Drastic Change of Magnetic Phase Diagram in Doped Quantum Antiferromagnet TlCu$_{1-x}$Mg$_x$Cl$_3$

0.2 MB·English

by  M. Fujisawa

Typeset with jpsj2.cls <ver.1.2> Letter
Drastic Change of Magnetic Phase Diagram in Doped Quantum Antiferromagnet
TlCu Mg Cl
1−x x 3
Masashi Fujisawa1∗, Toshio Ono1, Hideyasu Fujiwara1, Hidekazu Tanaka2, Vadim Sikolenko3,
Michael Meissner3, Peter Smeibidl3, Sebastian Gerischer3 and Hans A. Graf3
6
0 1Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551
0 2Research Center for Low Temperature Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 15-8551
2 3Hahn-Meitner-Institute, Glienicker Starasse 100, D-14109 Berlin, Germany

n
a
J TlCuCl3 is a coupled spin dimer system, which has a singlet ground state with an excita-
tion gap of ∆/gµB = 5.5 T. TlCu1−xMgxCl3 doped with nonmagnetic Mg2+ ions undergoes
8
impurity-inducedmagnetic ordering. Because triplet excitation with a finite gap still remains,
1
thisdopedsystemcanalsoundergomagnetic-field-inducedmagneticordering.Byspecificheat

measurements and neutronscattering experimentsunderamagnetic field, weinvestigated the
]
l phase diagram in TlCu1−xMgxCl3 with x∼0.01, and found that impurity- and field-induced
e
- ordered phases are the same. The gapped spin liquid state observed in pure TlCuCl3 is com-
r pletely wiped out bythe small amount of doping.
t
s
t. KEYWORDS: TlCuCl3, TlCu1−xMgxCl3, specific heat, neutron elastic scattering, magnetic-field-induced
a magnetic ordering, impurity-inducedmagnetic ordering, coupled spin dimer, spin gap
m
-
d
Recently, considerable attention has been paid to the TlCuCl . The easy axis lies in the (0,1,0) plane at an
n 3 ◦
quantum spin system with a gapped ground state. Such angleof13 fromthe[2,0,1]directiontothea-axis.Spin
o
c a spin gap system exhibits no magnetic ordering down flop transition was observed at Hsf ≈0.3 T, which is al-
[ to a zero temperature. Most gapped ground states arise most independent of x. Triplet excitation with a finite

fromthe dimerizationofspins thatarelocalizedinmag- gap, which can be interpreted as excitation from intact
2
v netic ions. Hence, when nonmagnetic ions are substi- dimers, was also observed.17 With decreasing tempera-
3 tuted for magnetic ions, unpaired spins are produced, ture, the gap increases below T in proportion to the
N
6 and staggered moments are induced around these un- order parameter. Mikeska et al.18 argued that the small
3
paired spins. Unpaired spins can interact through ef- staggered magnetic ordering induced in intact dimers
1
fective exchange interactions that are mediated by spin gives rise to the enhancement in triplet gap.
0
6 dimers in between.1–3 Three-dimensional (3D) magnetic Since the triplet gap still remains in TlCu1−xMgxCl3,
0 orderingcanoccurduetoeffectiveexchangeinteractions. we can expect the occurrence of field-induced magnetic
/ Such impurity-induced magnetic ordering is observed in ordering.Althoughtherearemanytheoreticalandexper-
t
a many spin gap systems.4–7 imentalstudiesofimpurity-inducedmagneticorderingin
m
This study is concerned with impurity- and field- doped spin gapsystems, the study of field-induced mag-
- induced magnetic orderings in the doped spin gap sys- netic orderingin doped spin gapsystems is limited. The
d
n tem TlCu1−xMgxCl3. The parent compound TlCuCl3 is relationshipbetweenimpurity-andfield-inducedordered
o a coupledspindimer system,whichhas a singletground phases has not been sufficiently understood. To investi-
c state with an excitation gap of ∆/k = 7.5 K.8–10 The gate a magnetic phase diagramfor temperature vs mag-
B
:
v small gapcomparedwith the intradimer exchange inter- netic field in TlCu1−xMgxCl3, we carried out a specific
i action J/k = 65.9 K is ascribed to strong interdimer heat measurement and a neutron scattering experiment
X B
exchange interactions.11,12 In a magnetic field, the gap in magnetic fields.
r
a is suppressed and closes completely at the critical field Before preparing the doped TlCu1−xMgxCl3 crystals,
(g/2)H =∆/gµ =5.5T.ForH >H ,TlCuCl under- we prepared single crystals of TlCuCl and TlMgCl .
c B c 3 3 3
goes magnetic ordering due to interdimer interactions.9 Mixing TlCuCl and TlMgCl in a ratio of (1 − x) :
3 3
Field-inducedmagneticorderinginTlCuCl3hasbeenex- x, we prepared TlCu1−xMgxCl3 by the vertical Bridg-
tensivelystudiedbyvarioustechniquesincludingneutron man method. We obtained single crystals of ∼ 0.5 cm3.
scattering.10,13 The resultsobtainedcanbe describedas The magnesium concentration x was analyzed by in-
aresultoftheBose-Einsteincondensationofspintriplets ductively coupledplasma−opticalemissionspectroscopy
(magnons).14,15 (ICP−OES) after the measurements. In the present
From a magnetization measurement and a neutron study, we use samples for with x = 0.0088 and 0.015.
scatteringexperiment,itwasfoundthatTlCu1−xMgxCl3 The TlCu1−xMgxCl3 crystal is cleaved easily parallel to
with x ≤ 0.03 exhibits impurity-induced magnetic or- the planes (0,1,0) and (1,0,¯2).
dering.16,17 The spin structure of the impurity-induced Specific heat measurements were performed for the
phase is the same as that of the field-induced mag- sample with x = 0.0088. Specific heat was measured
netic ordered phase for H k b in the parent compound down to 0.45 K at magnetic fields up to 9 T for H k b,
H ⊥ (1,0,¯2) and H k [2,0,1], using a Physical Prop-
∗E-mailaddress:[email protected]
2 J.Phys.Soc.Jpn. Letter AuthorName
erty Measurement System (Quantum Design PPMS) by T = 1.7 K. For H ≤ 3 T, T is almost independent
N N
therelaxationmethod.Thesamesamplewasusedinthe of temperature. However, for H > 3 T, T increases
N
measurements for H ⊥(1,0,¯2) and H k[2,0,1],and an- rapidly. A similar field dependence of T was also ob-
N
other sample that was taken from the same batch was served for H ⊥(1,0,¯2) and H k[2,0,1]. Figure 2 shows
used in the measurement for H k b. As will be shown a summary of the data of T obtained at various mag-
N
later, no difference was observed between the ordering netic fields for x=0.088 and those for TlCuCl . In Fig.
3
temperatures at a zero field obtained for both measure- 2,the magneticfieldis normalizedbytheg-factor.Here,
ments. This implies a good homogeneity in the same we use g = 2.06,2.23 and 2.06 for H k b, H ⊥ (1,0,¯2)
batch. and H k [2,0,1], respectively, which were determined
Neutron scattering experiments were carried out us- for TlCuCl by ESR.9 We see that phase boundaries for
3
ing the E1 spectrometer of the BER II Research Reac- these different field directions almost coincide. This fact
tor of the Hahn-Meitner Institute with the vertical field indicates that the phase boundary is independent of the
cryomagnet VM1. Incident neutron energy was fixed at externalfielddirection,whennormalizedbytheg-factor,
E =13.9 meV, and the horizontal collimation sequence and that the anisotropy of the exchange interaction is
i
′ ′ ′ ′
was chosen to be 40 −80 −40 −40. A single crystal negligible except in the low-field region (H < 0.5 T) in-
with x = 0.015 was used. The sample was mounted in cluding the spin flop field H ≈0.3 T.
sf
the cryostat with its (0,1,0) cleavage plane parallel to
∗ ∗
the scattering plane, so that reflections in the a − c
plane wereinvestigated.The sample wascooledto0.4K
12
using a 3He refrigerator. An external magnetic field of
H ⊥ (1,0,-2)
up to 12 T was applied along the b-axis.
H || [2,0,1]
Specific heatforTlCu1−xMgxCl3 withx=0.0088dis- 10 H || b
playsasmallcusplikeanomalybelow6Kindicatingmag- H || b, x = 0
netic phase transition at zero and finite magnetic fields.
To determine the transition temperature TN more accu- 8 AF
rately,weplottedthedifferenceC betweenthespecific
dif T)
heatC(H)forTlCu1−xMgxCl3inamagneticfieldH and H ( 6
C0 for TlCuCl3 at a zero field. Figure 1 shows the tem- 2)
perature dependence of Cdif for H ⊥(1,0,¯2) plane. The (g/
cusplike anomaly caused by phase transition is clearly Para
4
observed. Arrows in Fig. 1 denote the transition tem-
peratures. The transition temperature at a zero field is
2
TlCu MgCl
1-x x 3
x = 0.0088
0.6
0
TlCu MgCl
1-x x 3 0 1 2 3 4 5 6
x = 0.0088
0.5 H ⊥ (1,0,-2) T (K )

4) Fig. 2. Phase diagram for magnetic field vs temperature in
et 0.0 0.4 THlC⊥u(11−,x0M,¯2g)xaCnld3.HTkhe[2,m0,a1g]n.etic field is applied for H k b,
s
off
K) ( 0.3
ol- With increasing external field, the ordering temper-
m
C (J/dif 0.2 afiteuldreoTfN(g/in2c)rHeas∼es3raTpiidslycoanbsiodveera(bgl/y2)sHma≃ller3thTa.nTthhies
H = 0 T 5 T gap field (g/2)Hc ∼ 8 T corresponding to the triplet

1 T 6 T gap,whichisestimatedfromthetripletgapsinTlCuCl
0.1 2 T 7 T 3
3 T 8 T and TlCu1−xMgxCl3 with x ≈ 0.03.17 Since the triplet
4 T 9 T gapforintactdimersis enhancedwithincreasingdoping
0.0 rate x, the rapid increase in TN for H > 3 T does not
0 2 4 6 8 arisefromtheclosingofthetripletgapforintactdimers.
T (K) Theeffective exchangeinteractionJeff betweenunpaired
spins increases exponentially with decreasingtriplet gap
for intact dimers,1,2 which leads to an enhancement in
Fig. 1. TemperaturedependenceofCdif (=C(H)−C0)forH ⊥
(1,0,¯2),whereC(H)isthespecificheatforTlCu1−xMgxCl3 in orderingtemperature.Thus,the rapidincreaseinTN for
a magnetic field H and C0 is the specific heat for TlCuCl3 at H > 3 T should be attributed to the enhancement in
H =0.Arrowsdenote N´eeltemperatures. J due to the shrinkage of the triplet gap induced by
eff
the applied field.
A notable feature of the magnetic phase diagram is
J.Phys.Soc.Jpn. Letter AuthorName 3
thatthereisnoboundaryseparatingimpurity-andfield-
20 c)2.5
induced antiferromagnetic phases, i.e., these two phases 12 T 0se H = 0 T
alorwe c(ogn/t2ig)Huocus=.T5h.e4gTappinedpgurroeuTndlCsutaCtle3tihsatcoemxipstlestbeley- 18 1 08 TT unts/6021..05 T
16 o N
wiped out by the small amount of nonmagnetic impu- 6 T 30c1.0
iriPnsitbdi(deuNsicff.ie1eTd−rhexoneMrtdmgefrxare)god2nmVept2hiOtcahs8ape,t1hs9aaosriefendstewhiapehgairrcdaahomtpeidemfodbrpyuHTralaiCtlgydua-a1pn−apexneMddsygdfisxitseCeoldmlr3-- unts/600sec) 1142 0240 TTTT (4 K) Intensity (100..500.0 1.0 T2 (.K0) 3.0 4.0
dered phase. 3co 10
If the impurity- and field-induced ordered phases are y (10 8 Tx l=C u01.0-x1M5gxCl3
identical,thenthe orderparametersshouldbe the same. nsit Q = (1,0,-3)
Therefore, we can expect that the sublattice magneti- nte 6 T = 0.4 K
zation corresponding to the order parameter exhibits I
4
unusual field and temperature dependences. Then, we
performed a neutron elastic scattering experiment on
2
TlCu1−xMgxCl3 with x = 0.015, for which impurity-
induced magnetic ordering occurs at TN = 2.8 K as 0
shown in the inset of Fig. 3. Magnetic reflections with 58.5 59.0 59.5 60.0 60.5
a resolution-limited width were observedat Q=(h,0,l) 2θ (deg)
foranintegerhandanoddl.Thesereciprocalpointsare
the same as those for field- and pressure-induced trans-
Fig. 3. Intensityofθ−2θscansatT =0.4KforQ=(1,0,¯3)re-
verse N´eel orderings in TlCuCl .10,20 Figure 3 shows
3 flection in TlCu1−xMgxCl3 under various magnetic fields. The
θ−2θscansforthe(1,0,¯3)reflectionmeasuredatT =0.4 scan at the paramagnetic phase (T = 4.0 K) is also plotted.
K (< TN) under the various magnetic fields. We also Inset shows the temperature dependence of the magnetic peak
plotted in Fig. 3 the same scan for H = 0 at T = 4.0 intensityforQ=(1,0,¯3),wheretemperatureindependentback-
K (> T ). Since the parent compound TlCuCl be- groundissubtracted.
N 3
longs to the space group P2 /c, nuclear peaks are ex-
1
pected only at Q = (h,0,l) with an even l. However, as
sohdodwln. SininFceign.o3,stwrueacktunraulclpehaarspeetarkasnsairteioonbwsearsveodbsfeorrvaend 0sec) 9 TlCu1-xMgxCl3 9 Inten
ihsneeravTteldmCuaea1t−sQuxrMe=mg(xehCn,tl03s,,ltw)herwoiiunthgfeharnmthoaadgtdntelhtieazranetuidoculneeaartnopdtehasepkeslocoicfibac-l 30counts/80 6 xT == 00Q..04 1 =K5 (1,0,-3) 6 sity for Q =
disturbance of the lattice caused by Mg2+ doping. 3) (1 (0,0,1) (0,0
sHligA≥hstlsy6howTwi,nthtinhieFnciignre.tae3ns,ismnitgaygenixnetcterircenaBaslreasfigergladipnitduelpnys.ittoWyed4eicTnrv.eeaFsstoeirs- Q = (1,0,- 3 3 ,1) (10co3
gated the field dependence of magnetic Bragg intensity or un
cipnlleoadtrsetBfaoirrla.QgFgig=iunrt(ee1n,4s0i,st¯3hie)oswaansndtdh(e0b,ai0nc,tke1gn)rsomiutyangdvnseatrmiecasgpunebeattkrisca.cfitNeeuldd-. Intensity f 0 0 ts/480sec)
0 2 4 6 8 10
With increasing external field, the intensities of both
H (T)
magnetic peaks have a minimum at H ∼ 3.5 T and in-
crease rapidly. However, no anomaly indicative of field-
inducedphasetransitionisobserved.Thisresultconfirms Fig. 4. Magnetic field dependence of magnetic Bragg peak
thatthereisnoboundaryseparatingimpurity-andfield- intensities for Q = (1,0,¯3) and (0,0,1) reflections in
induced orderedphases.Since Braggpeak intensities for TlCu1−xMgxCl3.Dottedandbrokenlinesarevisualguides.
both Q = (1,0,¯3) and (0,0,1) exhibit similar field de-
pendences, these field dependences are attributed not to
are the intradimer and interdimer interactions, respec-
the change in spin direction, but to the change in the
tively, and Z is the coordination number. Their results
magnitudeoftheorderedmoment.Thepresentresultin-
are summarized as follows: doping causes the antifer-
dicates that impurity- and field-induced ordered phases
′
romagnetic order at a zero field. For smaller (ZJ /J),
in TlCu1−xMgxCl3 arethe same,and that the order pa-
there are three critical fields H , H and H . For
rameter has a minimum at H ≃3.5 T. c1 c2 s
H < H , the unpaired spins form an antiferromagnetic
Recently,Mikeskaetal.havetheoreticallyinvestigated c1
orderthroughtheeffectiveexchangeinteractionJ ,and
the interplay of the doping and the external field in the eff
a small transverse staggered order also occurs in intact
coupled S = 1/2 Heisenberg spin dimer system on the
dimers. Unpaired spins are fully polarized at H = H ,
basis of the mean-field approximation.18 For the ground c1
andthesmalltransversestaggeredorderinintactdimers
state,theypresentedtheschematicphasediagraminthe
(ZJ′/J,H/J) plane as shown in Fig. 5, where J and J′ vanishes.ThecriticalfieldHc1 isproportionaltotheim-
4 J.Phys.Soc.Jpn. Letter AuthorName
purity concentration x. Above H , the ground state is x∼0.01inmagneticfieldstoinvestigatetherelationbe-
c1
gapped and disordered. At the second critical field H , tween impurity- and field-induced ordered phases. Well-
c2
thetripletgapforintactdimersclosesandthetransverse defined phase transitions were observed. It was found
staggered order occurs again in intact dimers. With a that the impurity- and field-induced ordered phases are
further increase in magnetic field, the saturation takes contiguous, i.e., these two phases are the same. The
′
placeatH =H .Ontheotherhand,forlarger(ZJ /J), gapped spin liquid state observed in pure TlCuCl is
s 3
the field range of the disordered state shrinks. There is completely wiped out by the small amount of doping.
′ ′
a critical value (ZJ /J) , above which impurity- and This is because the interdimer exchange interaction J
c
field-induced ordered states merge. The point given by is so strong in TlCu1−xMgxCl3 that the triplet gap in
′
(ZJ /J)=1isthequantumcriticalpointthatseparates intact dimers closes before unpaired spins near impuri-
the gapped disordered state and the antiferromagnetic ties are fully polarized by the external field. From the
ordered state in the pure system. neutron scattering result, we found that the magnitude
ForTlCuCl ,thecriticalfieldcorrespondingtothegap of the ordered moment has a minimum at H ≃3.5 T. It
3
and saturationfield are (g/2)H = 5.5 T and (g/2)H ∼ is considered that this unique behavior of the order pa-
c s
90T,respectively.Hence,theexchangeparametershould rameter results from the competition between magnetic
be located at the point indicated by the arrowin Fig. 5. ordering and spin gap, the latter of which acts to sepa-
′
(ZJ /J) corresponding to TlCuCl is close to unity and rate impurity- and field-induced phases.
3
′
shouldbelargerthan(ZJ /J) forx≥0.0088.Inthispa- The authors would like to thank A. Oosawa and H.
c
rameter region, the field-induced disordered state is ab- -J. Mikeska for stimulating discussions. They are also
sent.The presentexperimentalresultthat the impurity- grateful to H. Imamura for his technical support. This
andfield-inducedorderedstatesareconnectedwithouta work was supported by a Grant-in-Aid for Scientific Re-
boundary in TlCu1−xMgxCl3 is in accordance with the search and the 21st Century COE Program at Tokyo
theory by Mikeska et al.18 In the present system, the Tech “Nanometer-Scale Quantum Physics” both from
interdimer interaction is fairly large so that the triplet the Ministry of Education, Culture, Sports, Science and
gap for intact dimers closes in a magnetic field before Technology of Japan.
unpaired spins are fully polarized. For this reason, the
impurity- and field-induced ordered states merge.
Accordingtothemean-fieldtheorybyMikeskaet al,18 1) M.SigristandA.Furusaki:J.Phys.Soc.Jpn.65(1996)12385.
(ZJ′/J) increases with decreasing impurity concentra- 2) M.ImadaandY.Iino:J.Phys.Soc.Jpn.66(1997) 568.
c
3) C.Yasuda,S.Todo,M.MatsumotoandH.Takayama,Phys.
tion x, and approaches unity for x → 0. However, it is
Rev.B64(2001) 092405, andreferencestherein.
also considered that for small x, there is a finite crit-
4) M.Hase,I.Terasaki,Y.Sasago,K.UchinokuraandH.Obara:
ical value (ZJ′/J)c being smaller than unity, because Phys.Rev.Lett.71(1993)4059.
field-inducedphenomenaatT =0shouldbe determined 5) T.Masuda,A.Fujioka,Y.Uchiyama,I.TsukadaandK.Uchi-
by the local interactions between unpaired spin and in- nokura:Phys.Rev.Lett. 80(1998)4566.
6) M.Azuma,Y.Fujishiro,M.Takano,M.NoharaandH.Takagi:
duced moments around the unpaired spin that are inde-
Phys.Rev.B55(1997)R8658.
pendent ofx for x→0.Thus,it is interesting to investi-
7) Y.Uchiyama,Y.Sasago,I.Tsukada,K.Uchinokura,A.Zhe-
gatewhether field-induceddisorderedstate is realizedin ludev,T.Hayashi,N.MiuraandP.Bo¨ni:Phys.Rev.Lett.83
TlCu1−xMgxCl3 with further decreasing x. (1999) 632.
8) K.Takatsu,W.ShiramuraandH.Tanaka:J.Phys.Soc.Jpn.
66(1997) 1611.
9) A.Oosawa,M.IshiiandH.Tanaka:J.Phys.:Condens.Matter
H/J 11(1999) 265.
Fully Saturated 10) H. Tanaka, A. Oosawa, T. Kato, H. Uekusa, Y. Ohashi, K.
KakuraiandA.Hoser:J.Phys.Soc.Jpn.70(2001) 939.
11) N.Cavadini,G.Heigold,W.Henggeler,A.Furrer,H.-U.Gu¨del,
K.Kra¨merandH.Mutka:Phys.Rev.B63(2001)172414.
1 Transverse N'eel Order 12) A. Oosawa, T.Kato, H.Tanaka, K.Kakurai, M.Mu¨ller and
H.-J.Mikeska:Phys.Rev.B65(2002) 5868.
13) Ch.Ru¨egg,N.Cavadini,A.Furrer,H.-U.Gu¨del,K.Kra¨mer,
TlCuCl H.Mutka,A.Wildes,K.HabichtandP.Vorderwisch:Nature
3
Disordered (London) 423(2003)62.
14) T.Nikuni,M.Oshikawa,A.OosawaandH.Tanaka:Phys.Rev.
Lett. 84(2000)5868.
(ZJ'/J) 1 ZJ'/J 15) M.Matsumoto,B.Normand,T.M.RiceandM.Sigrist:Phys.
c Rev.B69(2004) 054423.
16) A. Oosawa, T. Ono and H. Tanaka: Phys. Rev. B 66 (2002)
Fig. 5. Phase diagram of ground state proposed by Mikeska et 020405(R).
al.18 Solid and dashed lines are boundaries for the pure and 17) A. Oosawa, M. Fujisawa, K. Kakurai and H. Tanaka: Phys.
doped systems. Arrow denotes the (ZJ′/J) corresponding to Rev.B67(2003) 184424.
TlCuCl3. 18) H. -J. Mikeska, A. Ghosh, and A. K. Kolezhuk: Phys. Rev.
Lett. 93(2004)217204.
19) T. Masuda, K.Uchinokura, T.Hayashi and N.Miura:Phys.
In conclusion, we have performed specific heat mea- Rev.B66(2002) 174416.
20) A. Oosawa, M. Fujisawa, T. Osakabe, K. Kakurai and H.
surements and neutron elastic scattering experiments
Tanaka: J.Phys.Soc.Jpn.72(2003) 1026.
on the doped spin gap system TlCu1−xMgxCl3 with