Theoretical investigation on organic magnetoresistance based on Zeeman interaction

doi:10.1016/j.orgel.2011.07.017

Organic Electronics

Volume 12, Issue 11, November 2011, Pages 1835-1840

https://doi.org/10.1016/j.orgel.2011.07.017 Get rights and content

Abstract

Based on the magnetic field-spin Zeeman interaction, a mechanism is suggested to explain the organic magnetoresistance (OMR). It is found that a considerable magnetoresistance (MR) could be obtained in organic semiconductors (OSCs). The value of MR is sensitive to the carrier concentration and the mobility (or the charge-transfer integral). We speculate that the MR in organic materials should be phonon dependent. This investigation is consistent with the present experimental observations on OMR.

Graphical abstract

Highlights

►The peculiar properties of the organic materials are stressed in the study of OMR. ► The two important features of OMR can be obtained in our simulation. ► A well consistency with experimental results can also be obtained. ► We think that the specific MR in organic materials should be phonon dependent.

Introduction

Investigation on organic semiconductors (OSCs) has greatly been motivated by device applications such as organic light emitting diodes (OLEDs) [1], organic field effect transistors (OFETs) [2] and organic photovoltaic cells (OPVs) [3]. Recently, organic spintronics including spin injection, transport and detection in these materials has become a new hot subject of research [4], [5], [6]. Especially a strong organic magnetic-field effect (OMFE), i.e., a low magnetic field (in the scale of mT) can substantially change the electroluminescence, photoluminescence, photocurrent, and electrical-injection current, is relatively easy to be obtained in an OSC compared to its inorganic counterparts [7], [8]. The importance of OMFE is largely due to its fundamental science research and technology applications. Firstly, there is a belief that OMFE can be used as a powerful tool to probe microscopic process occurring in organic materials. Secondly, OMFE can also be used to develop new multifunctional organic devices integrating electronic, optical, and magnetic properties for energy conversion, optical communication and weak magnetic field sensing [9]. In the last few years, many groups in this community have done a lot of experiments, the results show that OMFE has the following surprising yet universal features: (1) the OMFE appears in vast different OSCs without any magnetic elements at room temperature. (2) The OMFE is sensitive to a very weak magnetic field and would be nearly saturated in a relative strong magnetic field. (3) Especially, the OMFE can often be fitted by two empirical formulas, (here we take the organic magnetoresistance (OMR) for example): ΔR(B)/R ∝ B²/(∣B∣ + B₀)² or $Δ R (B) / R \propto B^{2} / (B^{2} + B_{0}^{2})$ depending on the material [8], where ΔR(B) is the resistance difference with and without the external magnetic field, B₀ is a fitting constant.

Although some achievements have been obtained in experiments all of these days, the mechanism governing OMFE is highly debated and the origin has not been achieved with one voice. Three models have come to the forefront to explore the origin of the OMFE: (1) the electron–hole pair model [9], [10], which is based on spin-dependent singlet/triplet exciton formation from electron–hole pair. (2) The triplet exciton–polaron quenching model [11], which is based on the quenching action between the a triplet exciton and a polaron. (3) The bipolaron model [12], which treats the spin dependent formation of double occupied sites during the hopping transport through the organic film. All these models are based on an assumption that the localized carriers (charged polarons) are spin sensitive to the external magnetic field and the internal hyperfine field of the hydrogen nucleus [13]. For the Zeeman mechanism, researchers seem to be also puzzled that why an extremely small Zeeman energy $(| - g μ_{B} \vec{S} \cdot \vec{B} | \sim 10^{- 5} eV$ for 1 T) can beat the thermal energy (k_BT ∼ 0.026 eV at room temperature) to generate this OMFE. It is regretful that none of these models can give a quantitative explanation on the OMFE. Maybe a dynamic response theory of the spin to the magnetic field is needed to understand the OMFE, which there is not yet a report up to now. Recently the field-induced hopping mechanism has also been suggested [14], which believes that the hopping transport in OSCs is changed due to the Lorentz charge-magnetic field interaction but not the Zeeman spin-magnetic field one. However, the field-induced hopping mechanism still needs a further confirmation quantitatively for actual organic materials. In this paper, we try to give an analysis on the OMFE by calculating the magnetoresistance of an OSC based on the Zeeman mechanism. In our picture, the distinct properties of OSCs from that of inorganic counterparts are focused and it is found that the OMR is tightly related with these properties. We believe that this mechanism plays an important role in the understanding of OMFE. In the following section, the model and the method are presented. The results and discussions are shown in Section 3. Finally, in Section 4 a summary is given.

Section snippets

Model and method

Organic materials usually appear amorphous structure in the fabrication progress, such as spin coating or thermal evaporation. Theoretical investigation on the transport in an organic material or device is considered in two ways: one is based on the band transport mechanism and the disordered is partly included by considering the atomic position fluctuation [15]. Another is based on the hopping mechanism. In this mechanism, the transport is reflected by the Marcus formula of the hopping rate $κ_{ij} =$

Results and discussion

For a given carrier concentration n_e, the electronic eigenvalues ε_μ are solved with a self-consistently iteration method. The DOS is obtained by the Lorentz line shape formula, $ρ (ε) = \sum_{μ} \frac{1}{π} \frac{δ}{(ε - ε_{μ})^{2} + δ^{2}}$ where δ is the Lorentz parameter and $\sum_{μ}$ is sum over all the eigenvalues. The Fermi level of the system is determined by the total number of iterant electrons (carriers) and the MR is calculated from Eq. (5). In the following calculations, the electron–phonon coupling constant α is chosen as 110 meV/Å

Summary

In summary, we have performed a theoretical study on the mechanism of OMR based on the magnetic field-spin Zeeman interaction. Firstly we give a preliminary discussion based on the hopping mechanism and could not get a desired result. Then we performed a thorough investigation on the OMR based on the band conduction. It is found that the peculiar properties of the organic materials are important factors in the explanation of OMR. Also the value of OMR is found to be dependent on the

Acknowledgments

The authors would like to acknowledge the financial support from the National Basic Research Program of China (Grant Nos. 2009CB929204 and 2010CB923402) and the National Natural Science Foundation of the People’s Republic of China (Grant No. 10874100).

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Theoretical investigation on organic magnetoresistance based on Zeeman interaction

Abstract

Graphical abstract

Highlights

Introduction

Section snippets

Model and method

Results and discussion

Summary

Acknowledgments

Synth. Metals

Solid State Commun.

Synth. Metals

Appl. Phys. Lett.

Appl. Phys. Lett.

Nature

Appl. Phys. Lett.

J. Vac. Sci. Technol. A

Phys. Rev. B

Adv. Mater.

Synth. Metals

Phys. Rev. B

Phys. Rev. Lett.