Exploring Altermagnetism in Orthorhombic Pnma structure through Group Theory and DFT Calculations

Magnetism stands as a cornerstone in condensed matter physics,
playing a crucial role in various technological advancements. Magnetic
solids are typically divided into two broad categories: ferromagnet (FM)
and antiferromagnet (AFM). FM exhibits a net magnetization in direct
space, leading to intriguing phenomena stemming from the electronic spin
split band structure in the reciprocal space that breaks the time reversal
(T) symmetry in the non-relativistic (NR) limit. On the contrary, in a
conventional AFM, due to the compensating antiparallel magnetic ordering,
resulting in negligible small macroscopic magnetization, implying the
absence of spin split band structure, thereby preserving the T symmetry in
reciprocal space in the NR limit. However, recent research has sparked a
growing interest in exploring the T reversal symmetry-breaking macroscopic
phenomena and the existence of NR spin-splitting [1], characteristics
typically associated with FM, in compounds with vanishingly small
magnetization, which is characteristic of an AFM. This abundant and
previously unexplored magnetic phase has been termed Altermagnet (AM) [2].
Intriguingly, we identify two centrosymmetric materials, bulk orthorhombic
BiFeO3 (BFO) and CaMnO3 (CMO), that exhibit such NR spin-splitting
phenomena. Through Density Functional Theory (DFT), we unveil an
insulating state in both compounds with a preferred AFM order. Our DFT
calculations and the magnetic space group (MSG) symmetry analysis in the
NR limit uncover a substantial spin splitting phenomena observed only in
the ky − kz plane in the Brillouin zone (BZ) for both compounds. In
contrast, the spin degeneracy is maintained in the kx − ky and kx − kz
planes, respectively. Using the invariant theory, we also formulate the
governing Hamiltonian for the spin split pair of bands near the high
symmetry Γ point. Finally, we extend our findings to encompass two
possible MSGs falling within the Pnma space group that support such NR
spin-splitting phenomena along with the probable form of their Hamiltonian
[3]. In this talk, I will briefly provide
an overview of altermagnetism and its distinctions from the other two
conventional magnetic phases. Further, I will discuss our DFT findings and
symmetry analysis on two representative altermagnetic materials.

References:

[1] L. D. Yuan, Z. Wang, J. W. Luo, E. I. Rashba, and A. Zunger, "Giant
momentum-dependent spin splitting in centrosymmetric lowZ
antiferromagnets," Phys. Rev. B 102, 014422 (2020).

[2] L. Smejkal, J. Sinova, and T. Jungwirth, "Emerging Research Landscape
of Altermagnetism," Phys. Rev. X 12, 040501 (2022).

[3] S. Rooj, S. Saxena, and N. Ganguli, "Exploring Altermagnetism in
Orthorhombic Pnma structure through Group Theory and DFT Calculations,"
arXiv:2406.06232 (2024)