Effects of high magnetic fields on charge-density waves inNbSe3

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Abstract

The magnetotransport properties of ${\mathrm{NbSe}}_{3}$ in the temperature range below the second charge-density-wave (CDW) onset of 59 K have been studied in magnetic fields up to 230 kG. At liquid-helium temperatures giant magnetoquantum oscillations caused by magnetic breakdown (MB) between the normal Fermi surface (FS) and open orbits on the nested sheets of the FS dominate the magnetotransport and are extremely sensitive to the pinned CDW configuration. Spatial variations in the phase of the pinned CDW change the local Fermi level and CDW gap, giving rise to a distribution of FS cross-sectional areas. These variations in FS cross section and CDW gap produce frequency shifts, amplitude modulations, and beat structures in the quantum oscillations observed in both the magnetoresistance and Hall effect. A model conductivity tensor has been developed describing the open-orbit network and MB interference as well as the closed-orbit contribution. The adjustable parameters of the model are the frequency of oscillation, the frequency-distribution spread \ensuremath{\Delta}F, and critical MB parameter ${\ensuremath{\omega}}_{0}$\ensuremath{\tau}.The model has been used to study the detailed configurations of the pinned CDW in nominally pure ${\mathrm{NbSe}}_{3}$ crystals and in ${\mathrm{NbSe}}_{3}$ crystals doped with Fe, Ni, and Co. Unique fits to the data can be generated, and the resulting FS distributions provide direct information on the local CDW domain structure produced by pinning and repinning the CDW or by deliberately introducing impurities. At temperatures in the range 10--59 K, the oscillation amplitude decreases rapidly as the scattering time decreases, and a new magnetoresistance enhancement is observed. The dc resistance anomaly associated with the CDW is enhanced by up to a factor of 4 in a magnetic field of 226 kG and, if assigned exclusively to FS obliteration, it would require an increase from 60% obliteration at H=0 to 92% at H=227 kG. Accurate measurements also indicate a small increase in the transition temperature of \ensuremath{\sim}0.5 K in a magnetic field of 226 kG. These results have been analyzed in terms of a theory proposed by Balseiro and Falicov in which a transverse magnetic field induces a more perfect nesting of the FS.Magnetic-field modifications of the electronic spectrum at the Fermi level can become large when the cyclotron energy \ensuremath{\Elzxh}${\ensuremath{\omega}}_{c}$ is on the order of the CDW gap \ensuremath{\Delta}. Both the enhancement of the magnetoresistance and the sign change in the Hall effect can be related to this mechanism. In addition to the magnetic-field-induced changes in the static CDW state, studies of the dynamics of CDW motion have also been carried out in magnetic fields up to 230 kG. The magnetoresistance response to the CDW motion can be modeled with equations similar to those of the Bardeen tunneling model. At high electric fields the enhanced magnetoresistance in the range 10--59 K is quenched; in the quantum-oscillation regime the enhanced dc magnetoresistance is quenched while the oscillation amplitude saturates. The large magnetoresistance in the static CDW state allows measurement of the threshold electric field down to low temperatures. For the nominally pure crystals the temperature dependence of ${E}_{T}$ in high magnetic fields follows a thermal-fluctuation model similar to that observed at H=0, and the magnitude of ${E}_{T}$ is not significantly changed from the values observed at H=0. At very low temperatures a departure from the dynamics of the tunneling model can give rise to a large region of zero dynamic resistance. This behavior is observed in the highest-purity crystals and is rapidly modified by impurities. The magnetic field facilitates the study of a large range of both static and dynamic CDW effects at low temperature: A systematic classification has been accomplished. Adequate theoretical models have been developed for several of the effects, although further refinement of the models and additional experimental confirmation are needed.

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