faraday effect in sn_2p_2s_6 crystals

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  • Faraday effect in Sn2P2S6 crystals

    Oleh Krupych,1 Dmytro Adamenko,1 Oksana Mys,1 Aleksandr Grabar,2

    and Rostyslav Vlokh1,*1Institute of Physical Optics, 23 Dragomanov Street, 79005 Lviv, Ukraine

    2Institute for Solid State Physics and Chemistry, Uzhgorod National University,54 Voloshyn Street, 88000 Uzhgorod, Ukraine

    *Corresponding author: vlokh@ifo.lviv.ua

    Received 29 May 2008; revised 3 October 2008; accepted 3 October 2008;posted 8 October 2008 (Doc. ID 96761); published 5 November 2008

    We have revealed a large Faraday rotation in tin thiohypodiphosphate (Sn2P2S6) crystals, which makesthis material promising for magneto-optics. The effective Faraday tensor component and the Verdet con-stant for the direction of the optic axis have been determined by measuring the pure Faraday rotation inSn2P2S6 crystals with both the single-ray and small-angular polarimetric methods at the normal con-ditions and a wavelength of 632:8nm. The effective Verdet constant is found to be equal to 115 rad=T m. 2008 Optical Society of AmericaOCIS codes: 260.1180, 260.2130, 260.5430, 230.2240, 230.3810.

    1. Introduction

    The tin thiohypodiphosphate crystals belong to thefamily of ferroelectric semiconductor Sn2xpb21xS6ySe61y crystals (see [1]). These crystals are transpar-ent in a wide spectral range (0:538:0 m [2]) and pos-sess ferroelectric phase transition at Tc 337K,which changes the point group of symmetry accordingto the scheme 2=mFm. These crystals attract the in-terest of researchers because of their good electro-optic [3,4], piezo-optic [5,6], acousto-optic [7] andphotorefractive [8,9] properties. Previous researchhas shown that Sn2P2S6 crystals are characterizedby very high electro-optic coefficients (r11 174pm=V [4]) and an acousto-optic figure of merit(M2 1:7 0:4 1012 kg=s3 [7]).On the other hand, based on the natural assump-

    tion that the values of electro-optic and electrogyra-tion coefficients of any material must be of a similarorder of magnitude (see, e.g., [10]) and taking into ac-count that Sn2P2S6 crystals are proper ferroelectrics(that means that the changes in both optical birefrin-gence and optical activity occurring at the phasetransition are directly caused by spontaneous elec-

    tric polarization), it is possible to estimate roughlythe values of their electro-optic and electrogyrationcoefficients. Then, the electrogyration coefficientfor Sn2P2S6 could be estimated as 1010m=V[11],whereas, for most of the compounds studied pre-viously, it is of the order of 1012m=V. In general,all the data on the optical properties of Sn2P2S6 crys-tals obtained up to the present suggest high figuresof merit for different optical effects in these crystalsinduced by external fields. This means that the crys-tals may be applied when operating efficiently theoptical radiation. However, where the induced opti-cal activity effect and, in particular, the Faradayrotation are concerned, the experimental data havenot been presented in the literature. The reasonsfor the lack of the induced optical activity and theFaraday optical activity data for Sn2P2S6 crystalsare probably concerned with a low symmetry of thesecrystals. They are optically biaxial, thus assumingquite complicated experimental conditions for thecorresponding measurements.The optical gyration can exist below the phase

    transition temperature of Sn2P2S6 . Here, the do-mains with the opposite signs of spontaneous electricpolarization should be enantiomorphous, becausethe center of symmetry is lost during the phase tran-sition. In our recent report [11], we showed that the

    0003-6935/08/326040-06$15.00/0 2008 Optical Society of America

    6040 APPLIED OPTICS / Vol. 47, No. 32 / 10 November 2008

  • natural optical rotation in Sn2P2S6 crystals mea-sured along the optic axis reaches high values atroom temperature ( 44 1:5 deg =mm). The aimof the present work is to study the Faraday rotationin Sn2P2S6 crystals.

    2. Experimental

    As mentioned above, Sn2P2S6 crystals are opticallybiaxial. The axes of the Cartesian frame of reference[Fig. 1(a)] are very close to the crystallographic ones,with the only difference that the axes a and c of thelatter are slightly nonorthogonal. For room tempera-ture and a light wavelength of 632:8 nm, theplane of the optic axes is parallel to the b axis, beingrotated by 45 with respect to the a and c axes (see[12]). Under the same conditions, the angle betweenthe optic axes is equal to90. The optical rotation inpure form should manifest itself if the light propa-gates along one of the optic axes [see Fig. 1(b)] [11].As one can see fromFig. 1(b), optical rotation should

    have the same magnitude and opposite signs whenthe light propagates along different optic axes. Takinginto account the orientation of the plane of the opticaxes and denoting the angle between the plane of theoptic axes and the a axis as , one can derive the rela-tions for the angles and (where a sin cos,b sin sin, c cos, 1a, 2b, and 3c):

    arcsin

    cosV1 sin2Vsin2

    p;

    arccossin sinV;1

    where V means the angle between the optic axis andtheaaxis (i.e.,2V is the angle between the optic axes).For room temperature and 632:8nm, we have 45 deg, V 45 deg [12], 55 deg, and 57 deg (the conoscopic fringes appearing in the case

    when the light propagates along one of the optic axesin Sn2P2S6 crystals are presented in Fig. 2).The Faraday effect is described by the relations

    Bjk B0jk iejklFlmHm;l n3 FlmHm;

    VF n3 Flm; 2

    where l is the angle of the specific rotation of thelight polarization plane, Bjk is the actual optical-frequency dielectric impermeability tensor, B0jk isthe optical-frequency dielectric impermeability ten-sor before the application of magnetic field Hm, ejklis the unit LeviCivita tensor, n is the mean refrac-tive index, VF is the Verdet constant, and Flm is theFaraday tensor. For the point symmetry groupm, thelatter has the following form:

    H1 H2 H31 n

    3

    F11 0n3 F13

    2 0 n3

    F22 0

    3 n3

    F13 0n3 F33

    : 3

    Application of a magnetic field along the optic axisleads to three nonzero components of that field H1 H3 H cos 0:5H and H2 H cos 45 0:707H.Let the directions of the light propagation and themagnetic field be parallel to the optic axis. Thenthe rotation of the polarization plane inducedmagne-tically is equal to

    n3m

    F033H; 4

    where nm 3:0256 is the mean refractive index[12] and F033 is the effective Faraday component that

    Fig. 1. (Color online) (a) Cartesian and polar frames of reference and (b) shape of the gyration surface for Sn6P2S6 crystals in the crystal-lographic frame of reference. The outlets of the optic axes at the room temperature are also indicated. (k is the wave vector of light).

    10 November 2008 / Vol. 47, No. 32 / APPLIED OPTICS 6041

  • corresponds to the rotated reference frame, of whichthe Z0 axis coincides with the direction of the opticaxis:

    F033 12

    F22

    12F11

    12F33 F13

    =n3mH:

    5

    In our case, the Faraday rotation is not sensitive toswitching of the domains, thus permitting the studyof magnetically induced rotation on either single-domain or multidomain samples.Following from the above, we are able to determine

    the increment of optical activity for Sn2P2S6 crystalswith a direct technique for measuring the polariza-tion plane rotation, applied for the light propagatingalong one of the optic axes. For studies of the Faradayrotation, we have used both a single-ray polarimetryand a small-angular imaging polarimetry.While employing a single-ray polarimetric setup, a

    HeNe laser (optical power of P 0:18W=cm2 and aradiation wavelength of 632:8nm) was used as alight source. It is known that a photorefractive effecttakes place in Sn2P2S6 at the wavelength of632:8nm[13,14]. In the single-beam scheme used,this effect could manifest itself as optical damage,i.e., as a formation of a photo-induced lens producingdistortion of the beam spot or of images on the CCDcamera. In order to clarify whether the photorefrac-tive effect could influence the polarimetric measure-ments, we have used a 50mW HeNe laser and avariable attenuator. We have found that the intensityvariations of the light transmitted through aSn2P2S6 sample as large as one decade do not affectthe polarimetric results. Since in this work we usedan HeNe laser with the cw power of 1:5mW, we

    have, therefore, concluded that the influence of var-ious photo-induced effects in our case is negligi-bly small.The azimuth of the incident light was chosen such

    that it always remained perpendicular to the plane ofincidence when the magnetic field was applied. Thelongitudinal magnetic field was applied using anelectromagnet (shown in Fig. 3). The sample thick-ness was d0 1:68mm. The sample surface wasnot exactly perpendicular to the optic axis becausethe orientation of the optic axis is slightly sensitiveto environmental conditions, most of all the tempera-ture fluctuations. Therefore, the effective samplethickness was recalculated using the relation

    d d0= cosarcsin

    sin nm

    ;

    where is the angle of incidence nm 3:0256.The increment of the polarization plane rotation im-posed by the Faraday effect was studied in the geo-metry when the light propagated along the optic axisand the magnetic field was applied along the samedirection.A number of inevitable error sources exist in our

    case of magneto-optic measurements. The principalsources of errors are the angular distribution ofthe Faraday rotation and linear optical birefringencenear the optic axis, which appear even in a small-angular range of some degrees. Together with a smalldivergence of the laser beam (4 103 rad or0:23 deg), these factors could give rise to increasingmeasurement errors [15,16]. Using the small-a

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