Noncollinear magnetic modulation of Weyl nodes in ferrimagnetic ${\mathrm{Mn}}_{3}\mathrm{Ga}$

Noncollinear magnetic modulation of Weyl nodes in ferrimagnetic ${Mn}_{3} Ga$

Cheng-Yi Huang, Hugo Aramberri, Hsin Lin, and Nicholas Kioussis

Phys. Rev. B 102, 094403 – Published 2 September 2020

Abstract

The tetragonal ferrimagnetic ${Mn}_{3} Ga$ exhibits a wide range of intriguing magnetic properties. Here, we report the emergence of topologically nontrivial nodal lines in the absence of spin-orbit coupling (SOC) which are protected by both mirror and $C_{4 z}$ -rotational symmetries. In the presence of SOC, we demonstrate that the doubly degenerate nontrivial crossing points evolve into $C_{4 z}$ -protected Weyl nodes with chiral charge of $\pm 2$ . Furthermore, we have considered the experimentally reported noncollinear ferrimagnetic structure where the magnetic moment of the ${Mn}_{I}$ atom (on the Mn-Ga plane) is tilted by an angle $θ$ with respect to the crystallographic $c$ axis. The evolution of the Weyl nodes with $θ$ reveals that the double Weyl nodes split into a pair of charge-1 Weyl nodes whose separation can be tuned by the magnetic orientation in the noncollinear ferrimagnetic structure.

Received 1 April 2020
Revised 5 July 2020
Accepted 12 August 2020

DOI:https://doi.org/10.1103/PhysRevB.102.094403

Physics Subject Headings (PhySH)

First-principles calculations Magnetism Topological materials

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Cheng-Yi Huang^1,2, Hugo Aramberri ^2,*, Hsin Lin¹, and Nicholas Kioussis ^2,†

¹Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
²Department of Physics and Astronomy, California State University, Northridge, California 91330-8268, USA

^*hugo.aramberri@list.lu
^†nick.kioussis@csun.edu

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Vol. 102, Iss. 9 — 1 September 2020

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Figure 1
(a) The tetragonal cell of the $D O_{22}$ ferrimagnetic structure with [001] spin polarization. Arrows denote the magnetic moments of ${Mn}_{I}$ (purple) and ${Mn}_{I I}$ (red) sublattices which are coupled antiferromagnetically. (b) The first Brillouin zone of the primitive cell shown in panel (a). (c) Spin-polarized band structure without SOC along the high-symmetry directions of the primitive cell where the spin-up (spin-down) bands are denoted by blue (red).
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Figure 2
(a) Spin-polarized band structure along the $k_{z}$ axis ( $Γ - M$ symmetry direction) without SOC, where the blue (black) bands denote the spin-up states calculated from GGA ( $GGA + U$ ). The two nontrivial crossing points, denoted with the blue dots, are labeled with the pair of eigenvalues ( $\pm 1, \pm 1$ ) of the mirror $M_{[110]}$ and fourfold rotational $C_{4 z}$ symmetries, respectively, which protect them. Red dots denote the nontrivial crossing points when $U$ is turned on. (b) Three-dimensional landscape of the nodal lines where the two blue dots denote the two nontrivial crossing points in (a). The color bar represents the energy of the nodal points relative to the Fermi energy.
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Figure 3
(a) Band structure along the $k_{z}$ axis ( $Γ - M$ symmetry direction) with SOC, protected by $C_{4 z}$ symmetry. The two Weyl points, denoted with red dots, have chiral charges of $\pm 2$ . $e^{- i (π / 4)}$ and $e^{i (3 π / 4)}$ indicate the eigenvalues of $C_{4 z}$ for the crossing bands, respectively. (b) Two Fermi arcs on the (100) surface where the green (red) color denotes the spectral weight of the surface (bulk) states. The solid (hollow) white circle denotes positive (negative) chiral charge, and the white arrows indicate the Fermi arcs emerging from the Weyl nodes.
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Figure 4
(a) Noncollinear ferrimagnetic $D O_{22}$ structure of ${Mn}_{3} Ga$ [34] where the ${Mn}_{I}$ atoms [on the Mn-Ga (001) plane] carry a substantial in-plane magnetic moment leading to a tilt of their moments from the crystallographic $c$ axis. (b) Evolution of Weyl nodes in the 3D BZ as a function of tilt angle $θ$ where the red, green, and blue circles denote the Weyl nodes at $θ = 180^{\circ}, 170^{\circ}$ , and $160^{\circ}$ , respectively. The dashed arrows show the motion of the Weyl points with decreasing $θ$ . At $θ = 180^{\circ}$ (collinear case), the two charge-2 Weyl nodes lie on the $C_{4 z}$ -protected $k_{z}$ axis. For $θ \neq 180^{\circ}$ , each charge-2 Weyl node splits into two charge-1 Weyl nodes which, in turn, move away from the $k_{z}$ axis. The integer above each Weyl node denotes the chiral charge.
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Physical Review B

covering condensed matter and materials physics

Noncollinear magnetic modulation of Weyl nodes in ferrimagnetic ${Mn}_{3} Ga$

Cheng-Yi Huang, Hugo Aramberri, Hsin Lin, and Nicholas Kioussis

Phys. Rev. B 102, 094403 – Published 2 September 2020

Abstract

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Physical Review B

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Noncollinear magnetic modulation of Weyl nodes in ferrimagnetic Mn3Ga

Cheng-Yi Huang, Hugo Aramberri, Hsin Lin, and Nicholas Kioussis

Phys. Rev. B 102, 094403 – Published 2 September 2020

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Noncollinear magnetic modulation of Weyl nodes in ferrimagnetic ${Mn}_{3} Ga$