Engineering altermagnetic orders on the square-kagome lattice through sublattice interference

Abstract

We investigate the emergence of altermagnetic (AM) phases on the square-kagome lattice. Our analysis reveals that matrix element effects due to an orthogonal sublattice weight decomposition of Fermi level eigenstates known as sublattice interference enable decoupled magnetic ordering tendencies on distinct sublattices. Depending on which sublattice undergoes a magnetic instability, we identify a $d_{xy}$-type AM phase and a $d_{x^{2}-y^{2}}$-type AM phase originating from different sublattice polarization patterns. Using the Kotliar-Ruckenstein slave boson formalism we explore the stability of these AM phases as a function of interaction strength. Our findings demonstrate that sublattice-selective magnetic instabilities provide a versatile route to engineer the nature of AM order.

Figures (6)

• Figure 1: (a) Illustration of the square-kagome lattice. The unit cell [marked by gray square box] consists of six sites indicated by numbers $1,2,\dots,6$. Among these, sites $1,2,3,4$ belong to Wyckoff position $4f$ while the sites $5,6$ correspond to the Wyckoff position $2c$. The unit translational vectors are denoted by $\hat{a}^{}_x$ and $\hat{a}^{}_y$. Possible AM phases due to the magnetization on (b) $2c$ sites and (c) $4f$ sites. Here, yellow and green sites denote two different magnetic alignments, while blue sites denote nonmagnetic sites.
• Figure 2: Hopping amplitudes associated with the minimal models for the AM orders on (a) $2c$ and (b) $4f$ sites respectively.
• Figure 3: (a) Illustration of the tight-binding hopping parameters: $t$ (A-B hopping), $t^\prime$ (intra-unit-cell A-A hopping), and $t^{\prime\prime}$ (inter-unit-cell A-A hopping). (b) and (c) show the Fermi surfaces for $(t,t^\prime,t^{\prime\prime})=(1,0.5,0)$ and $(t,t^\prime,t^{\prime\prime})=(1,0.5,0.5)$ at fillings $n^{}_{f}\approx0.35$ and $n^{}_{f}\approx0.68$, respectively. The corresponding band dispersions are presented in (d) and (e), where the red line indicates the Fermi level (filling). The density of states (DOS) associated with each dispersion is shown on the right. For these two fillings, (f) and (g) display the sublattice weights along the paths $M\rightarrow M_1\rightarrow M_2\rightarrow M_3\rightarrow M$ and $\Gamma\rightarrow M_3\rightarrow\Gamma^\prime\rightarrow M\rightarrow\Gamma$, respectively.
• Figure 4: Non-relativistic lifting of Kramers degeneracy for $U=5$: (a) $(t,t^\prime,t^{\prime\prime})=(1,0.5,0)$ and (b) $(t,t^\prime,t^{\prime\prime})=(1,0.5,0.5)$. The dashed square indicates the boundary of the first Brillouin zone.
• Figure 5: Stability analysis for both altermagnetic saddle points with momentum-resolved response functions in arbitrary units (a.u.) calculated within the SRIKR Gaussian-fluctuation analysis. Shown along the high-symmetry path $\Gamma$--X--M--$\Gamma$ are the longitudinal spin susceptibility $\chi^{zz}_s$ (left), and charge susceptibility $\chi_c$ (right). The rows correspond to: (top) AFM order on B sites (Wyckoff $2c$) (stable, no instabilities), (middle) AFM order on A sites (Wyckoff $4f$) at $V=0$ (divergent charge/longitudinal-spin response indicating instability), and (bottom) AFM order on A sites with nearest-neighbor density interaction $V=2$ (suppressed instabilities indicating stabilized homogeneous phase).