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[Taichi Terashima](https://orcid.org/0000-0001-9239-0621), [Shinya Uji](https://orcid.org/0000-0001-9351-6388), [Hiroaki Ikeda](https://orcid.org/0000-0002-9258-9478), [Yuji Matsuda](https://orcid.org/0000-0001-9947-9418), [Takasada Shibauchi](https://orcid.org/0000-0001-5831-4924), [Shigeru Kasahara](https://orcid.org/0000-0002-6007-9617)

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[In-plane and Interlayer Magnetoresistances in FeSe](https://mdr.nims.go.jp/datasets/52a9444b-1927-4428-a117-34eb5aa0bd15)

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ver4p2In-plane and Interlayer Magnetoresistances in FeSeTaichi Terashima,1, ∗ Shinya Uji,1 Hiroaki Ikeda,2 YujiMatsuda,3, † Takasada Shibauchi,4 and Shigeru Kasahara5, ‡1Research Center for Materials Nanoarchitectonics (MANA),National Institute for Materials Science, Tsukuba 305-0003, Japan2Department of Physics, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan3Department of Physics, Kyoto University, Kyoto 606-8502, Japan4Department of Advanced Materials Science,University of Tokyo, Kashiwa, Chiba 277-8561, Japan5Research Institute for Interdisciplinary Science,Okayama University, Okayama 700-8530, Japan(Dated: September 11, 2025)AbstractWe report measurements of the in-plane and interlayer magnetoresistances of FeSe. The in-plane magnetoresistance ∆ρab/ρab(0) for B ‖ c is positive below Ts and increases with decreasingtemperature, exceeding 2.5 at T = 10 K andB = 14 T. The field-direction dependence indicates thatthe in-plane magnetoresistance is basically determined by the c-axis component of the magneticfield. The interlayer magnetoresistance ∆ρc/ρc(0) is negative below Ts but turns positive below∼18 K, which is probably due to the contamination by the large in-plane magnetoresistance. Thefield-direction dependence of the interlayer magnetoresistance can approximately be described by astandard formula for quasi-two-dimensional electron systems except near B ‖ ab. The experimentalmagnetoresistance near B ‖ ab is larger than the formula, which can be attributed to the so-calledinterlayer coherence peak. The large width of the peak indicates the correspondingly large interlayertransfer energy.11. IntroductionMagnetoresistance measurements have a long history as a technique for studying theelectronic state of metals1 and are still actively used today. In such measurements, themutual orientation of electrical current and magnetic field is important. By measuringmagnetoresistance as a function of magnetic field orientation, one can investigate the detailsof the Fermi surface. In a well-known example, the direction of open orbits can be determinedby such a measurement. In this study, we measure the magnetoresistance effects on the in-plane and interlayer resistivites of the iron-based superconductor FeSe with varying magneticfield directions, and we reveal the quasi-two-dimensional nature of the electronic structureof FeSe.FeSe is an intriguing iron-based superconductor parent compound.2 Unlike typical parentcompounds, FeSe exhibits a structural phase transition associated with electronic nematicordering at Ts ∼ 90 K, but not antiferromagnetic ordering. Furthermore, it becomes super-conducting below Tc ∼ 9 K. It is argued that this superconductivity is close to the BCS–BEC (Bardeen–Cooper–Schrieffer–Bose–Einstein condensate) cross-over regime.3 Quantumoscillation4–6 and angle-resolved photoemission spectroscopy studies6–10 have shown that theelectronic structure in the electronic nematic phase differs significantly from that predictedby density functional theory. The Fermi surface calculated by the density functional the-ory includes three hole cylinders and two electron cylinders, but the experimental studiesindicate that there are only one hole and one electron cylinder.4,11 The failure of the the-ory renders the experimental characterization of the electronic structure in FeSe vital. Inthis study, we confirm that the Fermi surface in the nematic phase consists of quasi-two-dimensional modulated cylinders by analyzing the magnetic-field direction dependence ofmagnetoresistance.2. Experimental Results and DiscussionHigh-quality single crystals of FeSe were grown by a chemical vapor transport method.12Electrical contacts were spot-welded and reinforced with conducting silver paint. A currentcontact and a voltage contact were attached to each (001) plane of a sample for interlayerresistivity measurements, whereas four contacts were attached to the same (001) plane for20.40.30.20.10.0ρ ab (mΩ cm)250200150100500T (K)I // ab B = 0 B = 14 T // ab B = 14 T // cIB // abB // c2.52.01.51.00.50.0Δρ ab / ρab(0)12080400T (K)FIG. 1. (Color online) Temperature dependence of in-plane resistivity ρab in FeSe sample 1 (0.64×0.8 × 0.02 mm3). The data for B = 0 and B = 14 T applied parallel to the ab plane and alongthe c axis are shown. The left inset shows the geometry of the current I and the magnetic field Bschematically. The in-plane field is approximately at a 50◦ angle from the current. The right insetshows the in-plane magnetoresistance ∆ρab/ρab(0) at B = 14 T for B ‖ ab and B ‖ c.in-plane resistivity measurements as usual. Because samples were not detwinned, they weretwinned below Ts, which basically obscured in-plane anisotropy arising from the orthorhom-bicity in the nematic phase. Samples were mounted on a two-axis rotation platform toenable the control of both the polar θ and azimuthal φ angles of the magnetic field. Resis-tivity measurements were performed in a 17-T superconducting magnet and a 4He variabletemperature insert.We begin with in-plane resistivity. Figure 1 shows the temperature dependence of the in-plane resistivity in sample 1 at zero field and at a field of 14 T applied along the ab plane andthe c axis. The current was parallel to the tetragonal [100] direction. The ab-plane field wasat an angle of about 50◦ to the current [φ = -15◦ in Fig. 2(b)]. Although this configuration isneither a transverse one nor a longitudinal one, the in-plane angle between the current andthe field is not very important, as we will see in Fig. 2(b). The measurements under magneticfield were performed at both the positive field (B = 14 T) and the negative field (B = −14T), and the measured voltages were symmetrized, i.e., Vsym = [V (14 T) + V (−14 T)]/2,to remove the contamination by the Hall voltage, although the contamination was foundto be negligibly small, as we will see in Fig. 2(a). The right inset of Fig. 1 shows themagnetoresistance ∆ρab/ρab(0), where ∆ρab is the difference between the resistivity at B =30.60.40.20.0Δρ ab / ρab(0)-10 -5 0 5 10B (T)I // ab B // c, T = 30 K fit to αBn0.60.40.20.0Δρ ab / ρab(0)-90 -60 -30 0 30 60 90θ (deg)φ = 90 to -75° in steps of 15°  α(Bcosθ)nI // abT = 30 K,  B = 14 T(a)(b)FIG. 2. (Color online) Magnetoresistance effects on in-plane resistivity in FeSe sample 1. (a)In-plane magnetoresistance ∆ρab/ρab(0) as a function of magnetic field along the c axis measuredat T = 30 K. A fit to αBn (broken line) gives α = 0.01433(2) and n = 1.512(1). (b) In-planemagnetoresistance at T = 30 K and B = 14 T as a function of θ, which is the polar angle of themagnetic field direction measured from the c axis. The azimuth angle φ specifies the rotation planeof the magnetic field and was varied from φ = 90 to -75◦ in steps of 15◦. The broken line showsα(B cos θ)n with the same values of α and n as in (a). The inset explains the field angles θ and φ.The origin of φ is defined with respect to the sample holder, not to a crystal axis.0 and 14 T and ρab(0) the resistivity at B = 0. The magnetoresistance is almost negligibleabove Ts (= 89.0 K for this sample) for both field directions, B ‖ ab and B ‖ c. For B ‖ c,the magnetoresistance increases rapidly with decreasing temperature below Ts, exceeding2.5 at T = 10 K. For B ‖ ab, the magnetoresistance is small even below Ts, being 0.15 at T= 10 K. The observed behavior is qualitatively consistent with those described in previousreports,13,14 although the magnitude of the magnetoresistance for B ‖ c is larger in the4present case.Figure 2(a) shows the magnetic field dependence of the in-plane magnetoresistance forB ‖ c measured at T = 30 K. The nearly perfect symmetry of the data with respect toB = 0 confirms that the Hall-voltage contamination is negligible. A fit to αBn (brokenline) gives n = 1.512(1). Although this exponent is smaller than n = 2 expected from asimple two-carrier model of compensated metals, a similar subquadratic magnetoresistanceis often observed in nominally compensated semimetals. On the basis of a detailed analysisof magnetoresistance in a compensated semimetal antimony, it has been argued in Ref. 15that the subquadratic magnetoresistance can be attributed to imperfect compensation andfield-dependent mobility.The magnitude and field dependences of the in-plane magnetoresistance are broadly con-sistent with our previous reports.16,17 It has been reported previously that the magnetore-sistance of FeSe does not follow Kohler’s rule,17,18 but in this study, we do not discuss thispoint owing to insufficient data collected on the matterFigure 2(b) shows the θ dependence of the magnetoresistance at B = 14 T and T = 30K, where the polar angle θ of the field direction was measured from the c axis. The rotationplane of the magnetic field was specified by the azimuth angle φ, and φ = 35◦ approximatelycorresponds to the tetragonal (010) plane, which is parallel to the current. Figure 2(b) showsthe data obtained for different φ values together, and they overlap each other. The brokenline shows α(B cos θ)n calculated with the same values of α and n as those in Fig. 2(a).It matches the experimental curves. This indicates that the in-plane magnetoresistance isbasically determined by the c-axis component of the magnetic field (B cos θ), as expectedfor quasi-two-dimensional electron systems. In Appendix A, we show the data presented inFigs. 2(a) and 2(b) together as a function of B cos θ.We now switch to interlayer resistivity. Figure 3(a) shows the temperature dependenceof interlayer resistivity in sample 2 at zero field and at B = 14 T parallel to the c axis.For B = 14 T, symmetrized data are shown. A schematic of the contact arrangement isshown in the upper left inset. The interlayer resistivity exhibits a maximum near 230 K,which is consistent with a previous report by Amigó et al.,14 but note that the presentpeak temperature Tmax = 233 K is slightly higher than 229 K reported in Ref. 14. Thelower right inset shows the interlayer magnetoresistance ∆ρc/ρc(0) at B = 14 T parallel toc, which becomes negative below Ts, showing a negative peak at around 35 K, and turns543210ρ c (mΩ cm)300250200150100500T (K)I // c B = 0 B = 14 T // cI+I- V-V+0.060.040.020.00-0.02-0.04Δρ c / ρ c(0)12080400T (K)0.080.060.040.020.00Δρ c / ρ c(0)14121086420B (T)T = 10 KI // c,  B // c (a)(b)cFIG. 3. (Color online) Temperature and magnetic-field dependences of interlayer resistivity in FeSesample 2 (1.02× 0.6× 0.135 mm3). (a) Temperature dependence of interlayer resistivity measuredat B = 0 and 14 T applied parallel to the c axis. The lower right inset shows the interlayermagnetoresistance ∆ρc/ρc(0) at B = 14 T parallel to c. The upper left inset is a schematic of thecontact arrangement. (b) Interlayer magnetoresistance as a function of magnetic field along the caxis measured at T = 10 K.positive below ∼18 K. The magnitude of the interlayer magnetoresistance is much smallerthan that of the in-plane one. Figure 3(b) shows the interlayer magnetoresistance ∆ρc/ρc(0)at T = 10 K as a function of the field applied along the c axis. Although it is positive atlow fields, a negative component appears above about 8 T.Amigó et al.14 reported that the interlayer magnetoresistance for B ‖ c was negative be-low Ts down to Tc. The positive magnetoresistance that we observed below ∼18 K probablyindicates that our measurements were contaminated by in-plane resistivity. An experimentalinterlayer resistivity may be contaminated by in-plane resistivity: for example, if cleavage60.40.30.20.1Δρ c / ρ c(0)-90 -60 -30 0 30 60 90θ (deg)-404d2(MR)/dθ2 (10-3)I // cT = 10 K, B = 14 Tφ = 0, 45, 90° calc.25°FIG. 4. (Color online) Interlayer magnetoresistance in FeSe sample 2 at T = 10 K and B = 14 Tas a function of the field angle θ. The upper curves are the corresponding second derivatives withrespect to θ [MR means ∆ρc/ρc(0)]. Three field rotation planes φ = 0, 45, and 90◦ were used. Thebroken line was calculated using Eq. (1) with ckF = 0.5 and ω0τ = 1.5.occurs inside a crystal, the electrical current has to flow along the in-plane direction toavoid the cleavage, which makes the measured voltages contaminated by an in-plane re-sistivity component. Amigó et al. pointed out that the peak temperature Tmax was agood measure of the contamination by in-plane resistivity.14 Because the in-plane resistivityincreases monotonically in a temperature range near Tmax, the apparent Tmax shifts to ahigher temperature as the contamination by in-plane resistivity increases. Because the in-plane magnetoresistance for B ‖ c is positive and large, especially at low temperatures (Fig.1), the apparent interlayer magnetoresistance becomes positive as the amount of contami-nation increases. The fact that the present Tmax = 233 K is larger than 229 K in Ref. 14suggests that our measurements were slightly more contaminated by the in-plane resistivitycomponent, which explains the present observation of the positive interlayer magnetoresis-tance for B ‖ c at low temperatures. In Appendix B, we show the results of ‘interlayerresistivity’ measurements on other samples, in which Tmax is still higher, and the interlayermagnetoresistance for B ‖ c appears positive and large because of the in-plane resistivitycontamination.Figure 4 shows the interlayer magnetoresistance at B = 14 T and T = 10 K as a functionof the polar angle θ of the field direction. The data are symmetrized with respect to θ7= 0. Three field-rotation planes, φ = 0, 45, and 90◦, were used, where φ = 45◦ approxi-mately corresponds to the tetragonal (100) plane. Although the three curves do not matchperfectly, which may partly be ascribed to the misalignment of the sample, the interlayermagnetoresistance is almost independent of φ. This is not surprising because the samplewas not detwinned. The field-angle dependence is quite different from that of the in-planemagnetoresistance in Fig. 2(b). The magnetoresistance is the largest at θ = ±90◦, wherethe field is perpendicular to the current. This is reasonable because the transverse magne-toresistance (B⊥I ‖ c) is usually larger than the longitudinal one (B ‖ I ‖ c). There is afinite magnetoresistance ∆ρc/ρc(0) = 0.065 at θ = 0, which might indicate a slight contam-ination by in-plane resistivity. However, the magnitude is much smaller than that observedin the in-plane resistivity measurements shown in Fig. 1, the right inset of which indicatesthat the in-plane magnetoresistance amounts to 2.6 at T = 10 K. The considerably smallermagnitude warrants that the contamination by in-plane resistivity is limited and that thefield-angle dependence in Fig. 4 captures that of the interlayer magnetoresistance withsufficient accuracy.For a quasi-two-dimensional metal with a weak c-axis energy dispersion of the formcos(ckz), the interlayer conductivity under magnetic field (except near θ = ±90◦) is givenby19σzz = σ0zz[J20 (ckF tan θ) +∞∑ν=12J2ν (ckF tan θ)1 + (ω0τν cos θ)2], (1)where σ0zz is the interlayer conductivity at zero magnetic field, Jν the ν-th order Besselfunction, kF the in-plane Fermi wave vector, ω0 = e/Bm∗ the cyclotron frequency for θ= 0, m∗ the effective mass, and τ the relaxation time.20 The quantum-oscillation data inRef. 4 indicate that ckF = 0.47 and 0.60 for two Fermi cylinders of FeSe (i.e., electronand hole). Accordingly, we set ckF = 0.5 and calculated the interlayer magnetoresistance∆ρc/ρc(0) = σ0zz/σzz−1 at various ω0τ values. The broken line in Fig. 4 was calculated withω0τ = 1.5. Because Eq. (1) gives ∆ρc/ρc(0) = 0 at θ = 0, we added a constant shift of 0.065so that the calculated curve and the experimental result match at θ = 0. The calculatedcurve reproduces the experimental result reasonably well except near θ = ±90◦. In Ref. 4,the mean free path of carriers was estimated for two quantum-oscillation frequencies, whichcorresponds to ω0τ = 0.8 and 1.2 at B = 14 T. Hence, the above assumption of ω0τ = 1.5is reasonable.8The experimental magnetoresistance near θ = ±90◦ is distinctly larger than the calcu-lated one. The enhancement of resistance becomes more evident in the second derivatives(upper curves). This is due to a so-called interlayer coherence peak. The approximationsused to derive Eq. (1) do not hold near θ = ±90◦, i.e., B ‖ ab, where the magnetoresis-tance is enhanced over Eq. (1) and peaks at θ = ±90◦ because of small closed orbits21or self-crossing orbits22 formed on the sides of quasi-two-dimensional Fermi cylinders. Theappearance of such a peak is an indication of coherent interlayer transport, and hence, thepeak was called the interlayer coherence peak. The width of the peak can be related tothe magnitude of the interlayer transfer energy tc. For a single Fermi cylinder withoutin-plane anisotropy and with a c-axis dispersion of the form cos(ckz), the relation is de-scribed by δθ ≈ 2ckF tc/EF .21 The interlayer coherence peak was initially found in organicconductors,23 but was also observed in the iron-based superconductor (parent) materialsKFe2As224 and CaFeAsF.25 In the present case, the width of the coherence peak, estimatedfrom the second derivatives (upper curves in Fig. 4), is about δθ ∼ 25◦. If we apply theabove relation to this width, we obtain tc/EF ≈ 0.4. However, this estimate should notbe taken literally because the Fermi-surface model used to derive the relation is very muchsimplified, as described above. Nonetheless the large magnitude of the interlayer transfer isreasonable because previous quantum-oscillation measurements indicated that the minimumand maximum cross-sectional areas of the Fermi cylinders considerably differ.4The field-angle dependence of the interlayer magnetoresistance in FeSe and KFe2As2 isnormal in the sense that the interlayer magnetoresistance is the smallest when B ‖ c, asexpected from Eq. (1).24 On the other hand, it is unusual in CaFeAsF in that the interlayermagnetoresistance is the largest when B ‖ c, although the observed behavior was reproducedby a detailed calculation based on a first-principles electronic band structure.25 The distinctbehavior may be related to the fact that the electronic structure in CaFeAsF is much moretwo-dimensional than those in FeSe and KFe2As2.25In summary, we studied the in-plane and interlayer magnetoresistances in FeSe. Thein-plane magnetoresistance ∆ρab/ρab(0) for B ‖ c was positive below Ts and increased withdecreasing temperature. It exceeded 2.5 at T = 10 K and B = 14 T for the present sample.Its dependence on the field direction indicated that it was basically determined by the c-axiscomponent of the magnetic field, as is expected for quasi-two-dimensional electron systems.The interlayer magnetoresistance ∆ρc/ρc(0) at B = 14 T was initially negative below Ts9but turned positive below ∼18 K, which is probably due to the contamination by the largein-plane magnetoresistance. The field-angle dependence of the interlayer magnetoresistancewas reasonably well described by a standard formula for quasi-two-dimensional electron sys-tems [Eq. (1)] with reasonable parameters ckF = 0.5 and ω0τ = 1.5 except near B ‖ ab. Theexperimental magnetoresistance near B ‖ ab was larger than the magnetoresistance calcu-lated with Eq. (1), which was attributed to the interlayer coherence peak. The large widthof the peak indicated the correspondingly large interlayer transfer, which is in agreementwith previous quantum-oscillation results.4ACKNOWLEDGMENTSThis work was supported by Grants-in-Aid for Scientific Research on Innovative Areas“Quantum Liquid Crystals” (Nos. JP19H05824 and JP22H04485), Grants-in-Aid for Sci-entific Research(A) (Nos. JP21H04443, JP22H00105, and JP23H00089), a Grant-in-Aidfor Scientific Research(B) (No. JP22H01173), a Grant-in-Aid for Scientific Research(C)(No. JP22K03537), and the Fund for the Promotion of Joint International Research (No.JP22KK0036) from Japan Society for the Promotion of Science. MANA is supported byWorld Premier International Research Center Initiative (WPI), MEXT, Japan.Appendix A: B cos θ DependenceFigure A1 shows the data presented in Figs. 2(a) and 2(b) as a function of B cos θ.All the curves roughly coincide, indicating that the in-plane magnetoresistance is mostlydetermined by the c-axis component of the magnetic field.Appendix B: Interlayer Resistivity Contaminated by In-Plane ResistivityFigure B1 shows the results of ‘interlayer resistivity’ measurements on sample 3. Themeasurements were markedly contaminated by in-plane resistivity, as explained below. Theresistivity versus temperature curve [Fig. B1(a)] shows a broad maximum at around Tmax ∼280 K, which is much higher than 233 K in Fig. 3. The magnitude of the resistivity ismuch larger than that in Fig. 3, suggesting the occurrence of an internal cleavage. The100.60.40.20.0Δρ ab / ρab(0)1050-5-10Bcosθ (T)I // ab, T = 30 K Data in Fig. 2(a) Data in Fig. 2(b) FIG. A 1. (Color online) In-plane magnetoresistance in FeSe sample 2 as a function of B cos θ.The data in Figs. 2(a) and 2(b) are plotted as a function of B cos θ, the c-axis component of theapplied field.2520151050ρ c (mΩ cm)300250200150100500T (K)"I // c" B = 0 B = 14 T // c0.80.60.40.20.0Δρ c / ρ c(0)12010080604020T (K)0.80.60.40.20.0Δρ c / ρ c(0)14121086420B (T)"I // c" B // c,  T = 10 K fit(a)(b) 0.50.40.30.20.1Δρ c / ρ c(0)-90 -60 -30 0 30 60 90θ (deg)"I // c"T = 20 K, B = 14 Tφ = 90, 45, 0° fit (c)FIG. B 1. (Color online) Interlayer resistivity contaminated by in-plane resistivity in FeSe sample 3(0.75×0.68×0.08 mm3). (a) ‘Interlayer resistivity’ versus temperature at B = 0 and 14 T appliedparallel to the c axis. The inset shows the corresponding magnetoresistance. (b) Magnetoresistanceat T = 10 K as a function of the magnetic field parallel to c. A fit to αBn (broken line) gives α =0.03052(4) and n = 1.2478(5). (c) Magnetoresistance at T = 20 K and B = 14 T as a function ofthe field angle θ. Three field rotation planes φ = 0, 45, and 90◦ were used. A fit to α(cosB)n + c(broken line) gives α = 0.470(1), n = 1.335(7), and c = 0.036(1).11151050ρ c (mΩ cm)300250200150100500T (K)"I // c"0.30.20.1Δρ c / ρ c(0)-90 -60 -30 0 30 60 90θ (deg)"I // c"T = 8 K, B = 14 Tφ = 90, 45, 0, -45°    (a) (b)FIG. B 2. (Color online) Interlayer resistivity contaminated by in-plane resistivity in FeSe sample4 (1.1× 0.64× 0.24 mm3). (a) ‘Interlayer resistivity’ versus temperature at B = 0. (b) Magnetore-sistance at T = 8 K and B = 14 T as a function of the field angle θ. Three field rotation planes φ= -45, 0, 45, and 90◦ were used.magnetoresistance for B ‖ c is positive and large below Ts down to Tc (inset), similar tothe in-plane magnetoresistance in Fig. 1. Figure B1(b) shows the magnetoresistance versusmagnetic field curve measured at T = 10 K, which can be fitted to αBn with α = 0.03052(4)and n = 1.2478(5), similar to the in-plane magnetoresistance in Fig. 2(a), although theexponent n is slightly smaller. Figure B1(c) shows the magnetoresistance at T = 20 Kand B = 14 T as a function of θ. Note that this field-angle dependence is unusual for theinterlayer magnetoresistance in that the longitudinal magnetoresistance at θ = 0 is muchlarger than the transverse one at θ = ±90◦. The broken curve is a fit to α(B cos θ)n+ c withα = 0.470(1) and n = 1.335(7). The exponent n is slightly different from the above valueprobably because of the temperature difference but is close enough, confirming that themagnetoresistance is mostly dominated by the c-axis component of the magnetic field as thein-plane magnetoresistance is. A close examination of the fit near θ = ±90◦ indicates thatthe experimental magnetoresistance is slightly larger than the fit, indicating a contributionfrom an interlayer coherence peak.Figure B2 shows results of ‘interlayer resistivity’ measurements on sample 4. The resistiv-ity maximum is located at Tmax = 263 K [Fig. B2(a)], which is in between the Tmax valuesin samples 2 and 3 (Figs. 3 and B1). The resistivity is not as high as that in sample 3 [Figs.B2(a) and B1(a)], indicating that the internal cleavage is not so serious. The field-angledependence of magnetoresistance [Fig. B2(b)] is qualitatively the same as that in sample 3[Fig. B1(c)], but the magnitude is smaller (note the temperature difference between T = 8K [Fig. B2(b)] and 20 K [Fig. B1(c)]).12In some previous papers on interlayer conductivity in layered materials, it is argued thatthe anomalous field-angle dependence of the interlayer magnetoresistance, like those in Figs.B1(c) and B2(b), originates from incoherent conduction along the interlayer direction.26,27In the present case, however, the clear correlation between the value of Tmax and the behav-ior of the apparent interlayer magnetoresistance strongly suggests that the anomalous angledependence in Figs. B1(c) and B2(b) is due to the contamination by in-plane resistivity.This is further corroborated by the following observations: First, as the temperature de-pendence of the apparent interlayer resistivity approaches the normal metallic conduction,i.e., dρ/dT > 0 at all temperatures, in the order of samples 2, 4, and 3 [Figs. 3(a), B2(a),and B1(a), respectively], the interlayer magnetoresistance becomes more anomalous [Figs.4, B2(b), and B1(c)]. Secondly, when the interlayer magnetoresistance is anomalous, itsfield and angle dependence is described well by (B cos θ)n with the exponent n close to thatfound for the in-plane magnetoresistance [Figs. B1(b) and (c)]. 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