A Large Faraday Effect Observed in An Atomically Thin Material

(From L to R): Dirk van der Marel, Alexey Kuzmenko, Julien Levallois and Iris Crassee of University of Geneva

A team of physicists from the University of Geneva (Switzerland) -- in collaboration with researchers in the University of Erlangen-Nuremberg (Germany) and Berkeley Advanced Light Source (USA) -- has recently measured the magnetically induced rotation of the polarization of light (Faraday rotation) [1] in graphene in the far-infrared range.

In contradiction to the common logics, the rotation angle, which is usually proportional to sample thickness, appears to be very strong – up to a few degrees in a single atomic layer. Such a large effect, which is due to the cyclotron resonance of ‘relativistic’ electrons in graphene, does not only provide a useful contact free tool to study the dynamics of the charge carriers in graphene, but also suggests that graphene can be used to manipulate the state of the optical polarization. This work is published in a recent issue of Nature Physics [2].

Graphene is a single layer of carbon atoms arranged in a honeycomb lattice. Electrons in graphene behave like massless relativistic particles moving with a velocity of about 300 times smaller than the speed of light [3]. A high mobility of charge carriers makes graphene potentially useful for electronics. Moreover, graphene shows unique optical properties such as the universal transparency [4], which in combination with excellent electrical conductivity favor its use in important optical applications, such as solar cells, infrared detection, computer screens and ultra fast lasers [5].

On the left: A schematic representation of the Faraday rotation. On the right: the Faraday rotation as a function of the photon energy and the magnetic field (This figure is reproduced from Reference [2]. We thank authors of the paper and 'Nature Physics' for their permission. -- 2Physics.com)

When an external magnetic field is applied over a medium it becomes magnetically polarized and the state of the optical polarization of light passing through the medium is affected: linearly polarized light is rotating gradually during its passage due to a difference in velocity and absorption of left- and right-handed polarized light. The rotation angle, also known as the Faraday angle, is proportional to the optical path length, to the applied magnetic field and a material specific parameter, the Verdet constant, which depends on the wavelength of the passing light. The ‘thickness’ of graphene is given by the inter atomic distance of graphite – stacked graphene layers; therefore an intriguing question is what happens to the optical polarization state if the optical path is as short as only one atom.

Iris Crassee, Julien Levallois, Dirk van der Marel and Alexey Kuzmenko at the University of Geneva have studied the Faraday rotation in the far-infrared range by graphene, epitaxially grown on SiC and characterized in the University of Erlangen-Nuremberg and Berkeley Advanced Light Source [2]. The experiments showed that even for such an extremely thin layer the Faraday rotation can reach 6 degrees in a moderate magnetic field of 7 Tesla (see the figure). If one could be able to stack several graphene layers at distances similar to interlayer spacing in graphite (about 0.35 nm) without changing their individual properties then the effective Verdet constant of such a material can in principle attain a few times of 10⁷ radian/(meter∙Tesla). For comparison, the Verdet constants of the magneto-optical materials used in the visible range, such as rare-earth garnets, are only of the order of 10²-10³ radian/(meter∙Tesla). A more appropriate, though, would be to compare the Faraday rotation in graphene and in the semiconductor-based two-dimensional electron gases (2DEGs) in the same spectral range (far-infrared and teraherz). The fact is that the effective Verdet constant in graphene is still at least one to two orders of magnitude larger!

The origin of the observed Faraday rotation is in a peculiar cyclotron orbital motion of nearly massless electrons in graphene in a magnetic field. A similar effect can also be observed in 2DEGs. However, the cyclotron mass and therefore the cyclotron frequency (at a given magnetic field) in 2DEGs are fixed. In graphene they can be varied with doping. Moreover, since graphene can be doped both positively and negatively either electrostatically or chemically, the cyclotron frequency, and therefore the direction of the Faraday rotation, can be inverted without changing the magnetic field.

The Faraday effect and the associated magneto-optical Kerr effect are already widely used in such vital applications as optical communications, data storage and laser systems, largely in the visible range. Although the Faraday rotation in graphene was shown to be strong in the by far less exploited far-infrared part of the electromagnetic spectrum, one can nevertheless think of using graphene for example, in ultrathin and ultra fast tunable ‘Faraday isolators’, in which light can travel in one direction, but is blocked in the other. In contrast to the existing devices, one should be able to tune the spectral range and also change the sign of the Faraday rotation in graphene by simply adjusting the gate voltage.

References
[1] M. Faraday, “On the magnetization of light and the illumination of magnetic lines of force”, Phil. Trans. R. Soc. 136, 104 (1846).
[2] I. Crassee, J. Levallois, A.L.Walter, M. Ostler, A. Bostwick, E. Rotenberg, Th. Seyller, D. van der Marel and A. B. Kuzmenko, “Giant Faraday rotation in single- and multi ayer graphene”, Nature Physics, 7, 48-51 (2011). Abstract.
[3] A. K. Geim and K. S. Novoselov, “The rise of graphene: Nature Materials, 6, 183 (2007). Abstract.
[4] R.R. Nair, P. Blake, A.N. Grigorenko, K.S. Novoselov, T.J. Booth, T. Stauber, N.M.R. Peres and A.K. Geim, “Fine structure constant defines visual transparancy of graphene”, Science 320, 1308 (2008). Abstract.
[5] F. Bonaccorso, Z. Sun, T. Hasan and A. C. Ferrari, “Graphene photonics and optoelectronics”, Nature Photonics, 4, 611 (2010). Abstract.