Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Zeeman-type spin splittings in strained d-wave altermagnets

Yahui Zhai, Longju Yu, Jian Lv, Wei Zhang, Hong Jian Zhao

TL;DR

The paper targets strain control of spin physics in $d$-wave altermagnets by predicting strain-induced nonrelativistic Zeeman-type spin splittings (ZSSs) that enable spin currents. It combines symmetry analysis of 58 collinear antiferromagnetic spin point groups to identify 15 SPGs capable of hosting ZSSs and derives two-band Hamiltonians $igl(\mathcal{H}(\bm{k},\eta)=\sum_{\gamma}\rho_{\gamma}k_{\gamma}^{2}+\sum_{\alpha\beta}\lambda_{\alpha\beta}k_\alpha k_\beta \sigma_\chi+\sum_{\alpha\beta}\tilde{\lambda}_{\alpha\beta}\eta_{\alpha\beta}\sigma_\chi\bigr)$ that capture both intrinsic $d$-wave spin splittings and strain-induced terms. First-principles calculations on CoF$_2$, LiFe$_2$F$_6$, and La$_2$O$_3$Mn$_2$Se$_2$ show that a $2\%$ shear strain $\eta_{xy}$ generates ZSSs up to $177$, $100$, and $102$ meV, respectively, with band dispersions near $\Gamma$ well described by the effective model. The work provides a concrete, symmetry-grounded route to engineer spin currents in altermagnets and informs design principles for altermagnetic spintronic devices, while suggesting experimental probes such as ARPES to observe the predicted ZSSs.

Abstract

Recently, altermagnetic materials have become rather attractive because such materials showcase combined advantages of ferromagnets (e.g., spin current) and antiferromagnets (e.g., low stray field and ultrafast spin dynamics). Symmetry arguments imply that $d$-wave altermagnets may host strain-induced nonrelativistic Zeeman-type spin splittings (ZSSs), and a theoretical, numerical, and experimental justification of such phenomena are of high necessity. In the present work, we work with collinear spin point groups (SPGs) and use symmetry analysis to identify 15 SPGs that host strain-induced nonrelativistic ZSSs. These 15 SPGs coincide with the cases associated with $d$-wave alternating spin splittings reported in literature. We further corroborate our analysis by first-principles numerical simulations, which indicate that a shear strain of $2\%$ creates sizable nonrelativistic ZSSs of up to 177, 100, and 102 meV in CoF$_2$, LiFe$_2$F$_6$ and La$_2$O$_3$Mn$_2$Se$_2$ $d$-wave altermagnetic semiconductors, respectively. Our work suggests an alternative route toward creating spin current in altermagnets, which may be used to design altermagnetic-based spintronic devices.

Zeeman-type spin splittings in strained d-wave altermagnets

TL;DR

The paper targets strain control of spin physics in -wave altermagnets by predicting strain-induced nonrelativistic Zeeman-type spin splittings (ZSSs) that enable spin currents. It combines symmetry analysis of 58 collinear antiferromagnetic spin point groups to identify 15 SPGs capable of hosting ZSSs and derives two-band Hamiltonians that capture both intrinsic -wave spin splittings and strain-induced terms. First-principles calculations on CoF, LiFeF, and LaOMnSe show that a shear strain generates ZSSs up to , , and meV, respectively, with band dispersions near well described by the effective model. The work provides a concrete, symmetry-grounded route to engineer spin currents in altermagnets and informs design principles for altermagnetic spintronic devices, while suggesting experimental probes such as ARPES to observe the predicted ZSSs.

Abstract

Recently, altermagnetic materials have become rather attractive because such materials showcase combined advantages of ferromagnets (e.g., spin current) and antiferromagnets (e.g., low stray field and ultrafast spin dynamics). Symmetry arguments imply that -wave altermagnets may host strain-induced nonrelativistic Zeeman-type spin splittings (ZSSs), and a theoretical, numerical, and experimental justification of such phenomena are of high necessity. In the present work, we work with collinear spin point groups (SPGs) and use symmetry analysis to identify 15 SPGs that host strain-induced nonrelativistic ZSSs. These 15 SPGs coincide with the cases associated with -wave alternating spin splittings reported in literature. We further corroborate our analysis by first-principles numerical simulations, which indicate that a shear strain of creates sizable nonrelativistic ZSSs of up to 177, 100, and 102 meV in CoF, LiFeF and LaOMnSe -wave altermagnetic semiconductors, respectively. Our work suggests an alternative route toward creating spin current in altermagnets, which may be used to design altermagnetic-based spintronic devices.

Paper Structure

This paper contains 8 sections, 7 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Results and discussion
  4. Effective Hamiltonians
  5. $d$-wave altermagnets with strain-induced nonrelativistic ZSSs
  6. Summary and outlook
  7. Note added
  8. Acknowledgement

Figures (5)

  • Figure 1: Schematic illustrations of the Brillouin zones and band structures for a $d$-wave altermagnet with nonrelativistic ASSs (a) and strain-induced nonrelativistic ZSSs (b). The spin-up and spin-down electronic states are colored in red and blue, respectively. In panel (b), $\mathbf{\Delta}$ indicates strain-induced nonrelativistic ZSSs at the zone center (i.e., $\Gamma$ point).
  • Figure 2: Panels (a), (b), and (c) sketch the collinear magnetic structures for $\mathrm{CoF_{2}}$, $\mathrm{LiFe_{2}F_{6}}$, and $\mathrm{La_{2}O_{3}Mn_{2}Se_{2}}$, respectively. The non-magnetic F, Li, La, Se and O ions are not displayed. Panels (d), (e), and (f) sketch the Brillouin zones for $\mathrm{CoF_{2}}$, $\mathrm{LiFe_{2}F_{6}}$, and $\mathrm{La_{2}O_{3}Mn_{2}Se_{2}}$, respectively. The black dashed boxes in panels (a), (b), and (c) demonstrate the cells that are used in our simulations, while the grey solid box in panel (c) represents the conventional unit cell that is employed in literature (see e.g., Ref. wei20252).
  • Figure 3: The band structures along $\mathrm{M}-\Gamma-\overline{\mathrm{M}}$ high-symmetry lines for $\mathrm{CoF_2}$ [(a), (b), and (c)], $\mathrm{LiFe_{2}F_{6}}$ [(d), (e), and (f)], and $\mathrm{La_{2}O_{3}Mn_{2}Se_{2}}$ [(g), (h), and (i)]. Panels (a), (d), and (g) are the band structures for the bulk materials without strain; Panels (b), (e), and (h) [respectively, (c), (f), and (i)] are the band structures for the strained materials with shear strain $\eta_{xy}$ of $+2\%$ [respectively, $-2\%$]. Insets in panels (b), (c) and (g) show the zoom-in band structures within the corresponding orange dashed circles. The spin-up and spin-down electronic states are colored in red and blue, respectively. The $E_{f}$ level is set as the top of the valence band.
  • Figure 4: The nonrelativistic ZSSs for $\mathrm{CoF_{2}}$, $\mathrm{LiFe_{2}F_{6}}$, and $\mathrm{La_{2}O_{3}Mn_{2}Se_{2}}$ induced by shear strain $\eta_{xy}$. The nonrelativistic ZSSs are extracted at the $\Gamma$ point for $\mathrm{CoF_{2}}$ (the two highest occupied valence bands), and at the $\Gamma$ point for $\mathrm{LiFe_{2}F_{6}}$ and $\mathrm{La_{2}O_{3}Mn_{2}Se_{2}}$ (the two lowest unoccupied conduction bands).
  • Figure 5: Panels (a), (b) and (c) are the band structures for $\mathrm{CoF_2}$, $\mathrm{LiFe_2F_6}$, and $\mathrm{La_2O_3Mn_2Se_2}$ under +2% shear strain. The solid and dashed lines indicate the results calculated by first-principles and fitted by Eq. (\ref{['eq_alter_cof']}), respectively. The $E_{f}$ level is set as the top of the valence band. The coordinates for the $\mathrm{H}$ and $\overline{\mathrm{H}}$ points, with respect to the corresponding reciprocal lattice vectors, are $(0.1, 0.1, 0)$ and $(-0.1, 0.1, 0)$, respectively.