PHYSICAL REVIEW B VOLUME 52, NUMBER 2 1 JULY 1995-II

Spin-density-wave transition and resistivity minimum of the Bechgaard salt (TMTSF)2NO3at high magnetic field, where TMTSF is tetramethyltetraselenafulvalene

Alain Audouard and Salomon AskenazyService National des Champs Magnetiques Pulses (CNRS UM-S 819) and Laboratoire de Physique des Solides (CNRS ERS 1-11),

Complexe Scientifique de Ranguei l, 31077 Toulouse, France(Received 21 March 1995)

Transverse magnetoresistance of the Bechgaard salt (tetramethyltetraselenafulvalcue)zNO3 has been mea-

sured up to 36 T, with the magnetic field parallel to the lowest conductivity direction c*. Data have beenrecorded at ambient pressure, in the temperature range from 2 to 77 K. Whereas the anion ordering temperatureremains field independent, the spin-density-wave transition temperature (Tsnw) increases by few tenths of a

percent at 32 T and the temperature at which the resistivity minimum occurs (T~;„) increases by nearly a factorof 3 at 36 T. The field dependence of TSD~ is studied in the framework of the mean-field calculations of Bjelisand Maki [Phys. Rev. B 45, 12 887 (1992)]while the T;„variation is discussed on the basis of field-induced

electron confinement.

In a previous paper,' both oscillatory and semiclassical

behaviors of the high-field magnetoresistance (MR) were re-ported in the ambient pressure spin-density-wave (SDW)ground state of the Bechgaard salt (BS) (TMTSF)2NO3.Among BS, (TMTSF)2NO3 exhibits several peculiar fea-tures. Indeed, contrary to most other salts with noncen-trosymmetric anions, the anion ordering (AO) wave vector isparallel to the best conduction axis a (Ref. 2) which shouldlead, below T AD=41 K, to a compensated two-dimensional(2D) semimetal with electron and hole closed tubes. In addi-

tion, the SDW order parameter at ambient pressure and zerotemperature is only about 8 K (Ref. 3) and the temperaturedependence of the resistivity below the SDW transition tem-perature (TsDw=9. 4 K) cannot be satisfactorily accountedfor by a thermally activated law. These features both suggestimperfect nesting of electron and hole tubes. Thus smallerclosed orbits should be further induced below TsD~. As amatter of fact, in the temperature range below 10 K,' twoseries of quantum oscillations with frequency at respectively63 and 246 T were observed above -5 and 16 T, respec-tively. Whereas the 246 T series was ascribed to the so-calledfast oscillations usually observed in most of BS, the 63 Tseries has no counterpart in other BS. It was shown to belinked to the SDW phase ' and might be related to theabove-mentioned small carrier pockets, ' ' although theLifshitz-Kosevitch equation fails to account for both the tem-perature and field dependence of the oscillations amplitude.On the other hand, the analysis of the semiclassical part ofthe MR has revealed a significant inhuence of the magneticfield on TsD~ which increases by 14% at 30 T.' This behav-ior which is the signature of the field-induced improvementof the imperfect nesting of the 2D orbits at the SDW transi-tion was satisfactorily accounted for by the mean-field cal-culations of Montambaux at low magnetic field. However,Bjelis and Maki have proposed more recently a generalequation for the field dependence of TsD~ w'hich holdswhatever the considered magnetic-field range. In the low-field range, this model predicts a quadratic variation ofTsD~, in agreement with Ref. 8. On the opposite side,

TsD~ is predicted to saturate at high field towards the valuewhich corresponds to the SDW transition temperature relatedto the case of perfect nesting. This feature is in agreementwith the idea that magnetic field improves the 1D characterof the Fermi surface. However, the above model did not yetreceive any quantitative verification since only lowmagnetic-field experiments or data analysis have been re-ported up to now. The purpose of this work is thus to presentexperimental evidence of the field dependence of TsD~, de-rived within the framework of the Bjelis and Maki model.

Experimental details were published previously. ' Toavoid cracks, a slow cooling rate was achieved (-0.1

103-3220

1025T-

C)10"

I—CQ

10o

OT

AO/

10"—10

T (K)

100

FIG. 1. Temperature dependence of the normalized resistance of(TMTSF)zNO3 recorded at several magnetic-field values. From thebottom to the top, the value of the magnetic field is 0, 2.5, 5, 7.5,10, 12.5, 15, 17.5, 20, 22.5, 25, 28, 30, 32, 34, and 36 T (some ofthese values are indicated on the figure). Solid lines are guides forthe eye.

0163-1829/95/52(2)/700(4)/$06. 00 52 700 1995 The American Physical Society

~ 'r, ~

'

/I/y g/ $) /1r ir, w/[ $)r1

52 SPIN-DENSITY-WAVE TRANSITION AND RESISTIVITY . . . R701

K min ') from 300 K down to 2 K so that the standardtemperature dependence of the resistance was obtained atzero field, ' as can be seen in Fig. 1 where a metallic be-havior is observed down to 12 K, followed by a steep resis-tance increase due to the condensation of the SDW phase.The temperatures at which SDW and AO transitions takeplace were conventionally estimated from the extrema ofd[ln(R)]/d(1/T). This parameter exhibits a minimum atTAo=41 K and a maximum at T so~=9.4 K, both in goodagreement with data of the literature. ' Magnetoresistancemeasurements were carried out in pulsed magnetic fields up

to either 32 or 36 T during the decay period (1.2 s) of thefield, in the transverse configuration (BJ a) with B parallelto c and 50 kHz ac current parallel to the best conductiondirection (a axis).

While TAo remain unaffected by magnetic field up to 36T, Fig. 1 shows that TsD~ increases: from 9.4 K in zero fieldup to 10.7 K at 32 T as evidenced in Fig. 2. As predicted, '

a quadratic behavior is observed at low field, followed by asaturating behavior. According to Maki, and for magneticfield 8 applied parallel to c*, the general equation given inRef. 9 can be approximated as

TsDwl 1) col /1 irub l (11—ln Re W —+q

TsDw) 2q

nip) y

2 2mTsnw)L2)

1 /eel'' /I irub4Re+ —+b) l

2 ~TSDW)

/1 inib—Re 8" —+i

2 mT sDw)

/11—3'P

The relevant parameters entering this equation are theSDW transition temperature corresponding to the perfectnesting case (TsDw ), the cyclotron pulsation (nlrb), and the

energy parameter which characterizes the deviation from per-fect nesting (eo), defined as'

and

qr (-,'+ ix) —4'(-,') = 2%(2ix) —4(i x)+'y

1Rer qr(ix)]= —y+x g n n +x (5)

ep = tb/t~ Q2, (2)

where t„and tb are transfer integrals in a and b directions,respectively. cob is written as

where y= —'P(-,') —2 ln(2) and qr(-,') = 1.963 51, the follow-ing analytical expression can be obtained:

O)b= VbeB, (3)Re 9 —+ix —0 ~—

) (2).

where p is the Fermi velocity in the a direction.In order to make Eq. (1) more easily tractable, an analyti-

cal approximation of Re('P(-,'+ix) —'P(-,')), where qr isthe digamma function, was calculated. Keeping in mind that

1 1 1=8x 2+ 2+1+4x 3(9+4x ) 5(25+4x )

11 1

147(49+4x ) 3(49+4x )

1 4x+ —ln 1+ (6)

10I I

20

B (T)

I

30

FIG. 2. Magnetic-field dependence of the spin-density-wavetransition temperature (T sow). The full line is the best fit to Eq. (1)(see text).

It is worthwhile to notice that Eq. (6) is accurate within4X10 in the whole magnetic-field range covered by theexperiments. The solid line in Fig. 2 is the best fit of Eq. (1)to experimental data: a very good agreement is obtained. Thefit yields ir=(2.4~0.3) 10 ms, TsDw =11.0~0.2 K, and

8p= 13~4 K. It can be noticed first that a reasonable valueis obtained for the Fermi velocity. On the other hand,

TsD~ is in excellent agreement with the value measured for0

(TMTSF)zPF6 for which the nesting can be regarded as per-fect. Indeed, for (TMTSF)zPFs crystals with best resistivityratio, the SDW transition temperature is 11.1 K. ' Let usconsider now the energy parameter ap which accounts for thedeviation from perfect nesting. This parameter is directlylinked to the transfer integrals t, and tb [see Eq. (2)]. Unfor-tunately, no data about transfer integral values in the SDWstate of (TMTSF)zNO3 are presently available in the litera-

R702 ALAIN AUDOUARD AND SALOMON ASKENAZY 52

35 I s I s / s s s s/

s s s s t s s

30

25

C:

E~ 20

15

0 s I s s s s I » s s I s s s s

0 10 20 30 40

FIG. 3. Magnetic-Geld dependence of the resistivity minimumtemperature (T~;„).The solid line is a guide to the eye.

ture. Nevertheless, the deduced value of sp can be comparedto that deduced from band-structure calculations related to(TMTSF)zPF6 at a temperature of 4 K.' These calculationsyield Rp=16 K, which is close to and even larger than thevalue deduced for (TMTSF)2NO3, and thus not consistent.This disagreement could be accounted for assuming either

ep [as defined in Eq. (2)] is not a relevant enough parameteror available band-structure calculations for BS are not fullyreliable. It must be remarked that, in the case of perfect nest-

ing, T sD~ should remain magnetic-field independent which,according to Eq. (1), would yield op= 0. In other words, Eq.(1) suggests that a SDW phase transition with perfect nestingof Fermi surface can only take place in BS for whichtb=o. This is in conflict with the theoretical model whichpredicts that electronic instability cannot be observed at fi-nite temperature in perfect 1D compounds. In any case, ac-curate band-structure calculations are needed to solve thisdiscrepancy. Nevertheless, it can be noticed that, althoughthis model neglects any infIuence of both electron correla-tions and AO, it nicely accounts for experimental data andyields satisfactory values for Fermi velocity and T sD~ .

0

Finally, it can be seen in Fig. 1 that the temperatureT;„at which the resistivity minimum occurs (T;„=12 Kin zero field) strongly increases as 8 increases. The fielddependence of T;„is displayed in Fig. 3.A similar behaviorhas already been observed in slowly cooled(TMTSF)2C104 (Ref. 18) for which a SDW phase is stabi-

lized at low field thus giving rise to a resistivity minimum,the temperature at which it occurs increasing up to 22 K at26 T. This phenomenon could be due to the predicted 'field-induced growth of antiferromagnetic fIuctuations. How-ever, this interpretation seems to be unlikely since in thepresent case the field dependence of the width of the SDWtransition' is not significant enough to account for such alarge increase of T;„.An alternate explanation could in-volve the field-induced decrease of the transverse interac-tions. Indeed, in tetramethyltetrathiafulvalene (TM1 I'I')

salts, for which ap is typically lower by a factor of 2 than in

BS,' the condensation of the charge degrees of freedom oc-curs at a temperature T which is higher than the condensa-tion temperature of the spin degrees of freedom leading to aresistivity minimum around T . In the present case, the fea-tures of the temperature dependence of the resistance at highfield (see Fig. 1) are quite similar to those observed at zerofield in, e.g. (TMTTF)2Br, although its T is well higher[T = 100 K (Ref. 20)] than T;„ in the present case(T;„=34 K at 36 T). This could be the signature of anincreased separation of charge and spin degrees of freedomin (TMTSF)2NO3. Since this separation is a general charac-ter of strongly correlated electron gas, it is suggested that theeffect of a field applied parallel to c* is to evidence theelectron correlation properties through the field-induced con-finement in the ab plane.

As a summary, we have shown that the mean-field calcu-lations of Bjelis and Maki ' nicely account for the field-induced increase of the SDW transition temperature of(TMTSF)2NO3 up to 32 T. Satisfactory values of both

TsD~ and Fermi velocity have been deduced from the analy-

sis. However, the deduced value of the energy parameterap is not consistent with the available data of transfer inte-grals in BS. This suggests that ap might not be the mostrelevant parameter to account for the deviation from perfectnesting in BS. We have also evidenced that magnetic fieldstrongly increases the temperature of the resistivity Inini-mum. As proposed in Ref. 18, this latter phenomenon islikely related to field-induced electron confinement.

The authors wish to acknowledge L. Brossard for hiscontinuous support and fruitful discussions, J. M. Fabre forpreparing the studied crystals, F. Goze for experimental help,J. P. Ulmet for initiating the study of (TMTSF)zNO3 in highmagnetic field, P. Auban and D. Jerome for communicatingtheir results on (TMTSF)2C104 prior to publication, and S.Tomic for discussions about inhuence of irradiation on spin-density-wave transition temperature. Special thanks are dueto K. Maki for enlightening discussions.

A. Audouard, F. Goze, J. P. Ulmet, L. Brossard, S. Askenazy, and

J. M. Fabre, Phys. Rev. B 50, 12 726 (1994).J. P. Pouget, R. Moret, and R. Comes, J. Phys. (Paris) Lett. 42,

543 (1981).S. Tomic, J. R. Cooper, W. Kang, D. Jerome, and K. Maki, J.

Phys. (France) I 1, 1603 (1991).A. Audouard, F. Goze, S. Dubois, J. P. Ulmet, L. Brossard, S.

Askenazy, S. Tomic, and J. M. Fabre, Europhys. Lett. 25, 363(1994).

N. Biskup, L. Balicas, S. Tomic, D. Jerome, and J. M. Fabre,Phys. Rev. B 50, 12 721 (1994).

K. Maki, Phys. Rev. B 49, 12 362 (1994).A. Audouard, F. Goze, J. P. Ulmet, L. Brossard, S.Askenazy, and

J. M. Fabre, Synth. Met. 70, 739 (1995).

52 SPIN-DENSITY-WAVE TRANSITION AND RESISTIVITY . . . R703

G. Montambaux, Phys. Rev. B 38, 4788 (1988).A. Bjelis and K. Maki, Phys. Rev. B 45, 12 887 (1992).J. F. Kwak, J. E. Schirber, P. M. Chaikin, J. M. Williams, H. H.

Wang, and L. Y. Chiang, Phys. Rev. Lett. 56, 972 (1986).S. Tomic, J. R. Cooper, D. Jerome, and K. Bechgaard, Phys. Rev.

Lett. 62, 462 (1989).' K. Maki, Synth. Met. 55-57, 2808 (1993).t3K. Yamaji, J. Phys. Soc. Jpn. 51, 2787 (1982).

It must be pointed out that, for (TMTSF)2PF6 crystals with resis-

tivity ratio in the range 90—150, TsD~ reaches 11.9 K. Thisvalue is close to that measured for best quality crystals (resistiv-

ity ratio 250; Tsnw= 11.1 K) subsequently irradiated at low flu-

ence (20 ppm irradiation-induced defects) for which Tsnw rise

up to 12.1 K (Ref. 3). Obviously, higher defect concentrationinduces a TsD~ decrease.

' L. Ducasse, M. Abderrabba, J. Hoarau, M. Pesquer, B. Gallois,and J. Gaultier, J. Phys. C 19, 3805 (1986).

K. Yamaji, J. Phys. Soc. Jpn. 55, 860 (1986).' H. Frohlich, Proc. R. Soc. London Ser. A 223, 296 (1954).sK. Behnia er al. , Phys. Rev. Lett. (to be published).A. Bjelis and K. Maki, Phys. Rev. B 44, 6799 (1991).C. Coulomb, J. Phys. (Paris) Colloq. 44, C3-885 (1983).