The dielectric tensor in incommensurately modulated crystal phases

Dijkstra, Edsger W.; Janner, A.; Meekes, Hugo

doi:10.1088/0953-8984/4/3/010

Cited by 20 publications

(60 citation statements)

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“…We avoid in (20) simplifying re-definitions for the reciprocal lattice vectors and the wave functions due to the selection rules and introducing the integer index m 0 (see formulae (12), (14) and (15)) just to show the structure of the solutions for the matrix elements, needed further to evaluate them and compare the microscopic dielectric components affected by the phason mode with those for the ''equilibrium" IC phase.…”

Section: Quantum-mechanical Calculationsmentioning

confidence: 99%

“…It has been shown that such long-wavelength vectors should not be simply discarded as in the case of ordinary (commensurate) crystals, for they can contribute to the total optical response of the IC crystal. Stasyuk and Shvaika [11] and Dijkstra et al [12] have analyzed the transition from a microscopic to a macroscopic description of the optical properties of the IC phases. It has been suggested that the IC phases should be considered as spatially inhomogeneous on the so-called mesoscopic scale, the mesoscopic period being related to the lowestindex non-zero reciprocal lattice vector [12,13].…”

Section: Introductionmentioning

confidence: 99%

“…Stasyuk and Shvaika [11] and Dijkstra et al [12] have analyzed the transition from a microscopic to a macroscopic description of the optical properties of the IC phases. It has been suggested that the IC phases should be considered as spatially inhomogeneous on the so-called mesoscopic scale, the mesoscopic period being related to the lowestindex non-zero reciprocal lattice vector [12,13]. Unfortunately, no attempt has been made in the mentioned works to obtain the microscopic dielectric tensor.…”

Section: Introductionmentioning

confidence: 99%

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Microscopic Dielectric and Gyration Tensors of Incommensurately Modulated Insulators

Kushnir¹,

Lokot²

2001

phys. stat. sol. (b)

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Subject classification: 64.70.Rh; Crystal optical properties of insulating materials possessing incommensurately modulated phases are studied in the framework of a microscopic model. Quantum-mechanical expressions for the microscopic dielectric permittivity tensor are derived. It is shown that the contributions from the long-wavelength reciprocal lattice vectors with the lowest microscopic indices should be taken into account in the optical response of the incommensurate crystals. This justifies, from the standpoint of microscopic theory, a mesoscopic approach to the problem of light propagation in incommensurate crystals adopted in a number of earlier studies. The mesoscopic tensors associated with the first-order spatial dispersion are obtained and analyzed in detail. The optical gyration is revealed to be described by the dielectric tensor components linear in both the light wave vector and the mesoscopic incommensurate modulation wave vector. The latter contributions correspond to the gyration mechanism related to the mesoscopic inhomogeneity of the optical medium under study.

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Section: Quantum-mechanical Calculationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Microscopic Dielectric and Gyration Tensors of Incommensurately Modulated Insulators

Kushnir¹,

Lokot²

2001

phys. stat. sol. (b)

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“…Optical activity is included in the description via birefringence (see, for example, Dijkstra (1991) and Dijkstra et al (1992b) …”

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The interpretation of HAUP measurements: a study of the systematic errors

Kremers¹,

Meekes²

1995

J. Phys. D: Appl. Phys.

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Please be advised that this information was generated on 2018-05-10 and may be subject to change. j Phys. d : Appl. Phys. 28 (1995) 1195-1211. Printed in the UK T h e i n t e r p r e t a t i o n o f h a u p m e a s u r e m e n t s : a s t u d y o f t h e s y s t e m a t i c e r r o r sM IntroductionThe merits of the high-accuracy universal polarimeter (HAUP), introduced by Kobayashi and Uesu (1983), lie in the possibility of measuring very accurately and simultaneously the optical activity and birefringence of crystals. In addition, the rotation of the optical indicatrix is detected with a high sensitivity. The measurements require optically transparent, birefringent platelets of single crystals, with flat (polished) plane-parallel faces. It is very important to perform the measurements as a function of some external parameter in order to separate systematic errors from the optical properties, In the experiments described in this paper, the wavelength k of the light is the external parameter* Additional parameters can be temperature, electric fields (electro-optics) or magnetic fields (magneto-optics).The presence and nature of structural phase transitions can often be revealed by the birefringence (Ivanov 1991, Gehring 1977). The point symmetry of a specific phase can be studied by measuring the optical activity in several directions in a crystal, since optical activity is a tensorial property, which is sensitive to the symmetry (Nye 1985). The HAUP is, therefore, a powerful instrument in crystal optics.A very interesting problem in this field is encountered for incommensurately modulated crystals, with a centrosymmetric paraelectric phase (Cummins 1990). The incommensurate phase is often a (small) periodic deformation of the centrosymmetric paraelectric phase. The wavelengths of the periodic deformation is incommensurate with the lattice of the average structure. Therefore, the lattice translational symmetry is broken in at least one direction. Of course, the question arises of whether this phase can be optically active, because optical activity is forbidden in a centrosymmetric crystal (Nye 1985 In order to exclude the possibility that these differences are caused by the way of measuring or the way of interpreting the measurements, we feel . it necessary to reconsider very precisely the working principles of the HAUP method. In this paper, we re-derive rigorously the HAUP intensity formula (section 2 ). Experiments have been performed both on a centrosymmetric crystal with zero optical activity and on the non-centrosymmetric room-temperature phase of quartz, which has a large optical activity (section 3). In section 4 the obtained results are used to re consider critically the fitting procedures with which the optical properties are extracted from the measurements. Moreover, in section 5, the behaviour and origin of the systematic errors will be studied thoroughly. The quality and sensitivity of HAUP measurements is addressed in section 6 . For all aspects of the HAUP method, we discuss and take into accoun...

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“…the domains is centrosymmetric it is still expected that the multi-domain state of the sample is optically active [25,26].…”

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confidence: 99%

The influence of incommensurate modulation on the optical properties of ((CH₃)₄N)₂CuCl₄

Kremers¹,

Meekes²

1995

J. Phys.: Condens. Matter

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Abstract. This paper reports on the measurement of the optical properties of incommensurately modulated ((CH3)4N)2CuCÎ4 by using the High Accuracy Universal Polarimeter. With this technique it is possible to measure, simultaneously, linear birefringence, linear dichroism, circular birefringence, circular dichroism and the rotation of the optical indicatrix. Two different samples are used. The orientation of the first sample allows for the measurement of the gyration tensor element #33. In the other sample #13 can be measured. The optical effects are studied as a function of temperature, both in a region of zero linear dichroism and in a region of finite linear dichroism. The measurements reveal that the crystals have a low defect concentration. The presence of the incommensurate modulation is clearly revealed by the linear birefringence. The linear dichroism, on the other hand, appears to be unaffected by the modulation. It is interesting that if one averages the effect of the incommensurate modulation a crystal structure is obtained that is believed to be orthorhombic and centrosymmetric. Two effects are observed that are forbidden by the symmetry of this average structure. One of them is the rotation of the optical indicatrix, which contradicts an orthorhombic symmetry. The other is the onset of non-zero optical activity, approximately halfway through the incommensurate phase. In centrosymmetric media this effect is not allowed to occur. The observed temperature dependence of the optical activity £ j3 differs from the behaviour measured by other authors. It is discussed whether the observed effects can be attributed to a symmetry breaking by the incommensurate modulation.

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The dielectric tensor in incommensurately modulated crystal phases

Cited by 20 publications

References 21 publications

Microscopic Dielectric and Gyration Tensors of Incommensurately Modulated Insulators

Microscopic Dielectric and Gyration Tensors of Incommensurately Modulated Insulators

The interpretation of HAUP measurements: a study of the systematic errors

The influence of incommensurate modulation on the optical properties of ((CH₃)₄N)₂CuCl₄

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The dielectric tensor in incommensurately modulated crystal phases

Cited by 20 publications

References 21 publications

Microscopic Dielectric and Gyration Tensors of Incommensurately Modulated Insulators

Microscopic Dielectric and Gyration Tensors of Incommensurately Modulated Insulators

The interpretation of HAUP measurements: a study of the systematic errors

The influence of incommensurate modulation on the optical properties of ((CH3)4N)2CuCl4

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The influence of incommensurate modulation on the optical properties of ((CH₃)₄N)₂CuCl₄