[Paper Review] Hidden altermagnetism

San-Dong Guo|arXiv (Cornell University)|Nov 21, 2024

Geomagnetism and Paleomagnetism StudiesBiochemistry, Genetics and Molecular Biology3 citations

TL;DR

This paper proposes 'hidden altermagnetism'—a novel state in $PT$-symmetric antiferromagnetic bilayers where individual inversion-partner sectors exhibit local altermagnetic spin-splitting despite zero net spin polarization. First-principles calculations on $\mathrm{Cr_2SO}$ demonstrate that an external electric field lifts the degeneracy, enabling experimental detection of momentum-dependent spin-splitting, thus enabling new avenues for spintronic materials with hidden spin-polarized states.

ABSTRACT

Hidden spin polarization (HSP) with zero net spin polarization in total but non-zero local spin polarization has been proposed in certain nonmagnetic centrosymmetric compounds, where the individual sectors forming the inversion partners are all inversion asymmetry. Here, we extend this idea to antiferromagnetic materials with $PT$ symmetry (the joint symmetry of space inversion symmetry ($P$) and time-reversal symmetry ($T$)), producing zero net spin polarization in total, but either of the two inversion-partner sectors possesses altermagnetism, giving rise to non-zero local spin polarization in the real space, dubbed "hidden altermagnetism". By first-principle calculations, we predict that $PT$-symmetric bilayer $\mathrm{Cr_2SO}$ can serve as a possible candidate showing altermagnetic HSP. By applying an external electric field to break the global $P$ symmetry, the hidden altermagnetism can be separated and observed experimentally. Our works extend the hidden physics, and will also advance the theoretical and experimental search for new type of spin-polarized materials.

Motivation & Objective

• To extend the concept of hidden spin polarization (HSP) to antiferromagnetic systems with $PT$ symmetry.
• To identify materials where local altermagnetism exists without net magnetization due to inversion symmetry.
• To propose a method for experimentally detecting hidden altermagnetism using an external electric field.
• To demonstrate the feasibility of hidden altermagnetism in a real material system, $\mathrm{Cr_2SO}$, via first-principles calculations.

Proposed method

• Theoretical framework is developed to define hidden altermagnetism as local altermagnetic spin-splitting in $PT$-symmetric antiferromagnets with inversion-partner sectors.
• First-principles density functional theory (DFT) calculations are performed using VASP on $\mathrm{Cr_2SO}$, including spin-orbit coupling (SOC).
• An external electric field is applied along the $z$-direction to break global $P$ symmetry and lift degeneracy, enabling detection of spin-splitting.
• The spin-splitting is analytically estimated using $eEd$, where $e$ is electron charge and $d$ is interlayer distance.
• Magnetocrystalline anisotropy energy (MAE) is calculated to assess the easy axis of magnetization.
• Valley polarization is evaluated by analyzing band splitting between $X$ and $Y$ valleys under in-plane magnetization and SOC.

Experimental results

Research questions

• RQ1 Can altermagnetic spin-splitting be hidden in a $PT$-symmetric antiferromagnetic system with zero net spin polarization?
• RQ2 How can hidden altermagnetism be experimentally accessed in a system with global inversion symmetry?
• RQ3 What role does an external electric field play in revealing local altermagnetic order in such systems?
• RQ4 What is the magnitude and field dependence of the spin-splitting in the proposed $\mathrm{Cr_2SO}$ bilayer?
• RQ5 Can intrinsic magnetization in $\mathrm{Cr_2SO}$ induce valley polarization when spin-orbit coupling is included?

Key findings

• The $\mathrm{Cr_2SO}$ bilayer exhibits hidden altermagnetism with non-zero local spin polarization in each inversion-partner sector despite zero net spin polarization.
• An external electric field of 0.03 V/Å induces a spin-splitting of approximately 203 meV, closely matching the analytical estimate of 207 meV via $eEd$.
• The spin-splitting increases linearly with electric field strength, confirming tunability via external control.
• The magnetization direction in $\mathrm{Cr_2SO}$ is in-plane, with negative magnetocrystalline anisotropy energy, indicating in-plane easy axis.
• With spin-orbit coupling, a valley splitting of 4.0 meV in the conduction band and 2.0 meV in the valence band is observed between $X$ and $Y$ valleys.
• Reversing the electric field direction reverses the layer-character and spin-splitting order, confirming controllability of the hidden state.