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 N\'eel operator $\tau$ such that a nonzero expectation value $\langle \tau \rangle$ 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 $\langle \tau \rangle$ 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 $\langle \tau \rangle$. 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.
Highlights
The technological viability of alternative spin-based electronics prototypes [1,2,3] hinges on the ability to efficiently manipulate magnetizations using electric currents or voltages
We present a detailed theoretical study of how magnetoelectricity arises in magnetically ordered quantum wells with broken time-reversal symmetry and broken space-inversion symmetry
Quasi-2D systems based on zincblende ferromagnets [Fig. 1(b)] and diamond-structure antiferromagnets [Fig. 1(c)] exhibit an analogous linear magnetoelectric response, i.e., an in-plane magnetization induced by a perpendicular electric field [Eqs. (34) and (77)], as well as a perpendicular electric polarization arising from an in-plane magnetic field [Eqs. (46) and (88)]
Summary
The technological viability of alternative spin-based electronics prototypes [1,2,3] hinges on the ability to efficiently manipulate magnetizations using electric currents or voltages. The magnetoelectric response of the antiferromagnetic system can be related to the modification of the quadrupolar equilibrium-current distribution associated with antiferromagnetic order by external electric and magnetic fields This is in line with the fact that the magnetoelectric tensor αi j behaves under symmetry transformations like a magnetic quadrupole moment [50], i.e., both of these second-rank material tensors require broken spaceinversion symmetry and broken time-reversal symmetry and these tensors share the same pattern of nonzero components, though microscopically they are generally not related to each other. Accurate numerical calculations utilizing realistic 8 × 8 and 14 × 14 k · p Hamiltonians establish a typically large, practically relevant magnitude of the electric-field-induced magnetization in holedoped quantum wells made from zincblende ferromagnets or diamond-structure antiferromagnets.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
