PHYSICAL REVIEW B 76, 214427 共2007兲

Impurity-induced singlet breaking in SrCu2„BO3…2
A. A. Aczel, G. J. MacDougall, J. A. Rodriguez, and G. M. Luke*
Department of Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S-4M1

P. L. Russo,† A. T. Savici,‡ and Y. J. Uemura
Department of Physics, Columbia University, 538 West 120th Street, New York, New York 10027, USA

H. A. Dabkowska
Brockhouse Institute for Materials Research, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S-4M1

C. R. Wiebe and J. A. Janik
Department of Physics, Florida State University, 211 Westcott Building, Tallahassee, Florida 32306, USA

H. Kageyama
Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto, 606-8502, Japan
共Received 1 March 2007; revised manuscript received 29 August 2007; published 26 December 2007兲
We have performed muon spin relaxation 共␮SR兲 studies on single crystals of SrCu2共BO3兲2, a quasi-twodimensional spin system with a spin-singlet ground state. We find evidence for two different muon sites which
we associate with muons located adjacent to the two inequivalent O sites. One site, presumably located in the
Cu-O-Cu superexchange path, exhibits a large increase in the frequency shift with decreasing temperature
which is unaffected by the onset of the singlet ground state, indicating that the muon has perturbed the Cu-Cu
interaction and created two quasifree spins. We have also performed ␮SR on single crystals of
SrMg0.05Cu1.95共BO3兲2, Sr0.96La0.04Cu2共BO3兲2, and Sr0.95Na0.05Cu2共BO3兲2. We have found that the frequency
shifts of these doped samples are equivalent and contain three branches at low temperatures. Two of thesebranches map onto the branches observed in the pure sample, and so we attribute the third branch to a dopant
effect. Specifically, this third branch represents the case when the muon resides at a site in the superexchange
path where a local singlet cannot form due to doping. This leads to the conclusion that doping this system bothin and out of the CuBO3 planes prevents the formation of some singlets.
DOI: 10.1103/PhysRevB.76.214427

PACS number共s兲: 76.75.⫹i, 75.50.⫺yI. INTRODUCTION

One example is CaV4O9,7 where the depleted square latticeconsists of plaquettes of four spins coupled to neighboring
plaquettes through one vertex. SrCu2共BO3兲2 is another quasitwo-dimensional spin system with a spin-singlet groundstate.8 The unit cell is tetragonal and the structure is characterized by layers consisting of Cu2+, O2−, and B3+ running
perpendicular to the c axis. These layers are separated fromeach other by planes composed of Sr2+ ions. All Cu2+ sites
have localized spin S = 1 / 2 moments and one nearest neighbor with which they form dimeric units, while each of theseunits is surrounded by four orthogonal dimers. This configuration of spins corresponds to the two-dimensional modelthat Shastry and Sutherland first introduced in 1981.9 Thismodel is topologically equivalent to a two-dimensional
Heisenberg model with nearest-neighbor coupling J andnext-nearest-neighbor coupling J⬘. With decreasing J⬘ / J, aphase transition from a four-sublattice Néel state to a gappedspin-singlet state was shown to take place at a critical valueof J⬘ / J ⬃ 0.7. The ratio of J⬘ / J in SrCu2共BO3兲2 is about 0.68,
a little bit smaller than the critical value.10 High-resolution
inelastic neutron measurements11 have identified one-, two-,and three-triplet excitations. These measurements clearlyshow the appearance of the energy gap in the spectrum of
excitations with decreasing temperature, and from them theenergy gap is evaluated to be ⬃34 K. The one- and twotriplet excitations both display a very large drop-off in inelastic intensity with increasing temperature. This temperature

Low-dimensional spin systems with spin-singlet groundstates have attracted considerable study over the past
15 years. These systems are interesting for a number of reasons, including possible relevance to high-temperature superconductivity and the existence of novel ground states. Mostof the systems studied to date have been limited to quasione-dimension. These include spin ladder systems 关e.g.,
SrCu2O3 共Ref. 1兲兴, spin-Peierls systems 关e.g., CuGeO3 共Ref.
2兲兴, and Haldane gap systems 关e.g., Y2BaNiO5 共Ref. 3兲兴.
These materials all have a spin gap in the energy spectrum,
which is associated with the spin-singlet ground states. Theoretical studies of spin ladders4 have predicted d-wave superconductivity at low concentrations of hole doping in thesesystems. In fact, the mixed ladder-chain system
Sr14−xCaxCu24O41 has been found to be a superconductor under pressure, specifically in the cases of x = 13.6 共Ref. 5兲 andx = 11.5 共Ref. 6兲 with the superconductivity thought to originate in the ladder layers. High-Tc cuprates have d-wave superconducting states and a partial spin 共or pseudospin兲 gap,
which provides further evidence for strong similiarities between doped ladders and doped CuO2 planes and motivates
study of the effects of perturbing spin gap systems.
Two-dimensional 共2D兲 systems with spin-singlet groundstates are comparatively rare and often involve lattices where
the active spins have a small number of nearest neighbors.
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ACZEL et al.

dependence is generally not seen in a system undergoing aphase transition, and no evidence of symmetry breaking has
been associated with the appearance of the spin-singlet
ground state. Another interesting feature of this system is themagnetization plateaus that are observed at 1 / 8, 1 / 4 共Ref.
8兲, and 1 / 3 共Ref. 12兲 of the saturation magnetization in highmagnetic fields 共⬎20 T兲. This is the first 2D system wherethese plateaus have been observed.
While superconductivity has been predicted and observedin some quasi-one-dimensional systems with a spin-singlet
ground state, it has also been predicted in the doped ShastrySutherland model.13–15 Liu et al. have recently investigated aseries of polycrystalline SrCu2共BO3兲2 samples, with dopants
added both in16 and out10 of the CuBO3 planes. They foundthat the spin gap behavior was strongly affected by doping,but did not find any evidence for superconductivity. The resistivity of the pure sample at room temperature was foundto be 41.73 M ⍀m,10 and the resistivity of all doped samples
was found to be only one or two orders of magnitude
smaller. This implies that all their samples were insulatorsand that the carriers introduced as a result of doping were notvery mobile, at least at room temperature. However, the theoretical predictions discussed above help to emphasize theimportance of better understanding Shastry-Sutherland systems such as SrCu2共BO3兲2 and their response to perturbations.
Muon spin relaxation 共␮SR兲 measurements of a spinsinglet state give a signal characteristic of a nonmagnetic
state. Zero-field measurements17 of the spin-Peierls system
CuGeO3 gave essentially a temperature-independent signal,with weak relaxation being ascribed to isolated defects associated with impurities. In the case of SrCu2共BO3兲2, Fukaya
et al.18 reported zero-field 共ZF兲 and longitudinal-field 共LF兲␮SR measurements of ceramic specimens. In contrast to
their expectations of seeing no spin relaxation associatedwith this state, the authors reported the onset of a large,
roughly constant relaxation for temperatures of 3 K and below. They attributed this relaxation to dilute defects or to␮SR detecting weak intrinsic magnetism that other probes
could not see. The authors also reported that dynamic fluctuations persisted in the system down to a base temperature
共20 mK兲 and that these fluctuations likely have a quantum
origin.
Lappas et al. also investigated ceramic samples of
SrCu2共BO3兲2 using the ␮SR technique.19 The authors reported the same anomalous relaxation in ZF as observed by
Fukaya et al. using a different batch of samples. They attributed this relaxation to an unusual spin-freezing process. The
authors went on to perform 0.6-T frequency shift measurements on their samples. They concluded that implanted
muons may liberate spin density in the spin gap regime thatspin freezes at very low temperatures.
II. EXPERIMENTAL DETAILS

We
grew
singlecrystalsof
SrCu2共BO3兲2,
Sr0.96La0.04Cu2共BO3兲2,
and
SrMg0.05Cu1.95共BO3兲2,
Sr0.95Na0.05Cu2共BO3兲2 in floating zone image furnaces at
Tokyo20 and McMaster21 Universities following slightly dif-

FIG. 1. dc volume susceptibility of single-crystal SrCu2共BO3兲2,
measured in an applied magnetic field H = 5 T 储 ĉ.

ferent procedures. Neutron-scattering measurements havebeen reported by Haravifard et al.22 on the system
SrMg0.05Cu1.95共BO3兲2. Aside from the original crystal growtharticle,21 this seems to be the only paper describing doped
single crystals of this system as they have proven to be quitedifficult to grow.
The dc susceptibility measurements of a McMaster crystalof SrCu2共BO3兲2 in a field of 5 T parallel to the c axis areshown in Fig. 1; the results for the Tokyo crystals are essentially identical. There is a sharp decrease in the susceptibility
below 15 K which provides evidence for the spin-singlet
ground state. A small upturn is seen in the susceptibility
curve below 4 K, which likely arises due to magnetic impurities and/or defects of Cu2+ ions in SrCu2共BO3兲2. The susceptibility data below 7.5 K were fit to the following functional form:

␹ = C/T + Be−⌬/T + ␹0 .

共1兲The first Curie term is due to the contribution of magnetic
impurities, the second term is to account for the spin gap,
and the third temperature-independent term accounts for Van
Vleck paramagnetism and core diamagnetism. The spin gap⌬ was found to be ⬃20.2共7兲 K in our field of 5 T, which isin line with other reported estimates. If we ascribe the Curie
term to free Cu spins, then this concentration would be only
0.12共4兲%.
We performed 5-T transverse-field 共TF兲 ␮SR measurements on pure and doped SrCu2共BO3兲2 samples to investigate the presumed nonmagnetic spin-singlet ground states inthese systems. These measurements were conducted on the
M15 surface muon channel at TRIUMF in Vancouver,
Canada, using a helium gas flow cryostat in the temperature
range 2 K ⬍ T ⬍ 150 K. The samples were mounted in a lowbackground spectrometer with the c axis parallel to the incoming muon momentum 共and the external field兲. In thishigh-field experiment, the measurements of the muon precession frequency signal in our samples and a reference material
共CaCO3兲 were taken simultaneously to allow for a precise
determination of the frequency shift.

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IMPURITY-INDUCED SINGLET BREAKING IN SrCu…

FIG. 2. 共Color online兲 Fast Fourier transform of the muon precession signal for SrCu2共BO3兲2 measured in an applied magnetic
field H = 5 T 储 ĉ at 20 K. The two peaks correspond to two magnetically inequivalent muon sites.

In addition, we performed ZF-␮SR and low TF-␮SR
measurements 共H ⬍ 1 T兲 on the pure sample. After observing
the anomalous relaxation previously seen by Fukaya et al.18
in the powder sample, we performed LF-␮SR measurementson our single crystal to characterize the nature of this relaxation. For these low-temperature measurements 共between
20 mK and 10 K兲, we used an Oxford Instruments dilution
refrigerator on the M15 beamline. The sample was mounted
on a silver sample holder, with the c axis parallel to theincoming muon beam, as in the case of the high-TF measurements.
III. DISCUSSION AND ANALYSIS

Implanted positive muons reside at sites which areminima in the electrostatic potential. Generally, in oxides,
muons are hydrogen bonded to O2− ions, roughly 1 Åaway.23–25 Figure 2 shows a fast Fourier transform of thetransverse-field muon precession signal measured in an applied magnetic field H = 5 T 储 ĉ at T = 20 K. Two peaks areclearly visible which correspond to two magnetically inequivalent muon sites in SrCu2共BO3兲2; we associate thesewith the two magnetically inequivalent oxygen sites in thesystem. From a simple electrostatic calculation treating all
the ions as point charges and assuming a muon-oxygen distance of 1 Å, we have determined the most probable muonstopping site associated with each O type. The results areshown in Fig. 3. To take these two sites into account, we
tried to fit these 5-T TF data to the sum of two damped
cosine functions. We considered the cases of both exponential and Gaussian relaxation, and since the latter yielded consistently higher ␹2 values, we adopted the former for all of
our fits. Our exact fitting function is given by

FIG. 3. 共Color online兲 The bottom half of the unit cell of
SrCu2共BO3兲2 viewed along ĉ. Listed in order of decreasing size, theions correspond to Sr2+ 共blue兲, B3+ 共red兲, Cu2+ 共black兲, and O2−
共yellow兲. The most probable muon-stopping sites 1 Å from each O
type are indicated by open circles. These sites have fractional coordinates of 共0.34, 0.04, 0.25兲 and 共0.44, 0.44, 0.08兲. Symmetryrelated equivalent sites 共one per O兲 are not shown.

tal degeneracy there should only be one true stable muonstopping site in a material, so the second muon site we observe may be a metastable site that is long lived in the time
range of our experiment.
The frequency shift is the fractional difference between
the applied field and the local field at the muon site, and it is
proportional to the local spin susceptibility. We see that for
one of the muon sites the frequency shift roughly follows aCurie-Weiss temperature dependence for T ⬎ 4 K 关represented by the crosses in Fig. 4共a兲兴, with the precise value of

A共t兲 = A1e−␭1t cos共␻1t + ␾1兲 + A2e−␭2t cos共␻2t + ␾2兲, 共2兲
where ␻1 and ␻2 are the average muon precession frequencies, ␭1 and ␭2 are the muon relaxation rates for the twosites, and A1 and A2 are the initial asymmetries. The ratio of
A1 and A2 was found to be ⬃3 : 2, with more muons stoppingat the site out of the superexchange path. Barring an acciden-

FIG. 4. Frequency shifts vs. temperature measured in an appliedfield of 5 T for 共a兲 SrCu2共BO3兲2, 共b兲 Sr0.96La0.04Cu2共BO3兲2, 共c兲
SrMg0.05Cu1.95共BO3兲2, and 共d兲 Sr0.95Na0.05Cu2共BO3兲2. The insets
show the temperature dependence of the frequency shift for themuon site outside of the superexchange path.

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ACZEL et al.

FIG. 5. Exponential relaxation rates vs temperature for zero applied field in SrCu2共BO3兲2.

the Curie constant depending on the temperature range being
fit. This is in contrast to 11B NMR frequency shiftmeasurements.26 In that case, the authors applied a field of
7 T perpendicular to the 关1 − 1 0兴 direction and observed adecrease in the frequency shift below the onset of the singlet
ground state. The lack of a similar decrease in our ␮+ frequency shift for this site indicates the presence of a larger
local field than expected in the singlet ground-state regime.
If we associate this muon site with the oxygen site in the
Cu-O-Cu superexchange path, then a possible explanation
for this is that the muon perturbs the system and essentiallyremoves the interaction between the two neighboring Cu
spins. Since this perturbation affects the Cu spin dynamics
even before the singlet state is the only existing state, we
begin to see an increase in the frequency shift for this site
well before the singlet ground-state sets in. We do not observe a decrease in the shift after entering the singlet groundstate regime because the lack of a nearest-neighbor Cu-Cu
interaction means a local singlet can no longer form. Instead,
we now have two quasifree spins in close proximity to themuon site.
The shift at the other muon site is considerably smaller
and negative 关see inset of Fig. 4共a兲兴. In this case, the frequency shift follows the temperature dependence of the bulk
susceptibility reasonably well, indicating the lack of any
strong muon perturbation. For this reason, this site likely
corresponds to the O2− ion out of the Cu-O-Cu superexchange path.
Motivated by the discovery of the two muon sites in
SrCu2共BO3兲2, we fit the ZF-␮SR data to the sum of two
terms, each taken to be the product of an exponential and astatic Gaussian Kubo-Toyabe relaxation function. The
Gaussian Kubo-Toyabe part represents relaxation due tonuclear moments that are oriented randomly in ZF. This is
generally a temperature-independent contribution to the relaxation and this was assumed in this case by fixing theGaussian Kubo-Toyabe relaxation rates. The ratio of theasymmetries of the two sites was fixed to the value obtained
when fitting the high-TF data. Figure 5 shows that the exponential relaxation of one site is roughly independent of tem-

FIG. 6. 共Color online兲 LF-␮SR line shapes for selected appliedfields at 20 mK. There is significant relaxation even in the case of
2 kG. The lines are a guide for the eye.

perature for T ⬎ 4 K, then rises sharply at 4 K, and saturates
for temperatures of 3 K and below. The other site has a verysmall, almost temperature-independent relaxation. The large
increase and saturation of the exponential relaxation for theone muon site at low temperatures may imply slowing downor freezing of the spins liberated by the muon perturbation
effect as previously suggested by Lappas et al.19
To see if this was a suitable description, it was necessary
to examine LF-␮SR data taken below the saturation temperature, specifically at 20 mK in this case 共Fig. 6兲. Values of⬃1 G and 13 G were estimated for the local fields at the twomuon sites from the ZF time spectrum at T = 20 mK using therelation B ⬃ ␭ / ␥␮ 共␥␮ = 135.5⫻ 2␲ MHz/ T兲 with ␭ representing the muon relaxation rate as before. Assuming these
local fields are static, a comparable LF 共up to one order ofmagnitude larger兲 should be enough to completely decouple
them. However, we are still seeing significant relaxationeven in the case of LF= 2 kG. This implies that the spins are
dynamic in the low-temperature regime and their behavior
cannot be described by spin freezing. These spin fluctuations
are fast for T ⬎ 4 K and then slow down substantially below
T ⬃ 4 K. The saturation of the relaxation at the low temperatures suggests that these fluctuations are not thermal but instead have a quantum origin. This is in agreement with what
Fukaya et al. reported on in the case of ceramic samples.18 If
the LF spectra are examined closely at early times, it becomes clear that they have a distinct Gaussian nature. In
general, dynamic spin fluctuations cannot be described by aGaussian line shape. This appears to be one of the rare casesof undecouplable Gaussian behavior in ␮SR studies, whichis still poorly understood. Such behavior has been previously
observed in frustrated and/or low-dimensional systems.27,28
Figure 7 shows a fast Fourier transform 共FFT兲 of thetransverse-field muon precession signal measured in an applied magnetic field H = 5 T 储 ĉ at T = 20 K for
SrMg0.05Cu1.95共BO3兲2. Similar FFTs were obtained for theLa- and Na-doped samples. There are clearly three frequency
peaks in this case as opposed to the two that were seen in the
FFT of the pure sample. For this reason, the data were fit to
the same functional form as given by Eq. 共2兲, but three exponentially damped cosine terms were included instead of

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IMPURITY-INDUCED SINGLET BREAKING IN SrCu…

FIG. 7. 共Color online兲 Fast Fourier transform of the precession
signal for SrMg0.05Cu1.95共BO3兲2 measured in an applied magnetic
field H = 5 T 储 ĉ at 20 K. There are now three peaks instead of two;
the third peak is due to the Mg2+ ions.

two. The frequency shifts calculated from these fits are given
in Figs. 4共b兲–4共d兲; the shifts for all three doped samples
examined appear to be essentially equivalent. The upper andlower branches are remarkably similar to the two branches in
the pure case, but the middle branch is new and so it seems
is associated with the dopants.
In one situation, we are substituting nonmagnetic Mg infor the Cu sites. This should prevent some singlets fromforming, as not all Cu spins have a nearest-neighbor Cu any
longer. In the other two cases, we are substituting La or Na
for the Sr sites. These are both forms of charge doping, witheach La introducing one electron into our system and each
Na introducing one hole. Each electron or hole introduced bydoping is expected to prevent the formation of one singlet
and make a localized spin 1 / 2. Resistivity measurements
performed by Liu et al.10 on La- and Na-doped polycrystalline samples verify the localized nature of these carriers. The
prevention of some singlet formation by the different dopants
is supported by dc susceptibility measurements performed on
our single crystals with an applied field H = 1 kG 储 ab plane.21
All three doped samples had much larger Curie tails than thepure sample, indicating the presence of many more free spin1 / 2 Cu’s in the singlet regime. We have calculated the spin
gap, Curie constant, and the resulting fraction of free spinsby fitting this data to Eq. 共1兲; the results are shown in Table
I. In all the doped cases, the spin gap has been supressed.
Also, the fraction of free spins is at least 5 times as great asin the pure case, but still lower than what we expect considering the concentration of our starting materials. This is
TABLE I. Estimated spin gaps, Curie constants, and fraction offree Cu spins by fitting susceptibility data with H = 1 kG 储 ab plane.

SampleSpin gap
共K兲

Curie
constant
共K兲

SrCu2共BO3兲2
SrMg0.05Cu1.95共BO3兲2
Sr0.96La0.04Cu2共BO3兲2
Sr0.95Na0.05Cu2共BO3兲2

27.8共8兲
20.4共6兲
23.2共6兲
24.4共5兲

3.4⫻ 10−5共8兲
5.5⫻ 10−4共1兲
3.09⫻ 10−4共1兲
1.67⫻ 10−4共1兲

Estimatedfractionof freeCu spins 共%兲
0.0585共1兲
0.95共2兲
0.53共2兲
0.29共2兲

likely due to difficulties involved in doping this system andsuggests that our doping concentrations should be viewed asnominal values.
Our ␮SR results complement the susceptibility measurements by providing microscopic evidence that some singlet
formation is prevented in this system when doping both inand out of the CuBO3 planes. There appear to be three distinct possibilities for muons in the doped samples. The muon
can either stop at the sites in or out of the superexchange
path as before. If the muon stops at the site in the superexchange path, it will perturb the Cu-Cu interaction and create
two quasifree spins in close proximity. However, in somecases the formation of a local singlet will have already been
prevented as a result of doping. In this case, the muon will
only be in close proximity to one quasifree spin and so asmaller frequency shift will be measured with decreasing
temperature, giving us the middle branch. In fact, Figs.
4共b兲–4共d兲 show that this middle branch gives about half theshift of the upper branch.

IV. CONCLUSION

We determined there are two different muon sites in
SrCu2共BO3兲2, which we associate with muons located adjacent to the two inequivalent O sites in the system. One site
exhibits a large increase in the frequency shift with decreasing temperature that is unaffected by the onset of the singlet
ground state, indicating that the muon resides in the CuO-Cu superexchange path and has essentially removed theinteraction between the two neighboring Cu spins, thus preventing the formation of a local singlet. The frequency shiftof the other site is considerably smaller and negative. Itroughly scales with the dc bulk susceptibility, indicating thelack of a strong perturbation effect in this case.
We also observe a large relaxation increase for the site in
the superexchange path in the singlet regime, which is incontrast to the weak, practically temperature-independent relaxation expected in such a state. Analysis of LF-␮SR data
has shown that this relaxation is likely due to slow but dynamic fluctuations of the liberated spins that persist down to
our base temperature of 20 mK.
Finally, all three doped samples studied have remarkably
similar frequency shifts. In each case, there are now threebranches at low temperatures instead of two as observed in
the pure sample. The upper and lower branches map on to
the two branches in the pure sample very well, and so thethird branch is attributed to the dopants. Specifically, thisthird branch represents the case when the muon resides at asite in the superexchange path where a local singlet cannot
form as a result of doping. Our results demonstrate that electron or hole doping of SrCu2共BO3兲2 by substituting on the Srsite gives the same result as substitution of Cu by nonmagnetic Mg: namely, the prevention of a local singlet fromforming and the liberation of a single Cu spin. We find thatthe number of free spins is significantly less than expectedfrom the nominal dopant concentration and that reaching
doping levels sufficient for metallic 共and superconducting兲
behavior may be difficult in this system.

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ACKNOWLEDGMENTS

We appreciate the hospitality of the TRIUMF Center for
Molecular and Materials Science where the ␮SR experiments were performed. A.A.A. and G.J.M. are supported by

15*luke@mcmaster.ca†Present address: TRIUMF, 4004 Wesbrook Mall, Vancouver, BC,

Canada, V6T 2A3.
‡Present address: Condensed Matter Physics and Materials Science

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NSERC CGS. Research at McMaster University is supported
by NSERC and the Canadian Institute for Advanced
Research Quantum Materials Program. Research atColumbia University is supported by Grants Nos. NSF
DMR-05-02706, NSF DMR-01-02752, and CHE-01-11752.

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