Ferroelasticity tunable altermagnets

Abstract

Altermagnets have garnered great interest due to their non-relativistic spin splitting and novel physical properties. However, the control of altermagnetic states remains underexplored. Here, we propose a unique multiferroic state, i.e. ferroelastic altermagnetic state, in which ferroelastic strain couples directly to the spin-splitting. Through symmetry analysis and first-principles calculations, we identify the ferroelastic $d$-wave altermagnetism of puckered pentagonal CoSe$_2$ monolayer. Interestingly, uniaxial stress can induce a ferroelastic phase transition, accompanied by a $90\degree$ rotation of the spin-splitting bands. Cooperative rotation of the lattice and Néel vectors preserves the sign of Kerr angle, whereas noncooperative rotation reverses it. Our work provides a general strategy for manipulating altermagnetism in multiferroic systems and opens other avenues for exploring emergent magnetoelastic phenomena.

Figures (6)

• Figure 1: Schematic illustration of ferroelastic altermagnetism and its switching. We postulate the lattice constants ($a_0$ and $b_0$) of the ground state of the ferroelastic system, with $a_0<b_0$. The horizontal coordinate is $a'=(2a-a_0-b_0)/(b_0-a_0)$, where $a$ is lattice constant of $a$-direction during the ferroelastic switching. To enhance the visual clarity, the unit cells of ferroelastic states are represented by transparent colored boxes: light red denotes ferroelastic state I with lattice constant $a=a_0$ ($a'=-1$), purple represents the paraelastic state with $a=(a_0+b_0)/2$ ($a'=0$), and light blue indicates ferroelastic state II with $a=b_0$ ($a'=+1$). The following diagrams are spin-momentum locking diagrams of two ferroelasctic states.
• Figure 2: (a) Top and side views of pentagonal CoSe$_2$ monolayer. $d$: the thickness. (b) Phonon spectrum of monolayer CoSe$_2$. (c) Orbital-projected density of state (PDOS) of one spin-up Co ion. Inset: schematic of electron occupation of Co$^{2+}$'s $3d$ orbitals under a quasi-tetragonal crystal field. The unpaired $d_{z^2}$ orbital can be visualized by the spin polarized electron cloud colored in green.
• Figure 3: (a) The MAE of CoSe$_2$ monolayer as a function of spin orientation in the $ab$ and $ac$ planes. The value of $ab$-plane has been amplified tenfold for better comparison. The radial axis represents the angle difference of the spin orientation relative to the $x$-direction. And $\theta$=$0^\circ$ indicates the $x$ directon in the $ab$ and $ac$ planes. (b) The MC simulation of antiferromagnetic-paramagnetic phase transition, indicated by the peak of heat capacity, which represents the total specific heat rather than per lattice site. Inset: a MC snapshot at $3$ K.
• Figure 4: (a) Spin charge density and symmetry operations connecting two opposite spins of pentagonal CoSe$_2$ monolayer with N-AFM order. The red and green sites are spin-up and spin-down. (b) The electronic band structure in the first Brillouin zone. Left panel: without splitting along high symmetry $k$-paths. Inset: 2D Brillouin zone. Right panel: with splitting along other $k$-paths. Inset: magnified view around the $\Gamma$ point.
• Figure 5: (a) The energy barrier of ferroelastic switching estimated by the CI-NEB method. The insets illustrate the two states before ($a$<$b$) and after ($a$>$b$) ferroelastic switching, along with a hypothetic intermediate state ($a$=$b$). The red (green) atoms represent spin-up (spin-down) magnetic moments. (b) Spin-resolved band structures of the top of valence band for the FES1 and FES2 states without spin-orbit coupling. Inset: the first Brillouin zone.