Ferromagnetism of the repulsive atomic Fermi gas: three-body recombination and domain formation

Abstract

The simplest model for itinerant ferromagnetism, the Stoner model, has so far eluded experimental observation in repulsive ultracold fermions due to rapid three-body recombination at large scattering lengths. Here we show that a ferromagnetic phase can be stabilised by imposing a moderate optical lattice. The reduced kinetic energy drop upon formation of a polarized phase in an optical lattice extends the ferromagnetic phase to smaller scattering lengths where three-body recombination is small enough to permit experimental detection of the phase. We also show, using time dependent density functional theory, that in such a setup ferromagnetic domains emerge rapidly from a paramagnetic initial state.The ground-state of a repulsive gas of fermions with contact interaction was first predicted by Stoner [1] in 1933 to be ferromagnetic and a precise value for the critical interaction strength in a homogeneous system was recently obtained with diffusion Monte Carlo simulations [2][3][4]. While ultracold fermionic gases should provide a controlled environment to study this phenomenon, the instability of a strongly repulsive gas towards molecule formation has so far prevented experimental realization of this phase. Repulsive fermions on the positive side of the Feshbach resonance live on the meta-stable repulsive branch [5]. When three atoms, one with the opposite spin of the other two, come close to each other two atoms with opposite spin will form bosonic molecules and the other one carries the binding energy away. The rate of such process increases rapidly with scattering length. The lifetime of the gas is therefore largely governed by the interaction strength and the spatial overlap between the two spin species.A recent experiment [6] presented evidence for a possible ferromagnetic state formed after rapid increase of the scattering length. The nature of this phase has, however, been questioned [7-9] as the peaks in kinetic energy, cloud size and loss rate observed in [6] are only indirect evidence for ferromagnetic domains [7], and it has been shown that molecule formation is dominant at large interaction strengths [8,9]. Several papers have proposed to reduce the recombination rate by using a polar molecular gas with dipole interactions and positive scattering range [10,11], narrower Feshbach resonances [8,9,12,13] and fermions with unequal mass [14,15]. Although these approaches might prove promising in future experiments, they all change the microscopic physics of the Stoner model.Here we suggest new strategies which achieve the same goal of stabilising the ferromagnetic phase, yet preserve the microscopic physics and thus pave the way towards experimental realization of Stoner ferromagnetism. Figure 1: Phase diagram of the homogeneous repulsive Fermi gas as a function of temperature T /T F and interaction strength k F as. The white dashed line indicates the paramagnet-ferromagnetic phase transition and the colour scale the polarization P = (n ↑ − n ↓ )/(n ↑ + n ↓ ).Firstly, the lifetime of the system can be incre...

Ferromagnetism of a Repulsive Atomic Fermi Gas in an Optical Lattice: A Quantum Monte Carlo Study

“…1), as well as the boundary between the partially and fully polarized ferromagnetic phases (black squares), rapidly decreases when V 0 increases. These results strongly support the idea of observing itinerant ferromagnetism in experiments with repulsive gases in shallow optical lattices [26]. A similar enlargement of the ferromagnetic stability region was obtained by means of DFT simulations based on the Kohn-Sham equations [27] with an exchange-correlation functional obtained within the local spin-density approximation (LSDA) [7,28].…”

Two-dimensional mixture of dipolar fermions: Equation of state and magnetic phases

“…This phenomenon was first predicted for the three-dimensional homogeneous electron gas [28], and represents a long-standing topic in quantum many-body physics. It was the subject of extensive theoretical investigations for the electron gas [29][30][31][32][33][34][35], for liquid 3 He [36][37][38] and for fermionic atoms with short-range interactions [39][40][41][42][43][44][45]. The case of shortrange-interacting atoms is the closest to the textbook model of magnetism introduced by Stoner [46].…”

Exploring emergent heterogeneous phases in strongly repulsive Fermi gases

“…The heterogeneous character of the resulting metastable phase investigated in this work links the physics of the repulsive Fermi gas to certain strongly correlated electron materials, where competing order parameters coexist in nanoscale phase separation [1,3]. The realization of such an exotic atom-pair quantum emulsion opens unforeseen new perspectives: In the future, it will be interesting to explore the finitemomentum response and the transport properties of atoms and pairs in such a spatially inhomogeneous gas, and to explore its robustness in weak optical lattices [39,40] or lower dimensions [41,42]. Further, quantum gas microscopes could uniquely explore the emergence of such a phase, with the competition between anti-ferromagnetic ordering favored by the undelying lattice structure and quantum emulsions of itinerant fermions.…”