Quantum oscillations and phase diagram of $\alpha -{\mathrm{}(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}-\mathrm{T}\mathrm{T}\mathrm{F})\mathrm{}}_2{\mathrm{TlHg}\left(\mathrm{SCN}\right)\mathrm{}}_4$

The interlayer magnetoresistance of the quasi-two-dimensional organic conductor $\alpha -{\mathrm{}(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}-\mathrm{T}\mathrm{T}\mathrm{F})\mathrm{}}_2{\mathrm{TlHg}\left(\mathrm{SCN}\right)\mathrm{}}_4$ was measured during both up and down sweeps of long-pulse magnetic fields extending up to 36 T. The temperature–magnetic-field phase diagram was extensively studied through the field and temperature dependences of both the background and the oscillatory parts of the magnetoresistance. The hysteretic behavior of the magnetoresistance, the field-dependent Peierls-like transition temperature ${(T}_P),$ and the temperature-dependent kink transition were investigated. The field sensitivity of $T_P$ is interpreted on the basis of a competition between the Pauli and orbital effects in a mixed-charge and spin-density-wave state. Besides, a splitting of the kink transition is observed when the magnetic field is strongly tilted with respect to the normal to the conducting plane. Analysis of the oscillatory part of the magnetoresistance reveals a hysteretic behavior of the amplitude of the oscillations linked to the α orbit around both the kink transition and $B_{\max }.$ Field-independent effective cyclotron mass parameters are derived in both the density wave and the normal metallic states.