Collinear Orbital Antiferromagnetic Order and Magnetoelectricity in Quasi-2D Itinerant-Electron Paramagnets, Ferromagnets and Antiferromagnets

Abstract

We develop a comprehensive theory for magnetoelectricity in magnetically ordered quasi-2D systems whereby in thermal equilibrium an electric field can induce a magnetization $m$ and a magnetic field can induce a polarization. This effect requires that both space-inversion and time-reversal symmetry are broken. Antiferromagnetic (AFM) order plays a central role in this theory. We define a Néel operator $\tau$ such that a nonzero expectation value $⟨\tau ⟩$ signals AFM order, in the same way $m$ signals ferromagnetic (FM) order. While $m$ is even under space inversion and odd under time reversal, $\tau$ describes a toroidal moment that is odd under both symmetries. Thus $m$ and $⟨\tau ⟩$ quantify complementary aspects of magnetic order in solids. In quasi-2D systems FM order can be attributed to dipolar equilibrium currents that give rise to $m$. In the same way, AFM order arises from quadrupolar currents that generate the moment $⟨\tau ⟩$. The electric-field-induced magnetization can then be attributed to the electric manipulation of the quadrupolar currents. We develop a $k\cdot p$ envelope-function theory for AFM diamond structures that allows us to derive explicit expressions for the operator $\tau$. Considering FM zincblende and AFM diamond, we derive quantitative expressions for the magnetoelectric responses due to electric and magnetic fields that reveal explicitly the inherent duality of these responses required by thermodynamics. Magnetoelectricity is found to be small in realistic calculations for quasi-2D electron systems. The magnetoelectric response of quasi-2D hole systems turns out to be sizable, however, with moderate electric fields being able to induce a magnetic moment of one Bohr magneton per charge carrier. Our theory provides a broad framework for the manipulation of magnetic order by means of external fields.

32 pages, 9 figures

References in corpus (6)

• Theory of ferromagnetic (III,Mn)V semiconductors
• Theory of orbital magnetoelectric response
• Intraband and interband spin-orbit torques in non-centrosymmetric ferromagnets
• Full magnetoelectric response of Cr2O3 from first principles
• Symmetry analysis of current-induced switching of antiferromagnets
• Spin order and dynamics in the diamond-lattice Heisenberg antiferromagnets CuRh2O4 and CoRh2O4

Cited by in corpus (9)

• Roadmap of spin-orbit torques
• Perspective on Metallic Antiferromagnets
• Theory of electric, magnetic, and toroidal polarizations in crystalline solids with applications to hexagonal lonsdaleite and cubic diamond
• Kinetic magnetoelectric effect in topological insulators
• Quantum theory of the Intrinsic Orbital Magnetoelectric Effect in itinerant electron systems at finite temperatures
• Magnetoelectricity in two-dimensional materials
• Orbital Gravito-Magnetoelectric response and Orbital magnetic quadrupole moment correction
• Standard model of electromagnetism and chirality in crystals
• Time inversion symmetry in the Dirac and Schrödinger-Pauli theories