Abstract

We study theoretically the magneto-optical properties of suspensions of magnetic nanoparticles within liquid crystalline matrices whose structure has been explored using off-lattice canonical Monte Carlo simulations. We find, in particular, that such systems exhibit a very strong magnetic circular-dichroism signal generated by morphological transformations of the structural motives of magnetic nanoparticles. These occur when the liquid crystalline matrix passes from isotropic to nematic states upon application of an external magnetic field. Moreover, we find that such hybrid magnetic-nanoparticle/liquid-crystalline systems demonstrate strong Faraday effect in the visible regime.

© 2016 Optical Society of America

1. Introduction

Creating suspensions of magnetic nanoparticles (MNP) in liquid crystalline (LC) matrices, i.e LC/MNP hydrid systems, is a non-trivial avenue for obtaining materials with programmable and controllable functions [1–3]. New interest on such systems was stimulated by the recent discovery of spontaneous magnetic ordering in a hybrid system of large, micron-sized magnetic plates embedded in a thermotropic low molar mass nematic LC [3]. In the present work, we focus on the opposite case of colloidal suspensions of LC rods and small MNPs, where the sizes of the species are of the same order of magnitude. An example of such systems are lyotropic suspensions of colloid pigment rods and magnetite MNPs which have been recently studied [4, 5]. Because of their chemical stability, magnetite nanostructures have become a key ingredient in technologically important applications in optoelectronics [6], magnetic storage [7] and bio-inspired devices [8]. More fundamental properties can also be probed via MNPs such as magnetic vortex formation [9].

Among the various magnetic functionalities possessed by LC/MNP hybrids, the magneto-optical (MO) response has, so far, received less attention. The MO properties of MNPs can differ markedly from those of the bulk magnetic materials [10, 11]. Furthermore, the LC/MNP hybrids offer further advances for potential MO applications in comparison to conventional ferrofluids [13]. In particular, the self-organization of MNP in anisotropic matrices, e.g. LC, provides a way of producing multi–stimuli responsive materials with controlled directional sensitivity to external fields. In the present work, we study theoretically the MO response of LC/MNP hybrids by means of rigorous electrodynamic calculations of the magneto-chiral dichroism (MCD) and the Faraday-rotation spectra. We find, in particular, that the MCD signal of a LC/MNP hybrid system may be significantly enhanced due to structural changes in the morphology of the MNP in the LC matrix upon application of an external homogeneous mag netic field. The latter can find application in monitoring the phase transitions of the LC matrices or enhancing the MCD signal of molecules attached to the MNPs.

2. Calculation methods

To explore these type of systems we have employed off-lattice canonical Monte Carlo simulations [14, 15] of a simple binary model system consisting of anisotropic Gay-Berne (GB) rodlike particles and MNPs, represented as dipolar soft repulsive spheres (DSS), i.e., spheres with an embedded central point dipole moment µi. Typical systems simulated here are shown in Fig. 1. A detailed analysis is presented in Refs. [14, 15]. In the systems of Fig. 1, the length (l)-to-width (σ) ratio of the rods is set to l/σ = 3 which is in the lowest accessible range for LC/MNP hybrids. The dipolar spheres have diameter σs = 1σ while they interact via a soft-sphere potential and standard dipole-dipole interactions. Finally, for the interactions between rods and spheres we consider a modified GB potential. For further details on the simulation methods and interaction potential see Refs. [14, 15] and references therein. The configurations (positions and orientations of the particles) obtained by MC simulations are used as input in the magneto-optic calculations that are described below.

 

Fig. 1 Representative simulation snapshots for mixtures with σs = 1σ in the absence of external magnetic field: (a) Isotropic and (b) nematic phase. In the bottom parts only the MNPs are shown for clarity. The nematic directors of the species are also indicated.

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The electromagnetic EM modeling of the suspensions of Figs. 1 and 2 is performed via the Discrete-Dipole Approximation (DDA) technique [16–18] for MO targets (scatterers) [19, 20]. A brief description of the method is provided in the appendix. In the calculations that follow, as an exemplary case we have considered magnetite MNPs of 5 nm radius whose dielectric tensor is taken from experimental measurements of bulk magnetite. For details on the parameterization that is used see appendix, Refs. [19–22] and references therein. The DDA method is employed for LC/MPNs hybrids consisting of 400 magnetite MNPs assumed to be embedded within a LC matrix. The LC matrix is treated as a homogeneous medium with a uniaxial dielectric tensor provided by ε^=2.1x^x^+2.1y^y^+2.5z^z^. In the isotropic case, we take ε^=[(2/3)×2.1+(1/3)×2.5](x^x^+y^y^+z^z^). One, of course, can perform a more realistic electrodynamic calculation by taking into account the microscopic nature of the LC. In this case, the LC molecules are considered as point dipoles similarly to the MNPs. At the positions of the LC molecules (as provided by the above MC calculations) one could assign, in principle, a corresponding electric-permittivity tensor according to the orientation of the LC particle at a given position in space [23–25]. This, however, would constitute an unnecessary complexity to our problem since the MO properties of the LC/MNP hybrids are exclusively determined by: (i) the positioning of the MNPs, and (ii) the orientation of the corresponding magnetic moments. The latter determine the electric-permittivity tensor of each MNP. We note that the description of the liquid crystal as a continuous medium rather than a coarse-grained, molecular material is the standard way to treat liquid-crystalline composite materials such as metallic nanoparticles embedded in a host material [26]. Even if one assumes an inhomogeneous director field for the nematic liquid crystal, its effect on much stronger resonance phenomena, e.g., surface plasmons, is rather marginal (a very slight shift of the resonance) [23, 24]. It is, therefore, fully justified to ignore the coarse-graining of the LC matrix at the level of electrodynamic calculations and assume having a homogeneous host surrounding the MNPs. Finally, we note that the parameterization we have used in this work is representative and corresponds to realistic values [27] for systems comprising of magnetic particles in LC matrices.

 

Fig. 2 Representative simulation snapshots for mixtures with σs = 1σ that are in the I-state (when the external magnetic field is off) and in the N-state (field-on): (a) [(T, ρ) = (1.1,0.34)] field-off S ≃ 0.0 (b) [(T, ρ) = (1.1,0.34)] field-on S ≃ 0.4 (c) [(T, ρ) = (2.2,0.40)] field-off S ≃ 0.0 (d) [(T, ρ) = (2.2,0.40)] field-on S ≃ 0.6.

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The MO response of the LC/MNPs hybrids is manifested via the MCD which is defined as MCD = CD(H) CD(H = 0), where CD is the circular dichroism defined as CD = 2(ARCP − ALCP)/(ARCP + ALCP) with ARCP being the absorbance for right-circularly polarized light (RCP) and ALCP for left-circularly polarized (LCP) (see appendix). Another typical MO quantity is the Faraday rotation which is substantiated via the azimuth and ellipticity rotation angles being calculated as the real and imaginary part, respectively, of the difference in the extinction coefficients between LCP and RCP incident light (see appendix).

3. Results and discussion

We begin with a brief description of the behavior of LC/MNP hybrids under or in the absence of a homogeneous magnetic field. Initially, we consider LC/MNP hybrids at various state points (T, ρ) in the absence of an external field: at the thermodynamic conditions considered (for details see ref. [15]), the LC matrix exhibits fully miscible isotropic (I), uniaxial nematic (N) and uniaxial smectic–B (SmB) states. Here we focus on the I– and N– states. These states are chosen as representative examples of the major effect of a magnetic field on the positional and orientational ordering of the magnetic and liquid crystalline components. In fact considerable structural changes occur, on application of an external field (see below). In dimensionless units, the temperature is T = kBT/ε (with kB being Boltzmann’s constant and ε is energy parameter), and the number density ρ*=Nσ03/V (total number of particles over volume). We have obtained various morphologies of the MNP within these states. In the I-state the MNP self assembly into chains, with the dipoles in a head-to-tail configuration; in turn they self-organized into either an isotropic network of wormlike chains (strong dipolar coupling λ = µ2/kB3 = 8.2) or isotropically distributed fragmented chains (weaker coupling λ = µ2/kB3 = 4.1) within the LC matrix. Representative illustrations of these structures are given in Fig. 1(a) and Fig. 2(c), respectively. Finally, in the N– state the ferromagnetic chains spontaneously ”unwrap” and align, on average, along the director of the LC matrix (i.e. the principal axis of the uniaxial state). A representative snapshot is given in Fig. 1(b). As a result, the director of the magnetic chains coincides with the LC director. Interestingly, the ferromagnetic chains are distributed randomly ”up” and ”down” within the LC host and therefore the overall magnetization is zero. Furthermore, the chains are translationally disordered lateral to the director of the phase. We finally note that the concentration of the magnetic particles in the LC host is relatively small (less than 4.2 vol%).

As an external perturbation we have applied a homogeneous magnetic field (H = µH/kBT) on the I- and N- states of the LC/MNP hybrids. The field is coupled to the permanent dipole µi of particle i through the potential Ui=μ^iH. When the field is off in the I–state of high [Fig. 2(a)] and low [Fig. 2(c)] dipolar coupling, the total magnetization is zero and the nematic order parameter S is essentially zero. The nematic order parameter S is calculated from the ordering matrix of the rods [15]. Under a small field of H*= 10, the nematic order parameter S jumps from nearly zero to 0.4 and the system becomes polar (macroscopic magnetization). The isotropic network [field-off see Fig. 2(a)] is replaced by nearly straight ferromagnetic chains that are oriented parallel to the direction of the magnetic field [see Fig. 2(b)]. Similar behavior is obtained for the systems of Fig. 2(c) and (d). As a general rule, the soft coupling between the magnetic particles and LC host generates a sterically-induced ordering, which can either be spontaneous (magnetic chains ordering caused by LC matrix) or forced by an external field (transformation of an isotropic state of the LC matrix caused by magnetic chains).

The magnetic nature of the LC/MNP hybrids means that these systems are expected to exhibit a nontrivial MO response. In Figs. 3(a), 3(b) we show the MCD signal for the systems of Fig. 2(b), 2(d). This is compared against the MCD signal obtained in the hypothetical case where the system of Fig. 2(a) does not undergo structural change to the system of Fig. 2(b) (N-state) under the presence of the magnetic field but remains in the I-state. Essentially, this hypothetical case corresponds to the pure MO effect stemming from the magnetite MNPs alone without taking into account the structural changes. Evidently, the actual MCD signal which incorporates the phase transition from the I- to the N-state [black curve of Fig. 3(a)] is on the average 50% higher than that of the hypothetical case (red line) without the structural changes (see also the corresponding insets). In the absence of structural changes to the LC/MNP hybrid, the MCD signal comes from the ferromagnetic contribution of the magnetite MNPs which is attributed to various electronic transitions taking place within the magnetite MNPs [28]. The external magnetic field promotes linear alignment of the chains along the field that in turn induce nematic ordering to LC matrix. The MCD signal incorporates this remarkable structural change in addition to the transitions within the magnetite MNPs leading to the enhancement of the MCD observed in Fig. 3(a). A more dramatic enhancement in the MCD signal is observed in Fig. 3(b) which corresponds to a transformation from an I-state [of smaller fragmented chains of Fig. 2(c)] to a N-state of Fig. 2(d). Namely, the actual MCD spectrum (black line) is on the average 4 times larger than the hypothetical MCD signal (red curve) if the structural change to N-state [Fig. 2(d)] does not occur and the system remains in the I-state of Fig. 2(c). The difference in the enhancement of the MCD signal between Figs. 3(a) and 3(b) may be attributed to the fact that in I-state of Fig. 2(a) there exists already an isotropic network of MNP long chains which promotes the magnetic interaction between the magnetite MNPs and shows a larger MCD signal. On the other hand, in the I-state of Fig. 2(c) (shorter) fragmented chains are formed. The presence of the MNP longer chains in the I-state of Fig. 2(a) also explains the much higher hypothetical MCD signal (about two orders of magnitude) compared to the corresponding hypothetical signal calculated for the isotropic phase of Fig. 2(c) [compare the red lines in Figs. 3(a) and 3(b)]. In the same fashion, the actual MCD signal (the one that can be measured experimentally) which encompasses the I-state to N-state transformation [black curve of Fig. 3(a)] is on the average 5 times larger than the MCD of the I-state to N-state transformation [black curve of Fig. 3(b)]. This is due to the fact the magnetic interactions in the N-state [Fig. 2(b)] are much stronger as the MNP chains are very ”tight” in comparison to the N-state of Fig. 2(d).

 

Fig. 3 (a) Red line: magnetochiral dichroism (MCD) signal for the hypothetical case where the configuration of Fig. 2(a) is not modified under the action of the magnetic field and the MNPs remain at the same positions (see inset). Black lines: MCD signal for the actual case where the configuration of Fig. 2(a) undergoes structural transformation to the configuration of Fig. 2(b) under the action of the magnetic field (see inset). (b) The same as (a) but for the configurations of Fig. 2(c) and 2(d), respectively. The magnetite MNPs have 5 nm radius.

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In Figs. 4(a), 4(b) we present the spectra of the (real and imaginary part of) azimuth and ellipticity rotation angles (which quantify the Faraday effect) for the systems of Figs. 2(b) and 2(d), respectively. We observe that both rotation angles assume values within, more or less, the same range of values. The arrangement of MNPs in the N-states does not affect much the Faraday effect since MNP linear chains are present in both cases, apart from the reversed sign in the angles which, however, depends on the spatial chirality of the particular configurations of the nematic samples of Figs. 2(b) and 2(d), respectively. In both cases, given the dimensions of a calculation cube (about 50 nm), the Faraday rotation is of the order of 10−2 milli-degrees per nanometer.

 

Fig. 4 Azimuth and ellipticity angles corresponding to Faraday rotation for (a) the system of Fig. 2(b) and 2(b) the system of Fig. 2(d) (also shown in the insets).

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4. Conclusions

In conclusion, we have shown numerically that liquid-crystalline/magnetite-nanoparticle hybrids show significant MCD upon application of an external magnetic field due to significant structural change the hybrids undergo from an isotropic to a nematic state. In these states a strong Faraday rotation is also observed due to the formation of long ferromagnetic chains (chains of magnetite nanoparticles) within the hybrids which favour the magnetic interactions among the nanoparticles. The enhanced MCD signal can be exploited experimentally to monitor liquid-crystalline transitions as well as to amplify the MCD signal of magnetic nanoparticles in order to keep track of the internal electron transitions in the nanoparticles.

Appendix

Our aim is to study the optical response of a collection of magnetic nanospheres within an anisotropic host based on the discrete dipole approximation (DDA) [16–18]. We consider a finite collection of point dipoles (i = 1, ···, N) each of which is located at the position ri and corresponds to a dipole moment Pi and a (position-dependent) polarizability tensor α˜i. The above quantities are connected by

Pi=α˜iEi
where Ei is the electric field at i-th dipole,
Ei=Einc,i+iiAijPj
which is the sum of the directly incident field Einc,i as well as the field scattered by all the other dipoles ji and it is incident on the i-th dipole [second term of Eq. (2)]. The interaction matrix Aij is given from
Aij=exp(ikrij)rij[k2(r^ijr^ij13)+ikrij1rij2(3r^ijr^ij13)],ij
where 13 is the 3 × 3 unit matrix, rij = ri rj, r^ij=rij/|rij|. By combining Eqs. (1) to (3) we obtain linear system of equations, i.e.,
j=1NAijPj=Einc,i
where the diagonal elements of the interaction matrix are essentially the inverse of the polarizability tensor of each dipole, i.e.,
Aij=[α˜i]1.

For a generally anisotropic sphere characterized by a dielectric tensor ε˜s and is immersed within an anisotropic host of dielectric tensor ε˜h, the polarizability tensor of the sphere is given by the Clausius-Mossoti formula for anisotropic spheres [26], i.e.,

α˜=Vs2εh;+εh;4π[ε˜sε˜h13][ε˜s+2ε˜h13]1.

For a gyrotropic material, the permittivity tensor is provided by [19,20]

ε˜s=(εxxiQmziQmyiQmzεyyiQmxiQmyiQmxεzz)
where Q is magneto-optical Voigt parameter and mx, my, mz are the direction cosines for the magnetization vector. For nematic LC host the corresponding tensor is written as
ε˜h=(ε000ε000ε)

Having determined the dipole moment Pi at each point dipole, one can calculate quantities such as the scattering, extinction and absorption cross sections, i.e.,

Csc=4πk|Einc|2i=1N[23k3|Pi|2(PiEself,i*)]
Cext=4πk|Einc|2i=1N(PiEinc,i*)
Cabs=4πk|Einc|2i=1N[(PiEi*)23k3|Pi|2]
where Eself,i = EiEinc,i. Evidently, Cext = Csc +Cabs.

The Faraday rotation, θ, and ellipticity, η, are provided by [20]

θ+iη=πkE0i=1N(PiLPiR)exp(ikz^ri)
where
PiL,R=Pie^L,R*
e^L,R=12(x^±iy^)

The absorption chiral dichroism is defined as

CD=CabsRCPCabsLCP
where RCP (LCP) stands for right (left-circularly polarized light. The magnetic chiral dichroism (MCD) is defined as
MCD=CD(H)CD(H=0).

References and links

1. S. Saliba, C. Mingotaud, M. L. Kahn, and J-D Marty, “Liquid crystalline thermotropic and lyotropic nanohybrids,” Nanoscale 5, 6641 (2013). [CrossRef]   [PubMed]  

2. B. Matt, K. M. Pondman, S. J. Asshoff, B. ten Haken, B. Fleury, and N. Katsonis, “Soft Magnets from the Self-Organization of Magnetic Nanoparticles in Twisted Liquid Crystals,” Angew. Chem. Int. Ed. 53, 12446–12450 (2014).

3. A. Mertelj, D. Lisjak, and M. Drofenik, “Ferromagnetism in suspensions of magnetic platelets in liquid crystal,” Nature (London) 504, 237–241 (2013). [CrossRef]  

4. K. May, R. Stannarius, S. Klein, and A. Eremin, “Electric-Field-Induced Phase Separation and Homogenization Dynamics in Colloidal Suspensions of Dichroic Rod-Shaped Pigment Particle,” Langmuir 30, 7070–7076 (2014). [CrossRef]   [PubMed]  

5. “Private communication with R. Stannarius,”

6. M. Salerno, J. R. Krenn, B. Lamprecht, G. Schider, H. Ditlbacher, N. Felidj, A. Leitner, and F. A. Aussenegg, “Plasmon Polaritons in Metal Nanostructures: The Optoelectronic Route to Nanotechnology,” Opto-Electron. Rev. 10, 217–224 (2002).

7. M. P. Sharrock and R. E. Bodnar, “Magnetic Materials for Recording: An Overview with Special Emphasis on Particles,” J. Appl. Phys. 57, 3919–3924 (1985). [CrossRef]  

8. A. Jordan, R. Scholz, P. Wust, H. Schirra, T. Schiestel, H. Schmidt, and R. Felix, “Endocytosis of Dextran and Silan-Coated Magnetite Nanoparticles and the Effect of Intracellular Hyperthermia on Human Mammary Carcinoma Cells in vitro,” J. Magnetism. Magn. Mater. 194, 185–196 (1999). [CrossRef]  

9. T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono, “Magnetic vortex core observation in circular dots of permalloy,” Science 289, 930–932 (2000). [CrossRef]   [PubMed]  

10. A. Demortiere, P. Panissod, B. P. Pichon, G. Pourroy, D. Guillon, B. Donnio, and S. Begin-Colin, “Size-dependent properties of magnetic iron oxide nanocrystals,” Nanoscale 3, 225–232 (2011). [CrossRef]  

11. H. Yao and Y. Ishikawa, “Finite Size Effect on Magneto-Optical Responses of Chemically Modified Fe3O4 Nanoparticles Studied by MCD Spectroscopy,” J. Phys. Chem. C 119, 13224–13230 (2015). [CrossRef]  

12. V. Yannopapas and A. G. Vanakaras, “Strong Magnetochiral Dichroism in Suspensions of Magnetoplasmonic Nanohelices,” ACS Photon. 2, 1030–1038 (2015). [CrossRef]  

13. S. Odenbach, Magnetoviscous effects in ferrofluids (Springer, 2002).

14. S. D. Peroukidis, K. Lichtner, and S. H. L. Klapp, “Tunable structures of mixtures of magnetic particles in liquid-crystalline matrices,” Soft Matter 11, 5999–6008 (2015). [CrossRef]   [PubMed]  

15. S. D. Peroukidis and S. H. L. Klapp, “Spontaneous ordering of magnetic particles in liquid crystals: From chains to biaxial lamellae,” Phys. Rev. E 92, 010501 (2015). [CrossRef]  

16. B. T. Draine, “The discrete-dipole approximation and its application to stellar graphite grains,” Astrophys. J. 333, 848–872 (1988). [CrossRef]  

17. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [CrossRef]  

18. M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spec. Rad. Transfer 106, 558–589 (2007). [CrossRef]  

19. D. A. Smith, Y. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, “Magneto-optical spectra of closely-spaced magnetite nanoparticles,” J. Appl. Phys. 97, 10M504 (2005). [CrossRef]  

20. D. A. Smith and K. L. Stokes, “Discrete dipole approximation for magnetooptical scattering calculations,” Opt. Express 14, 5746–5754 (2006). [CrossRef]   [PubMed]  

21. A. Schlegel, S. F. Alvarado, and P. Wachter, “Optical properties of magnetite (Fe3O4),” J. Phys. C: Solid State Phys. 12, 1157–1164 (1979). [CrossRef]  

22. X. Zhang, J. Schoenes, and P. Wachter, “Kerr-effect and dielecric tensor elements of magnetite (Fe3O4) between 0.5 and 4.3 eV,” Solid State Commun. 39, 189–192 (1981). [CrossRef]  

23. S. Y. Park and D. Stroud, “Surface-Enhanced Plasmon Splitting in a Liquid-Crystal-Coated Gold Nanoparticle,” Phys. Rev. Lett. 94, 217401 (2005). [CrossRef]   [PubMed]  

24. V. Yannopapas, N. Fytas, V. Kyrimi, E. Kallos, A. G. Vanakaras, and D. J. Photinos, “Light scattering by a metallic nanoparticle coated with a nematic liquid crystal,” Phys. Stat. Solidi A 210, 335–340 (2013). [CrossRef]  

25. S. D. Peroukidis, V. Yannopapas, A. G. Vanakaras, S. Droulias, and D. J. Photinos, “Plasmonic response of ordered arrays of gold nanorods immersed within a nematic liquid crystal,” Liq. Cryst. 41, 1430–1435 (2014). [CrossRef]  

26. O. Levy and D. Stroud, “Maxwell Garnett theory for mixtures of anisotropic inclusions: application to conducting polymers,” Phys. Rev. B 1997(56), 8035–8046 (1997).

27. T. Scharf, Polarized Light in Liquid Crystals and Polymers (Wiley, 2007).

28. V. Antonov, B. Harmon, and A. Yaresko, Electronic Structure and Magneto-Optical Properties of Solids (Kluwer, 2004).

References

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  1. S. Saliba, C. Mingotaud, M. L. Kahn, and J-D Marty, “Liquid crystalline thermotropic and lyotropic nanohybrids,” Nanoscale 5, 6641 (2013).
    [Crossref] [PubMed]
  2. B. Matt, K. M. Pondman, S. J. Asshoff, B. ten Haken, B. Fleury, and N. Katsonis, “Soft Magnets from the Self-Organization of Magnetic Nanoparticles in Twisted Liquid Crystals,” Angew. Chem. Int. Ed. 53, 12446–12450 (2014).
  3. A. Mertelj, D. Lisjak, and M. Drofenik, “Ferromagnetism in suspensions of magnetic platelets in liquid crystal,” Nature (London) 504, 237–241 (2013).
    [Crossref]
  4. K. May, R. Stannarius, S. Klein, and A. Eremin, “Electric-Field-Induced Phase Separation and Homogenization Dynamics in Colloidal Suspensions of Dichroic Rod-Shaped Pigment Particle,” Langmuir 30, 7070–7076 (2014).
    [Crossref] [PubMed]
  5. “Private communication with R. Stannarius,”
  6. M. Salerno, J. R. Krenn, B. Lamprecht, G. Schider, H. Ditlbacher, N. Felidj, A. Leitner, and F. A. Aussenegg, “Plasmon Polaritons in Metal Nanostructures: The Optoelectronic Route to Nanotechnology,” Opto-Electron. Rev. 10, 217–224 (2002).
  7. M. P. Sharrock and R. E. Bodnar, “Magnetic Materials for Recording: An Overview with Special Emphasis on Particles,” J. Appl. Phys. 57, 3919–3924 (1985).
    [Crossref]
  8. A. Jordan, R. Scholz, P. Wust, H. Schirra, T. Schiestel, H. Schmidt, and R. Felix, “Endocytosis of Dextran and Silan-Coated Magnetite Nanoparticles and the Effect of Intracellular Hyperthermia on Human Mammary Carcinoma Cells in vitro,” J. Magnetism. Magn. Mater. 194, 185–196 (1999).
    [Crossref]
  9. T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono, “Magnetic vortex core observation in circular dots of permalloy,” Science 289, 930–932 (2000).
    [Crossref] [PubMed]
  10. A. Demortiere, P. Panissod, B. P. Pichon, G. Pourroy, D. Guillon, B. Donnio, and S. Begin-Colin, “Size-dependent properties of magnetic iron oxide nanocrystals,” Nanoscale 3, 225–232 (2011).
    [Crossref]
  11. H. Yao and Y. Ishikawa, “Finite Size Effect on Magneto-Optical Responses of Chemically Modified Fe3O4 Nanoparticles Studied by MCD Spectroscopy,” J. Phys. Chem. C 119, 13224–13230 (2015).
    [Crossref]
  12. V. Yannopapas and A. G. Vanakaras, “Strong Magnetochiral Dichroism in Suspensions of Magnetoplasmonic Nanohelices,” ACS Photon. 2, 1030–1038 (2015).
    [Crossref]
  13. S. Odenbach, Magnetoviscous effects in ferrofluids (Springer, 2002).
  14. S. D. Peroukidis, K. Lichtner, and S. H. L. Klapp, “Tunable structures of mixtures of magnetic particles in liquid-crystalline matrices,” Soft Matter 11, 5999–6008 (2015).
    [Crossref] [PubMed]
  15. S. D. Peroukidis and S. H. L. Klapp, “Spontaneous ordering of magnetic particles in liquid crystals: From chains to biaxial lamellae,” Phys. Rev. E 92, 010501 (2015).
    [Crossref]
  16. B. T. Draine, “The discrete-dipole approximation and its application to stellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [Crossref]
  17. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
    [Crossref]
  18. M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spec. Rad. Transfer 106, 558–589 (2007).
    [Crossref]
  19. D. A. Smith, Y. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, “Magneto-optical spectra of closely-spaced magnetite nanoparticles,” J. Appl. Phys. 97, 10M504 (2005).
    [Crossref]
  20. D. A. Smith and K. L. Stokes, “Discrete dipole approximation for magnetooptical scattering calculations,” Opt. Express 14, 5746–5754 (2006).
    [Crossref] [PubMed]
  21. A. Schlegel, S. F. Alvarado, and P. Wachter, “Optical properties of magnetite (Fe3O4),” J. Phys. C: Solid State Phys. 12, 1157–1164 (1979).
    [Crossref]
  22. X. Zhang, J. Schoenes, and P. Wachter, “Kerr-effect and dielecric tensor elements of magnetite (Fe3O4) between 0.5 and 4.3 eV,” Solid State Commun. 39, 189–192 (1981).
    [Crossref]
  23. S. Y. Park and D. Stroud, “Surface-Enhanced Plasmon Splitting in a Liquid-Crystal-Coated Gold Nanoparticle,” Phys. Rev. Lett. 94, 217401 (2005).
    [Crossref] [PubMed]
  24. V. Yannopapas, N. Fytas, V. Kyrimi, E. Kallos, A. G. Vanakaras, and D. J. Photinos, “Light scattering by a metallic nanoparticle coated with a nematic liquid crystal,” Phys. Stat. Solidi A 210, 335–340 (2013).
    [Crossref]
  25. S. D. Peroukidis, V. Yannopapas, A. G. Vanakaras, S. Droulias, and D. J. Photinos, “Plasmonic response of ordered arrays of gold nanorods immersed within a nematic liquid crystal,” Liq. Cryst. 41, 1430–1435 (2014).
    [Crossref]
  26. O. Levy and D. Stroud, “Maxwell Garnett theory for mixtures of anisotropic inclusions: application to conducting polymers,” Phys. Rev. B 1997(56), 8035–8046 (1997).
  27. T. Scharf, Polarized Light in Liquid Crystals and Polymers (Wiley, 2007).
  28. V. Antonov, B. Harmon, and A. Yaresko, Electronic Structure and Magneto-Optical Properties of Solids (Kluwer, 2004).

2015 (4)

H. Yao and Y. Ishikawa, “Finite Size Effect on Magneto-Optical Responses of Chemically Modified Fe3O4 Nanoparticles Studied by MCD Spectroscopy,” J. Phys. Chem. C 119, 13224–13230 (2015).
[Crossref]

V. Yannopapas and A. G. Vanakaras, “Strong Magnetochiral Dichroism in Suspensions of Magnetoplasmonic Nanohelices,” ACS Photon. 2, 1030–1038 (2015).
[Crossref]

S. D. Peroukidis, K. Lichtner, and S. H. L. Klapp, “Tunable structures of mixtures of magnetic particles in liquid-crystalline matrices,” Soft Matter 11, 5999–6008 (2015).
[Crossref] [PubMed]

S. D. Peroukidis and S. H. L. Klapp, “Spontaneous ordering of magnetic particles in liquid crystals: From chains to biaxial lamellae,” Phys. Rev. E 92, 010501 (2015).
[Crossref]

2014 (3)

B. Matt, K. M. Pondman, S. J. Asshoff, B. ten Haken, B. Fleury, and N. Katsonis, “Soft Magnets from the Self-Organization of Magnetic Nanoparticles in Twisted Liquid Crystals,” Angew. Chem. Int. Ed. 53, 12446–12450 (2014).

K. May, R. Stannarius, S. Klein, and A. Eremin, “Electric-Field-Induced Phase Separation and Homogenization Dynamics in Colloidal Suspensions of Dichroic Rod-Shaped Pigment Particle,” Langmuir 30, 7070–7076 (2014).
[Crossref] [PubMed]

S. D. Peroukidis, V. Yannopapas, A. G. Vanakaras, S. Droulias, and D. J. Photinos, “Plasmonic response of ordered arrays of gold nanorods immersed within a nematic liquid crystal,” Liq. Cryst. 41, 1430–1435 (2014).
[Crossref]

2013 (3)

V. Yannopapas, N. Fytas, V. Kyrimi, E. Kallos, A. G. Vanakaras, and D. J. Photinos, “Light scattering by a metallic nanoparticle coated with a nematic liquid crystal,” Phys. Stat. Solidi A 210, 335–340 (2013).
[Crossref]

A. Mertelj, D. Lisjak, and M. Drofenik, “Ferromagnetism in suspensions of magnetic platelets in liquid crystal,” Nature (London) 504, 237–241 (2013).
[Crossref]

S. Saliba, C. Mingotaud, M. L. Kahn, and J-D Marty, “Liquid crystalline thermotropic and lyotropic nanohybrids,” Nanoscale 5, 6641 (2013).
[Crossref] [PubMed]

2011 (1)

A. Demortiere, P. Panissod, B. P. Pichon, G. Pourroy, D. Guillon, B. Donnio, and S. Begin-Colin, “Size-dependent properties of magnetic iron oxide nanocrystals,” Nanoscale 3, 225–232 (2011).
[Crossref]

2007 (1)

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spec. Rad. Transfer 106, 558–589 (2007).
[Crossref]

2006 (1)

2005 (2)

D. A. Smith, Y. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, “Magneto-optical spectra of closely-spaced magnetite nanoparticles,” J. Appl. Phys. 97, 10M504 (2005).
[Crossref]

S. Y. Park and D. Stroud, “Surface-Enhanced Plasmon Splitting in a Liquid-Crystal-Coated Gold Nanoparticle,” Phys. Rev. Lett. 94, 217401 (2005).
[Crossref] [PubMed]

2002 (1)

M. Salerno, J. R. Krenn, B. Lamprecht, G. Schider, H. Ditlbacher, N. Felidj, A. Leitner, and F. A. Aussenegg, “Plasmon Polaritons in Metal Nanostructures: The Optoelectronic Route to Nanotechnology,” Opto-Electron. Rev. 10, 217–224 (2002).

2000 (1)

T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono, “Magnetic vortex core observation in circular dots of permalloy,” Science 289, 930–932 (2000).
[Crossref] [PubMed]

1999 (1)

A. Jordan, R. Scholz, P. Wust, H. Schirra, T. Schiestel, H. Schmidt, and R. Felix, “Endocytosis of Dextran and Silan-Coated Magnetite Nanoparticles and the Effect of Intracellular Hyperthermia on Human Mammary Carcinoma Cells in vitro,” J. Magnetism. Magn. Mater. 194, 185–196 (1999).
[Crossref]

1997 (1)

O. Levy and D. Stroud, “Maxwell Garnett theory for mixtures of anisotropic inclusions: application to conducting polymers,” Phys. Rev. B 1997(56), 8035–8046 (1997).

1994 (1)

1988 (1)

B. T. Draine, “The discrete-dipole approximation and its application to stellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[Crossref]

1985 (1)

M. P. Sharrock and R. E. Bodnar, “Magnetic Materials for Recording: An Overview with Special Emphasis on Particles,” J. Appl. Phys. 57, 3919–3924 (1985).
[Crossref]

1981 (1)

X. Zhang, J. Schoenes, and P. Wachter, “Kerr-effect and dielecric tensor elements of magnetite (Fe3O4) between 0.5 and 4.3 eV,” Solid State Commun. 39, 189–192 (1981).
[Crossref]

1979 (1)

A. Schlegel, S. F. Alvarado, and P. Wachter, “Optical properties of magnetite (Fe3O4),” J. Phys. C: Solid State Phys. 12, 1157–1164 (1979).
[Crossref]

Alvarado, S. F.

A. Schlegel, S. F. Alvarado, and P. Wachter, “Optical properties of magnetite (Fe3O4),” J. Phys. C: Solid State Phys. 12, 1157–1164 (1979).
[Crossref]

Antonov, V.

V. Antonov, B. Harmon, and A. Yaresko, Electronic Structure and Magneto-Optical Properties of Solids (Kluwer, 2004).

Asshoff, S. J.

B. Matt, K. M. Pondman, S. J. Asshoff, B. ten Haken, B. Fleury, and N. Katsonis, “Soft Magnets from the Self-Organization of Magnetic Nanoparticles in Twisted Liquid Crystals,” Angew. Chem. Int. Ed. 53, 12446–12450 (2014).

Aussenegg, F. A.

M. Salerno, J. R. Krenn, B. Lamprecht, G. Schider, H. Ditlbacher, N. Felidj, A. Leitner, and F. A. Aussenegg, “Plasmon Polaritons in Metal Nanostructures: The Optoelectronic Route to Nanotechnology,” Opto-Electron. Rev. 10, 217–224 (2002).

Barnakov, Y. A.

D. A. Smith, Y. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, “Magneto-optical spectra of closely-spaced magnetite nanoparticles,” J. Appl. Phys. 97, 10M504 (2005).
[Crossref]

Begin-Colin, S.

A. Demortiere, P. Panissod, B. P. Pichon, G. Pourroy, D. Guillon, B. Donnio, and S. Begin-Colin, “Size-dependent properties of magnetic iron oxide nanocrystals,” Nanoscale 3, 225–232 (2011).
[Crossref]

Bodnar, R. E.

M. P. Sharrock and R. E. Bodnar, “Magnetic Materials for Recording: An Overview with Special Emphasis on Particles,” J. Appl. Phys. 57, 3919–3924 (1985).
[Crossref]

Demortiere, A.

A. Demortiere, P. Panissod, B. P. Pichon, G. Pourroy, D. Guillon, B. Donnio, and S. Begin-Colin, “Size-dependent properties of magnetic iron oxide nanocrystals,” Nanoscale 3, 225–232 (2011).
[Crossref]

Ditlbacher, H.

M. Salerno, J. R. Krenn, B. Lamprecht, G. Schider, H. Ditlbacher, N. Felidj, A. Leitner, and F. A. Aussenegg, “Plasmon Polaritons in Metal Nanostructures: The Optoelectronic Route to Nanotechnology,” Opto-Electron. Rev. 10, 217–224 (2002).

Donnio, B.

A. Demortiere, P. Panissod, B. P. Pichon, G. Pourroy, D. Guillon, B. Donnio, and S. Begin-Colin, “Size-dependent properties of magnetic iron oxide nanocrystals,” Nanoscale 3, 225–232 (2011).
[Crossref]

Draine, B. T.

B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
[Crossref]

B. T. Draine, “The discrete-dipole approximation and its application to stellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[Crossref]

Drofenik, M.

A. Mertelj, D. Lisjak, and M. Drofenik, “Ferromagnetism in suspensions of magnetic platelets in liquid crystal,” Nature (London) 504, 237–241 (2013).
[Crossref]

Droulias, S.

S. D. Peroukidis, V. Yannopapas, A. G. Vanakaras, S. Droulias, and D. J. Photinos, “Plasmonic response of ordered arrays of gold nanorods immersed within a nematic liquid crystal,” Liq. Cryst. 41, 1430–1435 (2014).
[Crossref]

Eremin, A.

K. May, R. Stannarius, S. Klein, and A. Eremin, “Electric-Field-Induced Phase Separation and Homogenization Dynamics in Colloidal Suspensions of Dichroic Rod-Shaped Pigment Particle,” Langmuir 30, 7070–7076 (2014).
[Crossref] [PubMed]

Felidj, N.

M. Salerno, J. R. Krenn, B. Lamprecht, G. Schider, H. Ditlbacher, N. Felidj, A. Leitner, and F. A. Aussenegg, “Plasmon Polaritons in Metal Nanostructures: The Optoelectronic Route to Nanotechnology,” Opto-Electron. Rev. 10, 217–224 (2002).

Felix, R.

A. Jordan, R. Scholz, P. Wust, H. Schirra, T. Schiestel, H. Schmidt, and R. Felix, “Endocytosis of Dextran and Silan-Coated Magnetite Nanoparticles and the Effect of Intracellular Hyperthermia on Human Mammary Carcinoma Cells in vitro,” J. Magnetism. Magn. Mater. 194, 185–196 (1999).
[Crossref]

Flatau, P. J.

Fleury, B.

B. Matt, K. M. Pondman, S. J. Asshoff, B. ten Haken, B. Fleury, and N. Katsonis, “Soft Magnets from the Self-Organization of Magnetic Nanoparticles in Twisted Liquid Crystals,” Angew. Chem. Int. Ed. 53, 12446–12450 (2014).

Fytas, N.

V. Yannopapas, N. Fytas, V. Kyrimi, E. Kallos, A. G. Vanakaras, and D. J. Photinos, “Light scattering by a metallic nanoparticle coated with a nematic liquid crystal,” Phys. Stat. Solidi A 210, 335–340 (2013).
[Crossref]

Guillon, D.

A. Demortiere, P. Panissod, B. P. Pichon, G. Pourroy, D. Guillon, B. Donnio, and S. Begin-Colin, “Size-dependent properties of magnetic iron oxide nanocrystals,” Nanoscale 3, 225–232 (2011).
[Crossref]

Harmon, B.

V. Antonov, B. Harmon, and A. Yaresko, Electronic Structure and Magneto-Optical Properties of Solids (Kluwer, 2004).

Hassdorf, R.

T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono, “Magnetic vortex core observation in circular dots of permalloy,” Science 289, 930–932 (2000).
[Crossref] [PubMed]

Hoekstra, A. G.

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spec. Rad. Transfer 106, 558–589 (2007).
[Crossref]

Ishikawa, Y.

H. Yao and Y. Ishikawa, “Finite Size Effect on Magneto-Optical Responses of Chemically Modified Fe3O4 Nanoparticles Studied by MCD Spectroscopy,” J. Phys. Chem. C 119, 13224–13230 (2015).
[Crossref]

Jordan, A.

A. Jordan, R. Scholz, P. Wust, H. Schirra, T. Schiestel, H. Schmidt, and R. Felix, “Endocytosis of Dextran and Silan-Coated Magnetite Nanoparticles and the Effect of Intracellular Hyperthermia on Human Mammary Carcinoma Cells in vitro,” J. Magnetism. Magn. Mater. 194, 185–196 (1999).
[Crossref]

Kahn, M. L.

S. Saliba, C. Mingotaud, M. L. Kahn, and J-D Marty, “Liquid crystalline thermotropic and lyotropic nanohybrids,” Nanoscale 5, 6641 (2013).
[Crossref] [PubMed]

Kallos, E.

V. Yannopapas, N. Fytas, V. Kyrimi, E. Kallos, A. G. Vanakaras, and D. J. Photinos, “Light scattering by a metallic nanoparticle coated with a nematic liquid crystal,” Phys. Stat. Solidi A 210, 335–340 (2013).
[Crossref]

Katsonis, N.

B. Matt, K. M. Pondman, S. J. Asshoff, B. ten Haken, B. Fleury, and N. Katsonis, “Soft Magnets from the Self-Organization of Magnetic Nanoparticles in Twisted Liquid Crystals,” Angew. Chem. Int. Ed. 53, 12446–12450 (2014).

Klapp, S. H. L.

S. D. Peroukidis, K. Lichtner, and S. H. L. Klapp, “Tunable structures of mixtures of magnetic particles in liquid-crystalline matrices,” Soft Matter 11, 5999–6008 (2015).
[Crossref] [PubMed]

S. D. Peroukidis and S. H. L. Klapp, “Spontaneous ordering of magnetic particles in liquid crystals: From chains to biaxial lamellae,” Phys. Rev. E 92, 010501 (2015).
[Crossref]

Klein, S.

K. May, R. Stannarius, S. Klein, and A. Eremin, “Electric-Field-Induced Phase Separation and Homogenization Dynamics in Colloidal Suspensions of Dichroic Rod-Shaped Pigment Particle,” Langmuir 30, 7070–7076 (2014).
[Crossref] [PubMed]

Krenn, J. R.

M. Salerno, J. R. Krenn, B. Lamprecht, G. Schider, H. Ditlbacher, N. Felidj, A. Leitner, and F. A. Aussenegg, “Plasmon Polaritons in Metal Nanostructures: The Optoelectronic Route to Nanotechnology,” Opto-Electron. Rev. 10, 217–224 (2002).

Kyrimi, V.

V. Yannopapas, N. Fytas, V. Kyrimi, E. Kallos, A. G. Vanakaras, and D. J. Photinos, “Light scattering by a metallic nanoparticle coated with a nematic liquid crystal,” Phys. Stat. Solidi A 210, 335–340 (2013).
[Crossref]

Lamprecht, B.

M. Salerno, J. R. Krenn, B. Lamprecht, G. Schider, H. Ditlbacher, N. Felidj, A. Leitner, and F. A. Aussenegg, “Plasmon Polaritons in Metal Nanostructures: The Optoelectronic Route to Nanotechnology,” Opto-Electron. Rev. 10, 217–224 (2002).

Leitner, A.

M. Salerno, J. R. Krenn, B. Lamprecht, G. Schider, H. Ditlbacher, N. Felidj, A. Leitner, and F. A. Aussenegg, “Plasmon Polaritons in Metal Nanostructures: The Optoelectronic Route to Nanotechnology,” Opto-Electron. Rev. 10, 217–224 (2002).

Levy, O.

O. Levy and D. Stroud, “Maxwell Garnett theory for mixtures of anisotropic inclusions: application to conducting polymers,” Phys. Rev. B 1997(56), 8035–8046 (1997).

Lichtner, K.

S. D. Peroukidis, K. Lichtner, and S. H. L. Klapp, “Tunable structures of mixtures of magnetic particles in liquid-crystalline matrices,” Soft Matter 11, 5999–6008 (2015).
[Crossref] [PubMed]

Lisjak, D.

A. Mertelj, D. Lisjak, and M. Drofenik, “Ferromagnetism in suspensions of magnetic platelets in liquid crystal,” Nature (London) 504, 237–241 (2013).
[Crossref]

Marty, J-D

S. Saliba, C. Mingotaud, M. L. Kahn, and J-D Marty, “Liquid crystalline thermotropic and lyotropic nanohybrids,” Nanoscale 5, 6641 (2013).
[Crossref] [PubMed]

Matt, B.

B. Matt, K. M. Pondman, S. J. Asshoff, B. ten Haken, B. Fleury, and N. Katsonis, “Soft Magnets from the Self-Organization of Magnetic Nanoparticles in Twisted Liquid Crystals,” Angew. Chem. Int. Ed. 53, 12446–12450 (2014).

May, K.

K. May, R. Stannarius, S. Klein, and A. Eremin, “Electric-Field-Induced Phase Separation and Homogenization Dynamics in Colloidal Suspensions of Dichroic Rod-Shaped Pigment Particle,” Langmuir 30, 7070–7076 (2014).
[Crossref] [PubMed]

Mertelj, A.

A. Mertelj, D. Lisjak, and M. Drofenik, “Ferromagnetism in suspensions of magnetic platelets in liquid crystal,” Nature (London) 504, 237–241 (2013).
[Crossref]

Mingotaud, C.

S. Saliba, C. Mingotaud, M. L. Kahn, and J-D Marty, “Liquid crystalline thermotropic and lyotropic nanohybrids,” Nanoscale 5, 6641 (2013).
[Crossref] [PubMed]

Odenbach, S.

S. Odenbach, Magnetoviscous effects in ferrofluids (Springer, 2002).

Okuno, T.

T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono, “Magnetic vortex core observation in circular dots of permalloy,” Science 289, 930–932 (2000).
[Crossref] [PubMed]

Ono, T.

T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono, “Magnetic vortex core observation in circular dots of permalloy,” Science 289, 930–932 (2000).
[Crossref] [PubMed]

Panissod, P.

A. Demortiere, P. Panissod, B. P. Pichon, G. Pourroy, D. Guillon, B. Donnio, and S. Begin-Colin, “Size-dependent properties of magnetic iron oxide nanocrystals,” Nanoscale 3, 225–232 (2011).
[Crossref]

Park, S. Y.

S. Y. Park and D. Stroud, “Surface-Enhanced Plasmon Splitting in a Liquid-Crystal-Coated Gold Nanoparticle,” Phys. Rev. Lett. 94, 217401 (2005).
[Crossref] [PubMed]

Peroukidis, S. D.

S. D. Peroukidis, K. Lichtner, and S. H. L. Klapp, “Tunable structures of mixtures of magnetic particles in liquid-crystalline matrices,” Soft Matter 11, 5999–6008 (2015).
[Crossref] [PubMed]

S. D. Peroukidis and S. H. L. Klapp, “Spontaneous ordering of magnetic particles in liquid crystals: From chains to biaxial lamellae,” Phys. Rev. E 92, 010501 (2015).
[Crossref]

S. D. Peroukidis, V. Yannopapas, A. G. Vanakaras, S. Droulias, and D. J. Photinos, “Plasmonic response of ordered arrays of gold nanorods immersed within a nematic liquid crystal,” Liq. Cryst. 41, 1430–1435 (2014).
[Crossref]

Photinos, D. J.

S. D. Peroukidis, V. Yannopapas, A. G. Vanakaras, S. Droulias, and D. J. Photinos, “Plasmonic response of ordered arrays of gold nanorods immersed within a nematic liquid crystal,” Liq. Cryst. 41, 1430–1435 (2014).
[Crossref]

V. Yannopapas, N. Fytas, V. Kyrimi, E. Kallos, A. G. Vanakaras, and D. J. Photinos, “Light scattering by a metallic nanoparticle coated with a nematic liquid crystal,” Phys. Stat. Solidi A 210, 335–340 (2013).
[Crossref]

Pichon, B. P.

A. Demortiere, P. Panissod, B. P. Pichon, G. Pourroy, D. Guillon, B. Donnio, and S. Begin-Colin, “Size-dependent properties of magnetic iron oxide nanocrystals,” Nanoscale 3, 225–232 (2011).
[Crossref]

Pondman, K. M.

B. Matt, K. M. Pondman, S. J. Asshoff, B. ten Haken, B. Fleury, and N. Katsonis, “Soft Magnets from the Self-Organization of Magnetic Nanoparticles in Twisted Liquid Crystals,” Angew. Chem. Int. Ed. 53, 12446–12450 (2014).

Pourroy, G.

A. Demortiere, P. Panissod, B. P. Pichon, G. Pourroy, D. Guillon, B. Donnio, and S. Begin-Colin, “Size-dependent properties of magnetic iron oxide nanocrystals,” Nanoscale 3, 225–232 (2011).
[Crossref]

Salerno, M.

M. Salerno, J. R. Krenn, B. Lamprecht, G. Schider, H. Ditlbacher, N. Felidj, A. Leitner, and F. A. Aussenegg, “Plasmon Polaritons in Metal Nanostructures: The Optoelectronic Route to Nanotechnology,” Opto-Electron. Rev. 10, 217–224 (2002).

Saliba, S.

S. Saliba, C. Mingotaud, M. L. Kahn, and J-D Marty, “Liquid crystalline thermotropic and lyotropic nanohybrids,” Nanoscale 5, 6641 (2013).
[Crossref] [PubMed]

Scharf, T.

T. Scharf, Polarized Light in Liquid Crystals and Polymers (Wiley, 2007).

Schider, G.

M. Salerno, J. R. Krenn, B. Lamprecht, G. Schider, H. Ditlbacher, N. Felidj, A. Leitner, and F. A. Aussenegg, “Plasmon Polaritons in Metal Nanostructures: The Optoelectronic Route to Nanotechnology,” Opto-Electron. Rev. 10, 217–224 (2002).

Schiestel, T.

A. Jordan, R. Scholz, P. Wust, H. Schirra, T. Schiestel, H. Schmidt, and R. Felix, “Endocytosis of Dextran and Silan-Coated Magnetite Nanoparticles and the Effect of Intracellular Hyperthermia on Human Mammary Carcinoma Cells in vitro,” J. Magnetism. Magn. Mater. 194, 185–196 (1999).
[Crossref]

Schirra, H.

A. Jordan, R. Scholz, P. Wust, H. Schirra, T. Schiestel, H. Schmidt, and R. Felix, “Endocytosis of Dextran and Silan-Coated Magnetite Nanoparticles and the Effect of Intracellular Hyperthermia on Human Mammary Carcinoma Cells in vitro,” J. Magnetism. Magn. Mater. 194, 185–196 (1999).
[Crossref]

Schlegel, A.

A. Schlegel, S. F. Alvarado, and P. Wachter, “Optical properties of magnetite (Fe3O4),” J. Phys. C: Solid State Phys. 12, 1157–1164 (1979).
[Crossref]

Schmidt, H.

A. Jordan, R. Scholz, P. Wust, H. Schirra, T. Schiestel, H. Schmidt, and R. Felix, “Endocytosis of Dextran and Silan-Coated Magnetite Nanoparticles and the Effect of Intracellular Hyperthermia on Human Mammary Carcinoma Cells in vitro,” J. Magnetism. Magn. Mater. 194, 185–196 (1999).
[Crossref]

Schoenes, J.

X. Zhang, J. Schoenes, and P. Wachter, “Kerr-effect and dielecric tensor elements of magnetite (Fe3O4) between 0.5 and 4.3 eV,” Solid State Commun. 39, 189–192 (1981).
[Crossref]

Scholz, R.

A. Jordan, R. Scholz, P. Wust, H. Schirra, T. Schiestel, H. Schmidt, and R. Felix, “Endocytosis of Dextran and Silan-Coated Magnetite Nanoparticles and the Effect of Intracellular Hyperthermia on Human Mammary Carcinoma Cells in vitro,” J. Magnetism. Magn. Mater. 194, 185–196 (1999).
[Crossref]

Scott, B. L.

D. A. Smith, Y. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, “Magneto-optical spectra of closely-spaced magnetite nanoparticles,” J. Appl. Phys. 97, 10M504 (2005).
[Crossref]

Sharrock, M. P.

M. P. Sharrock and R. E. Bodnar, “Magnetic Materials for Recording: An Overview with Special Emphasis on Particles,” J. Appl. Phys. 57, 3919–3924 (1985).
[Crossref]

Shigeto, K.

T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono, “Magnetic vortex core observation in circular dots of permalloy,” Science 289, 930–932 (2000).
[Crossref] [PubMed]

Shinjo, T.

T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono, “Magnetic vortex core observation in circular dots of permalloy,” Science 289, 930–932 (2000).
[Crossref] [PubMed]

Smith, D. A.

D. A. Smith and K. L. Stokes, “Discrete dipole approximation for magnetooptical scattering calculations,” Opt. Express 14, 5746–5754 (2006).
[Crossref] [PubMed]

D. A. Smith, Y. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, “Magneto-optical spectra of closely-spaced magnetite nanoparticles,” J. Appl. Phys. 97, 10M504 (2005).
[Crossref]

Stannarius, R.

K. May, R. Stannarius, S. Klein, and A. Eremin, “Electric-Field-Induced Phase Separation and Homogenization Dynamics in Colloidal Suspensions of Dichroic Rod-Shaped Pigment Particle,” Langmuir 30, 7070–7076 (2014).
[Crossref] [PubMed]

Stokes, K. L.

D. A. Smith and K. L. Stokes, “Discrete dipole approximation for magnetooptical scattering calculations,” Opt. Express 14, 5746–5754 (2006).
[Crossref] [PubMed]

D. A. Smith, Y. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, “Magneto-optical spectra of closely-spaced magnetite nanoparticles,” J. Appl. Phys. 97, 10M504 (2005).
[Crossref]

Stroud, D.

S. Y. Park and D. Stroud, “Surface-Enhanced Plasmon Splitting in a Liquid-Crystal-Coated Gold Nanoparticle,” Phys. Rev. Lett. 94, 217401 (2005).
[Crossref] [PubMed]

O. Levy and D. Stroud, “Maxwell Garnett theory for mixtures of anisotropic inclusions: application to conducting polymers,” Phys. Rev. B 1997(56), 8035–8046 (1997).

ten Haken, B.

B. Matt, K. M. Pondman, S. J. Asshoff, B. ten Haken, B. Fleury, and N. Katsonis, “Soft Magnets from the Self-Organization of Magnetic Nanoparticles in Twisted Liquid Crystals,” Angew. Chem. Int. Ed. 53, 12446–12450 (2014).

Vanakaras, A. G.

V. Yannopapas and A. G. Vanakaras, “Strong Magnetochiral Dichroism in Suspensions of Magnetoplasmonic Nanohelices,” ACS Photon. 2, 1030–1038 (2015).
[Crossref]

S. D. Peroukidis, V. Yannopapas, A. G. Vanakaras, S. Droulias, and D. J. Photinos, “Plasmonic response of ordered arrays of gold nanorods immersed within a nematic liquid crystal,” Liq. Cryst. 41, 1430–1435 (2014).
[Crossref]

V. Yannopapas, N. Fytas, V. Kyrimi, E. Kallos, A. G. Vanakaras, and D. J. Photinos, “Light scattering by a metallic nanoparticle coated with a nematic liquid crystal,” Phys. Stat. Solidi A 210, 335–340 (2013).
[Crossref]

Wachter, P.

X. Zhang, J. Schoenes, and P. Wachter, “Kerr-effect and dielecric tensor elements of magnetite (Fe3O4) between 0.5 and 4.3 eV,” Solid State Commun. 39, 189–192 (1981).
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A. Schlegel, S. F. Alvarado, and P. Wachter, “Optical properties of magnetite (Fe3O4),” J. Phys. C: Solid State Phys. 12, 1157–1164 (1979).
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White, S. A.

D. A. Smith, Y. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, “Magneto-optical spectra of closely-spaced magnetite nanoparticles,” J. Appl. Phys. 97, 10M504 (2005).
[Crossref]

Wust, P.

A. Jordan, R. Scholz, P. Wust, H. Schirra, T. Schiestel, H. Schmidt, and R. Felix, “Endocytosis of Dextran and Silan-Coated Magnetite Nanoparticles and the Effect of Intracellular Hyperthermia on Human Mammary Carcinoma Cells in vitro,” J. Magnetism. Magn. Mater. 194, 185–196 (1999).
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Yannopapas, V.

V. Yannopapas and A. G. Vanakaras, “Strong Magnetochiral Dichroism in Suspensions of Magnetoplasmonic Nanohelices,” ACS Photon. 2, 1030–1038 (2015).
[Crossref]

S. D. Peroukidis, V. Yannopapas, A. G. Vanakaras, S. Droulias, and D. J. Photinos, “Plasmonic response of ordered arrays of gold nanorods immersed within a nematic liquid crystal,” Liq. Cryst. 41, 1430–1435 (2014).
[Crossref]

V. Yannopapas, N. Fytas, V. Kyrimi, E. Kallos, A. G. Vanakaras, and D. J. Photinos, “Light scattering by a metallic nanoparticle coated with a nematic liquid crystal,” Phys. Stat. Solidi A 210, 335–340 (2013).
[Crossref]

Yao, H.

H. Yao and Y. Ishikawa, “Finite Size Effect on Magneto-Optical Responses of Chemically Modified Fe3O4 Nanoparticles Studied by MCD Spectroscopy,” J. Phys. Chem. C 119, 13224–13230 (2015).
[Crossref]

Yaresko, A.

V. Antonov, B. Harmon, and A. Yaresko, Electronic Structure and Magneto-Optical Properties of Solids (Kluwer, 2004).

Yurkin, M. A.

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spec. Rad. Transfer 106, 558–589 (2007).
[Crossref]

Zhang, X.

X. Zhang, J. Schoenes, and P. Wachter, “Kerr-effect and dielecric tensor elements of magnetite (Fe3O4) between 0.5 and 4.3 eV,” Solid State Commun. 39, 189–192 (1981).
[Crossref]

ACS Photon. (1)

V. Yannopapas and A. G. Vanakaras, “Strong Magnetochiral Dichroism in Suspensions of Magnetoplasmonic Nanohelices,” ACS Photon. 2, 1030–1038 (2015).
[Crossref]

Angew. Chem. Int. Ed. (1)

B. Matt, K. M. Pondman, S. J. Asshoff, B. ten Haken, B. Fleury, and N. Katsonis, “Soft Magnets from the Self-Organization of Magnetic Nanoparticles in Twisted Liquid Crystals,” Angew. Chem. Int. Ed. 53, 12446–12450 (2014).

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M. P. Sharrock and R. E. Bodnar, “Magnetic Materials for Recording: An Overview with Special Emphasis on Particles,” J. Appl. Phys. 57, 3919–3924 (1985).
[Crossref]

D. A. Smith, Y. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, “Magneto-optical spectra of closely-spaced magnetite nanoparticles,” J. Appl. Phys. 97, 10M504 (2005).
[Crossref]

J. Magnetism. Magn. Mater. (1)

A. Jordan, R. Scholz, P. Wust, H. Schirra, T. Schiestel, H. Schmidt, and R. Felix, “Endocytosis of Dextran and Silan-Coated Magnetite Nanoparticles and the Effect of Intracellular Hyperthermia on Human Mammary Carcinoma Cells in vitro,” J. Magnetism. Magn. Mater. 194, 185–196 (1999).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Phys. C: Solid State Phys. (1)

A. Schlegel, S. F. Alvarado, and P. Wachter, “Optical properties of magnetite (Fe3O4),” J. Phys. C: Solid State Phys. 12, 1157–1164 (1979).
[Crossref]

J. Phys. Chem. C (1)

H. Yao and Y. Ishikawa, “Finite Size Effect on Magneto-Optical Responses of Chemically Modified Fe3O4 Nanoparticles Studied by MCD Spectroscopy,” J. Phys. Chem. C 119, 13224–13230 (2015).
[Crossref]

J. Quant. Spec. Rad. Transfer (1)

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spec. Rad. Transfer 106, 558–589 (2007).
[Crossref]

Langmuir (1)

K. May, R. Stannarius, S. Klein, and A. Eremin, “Electric-Field-Induced Phase Separation and Homogenization Dynamics in Colloidal Suspensions of Dichroic Rod-Shaped Pigment Particle,” Langmuir 30, 7070–7076 (2014).
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S. D. Peroukidis, V. Yannopapas, A. G. Vanakaras, S. Droulias, and D. J. Photinos, “Plasmonic response of ordered arrays of gold nanorods immersed within a nematic liquid crystal,” Liq. Cryst. 41, 1430–1435 (2014).
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S. Saliba, C. Mingotaud, M. L. Kahn, and J-D Marty, “Liquid crystalline thermotropic and lyotropic nanohybrids,” Nanoscale 5, 6641 (2013).
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Nature (London) (1)

A. Mertelj, D. Lisjak, and M. Drofenik, “Ferromagnetism in suspensions of magnetic platelets in liquid crystal,” Nature (London) 504, 237–241 (2013).
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Opt. Express (1)

Opto-Electron. Rev. (1)

M. Salerno, J. R. Krenn, B. Lamprecht, G. Schider, H. Ditlbacher, N. Felidj, A. Leitner, and F. A. Aussenegg, “Plasmon Polaritons in Metal Nanostructures: The Optoelectronic Route to Nanotechnology,” Opto-Electron. Rev. 10, 217–224 (2002).

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O. Levy and D. Stroud, “Maxwell Garnett theory for mixtures of anisotropic inclusions: application to conducting polymers,” Phys. Rev. B 1997(56), 8035–8046 (1997).

Phys. Rev. E (1)

S. D. Peroukidis and S. H. L. Klapp, “Spontaneous ordering of magnetic particles in liquid crystals: From chains to biaxial lamellae,” Phys. Rev. E 92, 010501 (2015).
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S. Y. Park and D. Stroud, “Surface-Enhanced Plasmon Splitting in a Liquid-Crystal-Coated Gold Nanoparticle,” Phys. Rev. Lett. 94, 217401 (2005).
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Phys. Stat. Solidi A (1)

V. Yannopapas, N. Fytas, V. Kyrimi, E. Kallos, A. G. Vanakaras, and D. J. Photinos, “Light scattering by a metallic nanoparticle coated with a nematic liquid crystal,” Phys. Stat. Solidi A 210, 335–340 (2013).
[Crossref]

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T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono, “Magnetic vortex core observation in circular dots of permalloy,” Science 289, 930–932 (2000).
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S. D. Peroukidis, K. Lichtner, and S. H. L. Klapp, “Tunable structures of mixtures of magnetic particles in liquid-crystalline matrices,” Soft Matter 11, 5999–6008 (2015).
[Crossref] [PubMed]

Solid State Commun. (1)

X. Zhang, J. Schoenes, and P. Wachter, “Kerr-effect and dielecric tensor elements of magnetite (Fe3O4) between 0.5 and 4.3 eV,” Solid State Commun. 39, 189–192 (1981).
[Crossref]

Other (4)

T. Scharf, Polarized Light in Liquid Crystals and Polymers (Wiley, 2007).

V. Antonov, B. Harmon, and A. Yaresko, Electronic Structure and Magneto-Optical Properties of Solids (Kluwer, 2004).

S. Odenbach, Magnetoviscous effects in ferrofluids (Springer, 2002).

“Private communication with R. Stannarius,”

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Figures (4)

Fig. 1
Fig. 1 Representative simulation snapshots for mixtures with σs = 1σ in the absence of external magnetic field: (a) Isotropic and (b) nematic phase. In the bottom parts only the MNPs are shown for clarity. The nematic directors of the species are also indicated.
Fig. 2
Fig. 2 Representative simulation snapshots for mixtures with σs = 1σ that are in the I-state (when the external magnetic field is off) and in the N-state (field-on): (a) [(T, ρ) = (1.1,0.34)] field-off S ≃ 0.0 (b) [(T, ρ) = (1.1,0.34)] field-on S ≃ 0.4 (c) [(T, ρ) = (2.2,0.40)] field-off S ≃ 0.0 (d) [(T, ρ) = (2.2,0.40)] field-on S ≃ 0.6.
Fig. 3
Fig. 3 (a) Red line: magnetochiral dichroism (MCD) signal for the hypothetical case where the configuration of Fig. 2(a) is not modified under the action of the magnetic field and the MNPs remain at the same positions (see inset). Black lines: MCD signal for the actual case where the configuration of Fig. 2(a) undergoes structural transformation to the configuration of Fig. 2(b) under the action of the magnetic field (see inset). (b) The same as (a) but for the configurations of Fig. 2(c) and 2(d), respectively. The magnetite MNPs have 5 nm radius.
Fig. 4
Fig. 4 Azimuth and ellipticity angles corresponding to Faraday rotation for (a) the system of Fig. 2(b) and 2(b) the system of Fig. 2(d) (also shown in the insets).

Equations (16)

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P i = α ˜ i E i
E i = E i n c , i + i i A i j P j
A i j = exp ( i k r i j ) r i j [ k 2 ( r ^ i j r ^ i j 1 3 ) + i k r i j 1 r i j 2 ( 3 r ^ i j r ^ i j 1 3 ) ] , i j
j = 1 N A i j P j = E i n c , i
A i j = [ α ˜ i ] 1 .
α ˜ = V s 2 ε h ; + ε h ; 4 π [ ε ˜ s ε ˜ h 1 3 ] [ ε ˜ s + 2 ε ˜ h 1 3 ] 1 .
ε ˜ s = ( ε x x i Q m z i Q m y i Q m z ε y y i Q m x i Q m y i Q m x ε z z )
ε ˜ h = ( ε 0 0 0 ε 0 0 0 ε )
C s c = 4 π k | E i n c | 2 i = 1 N [ 2 3 k 3 | P i | 2 ( P i E self , i * ) ]
C e x t = 4 π k | E i n c | 2 i = 1 N ( P i E i n c , i * )
C a b s = 4 π k | E i n c | 2 i = 1 N [ ( P i E i * ) 2 3 k 3 | P i | 2 ]
θ + i η = π k E 0 i = 1 N ( P i L P i R ) exp ( i k z ^ r i )
P i L , R = P i e ^ L , R *
e ^ L , R = 1 2 ( x ^ ± i y ^ )
C D = C a b s R C P C a b s L C P
M C D = C D ( H ) C D ( H = 0 ) .

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