temperature paramagnetic Cu2⫹ signal or the24 cm⫺1 singlet to triplet transition. We exclude the possibility of the 52 cm⫺1 resonance being a phonon. The firstargument against being a phonon is the magnetic field effect.
We found that above 8 T this line starts to lose its intensity.
In the 12 T field the spectral weight is 1.4 times smaller thanin zero field. The magnetic field effect on this resonance lineis very similar to the effect of magnetic field on the singlet totriplet transition at 24 cm⫺1 共Fig. 5兲. The second argument isthe temperature dependence. The 52 cm⫺1 transition starts toshow up below 20 K 共Fig. 3兲. To explain this kind of T
dependence for a lattice mode one has to assume that a structural phase transition takes place and that the Brillouin zone
boundary phonon is folded back to the zone center. However, there is no clear onset temperature of the 52 cm⫺1resonance that could be identified as a structural phase transition temperature and also the width of the absorption line
changes by more than one order of magnitude. This is notconsistent with what is usually observed for a zone-folded
phonon. Also, the Raman scattering experiment11 has notshown any new phonon modes below 10 K and therefore
there is no structural phase transition. We assign the52 cm⫺1 line to a transition in the dimer spin system.

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14 345Creation of a single quasiparticle in the crystal by absorption of a light quantum is limited to long wavelengths ofquasiparticles, k⬇0. An inelastic neutron scattering study12
has found three branches of magnetic excitations in thedimerized state below 20 K. These excitations, in the k spacepoints that are equivalent to the center of the Brillouin zone,
are at 3, 5, and 9 meV. The 3 meV excitation corresponds tothe singlet to triplet transition observed in infrared absorption at 24 cm⫺1 and also by ESR. In the infrared absorption
there are two resonances at 37.6 and 43 cm⫺1 that are closein energy to the second branch at 5 meV. Two higher-energy
absorption lines at 69 cm⫺1 and 84 cm⫺1 are close in energy
to the third, 9 meV, branch. No magnetic excitations weredetected in the inelastic neutron scattering experiment in thecenter of the Brillouin zone at 52 cm⫺1 共6.5 meV兲. We
speculate that the 52 cm⫺1 absorption line in infrared corresponds to an electric dipole active transition where two triplet excitations are created simultaneously. In this type oftransition the spin and the total momentum of two magnetic
excitations is zero. For example, in antiferromagnets it has
been shown that the second-order electric dipole transition isstronger than the first-order magnetic dipole transition.13
The magnetic field suppresses the singlet to triplet transition and the 52 cm⫺1 absorption line 共Fig. 5兲. InSrCu2 (BO3 ) 2 the first gapless ground state is reached at 21 T共Refs. 1 and 14兲. We observe that already the 9 T field isaffecting the line intensities. Other experiments have established similar low-field effects. The magnetization starts toincrease from its zero value in low fields1,14 and in ESR 共Ref.
7兲 multiple magnetic resonances have been detected above
12 T. Our experiment provides conclusive evidence thatmagnetic fields smaller than the first critical field change thegapped ground state of the dimer system.
In conclusion, the spectrum of magnetic excitations inSrCu2 (BO3 ) 2 in the dimerized state has several infraredactive resonances. By their magnetic field dependence two ofthem have been identified as a triplet resonance at 24 cm⫺1and as a multiplet at 37.6 cm⫺1 . The third is a strong singlet
resonance polarized in the (ab) plane at 52 cm⫺1 . The otherthree weak resonances at 43, 69, and 84 cm⫺1 are singlet
resonances.

H. Kageyama et al., Phys. Rev. Lett. 82, 3168 共1999兲.
R.W. Smith and D.A. Keszler, J. Solid State Chem. 93, 430共1991兲.
3B.S. Shastry and B. Sutherland, Physica B 108, 1069 共1981兲.
4
S. Miyahara and K. Ueda, Phys. Rev. Lett. 82, 3701 共1999兲.
5
Z. Weihong, C.J. Hamer, and J. Oitmaa, Phys. Rev. B 60, 6608
共1999兲.
6E. Müller-Hartmann et al., Phys. Rev. Lett. 84, 1808 共2000兲.
7H. Nojiri et al., J. Phys. Soc. Jpn. 68, 2906 共1999兲.

812We thank Professor T. Timusk and Professor H. Nojiri for
helpful discussions. Work in Tallinn was partially supportedby Estonian Science Foundation Grant Nos. 3443 and 3437.
Work in Japan was supported by a Grant-in-Aid for Encouragement of Young Scientists from The Ministry of Education, Science, Sports and Culture.

Martin-Pupplett spectrometer SPS-200 is made by Sciencetech
Inc., Ontario, Canada.
9A. Abragam and B. Bleaney, Electron Paramagnetic Resonanceof Transition Ions 共Clarendon Press, Oxford, 1970兲, Vol. 1.
10T. Moriya, Phys. Rev. 120, 91 共1960兲.
11P. Lemmens et al., cond-mat/0003094 共unpublished兲.
12H. Kageyama et al., Phys. Rev. Lett. 共to be published兲.
13
R. Loudon, Adv. Phys. 17, 243 共1968兲.
14
H. Kageyama et al., J. Phys. Soc. Jpn. 67, 4304 共1998兲.