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Magnetoresistance studies of βμ-ET2AuBr2
Synthetic Metals, 41---43 (1991) 1903-1906
1903
MAGNETORESISTANCE STUDIES OF ,8"- ET2 AuBrz
M. DOPORTO, F.L. PRAFr, and W. HAYES Clarendon Laboratory, University of Oxford, Parks Road, Oxford (UK) J. SINGLETON and T. JANSSEN High Field Magnet Laboratory, Katholleke Unlversltelt Nljmegen, NlJrnegen (Netherlands) M. KURMOO and P. DAY Inorganic Chemistry Laboratory, University of Oxford, South Parks Road, Oxford (UK)
ABSTRACT Low-temperature transverse magnetoreslstance (MR) measurements have been made on the organic metal ,8"-ET 2 AuBr 2.
The MR was found to be highly anlsotroplc.
A 2-band model was used to
evaluate the carder mobllitles In the different sections of the Fermi surface.
Shubnlkov-de Haas (SdH)
oscillations of two dlstlnot frequencies were observed for current along the higher resistance direction. Analysis of the field and temperature dependence of these osclllaUons yields an effective mass of 4-5 m e and a Dingle temperature of 0.3-0.5 K. An Interpretation of the different oscillation frequencies gives an Inter-planar bandwidth of 4It-2.2--+0.3 meV.
INTRODUCTION The organic metal ,8"- ET2 AuBr 2 was first synthesized In 1986 by Morl et al. [1].
The donors form
stacks of dlmerlzed molecules which form 2-dimensional sheets parallel to the ab planes, separated by layers of the linear AuBr~ counterlons [2].
The band structure was calculated using the extended
HOckel method, giving a quasi-two-dimensional Fermi surface (FS) which consists of an open electron sheet and a closed hole orbit [1]. The ,8"- ET2 AuBr z samples were prepared electrochemically, forming crystals of typical dimensions 1xlx0.1 mm 3.
Gold contact pads were evaporated In 4-1n-line geometry onto the ab face and 10/~m
gold wires were attached to these using sliver paint. cut In two In order to measure current along a and b.
For the anlsotropy measurement a sample was The standard AC current technique was used.
The sub-Kelvin temperatures were provided by a He4/He3 dilution frldge for a 20T Bitter magnet at NlJmegen and a He3 system In a pulsed-field magnet at Leuven.
RESULTS Representative traces of the normalized MR, R(B)/R(0)-I, are shown In Fig. 1. No distinct saturation Is observed and the traces are far less temperature dependent than previously reported [3]. There Is no Indication of the negative MR observed In ref. 3, which was probably due to the the combined effect of the field dependent anlsotropy and the contact geometry [4]. SdH oscillations are visible only In the higher reslstanoe direction, at magnetic fields above ~9T and temperatures below ~1 K.
0379-6779/91/$3.50
© Elsevier Sequoia/Printed in The Netherlands
1904
s
. . . . . . . . . (a)
t5
(0)
/
/
Temp
~4
~
t0
N
N
L
~2
5
0
.
.
.
.
.
.
.
.
0
.
.
.
.
20
t0
i
i0
Magnetic Field {Tes]a}
i
I
i
I
I
I
I
I
20
30
Magnetic Field (Tesla)
Fig. 1. Normalized MR of .8"- ET2 AuBr~: (a) at 220 mK showing the anlsotropy within the conducting plane; (b) obtained for Jlla using a 35T pulsed field (at a base temperature of 350mK)
The following simple 2-band model [5] has been used to fit the background magnetoconductance for ilia (Fig. 2).
NeglecUng the Hall terms, the conductance a,, along a can be expressed as: oo=
ot
02
k
i+~,~) + 1 + - - ~ =-~=
O)
where 1 and 2 refer to the two bands, Ra Is the measured resistance along the a dlrecUon, and k Is a scaling factor which depends on the actual current paths inside the sample. From these fits one obtains for the average In-plane mobllltles/~1~ 5000 crnZ/Vs and ~2~ 800 cmZ/Vs, at 220 mK.
The
higher value Is associated with the closed-hole orbit, since the observation of SdH oscillations requires pB>l. If we Introduce %= ne n~,~ In Eq. 1, where n~ and #,~ are the fraction of the total carriers (n) and the mobility component along a for each orbit i, we can estimate the relative number of carders In the two bands.
From the fit we obtain %=0.91 (and n,=0.09), corresponding to FS areas of ~45% and ~5% of
the Brlllouin zone for the electron and the hole regions respectively. The SdH oscillations become clearer when one subtracts the fitted MR background (Fig. 3.). The Fourier Transform of the oscillatory part of the MR shows two strong peaks at fundamental fields of ~43T and ~180T together with weak sldebands of the latter at ~135T and ~220T. consistent with those previously reported by Pratt et al. [3]. slmUar frequency distribution but with 20% larger BF.
These values are
Swanson et al. [6] obtain a qualitatively
From the temperature and field dependence of
the amplitude of the osclllaUons In Fig. 3 an estlrnate of m'~(4.5±0.5)m, and To~(0.4±0.1)K Is obtained for the effective mass and Dingle temperature as opposed to the values ~2 and ~ I K obtained In [3] and [6].
It Is Interesting to note how the product m'To remains constant [7].
1905 1.0
0. i25 o
.
.
.
.
.
.
.
.
[b)
0. 100 0. 075
•=
m 1o
.
[a]
0.5 o.o5o
g~ 0. 025 0.000
..................... 5 i0 t5
20
25
30
0,0
~
Magnetic FielO (Tesla)
'
'
'
t0'
'
'
'
'
20
Magnetic FieiO (Tesla)
Fig. 2. Examples of 2-band model fits (Eq. 1) of the magnetoconductance of ,B'- ET2 AuBr 2. The traces w e r e obtained for ilia using (a) a 35T pulsed field magnet and (b) a 20T Bitter magnet.
O.iO
iO0
. . . . . . . . . . - 220mK
0.oo
~
50 ~600mK
-0. I0 0.05
0.06
0.07
0.08
Inverse Magnetic Field
0.09
0.t0
(t/Tee]a)
Fig. 3. SdH oscillations in p ' - E T 2 AuBr~at 220mK, 450mK and 800mK, obtained by back0roundsubtractlon.
0
0
a2
J00 200 300 400 500 600
SdH Frequency (Tesla] Fig. 4. Fourier transform of the oscillatory MR In Fig. 3.
DISCUSSION The MR anlsotropy can be understood In terms of the calculated FS to be due to the effect of the
open orbit.
The SdH oscillations are observed In the a direction, where the effect of the closed orbit Is
expected to clomlnate, and correspond to orbits of ~2% of the B.Z. derived from the room-temperature structure.
This Is somewhat smaller than the predicted value of ~4% using Morl's overlaps [1].
1906
The simplest explanation for the observed SdH frequencies Is In terms of a warped cylindrical Fermi surface due to dispersion along the c ° axis.
Following this Interpretation, the extremal Fermi surface
cross sections would correspond to the ~135T and ~220T oscUlaUons (Fig. 4.), with mixing between these frequencies leading to the observation of the average ~180T and the semi-difference (ztB~43T). The bandwidth In the c" direction can be estimated from the expression 4to= t'tn.:IBF/rn° [8]. Taking ABF=2,dB~86T and m'~4.5 m, one obtains an Inter-planar bandwidth of 4tc~(2.2_+0.3)meV, comparable to ~1.6 meV for ~-ETzCu(SCN)2 [8] and ~2.1 meV for ,8H- ETz 13[9].
It Is worth noting the similarity of m °,
TD and t c between/~'- ETz AuBr 2 and/~H- ET213 (see Ref. 9), the appearance of clearer beats In the MR of the latter being due to the larger size of the closed orbit [9]. The relatively large difference between the fundamental fields given In [6] and those obtained here seems unlikely to be due simply to sample mlsallgnment, as this would require angles of 35 °.
It may
point to the existence of a new low-temperature phase with a larger number of carriers in the closed section of the FS.
CONCLUSIONS The band structure and Fermi surface of ,8"- ET2 AuBr 2 given by the tight-binding method based on the extended H0ckel approximation are In fair qualitative agreement with the MR anlsotropy and the observation of SdH oscillations.
The size of the closed orbit estimated from these frequencies and a
simple 2-band model fit to the MR Is ~2-4% of the Brlllouln zone. Carder mobillUes of ~5000 cm2/Vs for the closed orbit and ~800 cmZ/Vs
for the open orbit are
estimated from the background MR fits at 200inK. Analysis of the temperature and field dependence of the SdH osclUaUons yields values of m *~ (4.5___0.5)me and TD~(0.4___0.1)K for the effective mass and Dingle temperature. The different frequencies observed In the SdH oscillations may be explained In terms of a warped Fermi
cylinder
resulting
from
the
non-negligible
Inter-sheet
overlap
and
a
bandwidth
of
4 tc ~ (2.2___0.3)meV Is deduced for the Interplane direction.
ACKNOWLEDGEMENTS The authors would like to thank Prof. F.Herlach and Dr. R.G. Clark for use of the pulsed-field equipment at the University of Leuven and the SERC (UK) for financial support.
REFERENCES 1.
T.Morl, F.Sakal, G.Salto and H.Inekuchl, Chem.Lett. 1037 (1986).
2.
MKurmoo et al; Sol. St. Comm. 88. (1987) 459.
3.
F.L.Pratt et al., Phvs.Rev.Lett. 81 (1988) 2721
4. 5.
W. Kang and D. J6rome, unpubllshod comment. see for example: N.W Ashcroft and N.D. Mermln, ~;011dState Phvslcs. HRW, Ch. 13, 1981.
6.
A.G. Swanson et al., to be published In the Proceedings of the International Conference on
7.
Organic Superconductors, South Lake Tahoe, (May, 1990), Plenum Press. N. Toyota, E.W. Fenton, T. Sasakl and M. Tachlkl, Sol. St. Commun. 72. (1989) 859.
8.
F.L Pratt et al., In G.Salto and S.Kagoshlma (eds.), The Phvslcs and Chemistry of Oreanlc Superconductors. Springer Proceedings In Physics, %1ol.51, Springer-Verlag, Berlin (1990) 200
9.
W.Kang et al., Phys. Rev. Lett. 62. (1989) 2559.
1903
MAGNETORESISTANCE STUDIES OF ,8"- ET2 AuBrz
M. DOPORTO, F.L. PRAFr, and W. HAYES Clarendon Laboratory, University of Oxford, Parks Road, Oxford (UK) J. SINGLETON and T. JANSSEN High Field Magnet Laboratory, Katholleke Unlversltelt Nljmegen, NlJrnegen (Netherlands) M. KURMOO and P. DAY Inorganic Chemistry Laboratory, University of Oxford, South Parks Road, Oxford (UK)
ABSTRACT Low-temperature transverse magnetoreslstance (MR) measurements have been made on the organic metal ,8"-ET 2 AuBr 2.
The MR was found to be highly anlsotroplc.
A 2-band model was used to
evaluate the carder mobllitles In the different sections of the Fermi surface.
Shubnlkov-de Haas (SdH)
oscillations of two dlstlnot frequencies were observed for current along the higher resistance direction. Analysis of the field and temperature dependence of these osclllaUons yields an effective mass of 4-5 m e and a Dingle temperature of 0.3-0.5 K. An Interpretation of the different oscillation frequencies gives an Inter-planar bandwidth of 4It-2.2--+0.3 meV.
INTRODUCTION The organic metal ,8"- ET2 AuBr 2 was first synthesized In 1986 by Morl et al. [1].
The donors form
stacks of dlmerlzed molecules which form 2-dimensional sheets parallel to the ab planes, separated by layers of the linear AuBr~ counterlons [2].
The band structure was calculated using the extended
HOckel method, giving a quasi-two-dimensional Fermi surface (FS) which consists of an open electron sheet and a closed hole orbit [1]. The ,8"- ET2 AuBr z samples were prepared electrochemically, forming crystals of typical dimensions 1xlx0.1 mm 3.
Gold contact pads were evaporated In 4-1n-line geometry onto the ab face and 10/~m
gold wires were attached to these using sliver paint. cut In two In order to measure current along a and b.
For the anlsotropy measurement a sample was The standard AC current technique was used.
The sub-Kelvin temperatures were provided by a He4/He3 dilution frldge for a 20T Bitter magnet at NlJmegen and a He3 system In a pulsed-field magnet at Leuven.
RESULTS Representative traces of the normalized MR, R(B)/R(0)-I, are shown In Fig. 1. No distinct saturation Is observed and the traces are far less temperature dependent than previously reported [3]. There Is no Indication of the negative MR observed In ref. 3, which was probably due to the the combined effect of the field dependent anlsotropy and the contact geometry [4]. SdH oscillations are visible only In the higher reslstanoe direction, at magnetic fields above ~9T and temperatures below ~1 K.
0379-6779/91/$3.50
© Elsevier Sequoia/Printed in The Netherlands
1904
s
. . . . . . . . . (a)
t5
(0)
/
/
Temp
~4
~
t0
N
N
L
~2
5
0
.
.
.
.
.
.
.
.
0
.
.
.
.
20
t0
i
i0
Magnetic Field {Tes]a}
i
I
i
I
I
I
I
I
20
30
Magnetic Field (Tesla)
Fig. 1. Normalized MR of .8"- ET2 AuBr~: (a) at 220 mK showing the anlsotropy within the conducting plane; (b) obtained for Jlla using a 35T pulsed field (at a base temperature of 350mK)
The following simple 2-band model [5] has been used to fit the background magnetoconductance for ilia (Fig. 2).
NeglecUng the Hall terms, the conductance a,, along a can be expressed as: oo=
ot
02
k
i+~,~) + 1 + - - ~ =-~=
O)
where 1 and 2 refer to the two bands, Ra Is the measured resistance along the a dlrecUon, and k Is a scaling factor which depends on the actual current paths inside the sample. From these fits one obtains for the average In-plane mobllltles/~1~ 5000 crnZ/Vs and ~2~ 800 cmZ/Vs, at 220 mK.
The
higher value Is associated with the closed-hole orbit, since the observation of SdH oscillations requires pB>l. If we Introduce %= ne n~,~ In Eq. 1, where n~ and #,~ are the fraction of the total carriers (n) and the mobility component along a for each orbit i, we can estimate the relative number of carders In the two bands.
From the fit we obtain %=0.91 (and n,=0.09), corresponding to FS areas of ~45% and ~5% of
the Brlllouin zone for the electron and the hole regions respectively. The SdH oscillations become clearer when one subtracts the fitted MR background (Fig. 3.). The Fourier Transform of the oscillatory part of the MR shows two strong peaks at fundamental fields of ~43T and ~180T together with weak sldebands of the latter at ~135T and ~220T. consistent with those previously reported by Pratt et al. [3]. slmUar frequency distribution but with 20% larger BF.
These values are
Swanson et al. [6] obtain a qualitatively
From the temperature and field dependence of
the amplitude of the osclllaUons In Fig. 3 an estlrnate of m'~(4.5±0.5)m, and To~(0.4±0.1)K Is obtained for the effective mass and Dingle temperature as opposed to the values ~2 and ~ I K obtained In [3] and [6].
It Is Interesting to note how the product m'To remains constant [7].
1905 1.0
0. i25 o
.
.
.
.
.
.
.
.
[b)
0. 100 0. 075
•=
m 1o
.
[a]
0.5 o.o5o
g~ 0. 025 0.000
..................... 5 i0 t5
20
25
30
0,0
~
Magnetic FielO (Tesla)
'
'
'
t0'
'
'
'
'
20
Magnetic FieiO (Tesla)
Fig. 2. Examples of 2-band model fits (Eq. 1) of the magnetoconductance of ,B'- ET2 AuBr 2. The traces w e r e obtained for ilia using (a) a 35T pulsed field magnet and (b) a 20T Bitter magnet.
O.iO
iO0
. . . . . . . . . . - 220mK
0.oo
~
50 ~600mK
-0. I0 0.05
0.06
0.07
0.08
Inverse Magnetic Field
0.09
0.t0
(t/Tee]a)
Fig. 3. SdH oscillations in p ' - E T 2 AuBr~at 220mK, 450mK and 800mK, obtained by back0roundsubtractlon.
0
0
a2
J00 200 300 400 500 600
SdH Frequency (Tesla] Fig. 4. Fourier transform of the oscillatory MR In Fig. 3.
DISCUSSION The MR anlsotropy can be understood In terms of the calculated FS to be due to the effect of the
open orbit.
The SdH oscillations are observed In the a direction, where the effect of the closed orbit Is
expected to clomlnate, and correspond to orbits of ~2% of the B.Z. derived from the room-temperature structure.
This Is somewhat smaller than the predicted value of ~4% using Morl's overlaps [1].
1906
The simplest explanation for the observed SdH frequencies Is In terms of a warped cylindrical Fermi surface due to dispersion along the c ° axis.
Following this Interpretation, the extremal Fermi surface
cross sections would correspond to the ~135T and ~220T oscUlaUons (Fig. 4.), with mixing between these frequencies leading to the observation of the average ~180T and the semi-difference (ztB~43T). The bandwidth In the c" direction can be estimated from the expression 4to= t'tn.:IBF/rn° [8]. Taking ABF=2,dB~86T and m'~4.5 m, one obtains an Inter-planar bandwidth of 4tc~(2.2_+0.3)meV, comparable to ~1.6 meV for ~-ETzCu(SCN)2 [8] and ~2.1 meV for ,8H- ETz 13[9].
It Is worth noting the similarity of m °,
TD and t c between/~'- ETz AuBr 2 and/~H- ET213 (see Ref. 9), the appearance of clearer beats In the MR of the latter being due to the larger size of the closed orbit [9]. The relatively large difference between the fundamental fields given In [6] and those obtained here seems unlikely to be due simply to sample mlsallgnment, as this would require angles of 35 °.
It may
point to the existence of a new low-temperature phase with a larger number of carriers in the closed section of the FS.
CONCLUSIONS The band structure and Fermi surface of ,8"- ET2 AuBr 2 given by the tight-binding method based on the extended H0ckel approximation are In fair qualitative agreement with the MR anlsotropy and the observation of SdH oscillations.
The size of the closed orbit estimated from these frequencies and a
simple 2-band model fit to the MR Is ~2-4% of the Brlllouln zone. Carder mobillUes of ~5000 cm2/Vs for the closed orbit and ~800 cmZ/Vs
for the open orbit are
estimated from the background MR fits at 200inK. Analysis of the temperature and field dependence of the SdH osclUaUons yields values of m *~ (4.5___0.5)me and TD~(0.4___0.1)K for the effective mass and Dingle temperature. The different frequencies observed In the SdH oscillations may be explained In terms of a warped Fermi
cylinder
resulting
from
the
non-negligible
Inter-sheet
overlap
and
a
bandwidth
of
4 tc ~ (2.2___0.3)meV Is deduced for the Interplane direction.
ACKNOWLEDGEMENTS The authors would like to thank Prof. F.Herlach and Dr. R.G. Clark for use of the pulsed-field equipment at the University of Leuven and the SERC (UK) for financial support.
REFERENCES 1.
T.Morl, F.Sakal, G.Salto and H.Inekuchl, Chem.Lett. 1037 (1986).
2.
MKurmoo et al; Sol. St. Comm. 88. (1987) 459.
3.
F.L.Pratt et al., Phvs.Rev.Lett. 81 (1988) 2721
4. 5.
W. Kang and D. J6rome, unpubllshod comment. see for example: N.W Ashcroft and N.D. Mermln, ~;011dState Phvslcs. HRW, Ch. 13, 1981.
6.
A.G. Swanson et al., to be published In the Proceedings of the International Conference on
7.
Organic Superconductors, South Lake Tahoe, (May, 1990), Plenum Press. N. Toyota, E.W. Fenton, T. Sasakl and M. Tachlkl, Sol. St. Commun. 72. (1989) 859.
8.
F.L Pratt et al., In G.Salto and S.Kagoshlma (eds.), The Phvslcs and Chemistry of Oreanlc Superconductors. Springer Proceedings In Physics, %1ol.51, Springer-Verlag, Berlin (1990) 200
9.
W.Kang et al., Phys. Rev. Lett. 62. (1989) 2559.