Interstitial-Electron Altermagnetism in Two Dimensions

Abstract

Altermagnetism has so far been associated with compensated magnetic moments carried by atoms. Here we introduce Stoner instability induced interstitial-electron altermagnetism, a distinct mechanism in which altermagnetic order is carried instead by interstitial anionic electrons in electrides. We show that, owing to the quasi-nucleus-free nature of interstitial electrons, the Stoner instability in electrides hosting two interstitial electrons can naturally stabilize an altermagnetic state rather than the conventional ferromagnetic one. This mechanism leads to a practical design principle for two-dimensional materials, from which we identify monolayers Zr2N and Ti2N as representative candidates. The strong sensitivity of interstitial electrons to cavity size enables efficient strain control of the altermagnetic order and a pronounced piezo-altermagnetic effect. Moreover, we investigate the evolution of the magnetism in Zr2N under ultrafast laser excitation, which exhibits dynamics distinct from those in all previously reported magnetic materials where magnetism is carried by real atoms. Our work not only offers a novel pathway to realize altermagnetism but also reveals an efficient non-magnetic route for its control.

Figures (5)

• Figure 1: (a-b) An ion with two electrons in the outermost shell. Since the electrons are tightly bound to the real ions, the electron clouds for the two electrons are confined in the same position. They have to choose suitable orthogonal orbits to lower the ground state energy. In (a) and (b), the outermost shells are the orbits with $\ell = 0$ and $\ell >0$, respectively. Accordingly to Hund's rule, the orbit with $\ell = 0$ ($\ell > 0$) is fully (partially) occupied, leading to a nonmagnetic (magnetic) state in (a) [(b)]. (c) In electrides, the IAEs are not tightly bound to certain ions, but actually delocalize throughout the unit cell, only with more weight distributed within certain cavities. Without the binding constraint imposed by the ions, the IAEs can adopt a fundamentally different way to lower the ground-state energy: under Stoner instability, the spin-degenerate IAE clouds can directly move in opposite directions. Such spatial separation of the spin-polarized IAE clouds lead to antiferromagnetism or altermagnetism.
• Figure 2: (a) Top and (b) side view of a modified monolayer Lieb lattice composed of three atomic species. The red region in (a) denotes a cavity in the lattice. The yellow region in (b) represents a possible IAE cloud in the cavities of the lattice.
• Figure 3: (a) The crystal structure and corresponding Brillouin zone of Zr$_{2}$N. (b-d) The properties of Zr$_{2}$N in the nonmagnetic state. (b) is the side view of the electron localization function (ELF), (c) plots the phonon spectrum, and (d) shows the electronic band structure and partial density of states (PDOS).
• Figure 4: (a) Electronic band structure and PDOS of Zr$_{2}$N in the AM state. (b) Spin density of Zr$_{2}$N in the AM order.
• Figure 5: (a) Evolution of the absolute magnetic moment of each IAE in the AM Zr$_{2}$N under biaxial strain. (b) Evolution of the net magnetic moment in Zr$_{2}$N under uniaxial strain along the x and y directions. (c) Schematic diagram of ultrafast laser-induced spin transfer and reversal in Zr$_{2}$N. (d) Time-dependent dynamics of the magnetic moments for Zr$_{1}$ atom (top layer, red), Zr$_{2}$ atom (bottom layer, blue) and N atom (middle layer, grey).