Luminescence properties of magnetic polarons in EuTe: Theoretical description and experiments in magnetic fields up to 28 T

Abstract

The recent discovery of a polaron-associated zero phonon line in the band-edge photoluminescence of high optical quality EuTe crystals opens up the prospect of answering long-standing questions about the polaron internal structure, thermal stability, and generation efficiency. Here, a Schrödinger equation for the polaron was formulated and resolved by using both variational and self-consistent methods. The theory is in good agreement with measurements of the zero phonon line as a function of magnetic field and temperature, and it could be applied to other polaronic systems. It is deduced that, in EuTe, at 0 K, a polaron carries a magnetic moment of 610μ B , and its binding energy is 27 meV. However, this binding energy does not carry the usual meaning of thermal stability, because it decreases drastically when the sample is warmed up. For instance, at T = 100 K, the binding energy is already reduced to only 6 meV. The thermal destruction of a polaron is brought about by thermal fluctuations of the spin lattice that suppress the electron's self-energy. Photoluminescence excitation spectra of EuTe demonstrate that the photogeneration of polarons becomes increasingly inefficient when the energy of the pumping photon is increased above the band gap.

Modeling huge photoinduced spin polarons in intrinsic magnetic semiconductors

“…SPs are formed due to the exchange interaction between between an electron in the photoexcited state state and the lattice spins. This interaction is described by an effective magnetic field, B Xf , acting on the lattice spins, which at a distance r from the electron is given by [5]…”

“…This equation shows that the greater the competing field B 0 , the smaller the radius of the SP. In EuTe, the magnetic anisotropy is described by a spin-flop field of magnitude about 0.1 T [5,16], hence it is reasonable to assume B 0 = 0. [4].…”

“…Recently, it was experimentally demonstrated that in the antiferromagnetic members of the europium chalcogenide series EuX (X=O, S, Se, Te), a single photon can generate a very large spin polaron (SPs), reaching hundreds, or even thousands of Bohr magnetons [1,[3][4][5][6][7]. In the ferromagnetic compound EuS, the size of the SPs surpasses 10,000 Bohr magnetons [2].…”

“…This paper presents the first theory ever reported on the temperature dependence of size of very large photoinduced SPs in magnetic semiconductors. The work developed here is based on an effective mass self-consistent Hamiltonian describing the photoinduced SP, which includes the kinetic energy of the photogenerated band electron, its Coulomb interaction with the hole, its exchange interaction with lattice spins, the exchange interaction between lattice spins, and an applied magnetic field [5]. The spin polarons induced by charge carriers can be described more fully by a Kondo Hamiltonian [12,13], but this more complex approach is beyond the scope of this paper, given that the simple effective mass Hamiltonian [5] describes sufficiently well the temperature dependence of the SP size analyzed in this work.…”

Indução ótica de magnetização em semicondutores magnéticos

“…onde a bé o raio de Bohr. Dessa forma, uma das maneiras de encontrar a energia do polaroń e tratar a energia da rede (interações de troca e energia Zeeman) como uma perturbação no sistema de umúnico elétron, e utilizar o raio de Bohr como parâmetro variacional para minimizar a energia [21]. A simetria esférica da função de Bohr simplifica o cálculo da energia de cada spin e a simplicidade do método variacional, que será discutido a seguir, permite o cálculo, sem muito esforço, de parâmetros relevantes do polaron em baixas temperaturas.…”