- Email: [email protected]
NMR Investigation of Spin Density Wave Critical Fluctuations in (TMTSF)2PF6
ELSEVIER
Synthetic Metals 103 (1999) 2166-2167
NMR Investigation of Spin Density Wave Critical Fluctuations in (TMMTSF)#F6 W.G. Clarka,M.E. Hansona, B. Alavia, W.G. Moultonb,P. Kuhnsb,andA. Reyesb ‘Dept. of PhysicsandAstronomy,University of Californiaat LosAngeles,Box 9.51547,LosAngeles,CA 90095-1547,USA bNationalHigh MagneticField Laboratory,1800E. PaulDirac Drive, Tallahassee, FL 32306,USA Abstract We report NMR measurements of the spindensitywave (SDW) transitioncritical fluctuationsin (TMTSF)zPFsat 14.9 MHz and 0.98 GHz. This contributionto 1/T, is nearly independentof the magneticfield alignmentand the frequencyon both sidesof the transition;abovethe transitionat TN it variesas IT - TN~’with 0 = -0.75 f 0.08. Theseobservations areconsistentwith dynamical scalingfor the 3D Heisenbergmodeland showthat the correlationtime for the critical fluctuationsresponsiblefor T, is lessthan 2 x lo-lo s for all temperaturesstudied.Suchbehavioris very di&ent from that observedin the orderedSDW phase,wherethe dominantcouplingis to SDWphasons whosecharacteristictimescovera very broadrange. Keywords:Nuclear magneticresonance,Metal-Insulatortransition,Magnetic phasetransitions,organic conductorsbasedon radical cationand/oranionsalts
1. Introduction One of the unresolvedquestionsregardingthe spin density wave (SDW) transition in Bechgaardsalts is the appropriate descriptionof the transition and its fluctuations.In this paper, we report measurements of the protonspin-latticerelaxationrate (l/TI) in the vicinity of the transitiontemperature(TN) over an unusually wide range of frequencies. By carrying the measurements to nearly 1 GHz, it is possibleto investigatea very broad range of kequenciesin the critical fluctuation
data that is subtractedto obtain the correspondingcritical contributionbelowTN. One of the moresignificantresultsis that there is very little difft’erence betweenthe relaxationrate for the two frequenciesin the critical regimeaboveTN 131.This meansthat the correlation time that characterizesthe critical fluctuationsis shorterthan 2 x lOBi s for all conditionsof thesemeasurements.
P,
Spectnun.
?F c,
0.98 GHz, 23.1 T
*O” j 0” o.ooo*oooo @ .“a
2. Experimental detailsand results The samples usedfor this work weresmall( < 1 mg), single crystalsof (TMTSF)2PF6that wereinvestigatedat 14.9MHz in an electromagnetat UCLA and at 0.98 Gfi in a resistive magnetat the NHMFL. The alignmentof the magneticfield was alongthe c*-directionfor the 14.9MHz measurements andat an undeterminedanglein the planeperpendicularto the a-direction for the 0.98GHz ones. The resultsfor thesetwo frequenciesare shownin Fig. 1. Other tiequencies,not discussed here, showa similarbehavior. The overall behavior can be divided into a low temperature regionstartinga few degreesbelowthe transition(TN f: 12.2K) where l/T1 is dominatedby SDW phasons[1,2J, the critical regioncioseto TN, andthe relaxationat highertemperatures that is usually attributed to methyl group rotation [ 13. The latter component[l] has been subtractedfrom the 14.9 MHz data, where it is a relatively large background,but not from the 0.98 GHz data, where it is not. The solid line is an empirical extrapolationof the SDW phasoncontributionfor the 0.98 GHz
l
‘I-I in(TMTSFAPF,
l
l
1
-5
6
0% cc
. l
l *:
l
9 10’ 2 3 4 r bmpe=-T(K) Fig. 1. ‘H l/T~in (TMTSF)-LPFh at 0.015 and0.98 GHz nearthe SDW transition. The solid line is an estimateof the SDW phasoncontributionin the orderedphase. 7
8
The critical behaviorcloseto TN is shownin Fig. 2, where l/T1 is plottedas a function of (T - TN\. The solid line, which corresponds to the powerlaw lITI 0: IT - TN[-‘-~‘, is a bestfit to the 0.98 GHz data above TN. Becauseno substantial backgroundsubtractionis requiredfor this data set, it provides
0379-6779/99/$ -see front matter 0 1999 Elsevier Science S.A. All rights reserved. PII: so379-6779(98)00742-5
W.G. Clark
et al. / Synthetic
Metals
the best resolution in these measurements. Although the 14.9 MHz data above TN andthe 0.98GHz databelowit havea much lower resolution, within the experimental error, they are consistentwith the sameexponent. There are severalcommentsthat shouldbe maderegarding the choicesof TN in Fig. 2. Although on the basisof Fig. 1 it is seenthat the transition temperaturecan be identified on the scaleof 0.1 K or better, the actual value of TNon a fmer scale hasbeenadjustedto give the straightestline in Fig. 2; i.e.; the bestfit to a power law. Becauseof the changesthat occurwith a reasonablevariation of TN, we estimatethat the error in the exponentfor the 0.98 GHz dataaboveTN is lessthan i 0.08. IOOLU -A
4
1”‘1”‘1”‘11”’ A
“I’
1 ‘1”“‘1”‘/“‘1
’ “1
’
“‘~“‘1
‘H in (TMTSF),PF,
10-1
2
3
4 5 6
100
2 /T-T,1
3
4 5 6
10’
2
3
4
6)
Fig. 2. Critical behavior for l/Trof protons in (TMTSF)sPF6. The solid line is a bestfit with exponent-0.75 to the 0.98 GHz dataaboveTN. 3. Discussionand comlusions One of the points to be noted regardingthe choiceof TN is that slightly different valueshavebeenusedto modelthe critical behaviorin the 0.98 GHz data aboveand below the transition. This behavior is consistentwith the observation that this transition has the characteristicsof a weakly first-order one [4,5], insteadof the second-ordertransition that is commonly usedto modelit [6]. A simple,phenomenological Landaumodel analysis[5] indicatesthat the divergenceabove TN is centered about80 n-X below it (minimumsupercoolingtemperature)and the divergencebelow TN is centeredabout 80 mK above it (maximum superheatingtemperature).The difference in the valuesassignedfor TN indicatedon Fig. 2 is in the samesense and within a factor of two of what is expectedon this basis. Such an interruption of the second-order transitionmay be the reasonthat the critical slowingis never enoughto generatea frequencydependence to l/T, within the range studiedin this work. Also, the closenessof the two divergencetemperatures suggests a free energybarrier that is low enoughto explainwhy no hysteresishasbeenseenin this transition. Another point is what physical situation might make the transition(weakly) fist order?One interestingpossibilityis that a combined SDW and charge density wave transition is responsible[7].
103 (1999) 2166-2167
2167
Now we apply the dynamicscalingmodelof Bourbonnais[8] for the 3D Heisenbergmodel to interpret the power law divergenceobservedfor l/T* : l/T
cc IT - Tj@‘+=‘,
(1)
where r is the critical index for the staggeredmagnetic susceptibility,v is the critical index, and z is the dynamical exponent.From the valuesv = 0.60-0.63, y = 1.25-1.30, and z = 2.0 + small correction 191, one obtains*/ - Du + zv in the range0.62-0.71, whichhassomeoverlapwith our measured value 0.75rt: 0.08. On the basisof this result, we concludethat our measurements of l/T] in the critical regimeare consistent with dynamicscalingfor the 3D Heisenberg modelon both sides of the transition. Our value for the exponentdiffers from the 3D RPA value -0.50 & 0.05 reportedearlier for comparablemeasurements in Bechgaardsalts [lo]. We do not have an explanationfor this difference. In conclusion,we havepresentedNMR measurements of the spin density wave (SDW) transition critical fluctuations in (TMTSF)2PF6at 14.9MHz and 0.98 GHz. This contributionto l/T, is nearly independentof the magneticfield alignmentand the frequencyon both sidesof the transition.Above TN it varies as IT - TNle with 0 = -0.75 f 0.08. A similar behavior is observed for the critical fluctuation contribution below the transition, but with lower resolution.These observationsare consistentwith dynamicalscalingfor the 3D Heisenbergmodel and show that the correlationtime for the critical fluctuations responsiblefor Tl is lessthan 2 x 10-l’ s for all temperatures studied. ACKNOWLEDGMENTS - We thank C. Bourbonnaisfor helpful discussions regardingthe useof the scalingmodelfor the critical behavior of lITI. The part of this work done by the UCLA participantswassupportedby NSF Grant DMR-9705369 Part of it wasdoneat the NHMFL, which is supportedby NSF Grant DMR-9527035andthe Stateof Florida. [I]
W.G. Clark,M.E. Hanson,W.H. Wong,andB. Alavi, J. Phys.ParisIV 3 (1993)235 andreferencescited therein. [2] S.E.Brown, W.G. Clark, andG. Kriza, Phys.Rev. B 56, (1997)5080. ]3] Fromour experiments,we cannot tell if the slight temperatureshift betweenthe two measurements is a real effect or an artifact of the thermometercalibration. [4] W.G. Clark, M.E. Hanson,W.H. Wong,andB. Alavi, PhysicaB 194-196(1994)2856. [5] M.E. Hanson,Ph.D. Thesis,University of Californiaat LosAngeles,unpublished. [6] For a recentreview of this subject,seeG. Grinner,Density Waves in Solids, AddisonWesley,Menlo Park, CA, 1994. [7] N. Kobayashi,M. Ogata,andK. Yonemitsu,J. Phys. Sot. Jpn.67 (1998) 1098. [8] C. Bourtonnais,J. Phys.I France3 (1993) 143. [9] Wethank C. Bourbonnaisfor providinguswith these values. [lo] P. Wzietek et al., J. Phys.IFrance 3 (1993) 171.
Synthetic Metals 103 (1999) 2166-2167
NMR Investigation of Spin Density Wave Critical Fluctuations in (TMMTSF)#F6 W.G. Clarka,M.E. Hansona, B. Alavia, W.G. Moultonb,P. Kuhnsb,andA. Reyesb ‘Dept. of PhysicsandAstronomy,University of Californiaat LosAngeles,Box 9.51547,LosAngeles,CA 90095-1547,USA bNationalHigh MagneticField Laboratory,1800E. PaulDirac Drive, Tallahassee, FL 32306,USA Abstract We report NMR measurements of the spindensitywave (SDW) transitioncritical fluctuationsin (TMTSF)zPFsat 14.9 MHz and 0.98 GHz. This contributionto 1/T, is nearly independentof the magneticfield alignmentand the frequencyon both sidesof the transition;abovethe transitionat TN it variesas IT - TN~’with 0 = -0.75 f 0.08. Theseobservations areconsistentwith dynamical scalingfor the 3D Heisenbergmodeland showthat the correlationtime for the critical fluctuationsresponsiblefor T, is lessthan 2 x lo-lo s for all temperaturesstudied.Suchbehavioris very di&ent from that observedin the orderedSDW phase,wherethe dominantcouplingis to SDWphasons whosecharacteristictimescovera very broadrange. Keywords:Nuclear magneticresonance,Metal-Insulatortransition,Magnetic phasetransitions,organic conductorsbasedon radical cationand/oranionsalts
1. Introduction One of the unresolvedquestionsregardingthe spin density wave (SDW) transition in Bechgaardsalts is the appropriate descriptionof the transition and its fluctuations.In this paper, we report measurements of the protonspin-latticerelaxationrate (l/TI) in the vicinity of the transitiontemperature(TN) over an unusually wide range of frequencies. By carrying the measurements to nearly 1 GHz, it is possibleto investigatea very broad range of kequenciesin the critical fluctuation
data that is subtractedto obtain the correspondingcritical contributionbelowTN. One of the moresignificantresultsis that there is very little difft’erence betweenthe relaxationrate for the two frequenciesin the critical regimeaboveTN 131.This meansthat the correlation time that characterizesthe critical fluctuationsis shorterthan 2 x lOBi s for all conditionsof thesemeasurements.
P,
Spectnun.
?F c,
0.98 GHz, 23.1 T
*O” j 0” o.ooo*oooo @ .“a
2. Experimental detailsand results The samples usedfor this work weresmall( < 1 mg), single crystalsof (TMTSF)2PF6that wereinvestigatedat 14.9MHz in an electromagnetat UCLA and at 0.98 Gfi in a resistive magnetat the NHMFL. The alignmentof the magneticfield was alongthe c*-directionfor the 14.9MHz measurements andat an undeterminedanglein the planeperpendicularto the a-direction for the 0.98GHz ones. The resultsfor thesetwo frequenciesare shownin Fig. 1. Other tiequencies,not discussed here, showa similarbehavior. The overall behavior can be divided into a low temperature regionstartinga few degreesbelowthe transition(TN f: 12.2K) where l/T1 is dominatedby SDW phasons[1,2J, the critical regioncioseto TN, andthe relaxationat highertemperatures that is usually attributed to methyl group rotation [ 13. The latter component[l] has been subtractedfrom the 14.9 MHz data, where it is a relatively large background,but not from the 0.98 GHz data, where it is not. The solid line is an empirical extrapolationof the SDW phasoncontributionfor the 0.98 GHz
l
‘I-I in(TMTSFAPF,
l
l
1
-5
6
0% cc
. l
l *:
l
9 10’ 2 3 4 r bmpe=-T(K) Fig. 1. ‘H l/T~in (TMTSF)-LPFh at 0.015 and0.98 GHz nearthe SDW transition. The solid line is an estimateof the SDW phasoncontributionin the orderedphase. 7
8
The critical behaviorcloseto TN is shownin Fig. 2, where l/T1 is plottedas a function of (T - TN\. The solid line, which corresponds to the powerlaw lITI 0: IT - TN[-‘-~‘, is a bestfit to the 0.98 GHz data above TN. Becauseno substantial backgroundsubtractionis requiredfor this data set, it provides
0379-6779/99/$ -see front matter 0 1999 Elsevier Science S.A. All rights reserved. PII: so379-6779(98)00742-5
W.G. Clark
et al. / Synthetic
Metals
the best resolution in these measurements. Although the 14.9 MHz data above TN andthe 0.98GHz databelowit havea much lower resolution, within the experimental error, they are consistentwith the sameexponent. There are severalcommentsthat shouldbe maderegarding the choicesof TN in Fig. 2. Although on the basisof Fig. 1 it is seenthat the transition temperaturecan be identified on the scaleof 0.1 K or better, the actual value of TNon a fmer scale hasbeenadjustedto give the straightestline in Fig. 2; i.e.; the bestfit to a power law. Becauseof the changesthat occurwith a reasonablevariation of TN, we estimatethat the error in the exponentfor the 0.98 GHz dataaboveTN is lessthan i 0.08. IOOLU -A
4
1”‘1”‘1”‘11”’ A
“I’
1 ‘1”“‘1”‘/“‘1
’ “1
’
“‘~“‘1
‘H in (TMTSF),PF,
10-1
2
3
4 5 6
100
2 /T-T,1
3
4 5 6
10’
2
3
4
6)
Fig. 2. Critical behavior for l/Trof protons in (TMTSF)sPF6. The solid line is a bestfit with exponent-0.75 to the 0.98 GHz dataaboveTN. 3. Discussionand comlusions One of the points to be noted regardingthe choiceof TN is that slightly different valueshavebeenusedto modelthe critical behaviorin the 0.98 GHz data aboveand below the transition. This behavior is consistentwith the observation that this transition has the characteristicsof a weakly first-order one [4,5], insteadof the second-ordertransition that is commonly usedto modelit [6]. A simple,phenomenological Landaumodel analysis[5] indicatesthat the divergenceabove TN is centered about80 n-X below it (minimumsupercoolingtemperature)and the divergencebelow TN is centeredabout 80 mK above it (maximum superheatingtemperature).The difference in the valuesassignedfor TN indicatedon Fig. 2 is in the samesense and within a factor of two of what is expectedon this basis. Such an interruption of the second-order transitionmay be the reasonthat the critical slowingis never enoughto generatea frequencydependence to l/T, within the range studiedin this work. Also, the closenessof the two divergencetemperatures suggests a free energybarrier that is low enoughto explainwhy no hysteresishasbeenseenin this transition. Another point is what physical situation might make the transition(weakly) fist order?One interestingpossibilityis that a combined SDW and charge density wave transition is responsible[7].
103 (1999) 2166-2167
2167
Now we apply the dynamicscalingmodelof Bourbonnais[8] for the 3D Heisenbergmodel to interpret the power law divergenceobservedfor l/T* : l/T
cc IT - Tj@‘+=‘,
(1)
where r is the critical index for the staggeredmagnetic susceptibility,v is the critical index, and z is the dynamical exponent.From the valuesv = 0.60-0.63, y = 1.25-1.30, and z = 2.0 + small correction 191, one obtains*/ - Du + zv in the range0.62-0.71, whichhassomeoverlapwith our measured value 0.75rt: 0.08. On the basisof this result, we concludethat our measurements of l/T] in the critical regimeare consistent with dynamicscalingfor the 3D Heisenberg modelon both sides of the transition. Our value for the exponentdiffers from the 3D RPA value -0.50 & 0.05 reportedearlier for comparablemeasurements in Bechgaardsalts [lo]. We do not have an explanationfor this difference. In conclusion,we havepresentedNMR measurements of the spin density wave (SDW) transition critical fluctuations in (TMTSF)2PF6at 14.9MHz and 0.98 GHz. This contributionto l/T, is nearly independentof the magneticfield alignmentand the frequencyon both sidesof the transition.Above TN it varies as IT - TNle with 0 = -0.75 f 0.08. A similar behavior is observed for the critical fluctuation contribution below the transition, but with lower resolution.These observationsare consistentwith dynamicalscalingfor the 3D Heisenbergmodel and show that the correlationtime for the critical fluctuations responsiblefor Tl is lessthan 2 x 10-l’ s for all temperatures studied. ACKNOWLEDGMENTS - We thank C. Bourbonnaisfor helpful discussions regardingthe useof the scalingmodelfor the critical behavior of lITI. The part of this work done by the UCLA participantswassupportedby NSF Grant DMR-9705369 Part of it wasdoneat the NHMFL, which is supportedby NSF Grant DMR-9527035andthe Stateof Florida. [I]
W.G. Clark,M.E. Hanson,W.H. Wong,andB. Alavi, J. Phys.ParisIV 3 (1993)235 andreferencescited therein. [2] S.E.Brown, W.G. Clark, andG. Kriza, Phys.Rev. B 56, (1997)5080. ]3] Fromour experiments,we cannot tell if the slight temperatureshift betweenthe two measurements is a real effect or an artifact of the thermometercalibration. [4] W.G. Clark, M.E. Hanson,W.H. Wong,andB. Alavi, PhysicaB 194-196(1994)2856. [5] M.E. Hanson,Ph.D. Thesis,University of Californiaat LosAngeles,unpublished. [6] For a recentreview of this subject,seeG. Grinner,Density Waves in Solids, AddisonWesley,Menlo Park, CA, 1994. [7] N. Kobayashi,M. Ogata,andK. Yonemitsu,J. Phys. Sot. Jpn.67 (1998) 1098. [8] C. Bourtonnais,J. Phys.I France3 (1993) 143. [9] Wethank C. Bourbonnaisfor providinguswith these values. [lo] P. Wzietek et al., J. Phys.IFrance 3 (1993) 171.