Magneto-optical effect in ferronematic cell with combined boundary conditions S .V.Burylov*, I.P.Pinkevich#, V.Yu.Reshetnyak# V.I.Zadorozhnii# *Institute of Transport Systems and Technologies, National Academy of Sciences of Ukraine, Pisargevskogo St., 5, Dnepropetrovsk, 49005, Ukraine # Physics Faculty, Kyiv Taras Shevchenko University, Prosp. Glushkova, 6, Kyiv, 03680, Ukraine Magnetic Fredericksz-like transition is theoretically investigated in a homeotropic ferronematic planeparallel cell with different director anchoring (strong and weak) on the cell walls. The optical birefringence of a ferronematic sample and its dependence on the value of applied magnetic field and anchoring energy is studied. Keywords : ferronematic, Fredericksz transition, optical birefringence 1. Introduction Suspensions of colloidal particles in nematic liquid crystals are very promising liquid-crystalline materials for technical applications. These heterogeneous systems combine anisotropic properties of the nematic host and specific (optical, magnetic etc.) properties ofthe disperse phase. As a result, composite liquid crystal materials differ essentially from pure nematics in a number of physical parameters. An example of such systems is a ferronematic (FN) where the role of the disperse phase is played by needle-shaped monodomain ferro- or ferrimagnetic particles (concentration — lO÷1O vol.%). The magnetic susceptibility of the FN's is several orders of magnitude higher than that of pure nematics. Therefore, this enables us to control the orientational state of the ferronematics with weak (1O Oe) magnetic fields [1—3]. In this paper we have theoretically investigated a magnetic Fredericksz-like transition in a homeotropic FN cell and calculated the optical birefringence of orientationally deformed FN sample. Note that this transition was studied in [4] for the case of infinitely strong director anchoring on the cell walls. Below we consider a more general case of combined boundary conditions, namely: one of the cell walls provides infinitely strong director anchoring while on the other wall the anchoring energy has some finite value. We calculate dependence of the optical birefringence on the value of applied magnetic field strength and anchoring energy. The paper is organised as follows. In Sec.2 we describe the geometry of the cell and discuss some general properties of FN. In Sec.3 we write down the total free energy functional and obtain equations for equilibrium state of FN. In Sec.4 we discuss the induced optical birefringence ofFN cell and analyse the results ofnumerical calculations. 2. Geometry of ferronematic cell Consider a planeparallel cell filled with homeotropically oriented FN. We assume that upper plane of the cell provides director anchoring with strength W and at the bottom plane director anchoring is infinitely strong. The magnetic particles of FN have a needle-shaped form. The characteristic sizes of the ferroparticles, i.e. their length L and diameter d — L/1O, are great in a comparison with the size a of the nematic molecules: L>>d>>a. Therefore, one can consider the ferroparticles as small but macroscopic objects. We suppose a homeotropic director anchoring on the particles surface with anchoring energy Wpat. In the absence of external fields the equilibrium orientation of long axes of the ferroparticles has been determined in paper [5]. It was theoretically predicted in [5], that if a dimensionless parameter 0pat = (Wpatd/2K), where K is the mean value of the nematic elastic constant, satisfies the condition Opat> o 1, the long axes of ferroparticles are oriented along the initial director n0, while for the opposite case (Opat4O* they are perpendicular to n0. For real termotropic FN with d71O6 cm, K—S 1 O dyn, Wpat —1 02 dynlcm one can obtain Wpat — 71 02 <<w* ; the corresponding experimental results [1-3] show that, in accordance with the theory [5], ferroparticles are oriented in the plane perpendicular to the unperturbed director n0. Note that in the case of real FN there is a magnetic anisotropy of the "easy-plane" type for the orientations of the magnetic moments , of the ferroparticles. So in the absence of external fields FN state is magnetically compensated, i.e. the Eighth International Conference on Nonlinear Optics of Liquid and Photorefractive Crystals, Gertruda V. Klimusheva, Andrey G. Iljin, Editors, Proceedings of SPIE Vol. 4418 (2001) © 2001 SPIE · 0277-786X/01/$15.00 1