Field-Dependent Differential Susceptibility Studies on Tetrathiafulvalene-AuS4C4(CF3)

13 Pages·2017·1.29 MB·English

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Physics Faculty Publications Physics
3-1-1982
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PPeeiieerrllss PPhhaassee DDiiaaggrraamm
J. A. Northby
University of Rhode Island, [email protected]
H. A. Groenendijk
L. J. de Jongh
Jill C. Bonner
University of Rhode Island
I. S. Jacobs
See next page for additional authors
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Northby, J. A., Groenendijk, H. A., de Jongh, L. J., Bonner, J. C., Jacobs, I. S., & Interrante, L. V. (1982).
Field-dependent differential susceptibility studies on tetrathiafulvalene-AuS4C4(CF3)4: Universal aspects
of the spin-Peierls phase diagram. Physical Review B, 25(5), 3215-3225. doi: 10.1103/PhysRevB.25.3215
Available at: http://dx.doi.org/10.1103/PhysRevB.25.3215
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AAuutthhoorrss
J. A. Northby, H. A. Groenendijk, L. J. de Jongh, Jill C. Bonner, I. S. Jacobs, and L. V. Interrante
This article is available at DigitalCommons@URI: https://digitalcommons.uri.edu/phys_facpubs/211
VOLUME 25,NUMBER 5 1MARCH 1982
Field-dependent differential susceptibility studies on tetrathiafulvalene-AuS4C4(CF3)&'.
Universal aspects of the spin-Peierls phase diagram
'
J.A. Northby, H. A. Groenendijk, and L.J.de Jongh
Karnerlingh Onnes Laboratorium, University ofLeiden, Leiden, The Netherlands
J.C, Bonner
Physics Department, University ofRhode Island, Kingston, Rhode Island, 02881
I.S.Jacobs and L, V.Interrante
General Electric Company, Corporate Research and Development, Schenectady, New York 12301
(Received 26October 1981)
An applied magnetic field is known to produce novel effects in the phase behavior ofmagne-
toelastic spin-Peierls systems. Hence we report measurements ofthe differential susceptibility
(X)and magnetization {M)in fields up to 40kOe (4T) on the spin-Peierls compound
tetrathiafulvalene (TTF)-AuS4C~(CF3)~ in the temperature region {11. K«T«4.2 K). This
range offield and temperature encompasses an interesting phase region, including the zero-field
spin-Peierls transition temperature T,(0)=2.03K. The measurements ofthe differential (ac)
susceptibility provide a more sensitive probe ofthe transition behavior than magnetization mea-
surements. The first definitive evidence for significant deviations from mean-field critical
behavior appear in these measurements, and the appropriate criteria for determining the precise
location ofthe transitions are thus provided by the thermodynamic theory of Xtransitions. Us-
ing the new criteria, qualitative and even quantitative agreement is obtained with current
theories ofthe field dependence ofspin-Peierls transitions. A novel contour plot ofX«in the
0-Tplane is shown to be useful for the delineation ofthe global phase-transition behavior. An
investigation ofthe role ofrelaxation effects in X„relative to the nature ofthe phase boun-
daries is conducted. A major feature is the observation ofa striking degree of"universality" in
the phase behavior ofthree spin-Peierls systems, TTF-AuSqC4(CF3) 4, TTF-CuS&C4(CF3)4, and
methylethylmorpholinium di-tetracyanoquinodimethane fMEM-(TC&Q)2l. These universal
features are preserved through considerable differences in lattice structure and avariation in
T,(0)ofafactor of10.
I. INTRODUCTION singlet ground state and (a band of) triplet excited
'
states. The gap is dependent on the degree ofalter-
The spin-Peierls (SP) transition is a topic ofhigh nation and vanishes in the uniform chain limit. As
current interest which'~brings together many subfields observed experimentally, in zero field, the transition
ofsolid-state physics. This transition marks the is second order, and the degree ofalternation in-
onset, as the temperature is lowered, ofa progressive creases as the temperature is lowered, reaching a
spin-lattice dimerization in a system ofquasi-one- maximum at T=0.
dimensional (quasi-1D) quantum antiferromagnetic The effect ofa magnetic field on an SP system is
(AFM) chains embedded in the 3D phonon field of quite dramatic and has"been the subject ofa number
the lattice. Theoretically the transition is observable oftheoretical papers. In simple terms, the mag-
in its simplest form when the magnetic chains are netic field lowers the energy ofthe magnetic excited
nonclassical; e.g., Heisenberg or XYin type. In prac- levels below the S=0zero-field ground state, des-
tice it has been observed experimentally only in good troying the energy gap and altering the character of
Heisenberg, spin- —,, systems characterized by gfac- the phase behavior. On the experimental side, neu-
tors close to the free electron value. By analogy with tron studies up to about '70 kOe have sho~n that
the well-known Peierls instability in a 1D metal, it T,(H") is depressed by application ofa magnetic
may be shown that a uniform AFM quantum chain is field. Magnetization studies have been performed
unstable with respect to an underlying lattice distor- in significantly higher magnetic fields (up to about
tion which dimerizes it into an alternating chain 200 kOe) on tetrathiafulvalene (TTF)-CuS4C4(CF3)
= K)" g
AFM. A quantum alternating chain AFM is charac- (T, 11 and on methylethylmorpholinium di-
terized by an energy gap between the nondegenerate tetracyanoquinodimethane [MEM-(TCNQ) 2]
3215 1982 The American Physical Society
"
=
(T, 18K). The data indicate the existence ofin- sweep (at T=1.250 K) an additional experiment at
teresting new phase boundaries in the high-field re- 0.94 kHz was performed which showed no detectable
gion, the nature ofwhich is not yet fully understood. differences from the highcr-frequency data. For
This is in addition to the second-order phase boun- measurements ofthe static magnetization (M) the
dary separating dimerized phase from uniform nonor- same coil system may be used, in which case the pri-
dered phase at lower fields. mary coil is disconnected and the induction voltages
In this paper we present and discuss both magneti- in the secondary arising from sample movement are
zation and also extensive differential susceptibility integrated electronically to yield the magnetization.
data on (deuterated) TTF-AuS4ti'.4(CFI)4 (T,=2.03 In Fig. 1 we show representative Xand Mdata as a
K). As a consequence ofthe much lower value of T, function oftemperature taken at different constant
in this Sp material, 2correspondingly lower applied fields. This figure clearly illustrates the power ofthe
fields are needed to bring about the field-dependent differential Xmeasurements. Whereas in the case of
transitions from the dimerized phase, It is therefore the high-field M(T) curves significant features are
easier to carry out a study ofthe differential suscepti- not apparent, the corresponding X(T) plots display
bility (X)over a large range ofrelative field. Since pronounced Illaxlllla (R1101118llcs)llldlcatiflg t11cpres-
X(H) measures the derivative with respect to the ence oftransitions. Note that the amplitudes of
flcld oftllc M(H) 1118gllctlzatloll curve, I't Is 8 111uc11 thcsc maxima 81'cstrongly flcld dcpcndcnt 8Qd van-
0
more sensitive probe for studying the nature ofthe ish as tends to8zero. As will be discussed in some
field-dependent transitions. As will be discussed in detail below, the =0 transition is better defined as
detail below, the differential Xdata give interesting a maximum in the temperature derivative of Xthan
new information on the nature ofthe phase transi- by a "kink" of "knee" in the Xvs Tplot. In mean-
tions in SP systems, and, ln con)unction with 8 thcl'- ficld theory, the second-order SP transition both in
modynamic theory ofsecond-order (A.-type) transi- zero and 1Q Qonzcl'o field ls given by a kncc cI'i-
tions, pl'ovidc prcclsc critcl'18 fol' thc location ofthc tcrion, as calculated theoretically by Bulacvski et al.7
magnetic phase boundaries in these materials. Novel and Tannous and Caille.' Our differential Xmea-
relaxation effects are observed which throw new light surements definitively demonstrate the breakdown of
on the character ofSp phases. Last, but not least, a mean-field picture very close to the transition.
the Xdata are instructive in an analysis ofphase The magnetization and susceptibility data measured
behavior which reveals some "universa" character as a function offield at different constant tempera-
to t11cH Tp118sc d-lagrams ofTTF-AuS4C4(CFI)g, tures arc given in Fig. 2. In this type ofplot pro-
TTF-Cus,c,(CF,),and MEM-(TCNg), . nounced maxima in the Xisothcrms are again ob-
served, and their amplitudes are in this case scen to
II. EXPERIMENTAL ASPECTS be strongly temperature dependent. In the magneti-
zation curves the transitions out ofthe dimcrizcd
Thc experiments werc performed on 8powdcrcd phase are marked by maxima in the slopes ofthe
sample of0.5 g ofdeuterated TTF-AuSqC4(CFl)q M(H) curves. In fact, the X(H) curves are the
prepared at General Electric R and 0,Schenectady. derivatives ofthe M(H) curves (apart from a reser-
The differential susceptibility was measured at Lciden vation to be discussed later). We remark, perhaps
by means ofa mutual inductance technique. The coil superfluously, that such a relationship is not the case
system consists of8primary and two secondary coils. in Fig. 1,as is apparent from the discussion in Sec.IV.
The latter are identical but oppositely wound and are At this point wc should point out that thc low-field
placed one above the other. Moving the sample from susceptibility measurements were affected by minor
thc center ofone ofthe secondary coils to thc center impurity effects, thought to be offerromagnetic ori-
ofthe other produces a change ofthe output voltage gin since the contribution is found to saturate in rela-
directly proportional to X. A steady field up to 40 tively low fields (=3kOe) and is independent of
0
kOe (4T) parallel to the ac field is provided by a su- temperature. This can be seen in Fig. 2 by the =0
perconducting solenoid. Temperatures werc mea- intercepts ofthe X(H) curves. A correction for this
sured by a calibrated carbon resistance thermometer. spurious signal (dotted cur~es in Fig. 2) was applied,
This apparatus, in principle, enables simultaneous and thc same correction was, in fact, applied to the
0
measurements to be made of the in-phase (X') and =0data shown in Fig. 1. %cbelieve that the im-
out-of-phase (X ) components ofthe complex sus- purity was not present in the sample itself, but that it
ceptibility. However, due to the low density ofspins arose from the sample holder (resulting, C.g., from
in the sample, the magnetic signals werc very weak. machining the holder or from impurity oxygen in the
Hence only X' could be studied (denoted by Xin He gas condensing on the holder). It was considered
%11Stfollows) S111ccflic X slg1181swerc too sII1811. unnecessary to correct the data for diamagnetism.
The signal-to-noise ratio also inhibited studies ofthe The estimated diamagnetic contribution is indicated
frequency dependence of X. All experiments report- in Fig. 1.
ed below were performed at 1.88 kHz. For one field The values for the critical fields and temperatures
25 FIELD-DEPENDENT DIFFERENTIAL SUSCEPTIBILITY. .. 3217
t I I I I I I I I I I I I I I I I I I I I I
x IO XIO
H(kOej 5.0
4.0
QP
CEO 6
E
CD
3.0
I—
—
2.0
CL
UJ (a)
CA
CA I I I I I I
IO 15 20 25 30 35 40 45
I.O MAGNET IC FIELD (k0ej
40
(EST. DIAMAGNETISM j
OI I I l I I I I I I I I I l I I I I I l I
I.O 1.5 2.0 2.5 3.0
TEMPERATURE (K)
I I I I I I l I I I I l I I 25
H (kOej
25— —
~ 28.16 20
~ 25.60
20— 23.04
l5
15
IO
IO—
IV
5
(b) 0 I I I I I I I
CD 0 5 IO I5 20 25 30 35 40 45
0I.O l i l i II.5 l l l l 2I.0l I I I 2I.5I I l I 3.I0 MAGNETIC FIELD (kOe)
TEMPERATURE (K) FIG.2.. (a) Differential susceptibility curves at constant
temperatures as a function offield. Those curves belonging
FIG. 1. (a) Differential susceptibility curves at various to the special low-temperature region are shown as dashed
constant fields as a function oftemperature for TTF- lines. At the lowest field, the dotted lines indicate a correc-
AuS4C4(CF3)4. The curves for the special high-field region tion for an impurity effect. The arrow is discussed in Sec.
are sho~n as dashed lines. (b) Magnetization (static) curves III. (b) Magnetization (static) curves at constant tempera-
as a function oftemperature at several fixed fields for TTF- tures as a function offield. The arrows indicate the location
AuS4C4(CF3)». The arrows indicate the location ofXH(T) ofX~(H) maxima from (a).
maxima from Fig. 1(a). The dotted curve shows the loca-
tion ofthe singularity using a mean-field knee criterion.
DU line in what follows, since it separates the (or-
dered) dimerized from the (nonordered) uniform
(H„T,) obtained from the plot in Figs. l and 2 have phase regions. The Bray calculation6 for the DU lines
been collected in Fig. 3, whe"re they are shown in is equivalent to that ofBulaev"skii et al.7 Hence both
cBoumlapeavrsiksoiin etwaitth.'tahnedthCeroorsest.ical AprlledtihcetioornesticaolfBprreadyi,c6- fthoeror(iHes,,',Tev,'a)l,uantaemdelyc,arepfuttlHly,,'"Iktgtiv=e0t.h7eSTsa,("m0e) avnadlues
tions give a second-order transition line extending T,"=0.54T,(0). Above H, and below T, (high-
from T,(0) to a special point (multicritical point) field, low-temperature region) Bulaevskii et al.
denoted (H,',T,'). We shall call this boundary the predict an intermediate (new) phase separating the
J.A.NORTHSY etaI.
I gl l ( I I I the experiment is T,(H =0), taken to be 2.03 K (see
BBK &. below). Secondly, the experiment also shows a bifur-
cation ofthe DU line, emanating from a mu'l=ticritical
INTERMEDIATE point located at H,'=21.4 +0.2 koe and T, (l.4
+0'=.003.) K or at p,sH,'/ks=0. 71T,(0) and
T, 69T,(0). (In later sections, we justify the pre-
cision ofthe determination ofthese parameters. )
"
The experimental T, lies midway between the two
theoretical predictions, as also does the experimental
DIMERlZED ',
H,
The IUline between intermediate and uniform re-
gions needs special discussion. The experimental
ISOTHERMS points shown are derived on the basis ofthe
+ lSOFIELDS TTF- H =23.04, 25.60 and 28.16kOC Xcurves in Fig. 1.
« Evidence for this phase line is not very apparent in
0.I5 i t l ) f.I0 l t l.l5 l i ~ l 2.I0„ tinhge apnlodtswoillfFbieg.di2s.cuTssheed reinasaonssubfsoerqutehnist arseecitniotenrest-
TEMPERATURE IK)
(III). We do note that the experimental data points
FIG.3. Magnetic phase diagram for TTF-AuS~C4(CF3)&, lie quite close to the Cross prediction, and the shape
constructed from susceptibility maxima ofFigs. 1and 2, (curvature) ofthe line, to the extent that it is experi-
Theoretical curves ofCross (C),Bray (B),and Bulaevskii mentally defined, is consistent with the shape ofthe
etal. (BBK)are shown along with their respective multicriti-
Cross curve.
cal points (starred). =1.
%Cconclude, therefore, that below T 4 K and
above H =21.4 kOe two distinct phase boundaries
(IUand Dl) are present in the experimental (H„T,)
phase diagram which encompass a new intermediate
dimerized and uniform phases, The calculated boun- phase such that magnetization and/or susceptibility
dary between intermediate and uniform phases (IU are generally lower than in the immediately adjacent
line) is shown in Fig. 3 and is second order. Bu- uniform chain or dimerized regions. The magnetic
laevskii eI:aI.3 predict the boundary between dimer- measurements, which have been carried out down to
ized and intermediate phases (DIline) to be first or- 1.1 K [0.54T,(0)],do not show explicit evidence of
der, but are not able to present a precise calculation, first-order character in the DIphase line, but this
This first-order boundary is therefore shown only possibility is not ruled out, as will be discussed below.
schematically in Fig. 3. The Cross theoretical predic-
tions (also shown in Fig. 3) show strong tluaiitative
similarities to those ofBray-Bulaevskii, The location III. SUSCEPTISII.ITY CONTOUR PLOT
of the multicritical point is slightly different, occur-
ring at psH,"/ks =0.69T,(0) and T,"=0.77T,(0). The extensive nature ofthe experimental Xvs T
The DU lines for both theories are very close, but the and Xvs Hdata allow us to present a new kind of
high-field IUtransition lines show significant differ- plot for illustrating phase behavior generally, and for
ences. In existing calculations the Cross line asymp- delineating phase boundaries. In Fig. 4 wc show con-
totically approaches 0.5T,(0) as H ~,whereas the tour lines ofconstant susceptibility (solid curves) in
Bulaevskii line asymptotically tends to a value close the H-Tplane. The plot extends only down to about
to T=0. However there is some possibility ofrecon- 0.5T,(0) owing to present experimental limitations.
ciliation, since the precise location ofthis line is sens- A major feature ofinterest is an essentially flat
itive to details ofthe assumed phonon spectrum. For "shelf" (shown shaded). In the H Tregion ofthe-
the DItransition between dimerized and intermediate shelf, transition (precursor) effects have disappeared
phases, Cross speculates on the order ofthe transi- and we are in a uniform chain region. Over the
tion, but gives no calculated values. Hence, we again ranges of temperature and field studied the uniform
show the transition line schematically in Fig. 3. chain susceptibility is constant since both ksT,(H)
Regarding the experimental data in Fig, 3 we can and gpsH, (T) are very small compared to J~„(from
make a @umber ofcomments. First we note that, as Ref. 2, JA„/ks =68 K). The dashed curve clearly
regards the DU curve, the experimental data are in corresponds to a "ridge" in the susceptibility con-
between the Bray-Bulaevskii and the Cross results. tours. It is also equivalent to the DUtransition line
%cconclude that, to present experimental accuracy, ofFig. 3 continued through the special point
the data do not really favor either theory, but are in (H,",T,")into the DIline, down to 1.1 K. Thus
gratifying agreement with both, especially since the phase boundar1cs arc dcflncd by ridges 1Q thc Xcon-
only adjustable parameter needed in fitting theory to tour plot. The high-field IUphase boundary (see
FIELD-DEPENDENT DIFPERENYIAL SUSCEPTIBILITY...
the isotherm crosses thc IUline at a very small angle
t t t
in this case, in which case the peak will not be
resolved since substantial broadening will occur. A
similar phenomenon can be inferred from data re-
ported for thc metamagnctic compound
'
CoBr2 2Hqo,
50
IV. THERMODYNAMIC DISCUSSION
25
The interesting question of the criteria to be used
in defining SP phase transitions over a range oftem-
perature and field, and the novel appearance ofthc X
plots in general, is best discussed in terms ofa ther-
modynamic theo"ry"ofsecond-order phase transitions
(h. transitions). The rationale for discussing our
experimental results in the light ofsuch a theory ar-
ises from the fact that the H =0 specific heat shows a
characteristic anomaly, and the Xdata do indicate
second-order (X) transitions along the DUline.
Theoretically one assumes that the specific heat at
constant field CH =—T(BS/BT)H has a singularity at
l.4 I.6 I.B 2.0 the field-dependent 8c-riTtical temperature, i.e,, along
rEMpERAruRE (K) the DU line ofthe phase diagram. By thermo-
dynamic arguments it then follows that the isother-
=
mal susceptibility Xr (BM/BH)s as well as the
0-FTIG.4. Contour plot ofacdifferential susceptibility in the quantity (BM/BT)0will display the same anomalous
plane for TTF-Aus4C4(CF3)4 (solid lines). Ridges in
behavior as CH. By contrast, the adiabatic suscepti-
the contours are shown as dashed or dot-dashed lines and
bility xs—=(BM/BH)s, the specific heat at constant
ctroarrryespuonnitds) tsoucphhatsheatbo1uanrdba.riuens.it cVorarleusepsonodfsXtaore1.i8n9(&ar1bi0-~ magnetization C~—=T(BS/B=T)~, and the slope of
emu/mole. the DU line itself (BH/BT)), (BH/BT)s, will
remain finite (display a much weaker singularity)
along the DU line. From thc thermodynamic theory
it follows that (Bxs/BT)H=—(CH/T) (B'T/BH )s.
Fig. 3) appears in Fig. 4 as a dash-dot line emanating Thus, although Xq sho~s only a weak anomaly along
from (H,",T,") Note that aga.in it is characterized by the DU line, its temperature derivative will display a
a ridge in the susceptibility contours, although this strong singularity (since the quantity (B T/BH )s, as
time the ridge is less sharply defined than for thc DU well as CH, diverges along the DU line). As Htends
and Dlbranches. The special point (multicritical to zero, M 0 and therefore Xq Xq and takes on
point) H,",T,",shown by the star in Fig. 4, appears as its characteristics, It follows that the experimental
an overall peak ofmaximum susceptibility in the en- criterion for defining T,(H) at low fields should be
tire H-Tplane. the temperature ofthe maximum slope of the X(T)
This contour plot illustrates why the high-field jU curves. Ifthis criterion is followed, the value of
phase line is visible only in the X(T) plots ofFig. 1 T,(0) obtained is (2.03 +0.02) K, which agrees with
and not in the X(H) plots ofFig. 2. The constant specific-heat studies as a function offield under~ay
field plots ofFig. 1 cross the high-field IUphase at Leidcn. Within the errors there appears to be no
ridge at a pronounced angle (almost perpendicular) difference between our value for the deuterated com-
and the effects ofthe ridge are clearly manifest. In pound and that reported in thc literaturc2 20for non-
=
Fig. 2 the pronounced maxima observed correspond deuterated TTF-AusqC4(CF3) 4 (T, 2.06 K). Note
to crossing the DU linc and the DIlinc at high and that use ofthe mean-field "knee" criterion would
low relative temperatures, respectively. It can be in- yield a value for T,(0) a few percent higher.
ferred from Fig. 2 that the IUline could only have Let us further investigate the interesting situation
been crossed by the X(H) field sweep at T=1.250 K. where T,(H) for low fields is derived from peaks in
The crossing point is indicated by the small arro~ (BXr/BT) whereas at higher fields, T,(H) is derived
(i). Although no separate peak is seen, there is a from peaks in X(T) itself. Consider the thermo-
substantial shoulder for H &H~I for this particular dynamic relation
=1.
iTso=th1er.m50 K(c)o.mTpharise mthaey cbuervaetstribfoutredT to t1h1e afnadct that xr—xs——(CH/T)(BT/BH),' .
3220 J.A.NORTHBY etal. 25
Since both Xs and (BT/BH)s are nonanomalous mal (dc), the susceptibility is measured with an ac
along the DU line, it follows that XTwill display a technique and the result can yield either XTor X~, or
peak similar to that in CH. However, the-amplitude indeed some intermediate quantity. The decisive fac-
ofthe peak in XTwill decrease and eventually vanish tor in this problem is the ratio ofthe ac frequency to
for H 0. This is precisely what is observed experi- the relevant relaxation time. The latter will in gen-
mentally. It is interesting to note that a similar situa- eral depend on both temperature and field, and may
tion arises in the case ofordered 3D antiferromag- in fact show anomalies at the field-induced transi-
nets.' There the zero-field antiferromagnetic order- tions. '8 Clearly, the nature ofthe susceptibility will
ing temperature, T~ is defined as an inflection point be important for the interpretation of the X-contour
in the plot of XTvs T, i.e., a singularity appears in plot described above. In the absence ofan extensive
'6's
(BXr/BT)H rather than in Xr itself. As the field frequency study, we resort to a direct test (for a
o
increases, a peak progressively develops in XT. This limited set ofexperimental conditions). The dc mag-
has been observed by direct calculation as well as ex- netization measurements ofFig. 2 are sufficiently de-
perimentally. '8 ' %e therefore note that although tailed to permit a direct evaluation of XTby differen-
the magnetoelastic SP antiferromagnetic chain and tiation of Mwith respect to H. XTevaluated this way
the regular 3D antiferromagnet represent two com- may then be compared with the observed X„. Alter-
pletely different physical systems, and accordingly natively, a new set ofmagnetization isotherms may
have characteristically different forms for the X be constructed by integrating X„(H). The various
curves, general aspects ofthe phase behavior are re- sets ofcurves may then be examined for consistency
markably equivalent. This should indeed be expect- with expected behavior.
ed, since it follows from basic therm' odynamics and H=e1n.ce, in Fig. 5, we show the X„vsHcurve for
the shape ofthe phase boundary. T 759 K in comparison with the Xr(H) derived
%ealso point out that similar thermodynamic ar- from the M(H) curve at T=1.76 K. The close
guments yield the criteria to be used in defining the agreement between these two curves demonstrates
DU transition from the isothermal Mr(H) or isofield that for this temperature, X„is in fact the isothermal
MH( T) magnetization curves. Obviously, since susceptibility (Xr). This tells us that the frequency cu
Xr=—(BM/BH) r, the transition in not too small of 1.88 kHz at which the X„measurements were per-
fields is defined by the maximum slope of the isoth- formed, is low with respect to the inverse relaxation
ermal magnetization curves. This is illustrated by the times v in this region, i.e., that the condition
Mr(H) curves in Fig. 2, where the arrows (f) indi- co~ &(1 obtains. This region is therefore character-
'
cate the temperatures at which the X~maxima are ized by a very short (&10 s) relaxation time, even
found to occur. Secondly, since (BM/BT)H when the second-order DU phase boundary is
=—(CH/T) (BT/BH)s it follows that for the isofield crossed. This result is unusual in comparison with
curves the transition is also defined to be the tem- observed phenomena in 3D ordered antiferromag-
perature ofmaximum slope. In Fig. 1 the vertical ar- nets, '8 for which the relaxation time goes through a
rows (f) indicate the temperature ofthe XH(T) maxi- pronounced maximum at the second-order boundary
ma. They are indeed seen to correspond to tempera- and may reach values of the order of 10 '—1 s. It
tures ofmaximum slope of the MH( T) curves. may reflect the fact that in the ideal magnetoelastic
Finally we note that since for not-too-small fields,
the singularity in XTreflects the singularity in CH,
the reverse is also true. Previous experimental SP
specific-heat data, have been analyzed in terms of I I I 1 I I I
mean-field cusps, as theoretically calculated, for ex- g I0-& I.76K (dMT/dH)
ample, in Ref. 9. Specific-heat experiments on TTF-
AuS4C4(CF3)4 at Leiden, at present in a preliminary E I j
stage, show anomalies which should be analyzed in W k
terms of (rounded) h. anomalies. Conversely, the !.759
consistency ofthe form ofthe CH and XTanomalies K
Xoc
provides a test ofexperimental data. CXl
El
LaJ
CD
Gh
V. RELAXATION PHENOMENA m 0 I
0 5 10 I5 20 25 50 55 40
MAGNETIC FIEID (k0e)
In the preceding we have discussed the expected
properties of Xr(H), XH(T), Mr(H), and MH(T) FIG.S. Comparison offield dependence ofdifferential
and we should now consider which of these quantities susceptibility, X„,at 1.759Kwith the isothermal susceptibil-
are in fact measured experimentally. Whereas the ity, (dMT/dH), obtained by differentiating the static mag-
magnetization measurements are necessarily isother- netization data of1.76K.
25 FIELD-DEPENDENT DIFFERENTIAL SUSCEPTIBILITY... 3221
SP system, the spins remain paramagnetically disor- available at four temperatures and are shown in Fig.
dered in the dimerized phase, i.e., the ordering is 7, By comparison with the directly measured mag-
manifested in the conformation ofthe lattice and not netization curves ofFig. 2, we might expect that
accompanied by long-range magnetic correlations. these curves should converge to a common line at
On the other hand, the equivalent comparison X„ the highest fields ofthese experiments. This condi-
at T=1.11K and Xr derived from M(H) at T=1.10 tion is met satisfactorily for T=2.1, 1.759, and 1.50
=1.
K, as shown in Fig. 6, presents a strong contrast. K, but fails notably for the curve for T 250 K.
Clearly X„is no longer isothermal when the DIline The "missing magnetization" is attributed to a
is crossed, as well as for a substantial region of failure ofthe condition X„=X~. The onset of the
X„(
higher field. We make a preliminary observation that inequality X~must thus occur between 1.5 and
the field region where X„&X~corresponds roughly 1.250 K. It is particularly' tempting to associate it
to the estimated field region spanned by the inter- with the special point T, at 1.4 K.
mediate phase at this temperature. The experimental We have already noted that our X-contour plot has
limitation in detecting X"signals does not allow us to the special feature that the special point (H,",T,")is
establish whether fully adiabatic conditions have been an absolute maximum, and further it is observed to
attained. Nevertheless, it is important to emphasize occur at the junction ofthe three ridges defining the
here that the most striking feature of this field re- DU, DIand IUphase boundaries. We deduce that
X„(
gion, namely, the DIphase boundary, is unambigu- the onset ofthe inequality X~with decreasing T
ously indicated as an anomaly in both susceptibilities or increasing Hbeyond (H,",T,') could explain the
Xy and X„. observed decreasing X,„. This feature is ofgreat
These two comparisons (at 1.76 and 1.1 K) do not uti'lity for a precise determination ofthe location of
").
tell us where, i.e., at what temperature, the cross T, (and also H, Figure 8 shows a plot of the am-
over from isothermal to nonisothermal behavior in plitude ofthe susceptibility peak versus the tempera-
X„takes place. Some information on this effect may ture along the DUand DI phase boundary lines.
X,
be obtained by examining a family ofmagnetization Along the DUline, „increases as Tdecreases, in
curves derived by integrating X„(H). Curves are agreement with our previous thermodynamic argu-
ments. Along the DIline, however, X,„progres-
sively decreases with decreasing temperature, attri-
butable to an increasingly longer relaxation time
II
I I I I I I I I I along this boundary. The intersection ofthe loci of
x IO10— X,„along the DUand DIlines presumably locates
I I I I I I
400
~
300
K
~
T/dHj 250
5—
cn
~ 200
Q
LLJ
CA I50
C)
~
l00
50
I I I I
0 5 IO I5 20 25 30 35 40
MAGNETIC FIELD (k0e)
l l I l l l l I
0 5 IO I5 20 25 30 35 40 45
MAGNETIC FIELD {k0e) FIG.7. Field dependence ofmagnetization as derived by
integration ofdifferential susceptibility curves for various
=1.
FIG.6. Same as Fig. 5, for T 1 K. temperatures.
J.A.NORTHBY etal. 25
II— I I I I I nevertheless, first order, we may'8 well associate with
it a new, rather slow, relaxation mechanism associat-
I03
x ed with transfer processes or nucleation effects
l0-
between the two coexisting phases. This mechanism
could explain the rather abrupt onset ofthe condition
X„&Xr and the "missing magnetization" (see Fig.
7) would correspond to the typical magnetization
OF'
discontinuity associated with the first-order transi-
& 8— tions, which would not be observable in X„. It could
CO equally well be attributable to a continuing series of
small jumps or discontinuities in magnetization as the
field increases through the intermediate phase region.
Such a phenomenon may be closely related to current
theoretical ideas on multiph"as"e phenomena'4 and
"staircase" phenomena. 9
VI. UNIVERSAL PHASE DIAGRAM
The precision susceptibility measurements on
TTF-AuC4Sq(CF3) 4, which reveal non-mean-field
characteristics ofthe SP transitions, have led us to
re-examine previous experimental phase boundary
data on TTF-CuSqC4(CF3)4 (Ref. 13)and MEM-
~ Xac (CONST.T) (TCNQ)2.' The data, reanalyzed along the lines dis-
+ Xsc (CONST, H ) cussed in the section on thermodynamics, are plotted
~ XT = dMT/dH in Fig. 9, along with the new "Au" data, in terms of
reduced variables H/T, (0) and T/'l, (0). The phase
boundaries for "Cu"and "MEM" differ quite con-
siderably (up to a 15'/o maximum) from those previ-
I I I I I I ously published, in consequence ofthe new criteria
I.O i.2 i.4 l.6 I.8 2.0 used in defining the transition points. The mutual
TEMPERATUR E (K) and individual consistency ofthe data on the three
FIG.8, Magnitude ofsusceptibility peaks, X«, along the materials is greatly improved. For instance, for
DUand DIphase boundary lines. Also shown are two X«
pea'.k points which agree with X«above T, and depaj.'t below
T, The discrepancy leaves questions which are difficult to
22
resolve owing to the sparseness ofX«data. 20-
C
IB- -.
INTERMEDIATE
BBK ~,
tThe,'=onls.e4t+o0f.0X3„K&,Xcorrraensdpohnednincge lotocat0es,=(2H1,.4,T+,0).2at 4P Il24—— ,~XW~q ~''-,oU0NIFORM
kOe, in agreement with, but more accurately than, IO
the determinations from Fig. 3 and 4. D1 DIMERIZED BB8K,
It is often difficult to understand the magnitudes + TTF-AuBDT
and microscopic mechanisms ofrelaxation processes. TTF-CljBDT DU
~ MEM~(TCNa)&
Tpahreameaxgisnteintigc listyesratetumrse dfooersorndoetreadppeaasroptopobseedastowell 0~~Oll i 0.2 i 0I5 i 0.I4 i 0.l5 i 0.I6 i 0I.7 i 0I.8 i 0.I9 I.O
developed. However, the dramatic change occurring Tc(H)/Tc(0)
over a narro~ range ofparameters in this experiment FIG.9. Composite normalized phase diagram for TTF-
AuS4C4(CF3)4, TTF-CuS4C4(CF3)4 and {MEM-TCNQ)
suggests a reasonably simple explanation. Theory 2
struagngseitsitosnst.hat%th'eemDigIhltinetheisreafolrieneeoxfpeficrtst-toordseere hpyhsa-se ppTeo,aw(kHde)vr/asT.lu,es(T0ho)e.fn(Wo8rMhmear/e8lizTep)doHssisboclarel,e(s8trMaarne/s8itHHio/)nTs,1.(a(0ore)raXlonadcea)tedFobry
teresis phenomena in the magnetic measurements. normalization, the values chosen for T,(0)are 2.03, 10.3,
Such phenomena have, indeed, been observed in the and 18,0Kfor the compounds as listed. The line designated
magnetization measurements on the SP sister com- (a) represents mean-field estimates for the high-field phase
pounds TT"F-CuS4C4(CF3)4 (Ref. 13)and MEM- boundary (for Cu) from data using a 10-MW solenoid
(TCNQ) 2—, but no—t in TTF-AuS4C4(CF3)4, at least (Hm,„=200kOe). The solid and dashed lines represent
down to 1.1 K [ 0.54T,(0)]. Ifthe DIline is, theoretical curves as in Fig. 3.