Spin-orbit density wave: a new phase of matter applicable to the hidden order state of URu₂Si₂

Abstract

We provide a brief review and detailed analysis of the spin-orbit density wave (SODW) proposed as a possible explanation to the ‘hidden order’ phase of URuSi. Due to the interplay between inter-orbital Coulomb interaction and spin-orbit coupling (SOC) in this compound, the SODW is shown to arise from Fermi surface nesting instability between two spin-orbit split bands. An effective low-energy Hamiltonian including single-particle SOC and two-particle SODW is derived, while the numerical results are calculated using density-functional theory (DFT)-based band-structure input. Computed gapped quasiparticle spectrum, entropy loss and spin-excitation spectrum are in detailed agreement with experiments. Interestingly, despite the fact that SODW governs dynamical spin-excitations, the static magnetic moment is calculated to be zero, owing to the time-reversal invariance imposed by SOC. As a consequence, SODW can be destroyed by finite magnetic field even at zero temperature. Our estimation of the location of the quantum critical point is close to the experimental value of  35 T. Finally, we extend the idea of SODW to other SOC systems including iridium oxides (iridates) and two-dimensional electronic systems such as BiAg surface and LaAlO/SrTiO interface. We show hint of quasiparticle gapping, reduction of pre-existing magnetic moment, large magneto-resistance, etc. which can be explained consistently within the SODW theory.

Keywords:

• spin-orbit density wave
• hidden order
• heavy fermion
• quantum phase transition
• URu₂Si₂

Acknowledgements

The author acknowledges valuable discussion with A. Leggett, J. Mydosh, P. Coleman, M. J. Graf, P. Woëlfle, J.-X. Zhu, J. Haraldsen, P. Riseborough, A. F. Santander-Syro. The author also expresses gratitude to A. V. Chubukov and A. Rahmanian for discussion of SODW formalism in iridates. The work is supported by the US DOE through the Office of Science (BES) and the LDRD Program and facilitated by NERSC computing allocation.