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Physical review. B./Physical review. B

Itinerant magnetic phases and quantum Lifshitz transitions in a three-dimensional repulsively interacting Fermi gas with spin-orbit coupling

Shang-Shun Zhang, Jinwu Ye, Wu-Ming Liu

Published Sep 9, 2016• 9 citations
Publisher

Abstract

Magnetic phenomena in itinerant electron systems have been at the forefront of materials science. Here we show that the Weyl spin-orbit coupling (SOC) in three-dimensional repulsively interacting itinerant Fermi systems opens up a platform to host new itinerant magnetic phases, excitations, and phase transitions. A putative ferromagnetic state (FM) is always unstable against a stripe spiral spin density wave (S-SDW) or a stripe longitudinal SDW (LSDW) at small or large SOC strengths, respectively. The stripe-ordering wave vector is given by the nesting momentum of the two SOC-split Fermi surfaces with the same or opposite helicities at small or large SOC strengths, respectively. The LSDW is accompanied by a charge density wave (CDW) with half of its pitch. The transition from the paramagnet to the SSDW or LSDW+CDW is described by quantum Lifshitz-type actions, in sharp contrast to the Hertz-Millis types for itinerant electron systems without SOC. The collective excitations and Fermi surface reconstructions inside the SSDW and LSDW+CDW are also studied. The effects of a harmonic trap in cold-atom experiments are briefly discussed. In view of recent ground-breaking experimental advances in generating two-dimensional SOC in cold atoms, these phenomena can be observed in current or near-future cold-atom experiments even at very weak interactions. They may also be relevant to some itinerant magnetic materials with a strong SOC.

DOI
10.1103/physrevb.94.115121

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Magnetic phenomena in itinerant electron systems have been at the forefront of materials science. Here we show that the Weyl spin-orbit coupling (SOC) in three-dimensional repulsively interacting itinerant Fermi systems opens up a platform to host new itinerant magnetic phases, excitations, and phase transitions. A putative ferromagnetic state (FM) is always unstable against a stripe spiral spin density wave (S-SDW) or a stripe longitudinal SDW (LSDW) at small or large SOC strengths, respectively. The stripe-ordering wave vector is given by the nesting momentum of the two SOC-split Fermi surfaces with the same or opposite helicities at small or large SOC strengths, respectively. The LSDW is accompanied by a charge density wave (CDW) with half of its pitch. The transition from the paramagnet to the SSDW or LSDW+CDW is described by quantum Lifshitz-type actions, in sharp contrast to the Hertz-Millis types for itinerant electron systems without SOC. The collective excitations and Fermi surface reconstructions inside the SSDW and LSDW+CDW are also studied. The effects of a harmonic trap in cold-atom experiments are briefly discussed. In view of recent ground-breaking experimental advances in generating two-dimensional SOC in cold atoms, these phenomena can be observed in current or near-future cold-atom experiments even at very weak interactions. They may also be relevant to some itinerant magnetic materials with a strong SOC.
Magnetic ordering of itinerant fermionic systems is at the forefront of condensed matter physics dating back to Stoner's instability. Spin-orbit coupling (SOC) which couples two essential ingredients of an itinerant fermionic system, namely spin and orbital motion, opens up new horizons to this long-standing problem. Here we report that the itinerant ferromagnetism is absent in 3D Fermi gas with a Weyl SOC and various itinerant spin density waves emerge instead, which is deeply rooted in the unique symmetry and spin-momentum locking effect in spin-orbit coupled systems. What is more appealing is that, the strong SOC provides a new and efficient mechanism to realize itinerant spin density waves at extremely weak repulsion---a significant benefit for present ultra-cold atom experiment. These novel phenomena can be probed by Bragg spectroscopy, time of flight imaging and {\sl In-Situ } measurements in ultra-cold atom experiment.
We investigate the itinerant ferromagnetism in a dipolar Fermi atomic system with the anisotropic spin–orbit coupling (SOC), which is traditionally explored with isotropic contact interaction. We first study the ferromagnetism transition boundaries and the properties of the ground states through the density and spin-flip distribution in momentum space, and we find that both the anisotropy and the magnitude of the SOC play an important role in this process. We propose a helpful scheme and a quantum control method which can be applied to conquering the difficulties of previous experimental observation of itinerant ferromagnetism. Our further study reveals that exotic Fermi surfaces and an abnormal phase region can exist in this system by controlling the anisotropy of SOC, which can provide constructive suggestions for the research and the application of a dipolar Fermi gas. Furthermore, we also calculate the ferromagnetism transition temperature and novel distributions in momentum space at finite temperature beyond the ground states from the perspective of experiment.
We consider a repulsive two-component Fermi gas confined in a two-dimensional isotropic harmonic potential and subject to a large Rashba spin-orbit coupling. The single-particle dispersion can be tailored by the spin-orbit-coupling term, which provides an opportunity to study itinerant ferromagnetism in this system. We show that the interplay among spin-orbit coupling, correlation effect, and mean-field repulsion leads to a competition between ferromagnetic and nonmagnetic phases. The weakly correlated nonmagnetic and the ferromagnetic phases can be well described by the mean-field Hartree-Fock theory, while the transition between the ferromagnetic and a strongly correlated nonmagnetic phase is driven by beyond-mean-field quantum correlation effect. Furthermore, the ferromagnetic phase of this system possesses a chiral current density induced by the Rashba spin-orbit coupling, whose experimental signature is investigated.
Recently the interest in non-Neel ground states for antiferromagnetically interacting localized spin systems has been revived. We discuss to what extent the generalization of such states is possible for itinerant electrons. Multiple spin correlation functions can be used to enumerate nontrivial order parameters for localized spins. This approach can be applied to itinerant systems without any modification. However, for the transition which breaks translational symmetry, electronic states far away from the Fermi surface are important and, hence, there is no distinct energetic mechanism for the nontrivial magnetic ordering. The only exception is the Fermi surface with the nesting property. As it is shown, among all phases known for localized spins only p-type spin nematic and chiral spin states can appear as a result of a Fermi liquid breakdown with respect to the electron-hole condensation near the Fermi surface. All other phases with zero local average spin known for localized systems, either are accompanied by the charge density wave or persistent orbital currents creating orbital magnetic moments, or can not appear as a result of a phase transition driven by such mechanism. Although two aforementioned phases are equivalent to their counterparts for localized spins from the symmetry viewpoint, the driving order parameter in an itinerant case is not a multiple spin average, but a wave function of the electron-hole condensate.
We clarify the ground-state phase diagram of the half-filled square-lattice Hubbard model with Rashba spin-orbit coupling (SOC) characterized by the spin-split energy bands due to broken inversion symmetry. Although the Rashba metals and insulating magnets have been studied well, the intermediate interaction strength of the system remained elusive due to the lack of appropriate theoretical tools to unbiasedly describe the large-scale magnetic structures. We complementarily apply four different methods (sine-square deformed mean-field theory, random phase approximation, Luttinger-Tisza method, and density matrix embedding theory) and succeed in capturing the incommensurate spin-density-wave (SDW) phases with very long spatial periods which were previously overlooked. The transition to the SDW phases from the metallic phase is driven by an unprecedented instability that nests the two parts of the Fermi surface carrying opposite spins. For large SOC, the spiral, stipe, and vortex phases are obtained, when the four Dirac points exist near the Fermi level and their whole linear dispersions nest by a wavelength $\ensuremath{\pi}$, opening a band gap. These two types of transition provide Fermiology that distinguishes the antisymmetric SOC systems, generating a variety of magnetic phases that start from the relatively weak correlation regime and continue to the strongly interacting limit.
The current efforts of studying many-body effects with spin-orbit coupling (SOC) using alkali-metal atoms are impeded by the heating effects due to spontaneous emission. Here, we show that even for SOCs too weak to cause any heating, dramatic many-body effects can emerge in a one-dimensional (1D) spin-12\frac{1}{2}21​ Fermi gas provided the interaction is sufficiently repulsive. For weak repulsion, the effect of a weak SOC (with strength $\ensuremath{\Omega}$) is perturbative, inducing a weak spin spiral (with magnitude proportional to $\ensuremath{\Omega}$). However, as the repulsion ggg increases beyond a critical value (${g}_{c}\ensuremath{\sim}1/\ensuremath{\Omega}$), the magnitude of the spin spiral rises rapidly to a value of order 1 (independent of $\ensuremath{\Omega}$). Moreover, near $g=+\ensuremath{\infty}$, the spins of neighboring fermions can interfere destructively due to quantum fluctuations of particle motion, strongly distorting the spin spiral and pulling the spins substantially away from the direction of the local field at various locations. These effects are consequences of the spin-charge separation in the strongly repulsive limit. They will also occur in other 1D quantum gases with higher spins.