Quantum fluctuations determine the spin-flop transition in hematite

Abstract

Magnetic phase transitions between ordered phases are often understood on the basis of semi-classical spin models. Deviations from the classical description due to the quantum nature of the atomic spins as well as quantum fluctuations are usually treated as negligible if long-range order is preserved, and are rarely quantified for actual materials. Here, we demonstrate that a fully quantum-mechanical framework is required for a quantitatively correct description of the spin-flop transition in the insulating altermagnet hematite between the collinear antiferromagnetic and the weakly ferromagnetic spin-flop phase at low temperature. By applying both exact diagonalization and density-matrix renormalization group theory to the quantum Heisenberg Hamiltonian, we show how a quantum-mechanical treatment of an ab initio parametrized spin model can significantly improve the predicted low-temperature spin-flop field over a classical description when compared to measurements. Our results imply that quantum fluctuations have a measurable influence on selecting the ground state of a system out of competing ordered magnetic phases at low temperature.

Figures (4)

• Figure 1: Out-of-plane ($m_z$) and in-plane ($m_{\mathrm{ip}}$) magnetization of hematite as a function of a magnetic field applied along the $z$-axis, calculated analytically at $T = 0$ within classical theory. The insets show the corresponding spin configurations within the primitive unit cell: (a) antiferromagnetic ground state, (b) spin-flop phase, (c) ferromagnetically polarized phase. The green arrows show the spin-flop field in the classical theory compared to mean-field (mf) and spin-wave theory (sw) calculations and dmrg results presented below. The red arrow shows the experimentally observed value.
• Figure 2: Magnetization curve for a system of $n$ spins with a quantum number $S = \tfrac{1}{2}$ computed with ed. The thicker gray line indicates the classical magnetization curve.
• Figure 3: Spin-flop field computed by ed and dmrg for clusters of different sizes $n$ and quantum numbers $S$. The colored points are dmrg results and the black crosses mark the corresponding ed results for the two smallest clusters. Uncertainty ranges for the dmrg results were also calculated but are smaller than the symbol size. The two lines are linear fits to the chain-like clusters used to extrapolate the critical field in the bulk limit.
• Figure 4: Spin-flop field for different quantum numbers calculated from mean-field theory (mf), both without and including on-site fluctuations, as well as spin-wave theory (sw), compared to the values extrapolated from the dmrg calculations and to experimental observations HematiteAbInitio.