content_image/430593.jpg content_image/430592.jpg
<img src='content_image/430593.jpg'>

tions of electrons for certain field directions on warped FSs [24, 25] and, thus, are field-independent. Peculiarly, the amplitude of observed oscillations decrease with in- creasing field above ∼ 8 T and disappear at higher fields. It turns out that the angular positions of the outer-most peaks (with respect to θ = 0 ◦ ), which are marked by ar- rows in Fig. 2, follow a simple geometrical law (inset of Fig. 2) related to the response of the 2D electrons resid- ing on the (2 ¯ 1 ¯ 1) plane perpendicular to the C 1 axis, as will be discussed later. Note that, because of the crys- tal symmetry, there are three equivalent C 1 axes in the plane perpendicular to the trigonal ( C 3 ) axis; hence, two of the three equivalent 2D FSs are at ± 30 ◦ to the rotation plane. The ρ$_{xx}$ ( θ ) measurements of the same sample in magnetic fields rotated within the trigonal-bisectrix ( C 3 - C 1 ) plane (not shown) reveal essentially similar angular dependences. 

In contrast to these “low-field’ oscillations, the “high- field” angular dependence of the transverse MR is devel- oping on a smooth field-dependent background coming from the anisotropy of ρ$_{xx}$ ( B ) along the different axes. An example of its fitting for B = 14 T is shown by the dashed line in Fig. 1(a). Because of a large MR back- ground in strong magnetic fields, only largest peaks in 

<img src='content_image/430592.jpg'>

ρ$_{xx}$ ( θ ) can be clearly seen in the raw data [Fig. 1(a)]. Subtracting the background would help to reveal smaller peaks, but it is not necessary, because the situation is much simpler in the Hall data as shown below. 

Figure 1(b) shows the ρ$_{yx}$ ( θ ) data, which also show pronounced angular-dependent oscillations at high fields. The “background ” for ρ$_{yx}$ ( θ ) is simply the angular de- pendence of the Hall effect, R$_{H}$B cos θ , where R$_{H}$ is the Hall coefficient. As can be clearly seen in Fig. 1(b), low- filed ρ$_{yx}$ ( θ ) data follow this expected angular dependence very closely (we use R$_{H}$ = − 37 cm $^{2}$/C, obtained from the Hall measurements), and the large deviation from this simple behavior is observed only in magnetic fields above 10 T. Figure 3 shows “pure” oscillations in Δ ρ$_{yx}$ ( θ ) af- ter subtracting the R$_{H}$B cos θ contribution from ρ$_{yx}$ ( θ ). One can clearly see a set of peaks, which are marked by short vertical ticks in Fig. 3. They are symmetric with respect to the C 3 axis and show a rather complicated magnetic-field dependence. 

To understand the origin of the observed angular- dependent oscillations, detailed knowledge of the FS is useful. We therefore measured the SdH oscillations on the present sample for a series of magnetic-field direc- tions in two high-symmetry planes, as shown in Fig. 4(a) for the C 3 - C 1 plane. Those SdH oscillations consist of three fundamental frequencies, which we call f 1 , f 2 , and f 3 . How these frequencies vary in the C 3 - C 1 plane is shown in Fig. 4(b), which is essentially consistent with what was observed with the dHvA oscillations [13] and indicates the presence of both 2D and 3D FSs. In the present sample, the radius of the circular 2D FS (given by f 1 ) is k$_{F}$ = 4.15 × 10 5 cm − 1 which is the same as in Ref. 13, while the 3D FS is somewhat smaller, the semi- axes of the three ellipsoidal 3D FSs (given by f 2 and 

