Exposing Altermagnetism through Momentum Density Spectroscopy

TL;DR

The paper addresses the challenge of fingerprinting altermagnetism, a zero-net-moment phase with spin-polarized momentum-space texture, by proposing bulk momentum-density probes. It develops a theoretical framework using spin-polarized MCP and spin-polarized 2D-ACAR to predict spin-resolved TPMDs, MCPs, and Fermi-surface signatures for RuO2, CrSb, and MnTe. The results indicate measurable antisymmetric MCPs, spin-resolved radial anisotropies, and the feasibility of reconstructing spin-resolved 3D Fermi surfaces via LCW folding, even in insulating cases. This approach provides concrete, bulk-compatible fingerprints for altermagnetism and enables direct mapping of spin-resolved Fermi surfaces, with potential for broad applicability to candidate materials.

Abstract

Materials which show a strong time-reversal symmetry-breaking response leading to spin-polarization phenomena, in conjunction with antiparallel magnetic alignments producing zero net magnetization, have recently been identified, classified, and been given the name 'altermagnets'. However, measuring and diagnosing possible candidates as altermagnetics still remains a challenge. From the uncertainty of the material being an altermagnet, additional experimental probes are essential to resolve this. Here, we propose using spin-dependent and magnetic momentum density probes such as spin-polarised positron annihilation and revisiting magnetic Compton scattering. By looking at the previously claimed altermagnetic candidates RuO2, CrSb and MnTe, we present theoretical altermagnetic calculations of the experimental quantities measured by these probes. We show that these quantities should produce a measurable signal and unequivocally confirm the altermagnetic state. We also highlight the additional benefits from these probes such as extracting spin-resolved Fermi surfaces which are key for further understanding the nature of the altermagnetic state.

Figures (4)

• Figure 1: (a)-(c) The altermagnetic Band structures for RuO$_2$, CrSb and MnTe, respectfully. The high symmetry points are defined in the Brilluoin zones shown in (j)-(k). The chosen paths highlight the breaking of the spin degeneracy in the altermagnetic state of each material. For RuO$_2$, the spin-up and spin-down Fermi surface sheets are shown in (d) and (e), and all of the Fermi surface sheets are shown in (f). For CrSb, (g), (h) and (i) show the spin-up, spin-down and all the Fermi surface sheets, respectfully. The Fermi surface topology of each spin are the same as each other but rotated in the $k_x$-$k_y$ plane by $\pi/2$ radians for RuO$_2$ and by $\pi/3$ radians for CrSb.
• Figure 2: Predicted MCPs of altermagnetic (a) RuO$_2$, (b) CrSb and (c) MnTe. Each show the scattering vectors along which a significant MCP signal with respect to the shown Ni [011] MCP from Ref. james2020magnetic. The legend labels of these vectors (which pass through $\Gamma$) are based on the symmetry points given in Fig. \ref{['bands']} (j) and (k). The altermagnetic MCPs of other directions along $\Gamma$ to a high symmetry point on the Brillouin zone edge results in $J_{\mathrm{mag}}(p_z)=0$ where the spins are degenerate. The inclusion of the Ni [011] MCP gives an indication of the expected experimental signal for these MCPs. We convolute our MCPs with the estimated experimental resolution.
• Figure 3: The 2D radial anisotropy of the 2D projected TPMDs along different projection vectors for (a)-(d) RuO$_2$, CrSb (e)-(h) and MnTe (i)-(l). The inset of each panel is a visual aid of the projection of the 3D TPMD along the vector (plane normal) going through the Brillouin zone. The $p_x$ and $p_y$ axes are labelled as such for convention. The $p_x$ axes are parallel to the vector linking the high symmetry points: (a) -- $\Gamma$ to M$_{\rm 2}$; (b) -- M$_{\rm 1}$ to $\Gamma$; (c)-(d) -- M$_{\rm 1}$ to X; (e), (g)-(i) and (k)-(l) -- M$_{\rm 1}$ to K; and (f) and (j) -- K to M$_{\rm 1}$. The $p_y$ axes varies between the panels and are not always parallel to a high symmetry path. The first two rows of the panels present the projections which clearly show the differences in the spins where the last two panel rows show the spin degeneracy, all clearly highlighting key features in the altermagnetic state.
• Figure 4: The 2D slices of the occupation distributions within the Brillouin zone of the metallic altermagnetics (a)-(d) RuO$_2$ and (e)-(h) CrSb. The left column shows the up spin distribution and the down spin is shown on the right column. Panels (a), (c) show the RuO$_2$ spin up and down electron occupation $n(k)$ slices in the k$_{\rm z} = 0$ plane. On the other hand, panels (b) and (d) show the spin up and down electron occupation as seen by the positron $n^{2\gamma}(k)$ in that plane. Panels (e) and (g) show the CrSb spin up and down $n(k)$ in the k$_{\rm x} = 0$ plane. Whereas panels (f) and (h) show the spin up and down $n^{2\gamma}(k)$ in that plane. For each panel, the Fermi surface contours from the energy eigenvalues are plotted for comparison. The Fermi surface are also located at the steps in the occupation distributions. These occupation distributions are not convoluted with an approximate experimental resolution function. The high symmetry points are labelled as per Fig. \ref{['bands']}.