Bi-altermagnetism unveiled by sublattice-specific circular dichroism in resonant inelastic X-ray scattering

Abstract

An altermagnet is a recently identified class of magnets that exhibit a zero net magnetic moment but break symmetry under the combined operations of parity and time reversal. It typically consists of two magnetic sites of opposite spins related by rotation within the unit cell. Here, we use circular dichroism (CD) in resonant inelastic X-ray scattering (RIXS) to identify a new form of altermagnetism, namely bi-altermagnetism, in the correlated insulator Fe2Mo3O8, which comprises two altermagnetic sublattices: one with alternating quasi-octahedral Fe environments and the other with alternating tetrahedral Fe environments. We experimentally revealed the emergence of CD in an achiral, zero-magnetization system, thereby probing mirror-symmetry breaking associated with altermagnetic order. Notably, the CD appeared at sublattice-specific excitations of the octahedral and tetrahedral sites, indicating symmetry breaking in both altermagnetic sublattices. Calculations based on a model with the bi-altermagnetic order along the c axis successfully reproduce the observed CD. Our findings provide compelling evidence for bi-altermagnetism in Fe2Mo3O8, and showcase the use of RIXS-CD as a probe of magnetic sublattices in systems with zero net magnetization.

Figures (4)

• Figure 1: Energy-dependent RIXS of Fe$_2$Mo$_3$O$_8$. a, Crystal structure of Fe$_2$Mo$_3$O$_8$. The unit cell outlined by a black cuboid contains two quasi-octahedral ($O_h$) and two tetrahedral ($T_d$) Fe$^{2+}$ sites, whose spin moments are antiparallel, as indicated by the white arrows. b, Illustration of the mirror planes in the magnetic point group $6'mm'$. Each of the $O_h$ and $T_d$ polyhedra in the plane $z=0$ form a triangular lattice and both together a hexagonal arrangement. Three vertical mirror planes, indicated by orange lines, correspond to the $m'$ planes, and the other three, shown in light blue, correspond to the glide planes $m$. The reciprocal lattice vectors $\mathbf{a}^{*}$ and $\mathbf{b}^{*}$ are shown by red arrows. c, Illustration of scattering geometry. The scattering plane, defined by the incident wave vector $\mathbf{k}_i$ and the scattered wave vector $\mathbf{k}_f$, lies in the $\mathbf{a}^{*}\mathbf{c}^{*}$ plane, i.e., one of the $m'$ planes. The momentum transfer is given by $\mathbf{Q} = \mathbf{k}_f-\mathbf{k}_i$. The light blue hexagon indicates the first Brillouin zone (BZ) of the reciprocal lattice. d, Fe $L$-edge XAS spectrum measured in the fluorescence yield mode. The XAS is plotted without corrections for self-absorption. e, RIXS intensity map plotted in the plane of energy loss vs. incident photon energy. Data were measured by using right-handed circularly polarized (RCP) X-rays at 32 K for incident photon energy across the $L_3$ peak of XAS. f, Corresponding theoretical RIXS intensity map.
• Figure 2: CD in RIXS of Fe$_2$Mo$_3$O$_8$. a, RIXS spectra measured with circularly polarized X-rays and with the scattering plane in the ${\bf a}^{*}{\bf c}^{*}$ plane ($m'$ plane) at 32 K, below the Néel temperature $T_{\rm N}$= 60 K. Red and blue curves, denoted by RCP and LCP, represent RIXS spectra excited with right- and left-handed circularly polarized incident X-rays, respectively. The RIXS data were recorded with momentum transfer $\mathbf{Q} = (0.05,0,0.65)$. In the RIXS spectra plotted in a, A indicates the low-energy spin-orbital excitations below 0.1 eV, predominantly originating from the $O_h$ site; B and C label the characteristic features of the crystal-field excitations around 0.5 eV and 1 eV at the $T_d$ and $O_h$ sites, respectively. Inset: Corresponding low-energy RIXS spectra with the scattering plane in the $ac$ plane ($m$ glide symmetry plane). b, c, Calculations for the quasi $O_h$ and $T_d$ sites, where the contributions from the two magnetic sublattices (up- and down-spin) are summed.
• Figure 3: Temperature-dependent circular dichroism (CD) in RIXS of Fe$_2$Mo$_3$O$_8$.a-d, CD in RIXS arising from spin-orbital excitations near 0.1 eV. e-h, CD in RIXS arising from $dd$ excitations. The spectra were measured at momentum transfer $\mathbf{Q} = (0.03,0,0.66)$ using circularly polarized X-rays at selected temperatures across the Néel temperature $T_{\rm N}$= 60 K. Red and blue curves (RCP and LCP) correspond to spectra excited with right- and left-handed circularly polarized incident X-rays, respectively. Additional RIXS-CD data at other temperatures are shown in Figs. S2 and S3 of the Supplementary Information.
• Figure 4: Spin-orbital excitations of Fe$_2$Mo$_3$O$_8$ probed by RIXS. a, Energy level diagram of Fe$^{2+}$ in an octahedral crystal field with spin-orbit coupling in first- and second-order approximations. For an atomic SOC constant $\zeta = 52~{\rm meV}$, atomic multiplet calculations show that the energies of the quintet substates ($E$ and $T_{1}$) are 23.7 and 25.6 meV, and those of the septet substates ($A_{1}$, $T_{1}$, and $T_{2}$) are 58.1, 62.1, and 64.8 meV. b, Energy-dependent RIXS measured at T = 32 K with RCP. c, Corresponding RIXS intensity map.