PHYSICAL REVIEW B

VOLUME 61, NUMBER 6

1 FEBRUARY 2000-II

First-order phase transition between dimerized-antiferromagnetic and uniform-antiferromagnetic
phases in Cu1Àx M x GeO3
T. Masuda,*† I. Tsukada,‡ and K. Uchinokura†
Department of Applied Physics, The University of Tokyo, 6th Engineering Building, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, JapanY. J. Wang, V. Kiryukhin, and R. J. Birgeneau
Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
共Received 8 June 1999兲
We have performed detailed magnetic susceptibility measurements as well as synchrotron x-ray-diffraction
studies to determine the temperature vs concentration (T-x) phase diagram of Cu1⫺x Mgx GeO3 . We observe
clear double peaks in the magnetic susceptibility implying two antiferromagnetic 共AF兲 transition temperaturesin samples with Mg concentrations in the range 0.0237⭐x⭐0.0271. We also observe a drastic change in the
inverse correlation length in this concentration range by x-ray diffraction. The drastic change of the AF
transition temperature as well as the disappearance of the spin-Peierls phase have been clarified; these results
are consistent with a first-order phase transition between dimerized AF and uniform AF phases as reported by
T. Masuda et al. 关Phys. Rev. Lett. 80, 4566 共1998兲兴. The T-x phase diagram of Cu1⫺x Znx GeO3 is similar tothat of Cu1⫺x Mgx GeO3 , which suggests that the present phase transition is universal for Cu1⫺x M x GeO3 .

I. INTRODUCTION

The discovery of the inorganic spin-Peierls 共SP兲 cuprate
CuGeO3 共Ref. 1兲 has made it possible to study systematicallythe effect of impurities on SP systems. The effect of substitution of Zn2⫹ (S⫽0) for Cu2⫹ was studied by Hase et al.2
and the appearance of an antiferromagnetic 共AF兲 phase attemperatures below the SP transition temperature (T S P ) was
reported.3,4 Both dimerization superlattice and AF magnetic
peaks were observed by neutron-diffraction measurements
below the AF transition temperature (T N ) 共Refs. 5–7兲; thecoexistence of these two seemingly exclusive order parameters was explained theoretically by using a phase Hamiltonian method.8 Recently, some of the present authors studied the transition temperature vs impurity concentration(T-x) phase diagram in Mg2⫹ (S⫽0)-doped CuGeO3 bymeans of dc susceptibility measurements.9 These authors observed the disappearance of the cusp due to the SP transition
and the sudden increase of the AF transition temperature at
an impurity concentration x⫽x c ⬃0.023. They therefore concluded that there was a first-order phase transition between
dimerized-antiferromagnetic
共DAF兲
and
uniformantiferromagnetic 共UAF兲 phases. The disappearance of thelong-range order 共LRO兲 of the dimerization above a critical
impurity concentration was tentatively explained theoretically as a second-order phase transition at T⫽0 K. 10 In thispaper we report detailed studies on the temperature dependence of the magnetic susceptibility and, consequently, theT-x phase diagram of Cu1⫺x M x GeO3 (M ⫽Mg and Zn兲
near x⬃0.024 (Mg) and 0.020 共Zn兲. We have obtained clear
evidence for a first-order phase transition between UAF andDAF phases in these nonmagnetic impurity-doped systems
thereby strengthening the conclusion of the previous work.9
We have also used high-resolution synchrotron x-raydiffraction techniques to clarify the SP phase region in thephase diagram. As a result we have confirmed the disappear0163-1829/2000/61共6兲/4103共6兲/$15.00

PRB 61ance of the SP-LRO at xⲏx c . More importantly, we havefound that the SP correlation length for a given x becomeslong range at a lower temperature11 (T ⬘S P ) than the SP transition temperature previously reported and T ⬘S P crosses theantiferromagnetic phase boundary at x⬃0.024; this gives aphenomenological explanation for the origin of the putative
first-order phase transition.

II. EXPERIMENTAL DETAILSAll the samples were high quality single crystals grownby the floating-zone 共FZ兲 method; the concentration of the
Mg2⫹ or Zn2⫹ dilutant x was determined by inductively
coupled plasma atomic emission spectroscopy 共ICP-AES兲.
To determine the phase boundary we paid special attention to
any possible inhomogeneity of the impurity concentration.
We show a rough sketch of typical bulk single crystals of
Cu1⫺x M x GeO3 (M ⫽Mg and Zn兲 in Fig. 1. The crystals
were grown by using small pure or slightly doped CuGeO3
single crystals as the seed crystals. When the seed crystal
contains a smaller concentration than that of starting polycrystalline material, the actual grown crystal rod has a concentration gradient at the end corresponding to the initial
growth stage and then the concentration saturate at the later
growth stage. For the measurements of physical properties
we used parts of the crystals in the saturated region, so thatthe concentration distribution along the c direction of thesamples we have studied is within the inhomogeneity along
the radial direction. We estimated the accuracy of the impurity concentration from the fluctuation of the saturated concentration in a few of the rods. From this we concluded thatany errors in the concentration are within 0.1% in
Cu1⫺x Mgx GeO3 and 0.3% in Cu1⫺x Znx GeO3 in the regionof 0.02⬍x⬍0.03. It is apparent that Mg-doped CuGeO3 ispreferable to Zn-doped CuGeO3 for studies of impurity effects because of the more accurate control of x. The use of4103©2000 The American Physical Society

T. MASUDA et al.

4104

PRB 61

FIG. 1. Sketches of bulk single crystals of
Cu1⫺x M x GeO3 (M ⫽Mg and Zn兲 grown by the
FZ method. In some cases we analyzed more than
one piece. The figures in the bottom show theconcentration determined by ICP-AES vs crystalgrowth length.

Mg2⫹ as a dilutant made it possible to observe unambiguously the phase transition between the DAF and UAF phases
in impurity-doped CuGeO3 . 9 Careful treatment ofZn2⫹ -doped samples also have made a similar observation
possible in the present study.
Measurements of the dc magnetic susceptibility were performed with a commercial super conducting quantum interference device magnetometer ( ␹ -MAG, Conductus Co.,
Ltd.兲. The synchrotron x-ray-diffraction measurements werecarried out at the MIT-IBM beamline X20A at the National
Synchrotron Light Source 共NSLS兲, Brookhaven National
Laboratory.11
III. EXPERIMENTAL RESULTS

The magnetic susceptibility in an applied field parallel tothe c axis 关 ␹ c (T) 兴 in Cu1⫺x Mgx GeO3 samples around x c in
the region of 2⬍T⬍5 K is shown in Fig. 2共a兲. We observe
clear double peaks in samples whose x’s are 0.0237, 0.0248,
0.0254, and 0.0271, while only one sharp peak is observed in
0.0229 and 0.0288 samples. In contrast to the previous
measurements,9 we took the data using temperature steps of
0.025 K; this reveals the detailed behavior of the susceptibility around x⬃x c . The inset in the bottom of Fig. 2共a兲 shows␹ c (T) over a wider temperature range. One can see the disappearance of the cusp in ␹ c (T) around 10 K in the x⫽0.0288 sample while the cusp exists in the x⫽0.0271
sample. This suggests that the SP transition still exists in thex⫽0.0271 sample and disappears in the x⫽0.0288 sample.
Here we define x c1 as the concentration x where the double
peaks first begin to appear, and x c2 as the concentration x,
where only one peak begins to be observed and at the sametime the cusp in ␹ c (T) corresponding to T S P disappears,
with increasing x. With these definitions, we obtain x c1
⫽0.0237 and x c2 ⫽0.0271. In cases when we do not distinguish x c1 and x c2 , we use simply x c , hereafter. We determined T S P from the crossing points of linear functions fitted
to ␹ c (T) above and below the putative transition. We
adopted Fisher’s theory12 to determine the AF transition temperature, according to which the AF transition temperature issignalled by a maximum in ⳵ ( ␹ 储 T)/ ⳵ T. When there are two
peaks in ⳵ ( ␹ 储 T)/ ⳵ T, we define T N1 and T N2 as the maxima
at lower and higher temperatures, respectively 关see the inset
in the upper left of Fig. 2共a兲兴. If there is only one peak, wedefine the Néel temperature simply as T N . In this way weobtained the T-x phase diagram of Cu1⫺x Mgx GeO3 near x cshown in Fig. 2共b兲.
In Ref. 9 the existence of a first-order phase transition
between the DAF and UAF phases was inferred from theobservation of a sudden increase of T N at x⫽0.023, thebroadening of ␹ c (T) around T N , and the disappearance ofthe cusp due to the SP transition. Instead of a single broadpeak, we now observe clear double peaks. T N below x c1 issmoothly connected to T N1 at x c1 , while T N2 is smoothly
connected to T N (x⬎x c2 ) at x c2 . Therefore T N1 and T N2 may
be confidently assigned as the AF transition temperatureswith respect to the DAF and UAF phases, respectively. The
lower T N curve never joins with the higher T N curve, whichshows more directly the presence of the proposed first-orderphase transition. Note that the double peaks are observed in
the finite concentration region, x c1 ⬍x⬍x c2 , where the lower
and upper boundaries are separated in x by amounts well
above our resolution of concentration.
The phase transition between the DAF and UAF phases
was also verified in neutron-diffraction experiments.13 Nakaoet al.13 determined x c as ⬃0.027 by the observation of apeak of the effective magnetic moment and the jump of themagnitude of dimerization. This value is approximately
equal to x c2 of the present paper. On the other hand, from themagnetic susceptibility measurements x c was deduced to beabout 0.023.9 To determine at what temperature true SPLRO is attained, synchrotron x-ray diffraction is a superior
technique to neutron diffraction, because of its naturally very
high resolution (⬃0.0002 Å ⫺1 ). The peak profiles of longitudinal scans at 共1.5, 1, 1.5兲 of samples with x⫽0.021 and
0.026 are shown in the inset of Fig. 2共c兲. We observe superlattice peak in the samples with x⭓0.023 but the peak widthis far wider than the resolution limit 共5000 Å兲 even at low
temperatures, that is, we determine that only SP-SRO exists
in these samples. The concentration dependence of the in-PRB 61

FIRST-ORDER PHASE TRANSITION BETWEEN . . .

4105

FIG. 2. 共a兲 The magnetic susceptibility of Cu1⫺x Mgx GeO3 near the AF transition temperature共s兲. The applied field is 1000 Oe. The datafor different x are shifted vertically. Double peaks are observed in the region of 0.0237ⱗxⱗ0.0271, while a single peak is observed in theregions of x⬍0.023 and 0.028⬎x. The arrows indicate the anomaly due to the AF transition. The inset in the upper left is ⳵ ( ␹ 储 T)/ ⳵ T for
determining T N1 and T N2 . The inset in the bottom shows the magnetic susceptibility in the same samples of x⫽0.0271, 0.0288, and 0.0299
for 2⬍T⬍15 K. 共b兲 The temperature vs concentration phase diagram determined by the magnetic susceptibility measurements. Opencircles, triangles, closed upward and downward triangles are T S P , T N , T N1 , and T N2 , respectively. Solid lines are guides to the eye. 共c兲 Mg
concentration dependence of the inverse correlation length of the lattice dimerization at T⫽4 K. The inset shows representative superlattice
peak profiles.

verse correlation length at 4 K is shown in Fig. 2共c兲. The
hatched zone corresponds to the double-peak region of the
DAF and UAF phases determined by the magnetic susceptibility measurements. The correlation length ( ␰ ) is larger than
the resolution limit of 5000 Å at low temperatures for x⬍x c1 , decreases drastically in the double peak region, andbecomes much shorter at x⬎x c2 .
We now discuss the Zn-doped CuGeO3 system. As one
might expect, the phase transition between the DAF andUAF phases exists not only in the case of Mg-doped

CuGeO3 but also in Zn-doped CuGeO3 . ␹ c (T) of
Cu1⫺x Znx GeO3 (x⫽0.016, 0.017, 0.019, 0.023, and 0.025兲
in the region of 2⬍T⬍5 K is shown in Fig. 3. Again we
observe double peaks in samples with Zn2⫹ concentrationsof x⫽0.017, 0.019, and 0.023, while a single peak is observed in the x⫽0.016 and 0.025 samples; generally, thepeak structure is not as clear as that of Cu1⫺x Mgx GeO3 .
⳵ ( ␹ 储 T)/ ⳵ T is shown in the inset in the upper left. The ambiguity seems to be due to the worse dilutant homogeneity in
the Zn-doped samples compared with that of the Mg-doped

4106

T. MASUDA et al.

FIG. 3. The magnetic susceptibility of Cu1⫺x Znx GeO3 aroundT N . Double peaks are observed in x⫽0.019, and 0.023 samples,while single peaks are observed in x⫽0.016 and 0.025 samples. Inx⫽0.017 the anomaly at T N2 is confirmed by Fisher’s methodthough it is not so clear in the raw susceptibility data. The inset in
the bottom shows the T-x phase diagram. The inset in the upper left
is ⳵ ( ␹ 储 T)/ ⳵ T.

samples as we explained in the previous section. In the caseof Zn-doped CuGeO3 we obtain x c1 ⯝0.017 and x c2
⯝0.023. The T-x phase diagram near x c is shown in theinset in the bottom. We observe a jump of T N in Zn-doped
CuGeO3 which is closely analogous to that in Mg-doped
CuGeO3 .
Now let us return to the SP transition in the Mg-doped
CuGeO3 system. Figures 4共a兲 and 共b兲 show the experimental
results of the magnetic susceptibility measurement and theheat-capacity measurement of Cu1⫺x Mgx GeO3 (x⫽0.017).
We observe a cusp due to the SP transition at T⬃11.5 K in
the magnetic susceptibility 关Fig. 4共a兲兴. As for heat capacity,
we observe an anomaly due to the SP transition at T
⬃10.7 K 关Fig. 4共b兲兴. From neutron-diffraction measurements on the same concentration sample, it is found that thesuperlattice peak intensity begins to increase at T⬃10.8 K
in Fig. 2 of Ref. 13. The coincidence of these temperatures isgood enough, and thus we concluded that T S P of the sample
is about 11 K.
On the other hand, high-resolution x-ray-diffraction measurements lead to rather different conclusions. We observethat the peak width of the superlattice reflection is not resolution limited at the T S P determined above but rather it continues to narrow as the temperature is lowered below T S P as
shown in Fig. 2 of Ref. 11. Here, we define the temperature
where the SP correlations become long range as T ⬘S P and it ismuch lower than T S P , especially for x near x c . The length
5000 Å, corresponding to the resolution limit of the measurement, is much longer than the average impurity distance andconsequently we may safely call the region of TⱗT ⬘S P as the
SP long-range order 共LRO兲 region.
Since T ⬘S P is lower than T S P , true SP-LRO only exists at

PRB 61

FIG. 4. The experimental results of 共a兲 the magnetic susceptibility and 共b兲 heat capacity in Cu1⫺x Mgx GeO3 (x⫽0.017) sample.

a temperature which is rather lower than the T S P deduced
from the susceptibility measurements. The difference between T S P and T ⬘S P does not reflect any experimental artifact
because the behavior of the x-ray integrated intensity shows
almost the same temperature dependence as the peak intensity of the neutron diffraction. We should note that the resolution of neutron diffraction is much less (⬃200–500 Å), 13
and actually the peak intensity of the neutron diffraction corresponds to the integrated intensity of the x-ray diffraction
within the temperature region of interest.
We show the T-x phase diagram of Cu1⫺x Mgx GeO3 in
Fig. 5. We have added T ⬘S P as closed diamonds and T S P
determined by the neutron diffraction13 as plusses there. The
T ⬘S P decreases with x and vanishes at x c ⬃0.024, i.e., thepeak width does not tend to the resolution limit at low temperatures in the x⬎x c region.

FIG. 5. T-x phase diagram of Cu1⫺x Mgx GeO3 obtained by susceptibility measurements, x-ray diffraction and neutron diffraction.
Neutron-diffraction data is from Fig. 6 of Ref. 13.

PRB 61

FIRST-ORDER PHASE TRANSITION BETWEEN . . .
IV. DISCUSSION

We find clear double peaks in ␹ c (T) 关Figs. 2共a兲 and 3兴
and a corresponding jump of T N in the T-x phase diagram关Fig. 2共b兲 and the inset of Fig. 3兴 of Cu1⫺x M x GeO3 in theregion x c1 ⬍x⬍x c2 . While the jump of T N is the strongest
evidence for the existence of a first-order phase transition
between the DAF and UAF phases, the double peaks suggest
the existence of spatial phase separation at a critical concentration, which is characteristic of a first-order phase transition. The measured phase separation region spreads over afinite region, x c1 ⬍x⬍x c2 , which is consistent with the phasetransition being of the first order. When a first-order phasetransition occurs, metastable phenomena, e.g., supercoolingand superheating, appear around the critical point in general.
The spread of the phase separation region over some nonzero
range suggests the existence of metastable states as is indeed
observed in the x-ray measurements.11 We should note that
this spread does not come from inhomogeneity of the impurity distribution in the case of Mg-doped CuGeO3 , because
the concentration fluctuation is within 0.1% as shown in Fig.
1.
The fact that T ⬘S P is much lower than T S P gives significant
insight into how the SP order collapses with increasing impurity concentration. T S P is the transition temperature inferred from the dip in the magnetic susceptibility, the jumpof the heat capacity, and the appearance of measurable diffraction intensity at the SP superlattice peak positions. The
coincidence of SP transition temperatures T S P in various
measurements, suggests that the correlation length of the
dimerization of ⬃500 Å, which corresponds to the resolution limit of the neutron diffraction, is sufficient for the opening of the SP energy gap. In contrast to the case of pure
CuGeO3 system where T S P and T ⬘S P are the same,14 the onedimensional spin chain is cut at the impurity site in the
Cu1⫺x M x GeO3 system. For T S P ⬎T⬎T ⬘S P , the phase of
dimerization is likely pinned at the impurity sites, which issimilar to the strong pinning interactions between the impurities and magnetic solitons which was suggested in the incommensurate phase in Cu1⫺x (Zn, Ni) x GeO3 . 15 However,
only local lattice rearrangements are needed to change thephase at an impurity site. As the temperature decreases andthe interchain interactions and spin-phonon coupling favoring the SP state become relatively more important, the individual finite SP domains begin to correlate with each otherover large distances, and at T ⬘S P LRO is finally established.
This model which could yield either a tricritical point with
its concomitant first-order phase transition or a more complicated reentrant scenario as in certain spin glass systems. Thisis discussed briefly in Refs. 11 and 16.
Therefore, for T S P ⬎T⬎T ⬘S P , the SP energy gap and thedimerization coexist though the lattice dimerization does not
attain LRO. Considering that the peak width determined in
x-ray-diffraction measurements decreases gradually with decreasing temperature and that there is no anomaly in thesusceptibility, heat capacity, and neutron peak intensity at
T ⬘S P , we cannot determine definitively whether the change
from SP-SRO to SP-LRO is a true phase transition or acrossover. The important point is that T ⬘S P , the temperature
where ␰ is much longer than the average impurity distance,
vanishes around x c 关Figs. 2共c兲 and 5兴. The jump of T N at4107

x c1 ⬍x⬍x c2 corresponds to the disappearance of SP-LRO,
which is the evidence for the phase transition between the
UAF and DAF phases by x-ray diffraction. When x is larger
than x c , SP-SRO is still present in the system. However, it
should be considered as the result of critical fluctuations of
the true SP state found for x⬍x c .
Recently, Nakao et al.13 have reported neutron-diffraction
measurements performed on Mg-doped CuGeO3 crystals.
This group of authors, which included some of the present
authors, deduced the existence of the phase boundary between the DAF and UAF phases from the sudden change in
SP lattice displacement ␦ and effective magnetic moment
␮ e f f at x c . They have also proposed the existence of anintermediate phase with SP-SRO which is reentrant at low
temperatures, and the existence of a phase transition between
the DAF and UAF phases at T⫽0 K. This reentrancy has
also been clearly seen in recent low-temperature synchrotron
x-ray measurements.16
While some of the extant theories provide a qualitativedescription of how impurity doping suppresses the SP phaseand how the AF phase is induced,17,18 they fail to explain thetransition between the DAF and UAF phases reported in ourpaper. Saito10 has recently proposed a model for the phasetransition between the DAF and UAF phases at T⫽0 K,
and very recently she showed that the order of the phasetransition depends on the ratio between the spin-lattice coupling and the interchain interaction.19 According to her work,
the phase transition between the DAF and UAF phases canbe of first order in the case of relatively large interchaininteraction.
While a detailed theoretical description of the two different AF phases at nonzero temperatures is still absent, thebehavior of T N as a function of x can be qualitatively explained as follows. The one-dimensionality of the spin interaction in CuGeO3 appears not to be as good20 as that ofconventional organic SP materials.21 The T-x phase diagramof CuGeO3 therefore would be that of a typical diluted antiferromagnet, i.e., a monotonic decrease of T N with x would
be observed, if the SP transition had not occurred in
CuGeO3 . Actually, the occurrence of the SP phase suppresses the AF phase completely in pure CuGeO3 . As x increases, the SP phase is suppressed and the DAF phase develops at an infinitesimally small impurity concentration,22
and at x c the SP-LRO disappears and the phase transition
from the DAF to UAF phase occurs. Since the SP-SRO,
however, still exists above x c , the AF phase is suppressed,
and T N exhibits a plateau for x c ⬍xⱗ0.04. For xⲏ0.04 any
SP-SRO is very weak 共Ref. 13兲 and therefore typical behavior of a diluted antiferromagnet, that is, a monotonic decrease of T N with x, is observed.

V. CONCLUDING REMARKS

We have confirmed the phase transition between the UAF
and DAF phases in Mg-doped CuGeO3 by detailed susceptibility measurements and high-resolution synchrotron x-raydiffraction studies. The results of previous neutrondiffraction experiments also suggested a similar phase

4108

T. MASUDA et al.

transition. We found clear double peaks in the magnetic susceptibility around x⬃x c . We have interpreted these peaks as
the result of two separate Néel transitions, in which casespatial phase separation between the DAF and UAF phases ispresent in the system. These features are interpreted as theresult of an intrinsic first-order transition.
Our x-ray-diffraction measurements show that the SP
dimerization attains long-range order only for x⬍x c . Thus
the transition from the DAF to UAF phase is characterized
by the loss of the SP long-range order.
Our
susceptibility
measurements
show
that
Cu1⫺x Znx GeO3 exhibits the same kind of behavior as
Cu1⫺x Mgx GeO3 , and the T-x phase diagrams of these compounds are very similar. We therefore conclude that the DAF
and UAF phases, and the corresponding transition between
these phases at x c , are also present in Zn-doped CuGeO3 .

*Electronic address: tmasuda@ap.t.u-tokyo.ac.jp†

Also at Department of Advanced Materials Science, The University of Tokyo, 6th Engineering Bldg., 7-3-1 Hongo, Bunkyo-ku,
Tokyo 113-8656, Japan.
‡
Present address: Central Research Institute of Electric Power Industry, Komae, Tokyo 201-8511, Japan.
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PRB 61ACKNOWLEDGMENTS

We would like to thank H. Nakao, Y. Fujii, M. Nishi, K.
Hirota, and G. Shirane for helpful discussions of the neutrondiffraction experiments. We are also grateful to M. Saito forvaluable discussion and for providing a preprint prior to publication. We would like to thank H. Fukuyama for general
discussions on the role of disorder in spin-gap systems. We
also acknowledge A. Fujioka for the growth of some of thesamples used. We thank S. LaMarra for assistance with thesynchrotron experiments. This work was supported in part by
a Grant-in-Aid for COE Research ‘‘SCP coupled system’’from the Ministry of Education, Science, Sports and Cultureof Japan, and T.M. would like to thank the Japan Society for
the Promotion of Science for Young Scientists. This work
was also supported by the NSF under Grant No. DMR9704532.

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12