Effect of applied pressure on the nonrelativistic spin splitting of the altermagnet FeSb 2 : A first-principles study

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We have investigated the pressure-dependent electronic structure, phonon stability, and anomalous Hall response of the recently discovered altermagnet <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>FeSb</a:mi> <a:mn>2</a:mn> </a:msub> </a:math> from density functional theory (DFT) and Wannier function analysis. From density functional perturbation theory (DFPT) calculations, we have found that <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>FeSb</b:mi> <b:mn>2</b:mn> </b:msub> </b:math> remains dynamically stable up to 10 GPa, evidenced by positive phonon frequencies. Our spin-polarized band structure reveals that the crossing nodes between the spin-up and spin-down bands near the Fermi energy occur precisely at the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi mathvariant="normal">Γ</c:mi> </c:math> and Z high-symmetry points. The Fermi crossing is mostly exhibited by band-24, band-25, and band-26. The nonrelativistic spin-splitting (NRSS) along <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msup> <e:mrow> <e:mi mathvariant="normal">M</e:mi> </e:mrow> <e:mo>′</e:mo> </e:msup> </e:math> - <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mi mathvariant="normal">Γ</g:mi> </g:math> -M and A-Z- <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:msup> <i:mrow> <i:mi mathvariant="normal">A</i:mi> </i:mrow> <i:mo>′</i:mo> </i:msup> </i:math> high symmetry paths is attributed to the symmetry operation [ <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mrow> <k:msub> <k:mi>C</k:mi> <k:mn>2</k:mn> </k:msub> <k:mrow> <k:mo>|</k:mo> <k:mo>|</k:mo> </k:mrow> <k:msub> <k:mi>C</k:mi> <k:mrow> <k:mn>2</k:mn> <k:mi>y</k:mi> </k:mrow> </k:msub> <k:mi>t</k:mi> </k:mrow> </k:math> ] and broken time-reversal symmetry ( <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mi mathvariant="script">T</l:mi> </l:math> ). Significant changes in the band structure are observed under applied pressure, as evidenced by the shift of the crossing node between bands 24 and 26 toward higher energies. The NRSS exhibited by band-24 along <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:msup> <n:mrow> <n:mi mathvariant="normal">M</n:mi> </n:mrow> <n:mo>′</n:mo> </n:msup> <n:mo>−</n:mo> <n:mi mathvariant="normal">Γ</n:mi> </n:math> -M symmetry is notably small. Although the strength of NRSS associated with band-26 along the A-Z- <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:msup> <q:mrow> <q:mi mathvariant="normal">A</q:mi> </q:mrow> <q:mo>′</q:mo> </q:msup> </q:math> path is substantial, it decreases under applied pressure. We have calculated and presented the anomalous Hall conductivity (AHC) over the energy range from <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"> <s:mrow> <s:mo>−</s:mo> <s:mn>1.5</s:mn> </s:mrow> </s:math> to 1.5 eV. The pronounced positive AHC peak at ambient pressure becomes spectrally broadened, and changes sign at 10 GPa as a result of pressure-induced modifications to the band structure and the associated redistribution of Berry curvature near the Fermi level. Furthermore, we quantify the orbital magnetization within the modern theory framework, which reaches a magnitude of 0.29 <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"> <t:msub> <t:mi>μ</t:mi> <t:mi>B</t:mi> </t:msub> </t:math> at zero pressure. Our results identify <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"> <u:msub> <u:mi>FeSb</u:mi> <u:mn>2</u:mn> </u:msub> </u:math> as a tunable altermagnetic candidate, where applied pressure can modulate both topological transport and dynamical stability, opening new avenues for strain-engineered Hall responses in compensated magnetic systems.