Experimental Studies of Magnetoresistance Tensor Components in Bismuth at Low Temperatures

Abstract

The monotonic and oscillating parts of the magnetoresistance tensor components are studied on a pure single crystals of bismuth. The nondiagonal-to-diagonal components ratio is shown to be sufficiently small a t helium tcmperatures, so that ozz = l/ezz with a high degree of accuracy, and thus the experimental deviations from the law ezz = aHn (m = 2 for u,t > 1) are independent of the electron-hole compensation disturbance in Bi.Within the framework of the ellipsoidal parabolic model taking account of the relaxation time anisotropy, the mobility tensor components at helium temperatures are found whose values coincide with data obtained by other authors in weak (uC.< 1) magnetic fields. It has been revealed that for magnetic field directions H near twinning planes the sign of an even constituent of the nondiagonal magnetoresistance tensor components becomes opposite t o t h a t for samples with no twinning interlayer. The twinning plane effect is essential up to 70 OK. It is also found that a t helium temperatures the even constituent eyz(H) changes its sign in high magnetic fields (10 kOe) near H 11 C,. It is shown that the transition in the H 11 C, direction under H rotation in the bisectrix plane causes the oscillation phase of the even constituent evz t o change. It is found that in the preultraquantum region of the magnetic fields the oscillating part of eyD turns out to be greater at certain H directions than the monotonic one.Die monotonen und oszillierenden Anteile der Tensorkomponenten der Magnetowiderstandsanderung werden an einem reinen Wismuth-Einkristall untersucht. Es wird gezeigt, daB das Verhaltnis der nichtdiagonalen zu den diagonalen Komponenten bei Heliumtemperaturen genugend klein ist, so daB ozD = l/ezz mit hoher Genauigkeit ist und somit sind die experimentellen Abweichungen vom Gesetz ezz = nHn ( n = 2 fur uCt 3 1) unabhangig von der Storung der Elektronen-Loch-Kompensation in Bi. I m Rahmen des parabolischen Ellipsoidmodells bei Berucksichtigung der Anisotropie der Relaxationszeit werden die Komponenten des Beweglichkeitstensors bei Heliumtemperatur gefunden, deren Werte mit den Werten anderer Autoren in schwachen Magnetfeldern (uCt < 1) ubereinstimmen.Es wird gefunden, daB fur Magnetfeldrichtungen H in der Nahe von Zwillingsebenen das Vorzeichen eines geraden Bestandteils einer nichtdiagonalen Tensorkomponente der Magnetowiderstandsanderung umgekehrt wird im Vergleich zu Proben ohne Zwillingszwischenflachen. Der EinfluB der Zwillingsebenen ist bis zu 70 O K wesentlich. Es wird auch gefunden, daB bei Heliumtemperaturen der gerade Bestandteil eyD(H) sein Vorzeichen in hohen Magnetfeldern (10 KOe) bei H 11 C, andert. Es wird gezeigt, daB der tfbergang in die H I I C,-Richtung bei H-Rotation in der Bisectrixebene eine Anderung der Schwingungsphase des geraden Bestandteils ell% verursacht. I m Pre-Ultraquantenbereich der Magnetfelder wird gefunden, daB der oszillierende Anteil von evZ bei bestimmten H-Richtungen groBer als der monotone Anteil ist.

Oscillations of the Hall Resistivity in Natural Single Crystals of Pyrrhotite Associated with the Orientation of the Elementary Magnetic Moments of Fe Atoms

“…The so called high temperature oscillations (HTO) appeared on high purity single crystals of Bi as well as on Bi doped with Sb, Sn, and Te over the temperature range 4-65 K and magnetic fields from 1 to 33 T. In the energy band scheme of these materials a hole band superimposes on an electron band. [24][25][26] This hole band splits into Landau sub-bands and its highest extreme lies near the bottom of the conduction band. With increasing B, the density of the electron states below the bottom of the conduction band is reduced periodically to zero.…”

Quantum oscillations of Bi resistance in high magnetic fields (quantum limit)

“…All measurements were taken using low frequency (o100 Hz) ac techniques. HTOs were detected reliably in the first, r 0 ik ðBÞ; or second, r 00 ik ðBÞ; derivative obtained as a result of computer processing of the corresponding r ik ðBÞ curve [10]. At temperatures 4-15 K the SdH oscillations prevail in the dependenciesr ik ðBÞ; while the HTO dominate above E15 K. The SdH oscillations and the HTO were measured with the magnetic field directed along the principal crystallographic axes C 3 (Fig.…”