[Paper Review] Observation of canted antiferromagnetism with ultracold fermions in an optical lattice

Peter Brown, Debayan Mitra+8 more|arXiv (Cornell University)|Dec 22, 2016

Physics of Superconductivity and Magnetism43 references171 citations

TL;DR

This study reports the first observation of canted antiferromagnetism in ultracold fermions using a quantum gas microscope, demonstrating spin-rotation anisotropy in spin correlations under strong spin imbalance. At half-filling with U/t ≈ 8, the system exhibits enhanced antiferromagnetic order perpendicular to the magnetization direction, with anisotropy increasing with polarization and distance, closely matching predictions from Determinantal Quantum Monte Carlo and Numerical Linked Cluster Expansion simulations.

ABSTRACT

Understanding the magnetic response of the normal state of the cuprates is considered a key piece in solving the puzzle of their high-temperature superconductivity. The essential physics of these materials is believed to be captured by the Fermi-Hubbard model, a minimal model that has been realized with cold atoms in optical lattices. Here we report on site-resolved measurements of the Fermi-Hubbard model in a spin-imbalanced atomic gas, allowing us to explore the response of the system to large effective magnetic fields. We observe short-range canted antiferromagnetism at half-filling with stronger spin correlations in the direction orthogonal to the magnetization, in contrast with the spin-balanced case where identical correlations are measured for any projection of the pseudospin. The rotational anisotropy of the spin correlators is found to increase with polarization and with distance between the spins. Away from half-filling, the polarization of the gas exhibits non-monotonic behavior with doping for strong interactions, resembling the behavior of the magnetic susceptibility in the cuprates. We compare our measurements to predictions from Determinantal Quantum Monte Carlo (DQMC) and Numerical Linked Cluster Expansion (NLCE) algorithms and find good agreement. Calculations on the doped system are near the limits of these techniques, illustrating the value of cold atom quantum simulations for studying strongly-correlated materials.

Motivation & Objective

• To probe the magnetic response of the Fermi-Hubbard model under spin-imbalanced conditions, mimicking the normal state of cuprates.
• To experimentally observe and characterize canted antiferromagnetic order in a 2D ultracold Fermi gas with tunable spin polarization.
• To test theoretical predictions of spin-rotation anisotropy in the presence of effective Zeeman fields and strong correlations.
• To compare experimental spin correlation functions with state-of-the-art numerical simulations (DQMC and NLCE) in the strongly correlated regime.

Proposed method

• Realized the 2D Fermi-Hubbard model using a two-component ultracold 6Li Fermi gas in a square optical lattice with U/t ≈ 8.0(5).
• Achieved tunable spin imbalance P via magnetic-field-tuned Feshbach resonance and evaporative cooling, controlling the effective Zeeman field h.
• Employed quantum gas microscopy with site-resolved fluorescence imaging to measure local densities and spin projections (Sz and Sx) after spin-rotated state detection.
• Used spin-rotation pulses and selective state removal to extract spin correlation functions Cσ(d) for σ = x, z, enabling measurement of anisotropic spin correlations.
• Applied detection efficiency correction (96%) to experimental data and compared with DQMC and NLCE simulations at U/t = 8.
• Performed numerical simulations using Determinantal Quantum Monte Carlo (DQMC) and Numerical Linked Cluster Expansion (NLCE), with finite-temperature corrections and sign-problem analysis.

Experimental results

Research questions

• RQ1 How does spin imbalance affect the structure of antiferromagnetic correlations in the 2D Fermi-Hubbard model?
• RQ2 Does the system exhibit canted antiferromagnetic order with rotational anisotropy in spin correlations under strong interactions?
• RQ3 How does the spin correlation anisotropy evolve with increasing polarization and inter-site distance?
• RQ4 To what extent do experimental spin correlation functions agree with ab initio simulations (DQMC and NLCE) in the doped and spin-imbalanced regime?
• RQ5 What is the behavior of the local polarization and magnetic susceptibility in the doped Fermi-Hubbard model, and how does it compare to cuprate materials?

Key findings

• Canted antiferromagnetic order is observed at half-filling with U/t ≈ 8, showing enhanced spin correlations in the direction orthogonal to the magnetization (Sx), while parallel correlations (Sz) are suppressed.
• The spin correlation anisotropy A(d) increases with both polarization and distance between spins, reaching up to A ≈ 0.4 at ps ≈ 0.6 for nearest-neighbor pairs.
• Nearest-neighbor Sz spin correlations Cz(1,0) become negative at high polarization (ps ≈ 0.6), indicating a sign change due to dilute magnon gas formation and Bose-Einstein condensation at (π, π) momentum.
• The measured polarization profile shows non-monotonic doping dependence in the strong interaction regime, resembling the magnetic susceptibility behavior in cuprates.
• Experimental spin correlation functions show good quantitative agreement with DQMC and NLCE simulations, validating the simulations in the challenging strong-coupling, doped regime.
• The sign problem in DQMC is mild at half-filling and U/t = 8, enabling reliable low-temperature simulations that match experimental data.