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The influence of magnetic order in quasi-2D organic conductors
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surface science
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ELSEVIER
Surface Science 305 (1994) 187-193
The influence of magnetic order in quasi-2D organic conductors M. Doporto *7a,J. Caulfield a, S. Hill a, J. Singleton a, F.L. Pratt a, M. Kurmoo b, P.J.T. Hendriks ‘, J.A.A.J. Perenboom ‘, W. Hayes a, P. Day b a Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK b Royal Institution, 21 Albemarle Street, London WIX 4BS, UK ’ High Field Magnet Laboratory, 6525 ED Nijtnegen, Netherlands (Received 4 May 1993; accepted for publication 4 June 1993)
Abstract We report extensive magnetoresistance (Y-(ET)~KH~(SCN)~. Our results indicate
(MR) measurements on the charge transfer salts /?“-(ET),AuBr, and that spin-density wave (SDW) groundstates in both of these materials
modify the Fermi surfaces calculated from room temperature crystal parameters. In the case of 0”-(ET),AuBr*, the shapes, sizes and orientations of three individual closed two-dimensional (2D) Fermi surface pockets have been deduced at 500 mK. The SDW groundstate in a-(ET),KHg(SCN), leads to the observation of a resistive “kink” made as a function of crystal orientation and temperature both above and transition at - 22 T. MR measurements below this “kink”, allow a qualitative assessment of the change in band structure at the “kink” to be made.
1. Introduction Many ET charge transfer salts have a Fermi surface (FS) consisting of a quasi-two dimensional (Q2D) hole pocket, plus a QlD electron section. The Q2D holes tend to dominate the low temperature conductivity of the salts, so that phenomena due to the QlD electrons, such as spindensity wave (SDW) formation (seen in, e.g. TMTSF charge-transfer salts, where the SDW leads to antiferromagnetic behaviour and a bandgap at the FS resulting in a metal-insulator transition), have been ignored by many workers. In this study, we report extensive magnetoresistance (MR) measurements on two metallic ET charge
* Corresponding author.
transfer salts, p”-(ET),AuBr, and a-(ET),KHg (SCN),, both of which exhibit low temperature SDW groundstates; the experiments show that the SDW leads to a modification of the simple Fermi surfaces deduced from band structure calculations.
2. Measurements
on /3”-(ET),AuBr,
The ET molecules in j?“-(ET>,AuBr, stack along the a crystal axis, forming conducting 2D sheets parallel to the UC plane, separated in the b direction by layers of linear AuBr; anions (see Ref. [l] and Fig. 3 below for definition of crystal axes). The j3” phase results in strong interactions between molecules in different stacks, so that p”-(ET>,AuBr, is less isotropic than many other
0039-6028/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI 0039-6028(93)E0695-Q
ii, ,,: i
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1. (a)
j”:(’ ~.
Magnetoresistance
!
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..__._
ri
i
and h” for all field orientations. The mechanism responsible for frequency mixing is indicated by the strong hysteresis in magnitude and in the phase of the SdHO between up and down sweeps of the magnetic field which is observed below 1 K when the field is parallel to b” [4]. This is indicativc of strong internal magnetic fields leading to domain formation. in view of this, effects due to the Shoenberg magnetic interaction (MI) [5] between two or more carrier pockets must be considered. These introduce a magnetic feedback term due to the fact that the field experienced by the carriers is 8 =,uJH + Mf, where N is the external applied field and M is the magnetisation containing the oscillatory (de Haas-van Alphen) components. This is thought to be the first observation of such an effect in an organic conductor
.
.1
: . ...
I
I _/‘,:I
.. .
1 rr
1?
70
111
of /3”-(ET)2AuBr,
for
Bllb”
(upper
trace) and for B tilted 30” from b” about a’ towards c
(lower
trace).
toresistance
(b) The
oscillatory
component
of the magne-
for the lower trace in (a). tcf Fourier
transform
of
0~). ln all cases T = 0.5 K.
metallic ET salts. Reliable calculations of the transfer integrals and band structure have not yet been established, and those estimated by differcnt groups disagree [2,3]. Evidence for a complex low temperature SDW groundstate is observed in the resistance, which drops sharply at - 20 K, and from ESR measurements, which reveal a change in g-value at - 6 K [l]. Fig. la shows the MR of /3”-tET),AuBr, for two different angles between the magnetic field and the normal to the 2D conducting planes tb”); the MR is seen to depend strongly on the field direction. Fig. lb shows the oscillatory component of the MR; Shubnikov-de Haas oscillations (SdHO) of several different frequencies are present. Fourier analysis (Fig. Icl reveals four strong frequencies (40, 140, 180 and 220 T), together with different harmonic combinations. To progress further, it is necessary to identity which frequencies correspond to actual carrier pockets, and which are merely an artefact of frequency mixing, or a result of crystal twinning* The latter possibility may be ruied out, as the frequencies of all the SdHO are inversely proportional to the cosine of the angle between the magnetic field
[61. The observed SdHO may be partly simulated using two Fermi surface (FS) pockets with areas corresponding to frequencies B,, = 40 T and B,, = 180 T and combinations such as B,, i: B,, and 2 x B,,> rir B,,. Simulations using the MI between the B,, and R,, series are successful in accounting for the sidebands at 180 + 40 T and 360 i: 40 T (Fig. lc), as well as the disappearance of the 180 T series under certain conditions, but cannot reproduce the dominance of the 40 T and the 220 T frequencies over the 180 T SdHO at higher tilt angles [6]. At large angles, the only surviving second harmonic observed corresponds to the 220 T frequency. Therefore, this frequency (B,:,l must also correspond to a real carrier pocket and is not merely an artefact of mixing. Having established that the SdHO frequencies B,, = 40 T, BFZ = 180 T and B,, = 220 T correspond to real closed 2D sections of FS, we turn to the angle dependence of the SdHO amplitudes. Fig. 2 shows an example of this for B,,, N,, and 1y,, as the sample is rotated about the w and u axes; strong oscillations in the amplitude are seen as a function of tilt angle. Rotations about the 4’ and c axes also reveal osciIlations in the SdHO amplitudes. These angle-dependent oscillations in SdHO strength are due to a mechanism first proposed by Yamaji 171, who showed that when a magnetic field is applied at certain angles, all the semi-classical k-space closed orbits around a
189
M. Doporto et al. /Surface Science 30.5 (1994) 187-I 93
I. -90
0
-45 Tilt
45
90
angle
Fig. 2. Fourier amplitudes of the three series of SdFIO corresponding to real 2D FS carrier pockets, for tilting about the w and Y directions (T = 0.5 KL
warped cylindrical FS have approximately the same area. Therefore, at these angles, the density of states at the Fermi energy is enhanced, resulting in a maximum in the background MR, and in the amplitude of the SdHO. The theory was
developed by Kartsovnik et al. [$I, who considered materials in which the plane of warping can be inclined with respect to the conducting plane. The tilt angles 8 at which the maxima occur are given by bk,,/ tan @I= ~(i - $) *A(4), where b is the interplane spacing, k,, is the radius of the warped cylindrical Fermi surface at a point where the tangent to the surface is perpendicular to the plane of rotation of the magnetic field, i is an integer and C#Jis the azimuthal angle describing the plane of rotation of the field. The gradient of a plot of 1tan 0 / against i may therefore be used to find one of the dimensions of the FS, and if the process is repeated for several 4, the complete FS shape in the conducting plane may be mapped out. (A(#) is determined by the inchnation of the plane of warping with respect to the 2D plane, and will not be discussed here.) Having rotated samples about various axes in the ac plane (a, c, a’, e’, v and w>, the SdHO amplitudes of each pocket are then plotted against tan 8, where 0 is the angle between the magnetic field and b*. From these data, the shape of the 2D FS pockets can be reconstructed (see Figs. 3c-3e), and, since the areas of the pockets are known from the SdHO frequencies, the unit cell size in the interplane direction can be estimated. In most cases, only a couple of oscillation periods in tan 8 are observed, as the resolution of the data does not permit more rapid oscillations to be resolved. It should be noted that the observation of these “Yamaji’” oscillations in /3”(ET),AuBr, is not necessarily expected since the
B
JOT
I SOT
220T
Fig. 3. (a) shows the room temperature Brillouin zone and FS for j3YETfzAuBrz calculated by Mori et al. 121.(b) Proposed low temperature FS, with two extra closed FS pockets produced by a 2c SDW. Cc), Cd) and (e) show the shapes (thin lines show worst case) of the different FS pockets, deduced from rotations about 6 crystal axes.
carrier pockets are very small. However, from the data, it is apparent that the Brillouin zone (BZ) boundary in the interplane direction is 2-3 times smaller than the room temperature value (i.e. the unit cell is 2-3 times longer in this direction). In theory, this should not alter the SdHO spectra significantly, as long as the interplane warping remains small. This suggests that there is some interplane component in the SDW ordering. The shapes of the FS pockets deduced from the angle-dependent oscillations in the SdHO are shown in Figs. 3c-3e. The caIculated FS that most resembles the SdHO data on p”-(ET), AuBr,, is due to Mori, and has just one closed hole pocket of - 5% of the room temperature BZ area centred on the X point, together with a pair of open sections [2] (Fig. 3a). Although the closed section is a factor of 2 too large to correspond to the B,, SdHO series, it shouid be remembered that this is close to the top of the hole band, so that small adjustments of, e.g., the band overlaps could result in a large reduction in pocket area. However, the FS calculation has no obvious candidate for the B,, and B,, series. In view of the magnetic ground state of p”that the additional (ET), AuBr, , we propose SdHO frequencies are the result of closed pockets produced by a SDW modulation with a conduction plane component of 2c, driven by the nesting properties of the QlD part of the FS. The result of such a modulation wouId be to fold back sections of the calculated FS leading to a small hole pocket close to V, together with a larger anisotropic closed section of FS (electronlike) (Fig. 3b). The band filling is such that there should be equal numbers of ciectrons and holes, so that the total area of the two hole pockets should be the same as the area of the electron pocket. In this way, if we identity the two hole pockets with the SdHO series B,, and B,, (Figs. 3c and 3d), the SdHO due to the eIectron pocket should then occur at the sum of these frequencies, namely B,, = 220 T (Fig. 3e). A comparison of Figs. 3c-3e and Fig. 3b shows that there is reasonable qualitative agreement between the experimental FS shapes and orientations and those of the proposed SDW groundstate.
3. Measurements
on cx-(ET),KHg(SCN.J,
Charge-transfer salts of the form cu-(ET& MHg(SCN),, where M may be K, Tl, Rb or NH,, were first synthesised as possible superconducting modifications of K-(ET),Cu(SCN), [9]. However, only cr-(ET),NH,Hg(SCN), is a superconductor. having a T,= 1.1 K f9]; the others are metals down to - 100 mK [lo], and in addition exhibit the onset of antiferromagnetic order at - 8- 10 K. probably due to the onset of a SDW groundstate [ 1 l-131. The materials are isostructural, with identical predicted Fermi surfaces consisting of a rather isotropic Q2D closed hole pocket and a Q 1D open eiectron section (see inset to Fig. 4). Fig. 4 illustrates the magnetoresistance of N(ET),KHg(SCN), for a variety of temperatures; the most noticeable feature is the so-called “kink” transition visibie as a dramatic fall in resistance between 22 and 23 T. (Similar “kinks” have now been observed in tr-(ET),TlHg(SCN), at _ 22 T [14] and in (r-(ET&RbHg(SCN), at - 35 T IlSl, but arc absent in the case of cr-(ET)?NH, Hg(SCN),.) Above the “kink” a single series of SdHO with a frequency of 670 i: 15 T is observed; however, below the “kink”, the MR exhibits hysteresis [ll], and the SdHO contain a
Fig. 4. Magnetoresistance of a-(ET), KHg(SCN), for several temperatures. SdHO and the field induced resistive “kink” at - 22 T can clearly be seen. The inset shows the predicted room temperature Fermi surface.
191
M. Doporto et al. /Surface Science305 (1994) 187-I 93
the “kink”. The “kink” would signal the destruction of the SDW state by the external field and the depopulation of the pocket would account for the fall in resistance. Others have noted that the complex behavior below the “kink” may be related to possible breakdown orbits between the open and closed sections of FS [15]. Recently, Kartsovnik et al. [14] have proposed a possible SDW groundstate for a-(ET),MHg (SCN), (M = K, Tl) with a nesting vector which leads to such a small FS pocket and a new 1D FS sheet inclined at N 26” to the 1D sheet shown in Fig. 4. In their scheme the SdHO with a fre-
prominent second harmonic component (see Fig. 4). In addition to the dominant SdHO series with a frequency of 670 _t 10 T, an apparent second series of SdHO, with a sample-dependent frequency between 700 and 870 T has also been observed at low fields [ll]. Several workers have linked these phenomena to the presence of the SDW groundstate [ll-131. It is thought that imperfect nesting in the SDW state could lead to the presence of an extra closed 2D carrier pocket in the Fermi surface (c.f. p”-(ET),AuBr, described above); the presence of this pocket would lead to the extra SdHO frequency at fields below
iO0
120 -
60
100 -
60
80 t
60
I
60
60 -
6C
-180
-120
-60 Angle
0
60
(degrees)
120
180
-180
-120
-60
Angle
0
60
120
180
(degrees)
Fig. 5. Magnetoresistance of a-(ET),KHg(SCN), at T = 1.5 K for fixed fields of 20 T (left-hand side) and 24 T (right-hand side) as a function of rotation angle (see text). The traces correspond to the following angles between the field and the rotation axis: left-hand side top to bottom 32”, 42” and 52”; right-hand side top to bottom 36”, 46” and 56”.
quency of N 670 T corresponds to a breakdown orbit between the small 2D FS pocket and the 1D sheet, whilst the 700-870 T series represents mixing between the 670 T frequency and SdHO due to simple orbits around the small pocket. Furthermore, the strong second harmonic observed below the ‘“kink” corresponds to a breakdown orbit of twice the area of that corresponding to the 670 T SdHO frequency, and not to the strong spin splitting proposed by other workers [12,13]. To test these assertions we have fitted data such as those shown in Fig. 4 using the LifshitzKosevich (LK) formula [S] in order to evaluate the carrier effective masses both above and below the “kink” field. Below the “kink” the fitting of the 670 T fundamental frequency is complicated by the presence of the second SdHO frequency _ 700-870 T, the amplitude of which has an anomalous temperature dependence. This results in a relatively large uncertainty in the effective mass determined, which lies in the range 2.02Sm,. However, the temperature dependence of the amplitude of the second harmonic at fields below the “kink” is much clearer, and may be fitted using the p = 2 term of the LK formula to reveai an effective mass of 2.40 + O.O5nz,. Above the “kink” the temperature dependence of the amplitude of the fundamental 670 T frequency yields a mass of 2.40 + 0.05~~~. It therefore appears that the effective mass associated with the FS pocket corresponding to the 670 T frequency is almost unchanged above and below the “kink”. In addition, the very strong second harmonic component seen below the “kink” also exhibits the same effective mass. The latter fact might support the proposal of Kartsovnik et al. [I41 that the second harmonic is due to a breakdown orbit of twice the area of the orbit corresponding to the 670 T frequency. Further information may be obtained by observing the MR as the sample is rotated in magnetic fields above and below the “kink” transition. The experiments were performed in a cryostat which allowed the sample’s axis of rotation to be itself tilted in the magnetic field. Typical data are shown in Fig. 5 for fixed fields of 20 T (below “kink”) and 24 T (above “kink”); the traces were obtained by setting the rotation axis (parallel to
the c axis of the crystal) at a fixed angle with respect to the fieId and then turning the sample about this axis through - 300” (the rotation angle). In this way, MR data are obtained in all four azimuthal angle quadrants; a disadvantage is that only a restricted range of azimuthal angles arc available. Several notable features are apparent in the data. Firstly, the MR oscillates, and shows minima which are found to be periodic in tan 0, but with a periodicity which is a very strong function of the azimuthal angle defining the plane of tilting of the magnetic field. This is especially notable when one compares data for rotation angles 0” to IgO”, corresponding to the azimuthal quadrants 90” I 4 2 180” and 270” I (b 2 360” with rotation angles 0” to - 180”, corresponding to quadrants 0” I 4 I 90 and 180” _< C$2 270”. The strong azimuthal angle dependence suggests that these oscillations are probably due to the presence of a QlD section of FS, rather than the 2D FS effect discussed above in the case of /I”Mechanisms for such oscillations (ET),AuBr,. have been proposed by several authors, invohing the velocities of electrons in a QlD band subjected to a magnetic field 1161. If the field is applied in a general direction, the velocity components perpendicular to the 1D direction sweep out all possible values. thus averaging to zero. However, if the field is oriented so that the electron’s k-vector is directed along a reciprocal lattice vector, the transverse velocity takes only a limited set of values determined by the electron’s initial position on the FS. Thus its time averaged velocity is non-zero, leading to dips in the MR periodic in tan(#). The period of these oscillations is determined by the projection of the plane of rotation of the magnetic field onto the 1D direction, and is proportional to l/cos(d -
M. Doporto et al. /Surface
determine the exact orientation of the QlD sections of the FS, the existing data do appear to indicate that there are no very drastic changes in band structure at the “kink” transition, and that similarly oriented QlD sections are present at all magnetic fields. This is supported by the similar carrier effective masses observed both above and below the “kink’. Thus, although some of our data give partial support to the band structure for a-(ET),KHg(SCN), proposed by Kartsovnik et al., much work remains to be done to clarify the mechanism responsible for the “kink” and the low temperature Fermi surface.
4. Note added in proof Recent measurements of the angle-dependent magnetoresistance in (u-(ET),KHg(SCN), have been carried out using fields up to 30 T. The data show conclusively that the high field “kink” represents a transition from a SDW groundstate, characterised by a quasi-one dimensional Fermi surface sheet tilted by N 21” with respect to the b*c plane, to a state with a cylindrical two-dimensional Fermi surface. The two states may be distinguished by the different character of the angle-dependent magnetoresistance oscillations observed above and below the “kink”. See “Magnetoresistance oscillations and field-induced Fermi surface changes in a-ET,KHg(NCS),“, J. Singleton, J. Caulfield, P.T.J. Hendriks, J.A.A.J. Perenboom, M.V. Kartsovnik, A.E. Kovalev, W.
Science 305 (1994) 187-193
193
Hayes, M. Kurmoo and P. Day, J. Phys.: Condensed Matter, submitted.
5. References [l] M. Kurmoo et al. Solid State Commun. 61 (1987) 459. 121 T. Mori, F. Sasaki, G. Saitoh and H. Inokuchi, Chem. Lett. (1986) 1037. [3] K. Kajita et al., Solid State Commun. 60 (1986) 811. 141 F.L. Pratt et al., Physica B 177 (1991) 333. I51 D. Shoenberg, Magnetic Oscillations in Metals (Cambridge University Press, Cambridge, 1984). 161 M. Doporto et al., Synth. Met., 56 (1993) 2572. [7] K. Yamaji, J. Phys. Sot. Jpn. 58 (1989) 1520. [8] M.V. Kartsovnik et al. J. Phys. I France 2 (1992) 89. [9] T. Ishiguro and K. Yamaji, Organic Superconductors (Springer, Berlin, 1990). [lo] H. Ito et. al., Solid State Commun. 85 (1993) 1005. [ill F.L. Pratt, J. Singleton, M. Doporto, T.J.B.M. Janssen, J.A.A.J. Perenboom, M. Kurmoo, W. Hayes and P. Day, Phys. Rev. B 45 (1992) 13904. 1121 J.S. Brooks et al., Phys. Rev. Lett. 69 (1992) 156. I131 T. Sasaki and N. Toyota, Solid State Commun. 82 (1992) 447. [14] M.V. Kartsovnik, A.E. Kovale and N.D. Kushch, J. Phys. I France, in press. [151 S.J. Klepper, J.S. Brooks, G.J. Athas, X. Chen, M. Tokumoto, N. Kinoshita and Y. Tanaka, Surf. Sci. 305 (1994) 181. [16] A.G. Lebed and P. Bak, Phys. Rev. Lett. 63 (1989) 315; G. Montambaux and P.B. Littlewood, Phys. Rev. Lett. 62 (1989) 953; V.M. Yakavenko, Phys. Rev. Lett. 68 (1992) 3607; M.J. Naughton, O.H. Chung, M. Chaparaba, X. Bu and P. Coppens, Phys. Rev. Lett. 67 (1991) 3712; T. Osada, S. Kagoshima and N. Miura, Phys. Rev. B 46 (1992) 1812.
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surface science
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ELSEVIER
Surface Science 305 (1994) 187-193
The influence of magnetic order in quasi-2D organic conductors M. Doporto *7a,J. Caulfield a, S. Hill a, J. Singleton a, F.L. Pratt a, M. Kurmoo b, P.J.T. Hendriks ‘, J.A.A.J. Perenboom ‘, W. Hayes a, P. Day b a Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK b Royal Institution, 21 Albemarle Street, London WIX 4BS, UK ’ High Field Magnet Laboratory, 6525 ED Nijtnegen, Netherlands (Received 4 May 1993; accepted for publication 4 June 1993)
Abstract We report extensive magnetoresistance (Y-(ET)~KH~(SCN)~. Our results indicate
(MR) measurements on the charge transfer salts /?“-(ET),AuBr, and that spin-density wave (SDW) groundstates in both of these materials
modify the Fermi surfaces calculated from room temperature crystal parameters. In the case of 0”-(ET),AuBr*, the shapes, sizes and orientations of three individual closed two-dimensional (2D) Fermi surface pockets have been deduced at 500 mK. The SDW groundstate in a-(ET),KHg(SCN), leads to the observation of a resistive “kink” made as a function of crystal orientation and temperature both above and transition at - 22 T. MR measurements below this “kink”, allow a qualitative assessment of the change in band structure at the “kink” to be made.
1. Introduction Many ET charge transfer salts have a Fermi surface (FS) consisting of a quasi-two dimensional (Q2D) hole pocket, plus a QlD electron section. The Q2D holes tend to dominate the low temperature conductivity of the salts, so that phenomena due to the QlD electrons, such as spindensity wave (SDW) formation (seen in, e.g. TMTSF charge-transfer salts, where the SDW leads to antiferromagnetic behaviour and a bandgap at the FS resulting in a metal-insulator transition), have been ignored by many workers. In this study, we report extensive magnetoresistance (MR) measurements on two metallic ET charge
* Corresponding author.
transfer salts, p”-(ET),AuBr, and a-(ET),KHg (SCN),, both of which exhibit low temperature SDW groundstates; the experiments show that the SDW leads to a modification of the simple Fermi surfaces deduced from band structure calculations.
2. Measurements
on /3”-(ET),AuBr,
The ET molecules in j?“-(ET>,AuBr, stack along the a crystal axis, forming conducting 2D sheets parallel to the UC plane, separated in the b direction by layers of linear AuBr; anions (see Ref. [l] and Fig. 3 below for definition of crystal axes). The j3” phase results in strong interactions between molecules in different stacks, so that p”-(ET>,AuBr, is less isotropic than many other
0039-6028/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI 0039-6028(93)E0695-Q
ii, ,,: i
,__.~_.I
tk:
Fig.
1. (a)
j”:(’ ~.
Magnetoresistance
!
!
..__._
ri
i
and h” for all field orientations. The mechanism responsible for frequency mixing is indicated by the strong hysteresis in magnitude and in the phase of the SdHO between up and down sweeps of the magnetic field which is observed below 1 K when the field is parallel to b” [4]. This is indicativc of strong internal magnetic fields leading to domain formation. in view of this, effects due to the Shoenberg magnetic interaction (MI) [5] between two or more carrier pockets must be considered. These introduce a magnetic feedback term due to the fact that the field experienced by the carriers is 8 =,uJH + Mf, where N is the external applied field and M is the magnetisation containing the oscillatory (de Haas-van Alphen) components. This is thought to be the first observation of such an effect in an organic conductor
.
.1
: . ...
I
I _/‘,:I
.. .
1 rr
1?
70
111
of /3”-(ET)2AuBr,
for
Bllb”
(upper
trace) and for B tilted 30” from b” about a’ towards c
(lower
trace).
toresistance
(b) The
oscillatory
component
of the magne-
for the lower trace in (a). tcf Fourier
transform
of
0~). ln all cases T = 0.5 K.
metallic ET salts. Reliable calculations of the transfer integrals and band structure have not yet been established, and those estimated by differcnt groups disagree [2,3]. Evidence for a complex low temperature SDW groundstate is observed in the resistance, which drops sharply at - 20 K, and from ESR measurements, which reveal a change in g-value at - 6 K [l]. Fig. la shows the MR of /3”-tET),AuBr, for two different angles between the magnetic field and the normal to the 2D conducting planes tb”); the MR is seen to depend strongly on the field direction. Fig. lb shows the oscillatory component of the MR; Shubnikov-de Haas oscillations (SdHO) of several different frequencies are present. Fourier analysis (Fig. Icl reveals four strong frequencies (40, 140, 180 and 220 T), together with different harmonic combinations. To progress further, it is necessary to identity which frequencies correspond to actual carrier pockets, and which are merely an artefact of frequency mixing, or a result of crystal twinning* The latter possibility may be ruied out, as the frequencies of all the SdHO are inversely proportional to the cosine of the angle between the magnetic field
[61. The observed SdHO may be partly simulated using two Fermi surface (FS) pockets with areas corresponding to frequencies B,, = 40 T and B,, = 180 T and combinations such as B,, i: B,, and 2 x B,,> rir B,,. Simulations using the MI between the B,, and R,, series are successful in accounting for the sidebands at 180 + 40 T and 360 i: 40 T (Fig. lc), as well as the disappearance of the 180 T series under certain conditions, but cannot reproduce the dominance of the 40 T and the 220 T frequencies over the 180 T SdHO at higher tilt angles [6]. At large angles, the only surviving second harmonic observed corresponds to the 220 T frequency. Therefore, this frequency (B,:,l must also correspond to a real carrier pocket and is not merely an artefact of mixing. Having established that the SdHO frequencies B,, = 40 T, BFZ = 180 T and B,, = 220 T correspond to real closed 2D sections of FS, we turn to the angle dependence of the SdHO amplitudes. Fig. 2 shows an example of this for B,,, N,, and 1y,, as the sample is rotated about the w and u axes; strong oscillations in the amplitude are seen as a function of tilt angle. Rotations about the 4’ and c axes also reveal osciIlations in the SdHO amplitudes. These angle-dependent oscillations in SdHO strength are due to a mechanism first proposed by Yamaji 171, who showed that when a magnetic field is applied at certain angles, all the semi-classical k-space closed orbits around a
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I. -90
0
-45 Tilt
45
90
angle
Fig. 2. Fourier amplitudes of the three series of SdFIO corresponding to real 2D FS carrier pockets, for tilting about the w and Y directions (T = 0.5 KL
warped cylindrical FS have approximately the same area. Therefore, at these angles, the density of states at the Fermi energy is enhanced, resulting in a maximum in the background MR, and in the amplitude of the SdHO. The theory was
developed by Kartsovnik et al. [$I, who considered materials in which the plane of warping can be inclined with respect to the conducting plane. The tilt angles 8 at which the maxima occur are given by bk,,/ tan @I= ~(i - $) *A(4), where b is the interplane spacing, k,, is the radius of the warped cylindrical Fermi surface at a point where the tangent to the surface is perpendicular to the plane of rotation of the magnetic field, i is an integer and C#Jis the azimuthal angle describing the plane of rotation of the field. The gradient of a plot of 1tan 0 / against i may therefore be used to find one of the dimensions of the FS, and if the process is repeated for several 4, the complete FS shape in the conducting plane may be mapped out. (A(#) is determined by the inchnation of the plane of warping with respect to the 2D plane, and will not be discussed here.) Having rotated samples about various axes in the ac plane (a, c, a’, e’, v and w>, the SdHO amplitudes of each pocket are then plotted against tan 8, where 0 is the angle between the magnetic field and b*. From these data, the shape of the 2D FS pockets can be reconstructed (see Figs. 3c-3e), and, since the areas of the pockets are known from the SdHO frequencies, the unit cell size in the interplane direction can be estimated. In most cases, only a couple of oscillation periods in tan 8 are observed, as the resolution of the data does not permit more rapid oscillations to be resolved. It should be noted that the observation of these “Yamaji’” oscillations in /3”(ET),AuBr, is not necessarily expected since the
B
JOT
I SOT
220T
Fig. 3. (a) shows the room temperature Brillouin zone and FS for j3YETfzAuBrz calculated by Mori et al. 121.(b) Proposed low temperature FS, with two extra closed FS pockets produced by a 2c SDW. Cc), Cd) and (e) show the shapes (thin lines show worst case) of the different FS pockets, deduced from rotations about 6 crystal axes.
carrier pockets are very small. However, from the data, it is apparent that the Brillouin zone (BZ) boundary in the interplane direction is 2-3 times smaller than the room temperature value (i.e. the unit cell is 2-3 times longer in this direction). In theory, this should not alter the SdHO spectra significantly, as long as the interplane warping remains small. This suggests that there is some interplane component in the SDW ordering. The shapes of the FS pockets deduced from the angle-dependent oscillations in the SdHO are shown in Figs. 3c-3e. The caIculated FS that most resembles the SdHO data on p”-(ET), AuBr,, is due to Mori, and has just one closed hole pocket of - 5% of the room temperature BZ area centred on the X point, together with a pair of open sections [2] (Fig. 3a). Although the closed section is a factor of 2 too large to correspond to the B,, SdHO series, it shouid be remembered that this is close to the top of the hole band, so that small adjustments of, e.g., the band overlaps could result in a large reduction in pocket area. However, the FS calculation has no obvious candidate for the B,, and B,, series. In view of the magnetic ground state of p”that the additional (ET), AuBr, , we propose SdHO frequencies are the result of closed pockets produced by a SDW modulation with a conduction plane component of 2c, driven by the nesting properties of the QlD part of the FS. The result of such a modulation wouId be to fold back sections of the calculated FS leading to a small hole pocket close to V, together with a larger anisotropic closed section of FS (electronlike) (Fig. 3b). The band filling is such that there should be equal numbers of ciectrons and holes, so that the total area of the two hole pockets should be the same as the area of the electron pocket. In this way, if we identity the two hole pockets with the SdHO series B,, and B,, (Figs. 3c and 3d), the SdHO due to the eIectron pocket should then occur at the sum of these frequencies, namely B,, = 220 T (Fig. 3e). A comparison of Figs. 3c-3e and Fig. 3b shows that there is reasonable qualitative agreement between the experimental FS shapes and orientations and those of the proposed SDW groundstate.
3. Measurements
on cx-(ET),KHg(SCN.J,
Charge-transfer salts of the form cu-(ET& MHg(SCN),, where M may be K, Tl, Rb or NH,, were first synthesised as possible superconducting modifications of K-(ET),Cu(SCN), [9]. However, only cr-(ET),NH,Hg(SCN), is a superconductor. having a T,= 1.1 K f9]; the others are metals down to - 100 mK [lo], and in addition exhibit the onset of antiferromagnetic order at - 8- 10 K. probably due to the onset of a SDW groundstate [ 1 l-131. The materials are isostructural, with identical predicted Fermi surfaces consisting of a rather isotropic Q2D closed hole pocket and a Q 1D open eiectron section (see inset to Fig. 4). Fig. 4 illustrates the magnetoresistance of N(ET),KHg(SCN), for a variety of temperatures; the most noticeable feature is the so-called “kink” transition visibie as a dramatic fall in resistance between 22 and 23 T. (Similar “kinks” have now been observed in tr-(ET),TlHg(SCN), at _ 22 T [14] and in (r-(ET&RbHg(SCN), at - 35 T IlSl, but arc absent in the case of cr-(ET)?NH, Hg(SCN),.) Above the “kink” a single series of SdHO with a frequency of 670 i: 15 T is observed; however, below the “kink”, the MR exhibits hysteresis [ll], and the SdHO contain a
Fig. 4. Magnetoresistance of a-(ET), KHg(SCN), for several temperatures. SdHO and the field induced resistive “kink” at - 22 T can clearly be seen. The inset shows the predicted room temperature Fermi surface.
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M. Doporto et al. /Surface Science305 (1994) 187-I 93
the “kink”. The “kink” would signal the destruction of the SDW state by the external field and the depopulation of the pocket would account for the fall in resistance. Others have noted that the complex behavior below the “kink” may be related to possible breakdown orbits between the open and closed sections of FS [15]. Recently, Kartsovnik et al. [14] have proposed a possible SDW groundstate for a-(ET),MHg (SCN), (M = K, Tl) with a nesting vector which leads to such a small FS pocket and a new 1D FS sheet inclined at N 26” to the 1D sheet shown in Fig. 4. In their scheme the SdHO with a fre-
prominent second harmonic component (see Fig. 4). In addition to the dominant SdHO series with a frequency of 670 _t 10 T, an apparent second series of SdHO, with a sample-dependent frequency between 700 and 870 T has also been observed at low fields [ll]. Several workers have linked these phenomena to the presence of the SDW groundstate [ll-131. It is thought that imperfect nesting in the SDW state could lead to the presence of an extra closed 2D carrier pocket in the Fermi surface (c.f. p”-(ET),AuBr, described above); the presence of this pocket would lead to the extra SdHO frequency at fields below
iO0
120 -
60
100 -
60
80 t
60
I
60
60 -
6C
-180
-120
-60 Angle
0
60
(degrees)
120
180
-180
-120
-60
Angle
0
60
120
180
(degrees)
Fig. 5. Magnetoresistance of a-(ET),KHg(SCN), at T = 1.5 K for fixed fields of 20 T (left-hand side) and 24 T (right-hand side) as a function of rotation angle (see text). The traces correspond to the following angles between the field and the rotation axis: left-hand side top to bottom 32”, 42” and 52”; right-hand side top to bottom 36”, 46” and 56”.
quency of N 670 T corresponds to a breakdown orbit between the small 2D FS pocket and the 1D sheet, whilst the 700-870 T series represents mixing between the 670 T frequency and SdHO due to simple orbits around the small pocket. Furthermore, the strong second harmonic observed below the ‘“kink” corresponds to a breakdown orbit of twice the area of that corresponding to the 670 T SdHO frequency, and not to the strong spin splitting proposed by other workers [12,13]. To test these assertions we have fitted data such as those shown in Fig. 4 using the LifshitzKosevich (LK) formula [S] in order to evaluate the carrier effective masses both above and below the “kink” field. Below the “kink” the fitting of the 670 T fundamental frequency is complicated by the presence of the second SdHO frequency _ 700-870 T, the amplitude of which has an anomalous temperature dependence. This results in a relatively large uncertainty in the effective mass determined, which lies in the range 2.02Sm,. However, the temperature dependence of the amplitude of the second harmonic at fields below the “kink” is much clearer, and may be fitted using the p = 2 term of the LK formula to reveai an effective mass of 2.40 + O.O5nz,. Above the “kink” the temperature dependence of the amplitude of the fundamental 670 T frequency yields a mass of 2.40 + 0.05~~~. It therefore appears that the effective mass associated with the FS pocket corresponding to the 670 T frequency is almost unchanged above and below the “kink”. In addition, the very strong second harmonic component seen below the “kink” also exhibits the same effective mass. The latter fact might support the proposal of Kartsovnik et al. [I41 that the second harmonic is due to a breakdown orbit of twice the area of the orbit corresponding to the 670 T frequency. Further information may be obtained by observing the MR as the sample is rotated in magnetic fields above and below the “kink” transition. The experiments were performed in a cryostat which allowed the sample’s axis of rotation to be itself tilted in the magnetic field. Typical data are shown in Fig. 5 for fixed fields of 20 T (below “kink”) and 24 T (above “kink”); the traces were obtained by setting the rotation axis (parallel to
the c axis of the crystal) at a fixed angle with respect to the fieId and then turning the sample about this axis through - 300” (the rotation angle). In this way, MR data are obtained in all four azimuthal angle quadrants; a disadvantage is that only a restricted range of azimuthal angles arc available. Several notable features are apparent in the data. Firstly, the MR oscillates, and shows minima which are found to be periodic in tan 0, but with a periodicity which is a very strong function of the azimuthal angle defining the plane of tilting of the magnetic field. This is especially notable when one compares data for rotation angles 0” to IgO”, corresponding to the azimuthal quadrants 90” I 4 2 180” and 270” I (b 2 360” with rotation angles 0” to - 180”, corresponding to quadrants 0” I 4 I 90 and 180” _< C$2 270”. The strong azimuthal angle dependence suggests that these oscillations are probably due to the presence of a QlD section of FS, rather than the 2D FS effect discussed above in the case of /I”Mechanisms for such oscillations (ET),AuBr,. have been proposed by several authors, invohing the velocities of electrons in a QlD band subjected to a magnetic field 1161. If the field is applied in a general direction, the velocity components perpendicular to the 1D direction sweep out all possible values. thus averaging to zero. However, if the field is oriented so that the electron’s k-vector is directed along a reciprocal lattice vector, the transverse velocity takes only a limited set of values determined by the electron’s initial position on the FS. Thus its time averaged velocity is non-zero, leading to dips in the MR periodic in tan(#). The period of these oscillations is determined by the projection of the plane of rotation of the magnetic field onto the 1D direction, and is proportional to l/cos(d -
M. Doporto et al. /Surface
determine the exact orientation of the QlD sections of the FS, the existing data do appear to indicate that there are no very drastic changes in band structure at the “kink” transition, and that similarly oriented QlD sections are present at all magnetic fields. This is supported by the similar carrier effective masses observed both above and below the “kink’. Thus, although some of our data give partial support to the band structure for a-(ET),KHg(SCN), proposed by Kartsovnik et al., much work remains to be done to clarify the mechanism responsible for the “kink” and the low temperature Fermi surface.
4. Note added in proof Recent measurements of the angle-dependent magnetoresistance in (u-(ET),KHg(SCN), have been carried out using fields up to 30 T. The data show conclusively that the high field “kink” represents a transition from a SDW groundstate, characterised by a quasi-one dimensional Fermi surface sheet tilted by N 21” with respect to the b*c plane, to a state with a cylindrical two-dimensional Fermi surface. The two states may be distinguished by the different character of the angle-dependent magnetoresistance oscillations observed above and below the “kink”. See “Magnetoresistance oscillations and field-induced Fermi surface changes in a-ET,KHg(NCS),“, J. Singleton, J. Caulfield, P.T.J. Hendriks, J.A.A.J. Perenboom, M.V. Kartsovnik, A.E. Kovalev, W.
Science 305 (1994) 187-193
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Hayes, M. Kurmoo and P. Day, J. Phys.: Condensed Matter, submitted.
5. References [l] M. Kurmoo et al. Solid State Commun. 61 (1987) 459. 121 T. Mori, F. Sasaki, G. Saitoh and H. Inokuchi, Chem. Lett. (1986) 1037. [3] K. Kajita et al., Solid State Commun. 60 (1986) 811. 141 F.L. Pratt et al., Physica B 177 (1991) 333. I51 D. Shoenberg, Magnetic Oscillations in Metals (Cambridge University Press, Cambridge, 1984). 161 M. Doporto et al., Synth. Met., 56 (1993) 2572. [7] K. Yamaji, J. Phys. Sot. Jpn. 58 (1989) 1520. [8] M.V. Kartsovnik et al. J. Phys. I France 2 (1992) 89. [9] T. Ishiguro and K. Yamaji, Organic Superconductors (Springer, Berlin, 1990). [lo] H. Ito et. al., Solid State Commun. 85 (1993) 1005. [ill F.L. Pratt, J. Singleton, M. Doporto, T.J.B.M. Janssen, J.A.A.J. Perenboom, M. Kurmoo, W. Hayes and P. Day, Phys. Rev. B 45 (1992) 13904. 1121 J.S. Brooks et al., Phys. Rev. Lett. 69 (1992) 156. I131 T. Sasaki and N. Toyota, Solid State Commun. 82 (1992) 447. [14] M.V. Kartsovnik, A.E. Kovale and N.D. Kushch, J. Phys. I France, in press. [151 S.J. Klepper, J.S. Brooks, G.J. Athas, X. Chen, M. Tokumoto, N. Kinoshita and Y. Tanaka, Surf. Sci. 305 (1994) 181. [16] A.G. Lebed and P. Bak, Phys. Rev. Lett. 63 (1989) 315; G. Montambaux and P.B. Littlewood, Phys. Rev. Lett. 62 (1989) 953; V.M. Yakavenko, Phys. Rev. Lett. 68 (1992) 3607; M.J. Naughton, O.H. Chung, M. Chaparaba, X. Bu and P. Coppens, Phys. Rev. Lett. 67 (1991) 3712; T. Osada, S. Kagoshima and N. Miura, Phys. Rev. B 46 (1992) 1812.