Semiclassical and non-classical angular effects of magnetoresistance in (TMTSF)2X

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Semiclassical and non-classical angular effects of magnetoresistance in (TMTSF),X Toshihito Osada*b, Nobuharu Kamiab, Ryusuke Kondo’, and Seiichi Kagoshimac Ynstitute for Solid State Physics, University of Tokyo, 7-22-I Roppongi, Minato-ku, Tokyo 106-8666, Japan bResearch CenterforAdvanced Science and Technology, University of Tokyo, 4-6-l Komaba, Megwo-ku, Tokyo 153-8904, Japan ‘Department ofBasic Science, University of Tokyo, 3-8-l Komaba, Megwo-ku, To&o 153-8902, Japan

Abstract We have studied the semiclassical and non-semiclassical behaviors of magnetoresistance (MR) in a quasi%n&imensiona1 (QID) conductor (TMTSF),ClO,. Based on the 3oltzmar111equation, we numerically investigated possible semiclassical “angular effects”, the characteristic patterns of the field-orientation-dependence of MR, iu the general QlD conductors. Particularly, we have clarifkd the complicated situation around B//lD-axis in which different angular effects are mixed up. The angular dependent MR features-b the metallic phase of (TMTSF),ClO, almost obey the semiclassical theory except a dip structure around B//b’. As for this non-semiclakical feature, we discuss the possibility of the one-body and many-body field-induced electron confinement onto a single conducting layer. Keywords: magnetotransport, organic conductors based on radical cation and/or anion salts

1. Introduction In the past several years, novel angular effects of magnetoresistance (MR) have been discovered in lowdimensional organic conductors. They are the characteristic structures which appear on the angular dependence of MR when the magnetic field orientation is rotated. Particularly, quasi-onedimensional (QlD) organic conductors such as (TMTSFJJ show rich angular effects. In addition to the three conventional angular effects, the “Lebed resonance”[l], the “Danner-Chaikin oscillations”[2], and the “third angular effect”[3], various angular effects have been reported[4]. The origins of these angular effects have not necessarily been established yet. Moreover, the fact that (TMTSF)J’F, shows anomalous angular dependence different from the others has attracted attention, and the possibility of a new electronic state has been discussed[5,6]. In the present study, we have tried to clarify the angular dependent features of MR in the QlD conductors, in other words, which effect can be explained by the conventional semiclassical magnetotransport picture, and which effect is essentially a new phenomenon. First, we have numerically surveyed all possible semiclassical angular effects originating from the Fermi surface topology. Then, we experimentally search for the non-classical features of MR by studying deviation from the numerical results, and discuss their possible origins. 2. Semiclassical Angular Effects of Magnetoresistance Firs4 based on the semiclassical magnetotransport theory, we carried out the numerical calculation of MR in the QlD 0379~6779/991$ - see front matter PII: SO379-6779(98)00289-6

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conductors with a pair of the sheetlike Fermi surfaces (FS’s). We employ the following tight-binding band model for the QlD conductor: E(k) = -2t, cos ak, - 21, cos bk, - 2t, ~0s ck, -E,.

(1)

Here, we take the x-axis and the q-plane for the lD-axis and the conducting plane, respectively; t>>tb>>tc. In the present calculations, we chose the band parameters so as to simulate (TMTSF)$lO,; 4t,:4t,:4t,=1000:100:3, a:b:c=3.5:7.1:13.6, and Ep=-J-%n (quarter ffiled). The semiclassical electron orbital motion obeys the following equation of motion: Al&(-e)vxB,

v = (‘/~~~(~>/~)

(2)

According to the semiclassical magnetotransport theory, the conductivity is calculated f?om the electron orbital motion by the kinetic form of the Boltzmann equation: (3) Here, the relaxation time z is assumed as a constant- (the relaxation time approximation). We can calculate the MR for given conditions by evaluating above formulas numerically. In the present calculations, we always assumed zero temperature. Figure 1 shows the calculated angular dependence of the interlayer resistivity p, when the magktic field orientat& is rotated in the p-plane (a), xz-plane (b), and v-plane (c). Several

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traces for different values of rM~2eBazt,2&z are shown, The Lebed resonances (a), the Danner-Chaikin oscillations (b), and the third angular effect (c) are clearly reproduced numerically. This fact means that these three angular effects are essentially semiclassical Fermi surface topological effects[3]. They relate to periodic orbits in the k-space, orbits with the width of n x2nfc (ninteger), and closed orbits, respectively. The resistance peak at B//x in Fig. l(b) is basically same effect of the third angular effect. It relates to closed orbits, too. (a) 0= 90 deg

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generalized Lebed resonances, where the electron orbit is periodic in the k-space. The blight diamond patterns correspond to the generalized Danner-Chaikin oscillation peaks. The blight horizontal bar in the center is the knife-edge-like resistance peak where the closed electron orbit exists. This is the generalized third angular effect. In this way, the three angular effects are mixed up generating the complicated angular dependence near the lD-axis.

(c)p=Ocieg

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Fig. 1. Calculated three angular effects of MR in the QlD conductor. Previously, we explained the Lebed resonance by the semiclassical picture employing the linearized band model[7]. This theory has not necessarily accepted since artificial interchair transfers appear in the linearized model. However, the presenl result clearly shows that the detail of the band model is not important. In contrast to the interlayer resistivity pm the in-planf interchain resistivity pm shows no clear angular effects. The 1D. axis resistivity p, has no magnetic field effect since the relaxation time approximation cannot lead MR in the 1D. direction Figure 2 shows the interlayer resistivity p, as a function 01 general field orientation. The field strength was fixed to ~~~50 (Bz;35O[T.ps]). In this diagram, the direction and the distance from the origin indicate the field orientation and the resistivity value, respectively. Rich angular effects are superposed on the moderate background angular dependence of interlayer resistivity p=. The three conventional angular effects are seen on theyz-, xz-, and xy-plane. Note that the semiclassical magnetotransport theory concludes that the interlayer resistivity pa takes the maximum value at B//y where the magnetic field is parallel to the current. Figure 2 contains the information of general angular effects for general field orientations. We can see that the Lebed resonances are the major angular effect in most field orientations except near the lD-axis (x-axis), Around the x-axis, p= shows complicated angular dependence, which becomes to the DannerChaikin oscillations and the third angular effect on the xz- and xyplane, respectively. To clarify this complicated behavior, we performed the detailed calculation for the field orientations around the lD-axis. Figure 3 shows the density plot of the angular dependence of p= near the ID-axis, where the brightness indicates the resistivity value. We can fmd the clear regularity in the apparently complicated behavior, The radiating dark lines are the

Fig.2. Angular dependence of interlayer resistivity as a function of the magnetic field orientation.

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Fig.3. Densityplot of interlayerresistivity for the magnetic field orientationsaroundthe ID-direction.

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Recently, the “out-of-plane effects”, in which the magnetic field is rotated with a fixed off-angle from the plane, have been studied, and various angular effects have been reported[4]. Naughton et al. observed complicated oscillations for the xyplane rotation with a fured off-plane angle. They claimed that the third angular effect does not vanish even at large off-plane angles where no closed orbit exists. The experiment by Nat&ton et al. is numerically simulated in Fig.4. Most of features are qualitatively reproduced well. The double minima of the third effect apparently seem to still remain at large off-plane angles. However, the resistance peak due to the third effect has already vanished at large off-plane angles. As mentioned above, most of the semiclassical angular dependent feature in the Q1D system can be interpreted as the mixture of the three angular effects. However, strictly to say, additional fine patterns which cannot be explained by the three effects exist in the field orientation where the off-plane angle is very small (]@Gdeg.)

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expectedto breakdown.Thisis a non-semiclassical but one-body effect Stronget al. theoreticallydiscussed the many-bodyeffect on the electronconfmement[5].Accordingto -theirtheory, the strong electroncorrelationeffectively reducesthe interlayer transfert, and enhancesthe field-inducedelectron-confinement.In this many-body confinement state, each conducting layer is decoupledinto 2D non-Fermiliquid incoherentwith eachother, and the resistanceis scaledby the magneticfield component normalto the 2D plane:

Stronget al. proposedtheir theory as an explanationfor the anomalousangulardependence of MR m (TMTSF);PF,, which does not obey the semiclassical theory[5]. Experimentaliyin (TMTSF)J’F,, it has been reported that I?, and & obey the scalinglaw andR, showsinsulatingtemperaturedependence in mostfield orientationsexceptthosearoundthe Lebedresonances [6]. In (TMTSF)J’F,, also the possibility of the field-induced superconductivityis experimentallydiscussed in the parallelfield contiguration[8]. We have experimentallystudiedan QID organicconductor (TMTSF),ClO,, a sistercompoundof (TMTSF)pF,, in orderto explore the non-semiclassical parallel field effect in the “standard”QlD conductorwhich showsthe semiclassical MR. The one-bodyconfinementfield B,,, are estimatedas 12.3Tfor (TMTSF),ClO,. Figure5 showsthe angulardependence of the interlayerMR whenthe field is rotatedin the planenormalto the lD-axis (yzplane rotation). Here, in the region la&led as “FISDW”, the electron systemis not in the normal metallic phasebut in the field-inducedspin-density-wave phase.In the normalphase,there appeara few Lebed resonances. We can seethat the angular dependence of MR in the normalphaseis almostsemiclassical in contrastto (TMTSF)zF,. Only oneexceptionis the dip structure aroundB//b’ (y-axis). This dip structurecannotbe explainedby the semiclassical picture sincethe interlayer MR shouldtake the maximumvalueat B//y asnotedbefore.

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Fig.4. Numerical simulation of the out-of-plane rotation experiment. 3. Parallel

Field Effect in (TMTSF),CIO,

Whenthe magneticfield is appliedparallelto they-axis, the semiclassical width of the z-componentof real spaceelectron orbits is given by 4t/v,+eB. Here, vP=nt&#i is the Fermi velocity. If the magnetic field becomeslarger than the “confinementfield” =AL, BCOrLf vFec

(4)

the width becomeslessthan the interlayerdistancec, sothat the electronmotion is effectively confiied in a single conduction layer &-plane). In this situation,the semiclassical treatmentof the electronkinetics,that is, the effective massapproximationis

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Angle P W-M Fig.5. Angular dependence of the intglayer MR in ~~ (‘IMlSF),CIO., whenthe magneticfield is rotated in the b’c*-plane.

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perfectly realizedin the presentcaseevenif it exists. It is considered that the electroncorrelationis lesseffective in (TMTSF),ClO., comparedto (TMTSF)$F, since these two compoundshave one-bodyconfinementfields of almostsame value.The field-inducedconfinementhasrecently beendiscussed alsoin an oxide QlD conductorYBa&u,O,[9].

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4. Acknowledgement This work wassupportedby the Torey ScienceFoundation.

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Fig.6. Scalingplot of the interlayerMR in (TMTSF),CIO, The confimement is one of the plausibleexplanationsfor the dip aroundB//b’. In (TMTSF),ClO,, the one-bodyconfinementis expectedunder the parallel field (B//b’) above B,,fll2T. The many-bodyeffect mightbe expectedin lower field. So, somesign of confinementis expectedto appeararoundB//b’ in the present experiment(maximumtield=12T). The confinementis consideredto leadthe decreasefrom the semiclassical MR, that is, a dip aroundB//y. According to the semiclassicalpicture, the interlayer MR R, has linear field dependence in parallelhigh fields(B//y), andshowsno saturation. It is consideredthat the contiiement suppresses the increaseof interlayerMR. Particularly in the many-bodyconfiiement state, R, losesB, dependence. In order to study the possibility of the many-body confmementstate,we testthe scalinglaw (5). Figure 6 showsthe plot of the interlayer MR vs. the normal field B, The parallel field B,,=Bcospis regardedas almostconstantduring eachfield rotation in dip region(]#lOdeg). The interlayer MR seemsto obey the BzM-law in the dip region. But it is not necessarily scaledby B, sincethe different rotationdata do not align on the singlecommonline. In other words,the MR still dependsonB,. This fact means that the many-body confinement is not

PI T.Osada,A.Kawasumi,SKagoshima,NMiura, and G.Saito,

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