“Rectangular samples with $L_x eq L_y$ host a finite spin polarization, which vanishes in the symmetric limit $L_x=L_y$ and in the thermodynamic limit.”

“The paper formulates a gauge-invariant expression for the orbital magnetic octupole moment and links it to a higher-rank Hall response induced by spatially nonuniform electric fields.”

“Atomic-scale visualization of d-wave altermagnetism is the core achievement.”

“The switching polarity is dictated by chirality rather than charge current polarity.”

“The paper finds a g-wave altermagnetic spin liquid as the unique ground state for the spin-3/2 model and a richer phase diagram for the spin-7/2 model, including d-wave altermagnetic spin liquids and chiral spin liquids.”

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“The paper highlights the creation of coexisting helical Fermi arcs with opposite chirality on the same surface, a phenomenon not found in conventional magnetic Weyl semimetals.”

“Cr doping drives a transition to an A-type AFM phase that breaks Kramers spin degeneracy and realizes a g-wave altermagnetic state with large nonrelativistic spin splitting near the Fermi level. Importantly, this spin splitting can be deterministically reversed by polarization switching, enabling electric-field control of altermagnetic electronic structure without reorienting the Neel vector or relying on spin-orbit coupling.”

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“The article likely discusses the experimental setup, the theoretical framework, the results of the spin sensing, and the implications of the findings for understanding altermagnetism and potential applications.”

“Ultrahigh Charge-to-Spin Conversion and Tunneling Magnetoresistance are observed.”