PHYSICAL REVIEW B 66, 174416 共2002兲

Impurity-induced antiferromagnetic phase in a doped Haldane
system Pb„Ni1Àx Mgx … 2 V2 O8
T. Masuda* and K. Uchinokura
Department of Advanced Materials Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

T. Hayashi and N. Miura
Institute for Solid State Physics, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba 277-8581, Japan
共Received 14 August 2002; published 8 November 2002兲
The impurity-induced antiferromagnetic phase in Pb共Ni1⫺x Mgx ) 2 V2 O8 (x⫽0.020, 0.010, and 0.0050兲 isstudied by means of heat-capacity and magnetization measurements. One S⫽1 spin is induced by one nonmagnetic impurity, which contributes to the antiferromagnetic phase. The effective interaction between these
impurity-induced spins is weak and the number of the spins is a few percent of all spins, which results in thedisappearance of the antiferromagnetic phase at an anomalously low magnetic field in the H-T phase diagram.
DOI: 10.1103/PhysRevB.66.174416

PACS number共s兲: 75.10.Jm, 75.30.Kz, 75.50.Ee

I. INTRODUCTION

Recent interest in quantum-spin systems is focused on
spin-gap systems, which are classified into spin-Peierls, spin
alternation, dimer, two-leg ladder, and Haldane1 systems.
The ground state of these systems is a nonmagnetic singlet
state and, therefore, the spin correlation decays rapidly. In
the valence bond solid 共VBS兲 model, which is an approximate model for the one-dimensional S⫽1 共1D兲 Heisenberg
model, it decays exponentially.2 A numerical study of the S⫽1 1D Heisenberg model with open boundary conditions
shows that the staggered moment induced at the edge decays
exponentially,3,4 which is consistent with the VBS model.
Experimentally, impurity doping to the spin site is a goodprobe for the degree of freedom of edge spins. An electron
spin resonance 共ESR兲 study on impurity-doped NENP
showed the S⫽1/2 states at Ni2⫹ sites around the impurity.5,6
To simplify the situation we draw a picture that one nonmagnetic ion induces two S⫽1/2 spins, which is shown in Fig.
1共a兲.
There are several cases for the impurity-induced spins. If
the next-nearest-neighbor interaction is negligible, one nonmagnetic impurity induces two free S⫽1/2 spins which isshown in Fig. 1共a兲. This was reported in NENP doped withnonmagnetic impurities6 and many other Haldane materials.
If there is a strong coupling between the edge spins in one
separated chain, the configuration of impurity-induced spinsis shown in Fig. 1共c兲. The total spin in a chain with an evennumber of spins is 0 and the one in a chain with an odd
number of spins is 1. In this case two nonmagnetic impurities
induce one S⫽1 spin on the average, which was observed
only in Y2 BaNi1⫺x Znx O5 . 7 If the next-nearest-neighbor interaction is ferromagnetic and strong, the adjacent impurityinduced spins will be coupled and form an S⫽1 spin. In thiscase one nonmagnetic impurity will induce one S⫽1 spin.
This case has not been reported experimentally in a real material. In any case most of the spins are in a singlet state andthe system would be mapped to the paramagnetic state witha reduced number of spins at low temperatures and at low
magnetic fields compared to the spin gap energy.
0163-1829/2002/66共17兲/174416共7兲/$20.00

To observe the degree of freedom of spins or to estimate
the number of spins, the heat capacity is one of the best
tools. The heat capacity of free spins is expressed by the
Schottky heat capacity:C⫽N⫺

共 g ␮ BH 兲 2

k BT 2

冋共 S⫹1/2兲 2

sinh2 关 ␤ g ␮ BH 共 S⫹2/1兲兴

共 1/2兲 2

sinh2 共 ␤ g ␮ BH 兲

册

.

共1兲

The temperature dependences of the Schottky heat capacity
are shown in Fig. 2共a兲 for S⫽1/2, 1, and 2. The shapes arequite different among those for different sizes of spins andone can estimate the size of spins, the number of spins, andthe g value from the Schottky heat capacity. The magnetic
susceptibility also tells us information on the number of
spins, the size of spins, and the g value. Figure 2共b兲 shows
the inverse magnetic susceptibility of free spins for four S⫽1/2 spins, two S⫽1 spins, and one S⫽2 spin. In this case,

FIG. 1. 共a兲 VBS description when the next-nearest-neighbor interaction is neglected. 共b兲 VBS description when the next-nearestneighbor interaction is ferromagnetic. 共c兲 Singlet-triplet model.

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T. MASUDA, K. UCHINOKURA, T. HAYASHI, AND N. MIURA

FIG. 2. 共a兲 The Schottky heat capacities for four S⫽1/2 spins,
two S⫽1 spins, and one S⫽2 spin. 共b兲 The inverse magnetic susceptibilities for four S⫽1/2 spins, two S⫽1 spins, and one S⫽2
spin.

however, the Curie constant is the product of the number of
spins, the size of spins, and the g value and we cannot knoweach value separately.
In doped Haldane materials the paramagnetic state isstrongly fluctuated by quantum effects and the impurityinduced spins are usually not in the ordered state even at low
temperatures.5– 8 If the interchain spin interaction is rather
large, however, the impurity-induced spins may be in theordered state as was observed in a different spin-gap material
doped with nonmagnetic impurities Cu1⫺x M x GeO3 . 9–12
Pb共Ni1⫺x Mgx ) 2 V2 O8 (Ni2⫹ : S⫽1, Mg2⫹ : S⫽0) 共Refs. 13
and 14兲 is an example of the impurity-induced antiferromagnetic 共AF兲 ordered phase in the doped Haldane system because the interchain spin interaction is rather large and PbNi2
V2 O8 is located in the vicinity of the phase boundary between the ordered phase and Haldane phase.15 The authors ofRefs. 13 and 14 observed the AF transition by means ofmagnetic susceptibility and heat capacity measurements at
T⭓2 K in Pb共Ni1⫺x Mgx ) 2 V2 O8 . However, the Néel temperature of this material is Tⱗ3.5 K and a lower temperature
will be required to study the AF phase in more detail. If asmall number of spins induced by nonmagnetic ions contribute to the antiferromagnetic order, we can map the original
spin system to the antiferromagnetic spin system with a reduced number of spins. In this mapped system the number of
共impurity-induced兲 spins and the 共impurity-induced兲 spin interaction would be small. Therefore, all 共impurity-induced兲
spins would be along the magnetic field and the impurityinduced AF phase would disappear at an anomalously low
magnetic field.
In Sec. III we performed the heat capacity measurements
down to 0.45 K in Pb共Ni1⫺x Mgx ) 2 V2 O8 (x⫽0.020) in themagnetic field and observed the disappearance of the
impurity-induced AF phase at 3– 4 T. To complete themagnetic-field–temperature (H-T) phase diagram we performed a magnetization measurement in Pb共Ni1⫺x Mgx ) 2 V2
O8 up to 38 T. We confirmed the spin-gap phase at the lowest
temperature and the disappearance of the spin gap at highmagnetic field. The H-T phase diagram is explained bymeans of the molecular-field theory very well.
To estimate the degree of freedom of the impurityinduced spins, a heat capacity measurement at lower temperature range would be required. In Sec. IV, therefore, we
prepared lower-concentration samples Pb共Ni1⫺x Mgx ) 2 V2 O8(x⫽0.005 and 0.010兲 which have a lower Néel temperatureand performed the heat capacity measurements. Fitting theexperimental data to the Schottky heat capacity shows that
one nonmagnetic impurity induces one S⫽1 spin. The obtained H-T phase diagrams are explained by the molecularfield theory as well as that in Pb共Ni1⫺x Mgx ) 2 V2 O8(x⫽0.020).
Neutron scattering, of course, will be required for a detailed study of the impurity-induced AF phase but a single
crystal of PbNi2 V2 O8 has not been obtained. This material isincongruent and it is difficult to find an adequate condition
for the crystal growth. The intensity of the spin-wave excitation in the impurity-induced AF phase is expected to bevery small and neutron scattering by means of a polycrystalline sample would not be an effective method to obtain theinformation on the impurity-induced antiferromagnetic
phase.
II. EXPERIMENTAL DETAILS

Polycrystalline
samplesof
Pb共Ni1⫺x Mgx ) 2 V2 O8(x⫽0.0050, 0.010, and 0.020兲 were prepared by the solidstate reaction method for heat capacity measurements. For
the magnetization measurements, an aligned polycrystalline
sample of Pb共Ni1⫺x Mgx ) 2 V2 O8 (x⫽0.020) was prepared in
the same way as in Ref. 13. Heat capacity measurements
were performed down to 0.45 K and up to 14.0 T using acommercial heat capacity measurement system PPMS
共Quantum Design Co. Ltd.兲. The magnetization measurements up to 38 T were performed by means of an induction
method using a pair of coaxial pickup coils.
III. PB„NI1Àx MGx … 2 V2 O8 „xÄ0.020…
A. Experimental results

The disappearance of the AF phase by a magnetic field isobserved in the magnetic heat capacity measurements in
Pb共Ni1⫺x Mgx ) 2 V2 O8 (x⫽0.020), which is shown in Fig.
3共a兲. The magnetic heat capacity is obtained by subtracting
the heat capacity in PbMg2 V2 O8 from that in Pb共Ni1⫺x Mgx )2 V2 O8 so as to eliminate approximately the contribution of
the lattice heat capacity. The reference compound PbMg2 V2
O8 is isostructural with PbNi2 V2 O8 and the magnetic Ni2⫹
ions are replaced by nonmagnetic ions Mg2⫹ . A sharp peak
due to the AF transition is observed at T⫽2.2 K and at 0 T.
The peak is suppressed by the magnetic field and it disappears at H⬃4 T. At H⭓4 T broad anomalies are observed
and their magnetic field dependence is qualitatively consistent with the Schottky heat capacity assuming that S⫽1/2, g

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IMPURITY-INDUCED ANTIFERROMAGNETIC PHASE IN . . .

FIG. 3. 共a兲 共Color兲 Heat capacity in Pb共Ni1⫺x Mgx ) 2 V2 O8 (x⫽0.020). The suppression and disappearance of the AF transition
by applying a magnetic field is observed. The broad anomaly atH⭓ 4 T is the Schottky-like anomaly and it is not due to a phasetransition. The inset is the enlargement of the low-temperature andlow-magnetic field region. 共b兲 Magnetic entropy estimated from theheat capacity measurements.

⫽ 2.1, and the reduced number of free spins, N, is N⫽2⫻0.020⫻N A 关 Ni mol⫺1 兴 or S⫽1, g⫽2.1, and N⫽1⫻0.020⫻N A 关 Ni mol⫺1 兴 . Here N A is the Avogadro number.
The Schottky heat capacity, hence, is due to Zeeman splittingof impurity levels. The temperature of the broad anomalies(T Schottky) in the higher magnetic field is 3 K ⱗT Schottkyⱗ 10
K. The contribution of the spin-gap excitation to heat capacity may not be completely negligible, which results in a difficulty of quantitative consistence.
The magnetic entropy is shown in Fig. 3共b兲. The solid,
dashed, and dotted lines in Fig. 3共b兲 are the entropies on theassumption of the models described in Figs. 1共a兲, 1共b兲, and1共c兲, respectively. The magnetic entropy at H⫽0 T increases
drastically at 0.45 K, ⱗTⱗT N , because of the antiferromagnetic order. At T NⱗT the increase of the entropy is due to the
AF fluctuation of impurity-induced spins and spin-gap excitation. The spin gap of PbNi2 V2 O8 estimated in Ref. 13 isabout 14 K and it is rather difficult to separate the contributions of the AF fluctuation and the spin-gap excitations.
However, the magnetic entropy at T N is well above the dotted line in Fig. 3共b兲 and the model of either Fig. 1共a兲 or 1共b兲is more adequate than that in Fig. 3共c兲. We can safely conclude that one nonmagnetic ion induces two S⫽1/2 spins or
one S⫽1 spin in this system. The degrees of freedom ofthese spins freeze below T N , which means that a small number of impurity-induced spins interact with each otherweakly and are in an ordered state below T N . The rest of thespins do not contribute to the entropy or heat capacity at low
temperatures, which means that they are in the singlet stateand form a spin-gap mode. Hence, spin-gap and antiferromagnetic spin-wave excitations coexist.

FIG. 4. 共a兲 Magnetization measurements up to 37.5 T in a fieldparallel to the chain axis. The arrow indicates the magnetic field
where the impurity-induced AF phase disappears. 共b兲 Magnetization
in a field perpendicular to the chain axis.

The magnetization in Pb共Ni1⫺x Mgx ) 2 V2 O8 (x⫽0.020) ina field parallel 关 M 储 (H) 兴 and perpendicular 关 M⬜ (H) 兴 to thechain axis 共the c axis兲 is shown in Fig. 4. Here the chain axis
is also the magnetic easy axis.13 The slope of the magnetization curve of 2 K changes at 2–3 T in both cases of H 储 c andH⬜c, which is indicated by arrows in Fig. 4. This corresponds to the disappearance of the AF phase which is observed in the heat capacity measurement. At Hⲏ4 T the
impurity-induced spins are along the magnetic field.
At high field an abrupt increase of the magnetization isobserved at around 20 T 共depending on temperature兲. Now
let us compare this result with the magnetization vs magnetic
field (M -H) curve of pure PbNi2 V2 O8 shown in Fig. 2 ofRef. 13. In that figure a sharp change of dM /dH at 4.2 K
was observed. This fact was one of the clearest pieces ofevidence of the existence of a Haldane gap in pure PbNi2 V2O8 and the authors of Ref. 13 concluded that PbNi2 V2 O8 is a
Haldane-gap system.
The present experiment in Pb共Ni1⫺x Mgx ) 2 V2 O8 does notshow such a sharp change of dM /dH at the same temperature 4.2 K. However, the magnetic fields of the kinks in both
samples are almost the same and the overall behavior 共except
for the low-field region兲 is very similar. These facts clearlysuggest that both of the kinks in pure PbNi2 V2 O8 and
Pb共Ni1⫺x Mgx ) 2 V2 O8 originate from the same phenomenon.
It leads to the conclusion that even the doped sample has a
Haldane-gap-like excitation, at least just below the magnetic
field of the kink.
The critical fields parallel to the c axis 关 H c储 (2 K) 兴 andperpendicular to the c axis pH⬜c (2 K)] were 20.8 T and 18.7

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T. MASUDA, K. UCHINOKURA, T. HAYASHI, AND N. MIURA

FIG. 5. The magnetic-field–temperature (H-T) phase diagramin Pb共Ni1⫺x Mgx ) 2 V2 O8 (x⫽0.020).

T, respectively. Using Eq. 共2.13.2兲 in Ref. 16, which relates
the critical fields H c储 and H⬜c to the doublet and singlet gap
energies ⌬ 储 and ⌬⬜ for Pb共Ni1⫺x Mgx ) 2 V2 O8 (x⫽0.020),
we obtain ⌬ 储 ⫽1.9 meV, ⌬⬜ ⫽2.4 meV, the mean gap energy ⌬⫽(2⌬⬜ ⫹⌬ 储 )/3⫽2.3 meV, and the anisotropy termD⫽⫺0.23 meV. 17 ⌬ is larger than that of pure PbNi2 V2 O8
关 ⌬ pure ⫽1.9 meV 共Ref. 13兲兴, which is due to the finite chain
effect.18 It is observed that H c decreases with decreasing
temperature and, hence, ⌬ also decreases with decreasing
temperature as was observed in pure PbNi2 V2 O8 , 19 SrNi2 V2O8 , 15 and other Haldane materials.20
The magnetic-field–temperature (H-T) phase diagram is
obtained by heat capacity measurements and magnetization
measurements, which is shown in Fig. 5. The suppression
and disappearance of the impurity-induced AF phase are observed but this behavior is quite different from that in theconventional AF phase in a quasi-1D AF magnet 共halfinteger spins兲. The conventional one is, generally, suppressedby the quantum fluctuation of the spins. The magnetic field
suppresses the quantum fluctuation and, therefore, the AF
phase in the quasi-1D AF magnet is enhanced by thefield.21,22 The qualitative behavior of the AF phase in the
integer-spin quasi-1D AF material, CsNiCl3 is the same.23
Pb共Ni1⫺x Mgx ) 2 V2 O8 is, however, quite different.
B. Discussion

The reason for the anomalous behavior of the impurityinduced AF phase is that the staggered spins which contribute to the AF order are strongly fluctuated by quantum effects and that the induced staggered spins decay
exponentially.2– 4 Hence, we can map the original system tothe simplified model: the system with a reduced number of
spins, which is shown in Fig. 1共a兲 or 1共b兲. In model 共a兲 thespin is S⫽1/2 and the number of spins is N⫽2⫻x⫻N A or
共b兲 S⫽1, N⫽1⫻x⫻N A , either of which is adequate for the
impurity-induced spin system inPb共Ni1⫺x Mgx ) 2 V2 O8 . Theinteraction between the induced spins is different from theoriginal spin interaction between adjacent spins. We assume
here that the effective interaction is isotropic and we adopt avery simple model: the molecular-field approximation. The
model Hamiltonian isFIG. 6. The inverse magnetic susceptibility in Pb共Ni1⫺x Mgx ) 2
V2 O8 (x⫽0.020). The inset is the magnetic susceptibility.

H⫽zJ eff兺i苸 ␣ , j苸 ␤

⫺g ␮ B H z

共 具 S典 ␣ Si ⫹ 具 S典 ␤ S j ⫺ 具 S典 ␣ 具 S典 ␤ 兲

兺 S zi .

共2兲Here z is the coordination number of adjacent spins and J eff
is the interaction between the impurity-induced spins. ␣ and␤ mean the sublattice. There are some relations between
molecular-field parameters:1␪ ⫽ CA,
2
A:
M:

molecular field constantsaturation moment

共3兲

A⫽

2zJ eff
Ng 2 ␮ B2,

M ⫽Ng ␮ z S.

共4兲
共5兲

Here ␪ is the Weiss temperature and C is the Curie constant.
Using these parameters the saturation field H 0 is
H 0 ⫽2AM .

共6兲

From the heat capacity measurements we assumed that 共a兲
S⫽1/2 and N⫽2⫻x⫻N A or 共b兲 S⫽1 and N⫽1⫻x⫻N A .
We need not make difference between models 共a兲 and 共b兲when we estimate H 0 in Eq. 共6兲. The molecular field A,
which corresponds to the effective interaction, is estimatedfrom the Weiss temperature and the Curie constant. These are
obtained by Curie-Weiss fitting in the inverse magnetic susceptibility which is shown in Fig. 6. Half of the molecularfield constant A/2 is the y-axis intercept in Fig. 6 and A⫽63⫾15 emu⫺1 Ni mol is obtained. Hence, H 0 ⫽3.1
⫾0.8 T is obtained. This magnetic field is consistent with thevalue of H, where the impurity-induced AF phase disappears.
IV. PB„NI1Àx MGx … 2 V2 O8 „xÄ0.0050 AND 0.010…
A. Experimental results

In the previous section we showed the disappearance of
the impurity-induced AF phase at rather low magnetic field.
The size of the impurity-induced spins, however, has notbeen obtained because the temperature and magnetic field
ranges are rather high. At higher temperature and magnetic

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IMPURITY-INDUCED ANTIFERROMAGNETIC PHASE IN . . .

FIG. 9. 共Color兲 The heat capacity in Pb共Ni1⫺x Mgx ) 2 V2 O8(x⫽0.0050) scaled by the magnetic field. The temperature range
which is displayed here is 0.40 K ⱗTⱗ2.0 K at higher magnetic
fields.
FIG. 7. 共Color兲 The heat capacity in Pb共Ni1⫺x Mgx ) 2 V2 O8 (x⫽0.010).

field the contribution from Haldane-gap excitation cannot be
neglected and a quantitative explanation for the Schottky
heat capacity was difficult. We therefore performed the heat
capacity measurements in the samples Pb共Ni1⫺x Mgx ) 2 V2 O8(x⫽0.010 and 0.0050兲, which have lower Néel temperature.
Figures 7共a兲 and 7共b兲 show the heat capacity and entropyof the impurity-induced spins, respectively. These data wereobtained by subtracting the heat capacity inPbNi2 V2 O8 at
H⫽0 T from that in Pb共Ni1⫺x Mgx ) 2 V2 O8 (x⫽0.010) toeliminate the contribution from phonon and Haldane-gap excitations. The minimum spin gap in Pb共Ni1⫺x Mgx ) 2 V2 O8(x⫽0.020) in global reciprocal space is estimated as about
20 T in Fig. 5. The temperature and magnetic field are too
low for the spin-gap excitation to contribute much to the heat
capacity and the subtraction would be valid. An anomaly due
to the Néel transition is observed at T⫽1.3 K and at H
⫽0 T in Fig. 7共a兲. This anomaly is suppressed with increasing magnetic field and disappears at H⬃1.75 T. The
Schottky anomaly, in turn, is observed at Hⲏ1.75 T. The
qualitative behavior is the same as in Pb共Ni1⫺x Mgx ) 2 V2 O8(x⫽0.020).
The Schottky heat capacity is scaled by the magnetic field
as we can see in Eq. 共1兲. We hence show the heat capacity

FIG. 8. 共Color兲 The heat capacity in Pb共Ni1⫺x Mgx ) 2 V2 O8(x⫽0.010) scaled by the magnetic field. The temperature range
which is displayed here is 0.40 K ⱗTⱗ 5.0 K at higher magnetic
fields.

scaled by the magnetic field in Fig. 8. At Hⱗ1.75 T the peak
position changes with increasing magnetic field and, on theother hand, at Hⲏ1.75 T the heat capacities overlap in thisscaled temperature. This means that at H⬃1.75 T the applied field is comparable to or larger than the effective field
due to the interaction between the impurity-induced spins
and the impurity-induced spins are along the magnetic field.
At higher magnetic field the interaction between the
impurity-induced spins can be negligible and the heat capacity can be fitted by the Schottky heat capacity which is expressed by Eq. 共1兲. The dashed line in Fig. 8 is the best fit
when S⫽1. The fitting parameters are g⫽2.24 and N⫽1⫻0.013⫻N A . The dotted line is the best fit when S⫽1/2 andg⫽2.2. The fitting parameter is N⫽2⫻0.010⫻N A . We obtain a better result when S⫽1/2, g⫽2.7, and N⬃2⫻0.01⫻N A than dotted line in Fig. 8 but the g value deviates from2 very much and we fixed the g value at 2.2. The dashed line
is a much better fitting than the dotted line. The imperfectionof eliminating the contribution from Haldane-gap excitations
may result in a small deviation at higher temperature. Hence,
it is concluded that one nonmagnetic ion induces one S⫽1spin. The model which is described in Fig. 1共b兲 is adequate
for this material.
The estimated value of N⫽1⫻0.013⫻N A deviatesslightly from N⫽1⫻0.010⫻N A . The impurity concentration is low in this sample and the contribution from the intrinsic vacancies may not be neglected, which would resultin the small deviation.

FIG. 10. The H-T phase diagram in Pb共Ni1⫺x Mgx ) 2 V2 O8 .
Solid circles, triangles, and squares show the Néel temperatures inthe samples of x⫽0.020, 0.010, and 0.0050.

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T. MASUDA, K. UCHINOKURA, T. HAYASHI, AND N. MIURA

FIG. 11. The
Pb共Ni1⫺x Mgx ) 2 V2 O8 .

inversedmagnetic

susceptibility

inFigure 9 is the heat capacity of the impurity-induced spinsin Pb共Ni1⫺x Mgx ) 2 V2 O8 (x⫽0.0050) which is obtained in
the same way as in Pb共Ni1⫺x Mgx ) 2 V2 O8 (x⫽0.010). The
temperature is scaled by the magnetic field. The heat capacities overlap with one another at Hⲏ1 T and they can be
fitted by the Schottky heat capacity at this magnetic fieldregion. The obtained parameters are g⫽2.15 and N⫽1⫻0.0061⫻N A when S⫽1 共dashed line兲. When S⫽1/2, theobtained parameter is N⫽2⫻0.0049⫻N A 共dotted line兲. The
dashed line is a much better fitting than the dotted line andthe result is consistent with that in Pb共Ni1⫺x Mgx ) 2 V2 O8(x⫽0.010).
The H-T phase diagram at the low magnetic field isshown in Fig. 10. The qualitative behavior is all the same in
Pb共Ni1⫺x Mgx ) 2 V2 O8 . The Néel phases disappear at an
anomalously low magnetic field.
B. Discussion

Here we will estimate the critical field H 0 in Eq. 共6兲 forthe disappearance of the Néel phase by means of themolecular-field theory as we did in Sec. III. The molecularfield constant A in Eq. 共4兲 is estimated to be A⫽89
⫾20 emu⫺1 Ni mol from the magnetic susceptibility measurement which is shown in Fig. 11. By means of Eq. 共6兲,
H 0 ⫽2.2⫾0.6 T is obtained in Pb共Ni1⫺x Mgx ) 2 V2 O8(x⫽0.010) and this magnetic field is consistent with thevalue of H where the impurity-induced AF phase disappears.
The same result is obtained in the sample of x⫽0.0050.
We can see that the molecular-field constant A is almost
independent of the impurity concentration in Fig. 11. Notethat A/2 is the y-axis intercept in Fig. 11. Therefore, thecritical field H 0 for the disappearance of the Néel phase only
depends on the number of impurity-induced spins. The number of spins is the same as that of impurity ions and we cansee the approximately proportional relation between the impurity concentration x and the critical field H 0 in Fig. 10.

V. SUMMARY

共i兲 Pb共Ni1⫺x Mgx ) 2 V2 O8 (x⫽0.020): we observed that asmall number of spins are induced by nonmagnetic ions andthey contribute to the impurity-induced AF phase. The disappearance of the AF phase at very low field, 3– 4 T, isobserved. This is because the number of impurity-induced
spins is small and the effective interaction is also small.
共ii兲 Pb共Ni1⫺x Mgx ) 2 V2 O8 (x⫽0.010 and 0.0050兲: the heat
capacity of the impurity-induced spins is explained very well
if it is assumed that one nonmagnetic ion induces one spinS⫽1. The existence of a ferromagnetic NNN inchain interaction is suggested. The magnetic field for the disappearanceof the AF phase is explained by means of molecular-field
theory.

ACKNOWLEDGMENTS

The authors thank I. Tsukada, Y. Uchiyama, and A. Zheludev for cooperation in the various aspects of this work.
This work was supported in part by a Grant-in-Aid for COE
Research ‘‘Phase Control of Spin-Charge-Photon Coupled
System’’ from the Ministry of Education, Culture, Sports,
Science, and Technology.

5*Electronic address: tmasuda@k.u-tokyo.ac.jp
F. D. M. Haldane, Phys. Rev. Lett. 50, 1153 共1983兲.
2
I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett.
59, 799 共1987兲.
3
J. Kennedy, J. Phys.: Condens. Matter 2, 5737 共1990兲.
4
S. Miyashita and S. Yamamoto, Phys. Rev. B 48, 913 共1993兲.
1

The disappearance of the ‘‘impurity-induced AF phase’’ atanomalously low magnetic field may be observed in doped
CuGeO3 . The appearance of the AF phase by impurity doping was reported in the two-leg ladder material SrCu2 O3
共Ref. 24兲 and dimer material TlCuCl3 共Ref. 25兲. If the AF
phase of these materials is of the same type as doped PbNi2
V2 O8 orCuGeO3 , the same phenomenon might be observed.
These are future problems.
The fact that one nonmagnetic impurity induces one S⫽1 spin means the existence of a ferromagnetic nextnearest-neighbor 共NNN兲 inchain interaction, which is described in Fig. 1共b兲. The origin of the NNN interaction is
ascribed to the crystal structureofPbNi2 V2 O8 . In this material the edge-shared NiO6 octahedra forms a fourfold screw
chain along the b axis.13 In this case the nearest-neighbor
共NN兲 and NNN interactions would be comparable and a relatively large NNN interaction is expected. The existence of
the NNN interaction (J NNN ) is, actually, proposed by Zheludev et al. to explain the spin dispersion in PbNi2 V2 O8 . 26
Their discussion is qualitatively consistent with our experimental result. Our fits to the data are good if S⫽1 is assumed at 0.40 KⱗTⱗ 5.0 K in the sample of x⫽0.010 andat 0.40 KⱗTⱗ2.0 K in the sample of x⫽0.0050. We cannot
estimate J NNN from the heat capacity measurements but thesuccess of the fits indicates that J NNN is larger than 5.0 K.

M. Hagiwara, K. Katsumata, I. Affleck, B. I. Halperin, and J. P.
Renard, Phys. Rev. Lett. 65, 3181 共1990兲.
6
S. H. Glarum, S. Geschwind, K. M. Lee, M. L. Kaplan, and J.
Michel, Phys. Rev. Lett. 67, 1614 共1991兲.
7
A. P. Ramirez, S-W. Cheong, and M. L. Kaplan, Phys. Rev. Lett.
72, 3108 共1994兲.

174416-6

PHYSICAL REVIEW B 66, 174416 共2002兲

IMPURITY-INDUCED ANTIFERROMAGNETIC PHASE IN . . .
8

K. Kojima, A. Keren, L. P. Le, G. M. Luke, B. Nachumi, W. D.
Wu, Y. J. Uemura, K. Kiyono, S. Miyasaka, H. Takagi, and S.
Uchida, Phys. Rev. Lett. 74, 3471 共1995兲.
9
M. Hase, I. Terasaki, and K. Uchinokura, Phys. Rev. Lett. 70,
3651 共1993兲.
10
M. Hase, I. Terasaki, Y. Sasago, K. Uchinokura, and H. Obara,
Phys. Rev. Lett. 71, 4059 共1993兲.
11
T. Masuda, A. Fujioka, Y. Uchiyama, I. Tsukada, and K. Uchinokura, Phys. Rev. Lett. 80, 4566 共1998兲.
12
K. Manabe, H. Ishimoto, N. Koide, Y. Sasago, and K. Uchinokura, Phys. Rev. B 58, R575 共1998兲.
13
Y. Uchiyama, Y. Sasago, I. Tsukada, K. Uchinokura, A. Zheludev,
T. Hayashi, N. Miura, and P. Böni, Phys. Rev. Lett. 83, 632
共1999兲.
14
K. Uchinokura, Y. Uchiyama, T. Masuda, Y. Sasago, I. Tsukada,A. Zheludev, T. Hayashi, N. Miura, and P. Böni, Physica B 284288, 1641 共2000兲.
15A. Zheludev, T. Masuda, I. Tsukada, Y. Uchiyama, K. Uchinokura, P. Böni, and S.-H. Lee, Phys. Rev. B 62, 8921 共2000兲.
16O. Golinelli and Th. Jolicoeur, J. Phys.: Condens. Matter 5, 7847
共1993兲.
17
We should note that these values are not directly related to theintrinsic Haldane gap but to the minimum in the dispersion
caused by the interchain interaction. This is the same assumption
in Ref. 13. Details are discussed in Ref. 15.
18
S. Yamamoto and S. Miyashita, Phys. Rev. B 50, 6277 共1994兲.
19
Y. Uchiyama 共unpublished兲.
20
A. Zheludev, S. E. Nagler, S. M. Shapiro, L. K. Chou, D. R.
Talham, and M. W. Meisel, Phys. Rev. B 53, 15 004 共1996兲; T.
Sakaguchi, K. Kakurai, T. Yokoo, and J. Akimitsu, J. Phys. Soc.
Jpn. 65, 3025 共1996兲.
21
W. J. M. de Jonge, J. P. A. M. Hijmans, F. Boersma, J. C.
Schouten, and K. Kopinga, Phys. Rev. B 17, 2922 共1978兲.
22
J. Villain and J. M. Loveluck, J. Phys. 共France兲 Lett. 38, L77
共1977兲.
23
D. Beckmann, J. Wosnitza, H. v. Löhneysen, and D. Visser, Phys.
Rev. Lett. 71, 2829 共1993兲.
24
M. Azuma, Y. Fujishiro, M. Takano, M. Nohara, and H. Takagi,
Phys. Rev. B 55, R8658 共1997兲.
25
A. Oosawa, T. Ono, and H. Tanaka, cond-mat/0202004 共unpublished兲.
26
A. Zheludev, T. Masuda, K. Uchinokura, and S. E. Nagler, Phys.
Rev. B 64, 134415 共2001兲.

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