research article induced magnetic anisotropy in liquid...

Research ArticleInduced Magnetic Anisotropy in Liquid Crystals Doped withResonant Semiconductor Nanoparticles

Vicente Marzal Juan Carlos Torres Isabel Peacuterez Joseacute Manuel Saacutenchez-Penaand Braulio Garciacutea-CaacutemaraDisplays and Photonic Applications Group Electronic Technology Department Carlos III University of Madrid Leganes28911 Madrid Spain

Correspondence should be addressed to Braulio Garcıa-Camara brgarciainguc3mes

Received 10 April 2016 Accepted 28 June 2016

Academic Editor Nathan C Lindquist

Copyright copy 2016 Vicente Marzal et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Currently there are many efforts to improve the electrooptical properties of liquid crystals by means of doping them with differenttypes of nanoparticles In addition liquid crystals may be used as activemedia to dynamically control other interesting phenomenasuch as light scattering resonances In this sense mixtures of resonant nanoparticles hosted in a liquid crystal could be a potentialmetamaterial with interesting properties In thiswork the artificialmagnetism induced in amixture of semiconductor nanoparticlessurrounded by a liquid crystal is analyzed Effective magnetic permeability of mixtures has been obtained using the Maxwell-Garnett effectivemedium theory Furthermore permeability variations with nanoparticles size and their concentration in the liquidcrystal as well as the magnetic anisotropy have been studied

1 Introduction

Plasmonics is a consolidated research field due to its potentialapplications in many nanotechnology domains [1ndash3] Plas-mon resonances occur when the photon frequency of anincident radiation is resonant with the collective oscillationof the conduction electrons in a metal This process involvesthe concentration of light in subwavelength dimensionswhich allows the manipulation of light at nanoscale Thisphenomenon is the basis of a myriad of applications rangingfrom new all-optical devices [4 5] to the design of metatomsto performmetamaterials with tunable optical properties [6ndash8]

Although huge efforts have been made on plasmonnanoparticles and plasmonic applications [9] metallic sam-ples have the inherent problem of absorption in the visiblerange This absorption produces thermal effects leading tomaterial degradation Semiconductor materials with highrefractive index can be the alternative to plasmonic materials(eg gold and silver) in this kind of applications Themagnetic and electric Mie resonances in light scattering ofsemiconductor materials [10 11] are analogous to the local-ized surface plasmon resonances in metallic nanoparticles

These semiconductor nanoparticles can act as photonicnanoresonators due to the high-refractive-index contrastbetween them and the surrounding medium and the ratiobetween their size and the incident radiation wavelengthThese properties lead to the appearance of bothmagnetic andelectric resonances in the visible range of the electromagneticspectrum [12] The excitation of these resonances is beingdeeply studied nowadays For instance astonishing phenom-ena like scattering directionality have been reported [13 14]in these systems In addition the low optical absorption ofsemiconductors has overcome in part thermal issues [15]

The tunability of resonances of these nanostructures is akey aspect for several applications For instance the spectralcoincidence of these resonances with the absorption peak ofdifferent molecules is the basis of chemical sensors [16] As inplasmonicsMie resonances of dielectric nanoparticles can betuned changing their size shape composition or the opticalproperties of the surrounding medium The variation of theproperties of the nanoparticles is a static method it involvesthe fabrication of new ones in order to change the outputresponse limiting its application Nevertheless the changeof the surrounding medium properties may be dynamicBy using an active material as surrounding medium its

Hindawi Publishing CorporationJournal of NanomaterialsVolume 2016 Article ID 7659074 9 pageshttpdxdoiorg10115520167659074

2 Journal of Nanomaterials

optical properties can be changed with real time control andreversibility capacity changing the resonant wavelength inthe same way This dynamic response is very interesting forapplications such as active polarizers [17] or new tools foractive photonic circuits [18]

Among all the active media used in plasmonic devicesliquid crystals are a good choice they have capacity to easilymodify their refractive index by electrical [19] optical [20]or thermal techniques [21] because of their high birefringenceand small elastic constants This control feature besides theirhigh compatibility with optoelectronic materials makes themthe perfect option as active dielectric media Liquid crystalproperties have also led to the development of a large varietyof photonic devices (modulators filters optical switches andso on) [22ndash24]

While liquid crystals have a remarkable dielectricanisotropy their magnetic properties in the visible range donot have a noticeable behavior In this sense this work isdevoted to analyze the magnetic properties of mixtures com-posed of a liquid crystal doped with semiconductor nanopar-ticles with magnetic resonances The magnetic permeabilityof the nanoparticles and the effective magnetic permeabilityof the mixture have been studied in a set of simulationsThe Maxwell-Garnett effective medium approach has beenconsidered in the calculus of the permeability [25] Searchinga noticeable magnetic anisotropy several liquid crystals andsemiconductor nanoparticles have been considered

2 Theory

The effective permeability 120583eff of mixtures composed of aliquid crystal (LC) doped with resonant nanoparticles (NPs)can be obtained through several effective medium approx-imations In particular a generalization of the Maxwell-Garnett Theory (MG) [25] has been considered in this workThis theory establishes that the effective dielectric function120598eff of a matrix with homogeneous spherical inclusions canbe expressed in terms of the optical properties of eachcomponent and the volume fraction of the inclusions (119891) [26]as follows

120598eff = 120598119898 [1 +3119891 ((120598 minus 120598

119898) (120598 + 2120598

119898))

1 minus 119891 ((120598 minus 120598119898) (120598 + 2120598

119898))] (1)

where 120598 and 120598119898are the dielectric permittivity of the inclusions

and the matrix material respectivelyDue to the symmetric nature of the electromagnetic

field an analogue expression can be derived for the effectivemagnetic permeability 120583eff

120583eff = 120583ℎ [1 +3119891 ((120583

119904minus 120583ℎ) (120583119904+ 2120583ℎ))

1 minus 119891 ((120583119904minus 120583ℎ) (120583119904+ 2120583ℎ))] (2)

where 120583ℎand 120583

119904are the magnetic permeability of the host

medium and the inclusion respectivelyIn this work a LC host medium with high-refractive-

index semiconductor nanoparticles as inclusions is consid-ered Selected NPs have both electric and magnetic reso-nances in the visible range although they are composed of

nonmagnetic materials (eg silicon and germanium) [11]Thus effective optical constants can also be derived for theindividual nanoparticles Focusing attention on the mag-netic properties the effective magnetic permeability of thesenanoparticles has been obtained through theMie theory [26]

The scattered electromagnetic field (119864119904 119867119904) of a spherical

particle (of radius 119877) made of a certain material embeddedin a homogeneous and isotropic media can be calculatedthrough theMie theory [26]This theory considers an expan-sion of the scattered fields in vector spherical harmonics(11987311989011198991198721199001119899 11987311990011198991198721198901119899

) when the sphere is radiated with anincident electromagnetic plane wave with wavelength 120582 andamplitude 119864

0

119864119904= 1198640

infin

sum

119899=1

1198941198992119899 + 1

119899 (119899 + 1)(1198941198861198991198731198901119899minus 1198871198991198721199001119899)

119867119904=119896

1205961205831198640

infin

sum

119899=1

1198941198992119899 + 1

119899 (119899 + 1)(1198941198871198991198731199001119899+ 1198861198991198721198901119899)

(3)

where 119896 is the wave vector and 120596 is the frequency of theincident field 120583 is themagnetic permeability of the surround-ing medium and 119886

119899 119887119899 are the so-called Mie coefficients

for the scattered field Applying the boundary conditionsbetween the sphere and the surrounding medium analyticalexpressions for these coefficients can be deduced [26]

119886119899=Ψ119899(119898119909)Ψ

1015840

119899(119909) minus Ψ

119899(119909)Ψ1015840

119899(119898119909)

Ψ119899(119898119909) 1205851015840

119899(119909) minus 120585

119899(119909)Ψ1015840119899(119898119909)

119887119899=Ψ119899(119898119909)Ψ

1015840

119899(119909) minus Ψ

119899(119909)Ψ1015840

119899(119898119909)

Ψ119899(119898119909) 1205851015840

119899(119909) minus 120585

119899(119909)Ψ1015840119899(119898119909)

(4)

Ψ119899and 120585

119899are the Riccati-Bessel functions and 119898 = 119899

119904119899

is the relative refractive index between the sphere (119899119904) and

the surrounding medium (119899) The factor is given by =119898120583119904 where 120583

119904is the magnetic permeability of the sphere

material The size parameter is 119909 which is given by therelation 119909 = 2120587119877119899120582 where 119877 is the radius of the sphereand 120582 the incident wavelength as was commented While 119886

119899

coefficients are related to the electric response of the system119887119899are usually related to the magnetic character In addition1198861and 1198871correspond to the dipolar behavior 119886

2and 1198872with

the quadrupolar one and so onThese complex expressions can be simplified under

certain assumptions for instance applying the Rayleighapproximation which is satisfied when

119909 ≪ 1

|119898| 119909 ≪ 1

(5)

Journal of Nanomaterials 3

450 500 550 600 650 700 750400

120582 (nm)

a1b1

a2b2

00

02

04

06

08

10M

ie co

effici

ents

(a)

450 500 550 600 650 700 750400

120582 (nm)

a1b1

a2b2

00

02

04

06

08

Mie

coeffi

cien

ts

(b)

Figure 1 First four Mie coefficients of an AlAs nanoparticle with a radius of 58 nm embedded in liquid crystal (UCF-N3b) as a function ofthe incident wavelength

In this case only the dipolar components remain and theexpressions of Mie coefficients can be simplified as follows[26]

1198861= minus11989421199093

3

120598 minus 1

120598 + 2 (6)

1198871= minus11989421199093

3

120583 minus 1

120583 + 2 (7)

119886119899asymp 119887119899asymp 0 119899 ge 2 (8)

This approximation is only satisfied by dipole-like spheresAlthough the magnetic response of semiconductor nanopar-ticles has been observed in large nanoparticles (diameter gt50 nm) a simple analysis of the Mie coefficients shows thatthe dipolar character dominates in these nanoparticles inthe visible wavelength range Figure 1 shows the first fourMie coefficients (119886

1 1198862 1198871 1198872) of an AlAs nanoparticle with a

radius of 119877 = 58 nm as a function of the incident wavelengthconsidering the ordinary refractive index (a) and the extraor-dinary refractive index (b) for the surrounding UCF-N3b LChost [27] Although liquid crystals are not isotropic mediathey can be approximated as isotropic considering eithertheir ordinary or extraordinary refractive index For thewavelength range where the magnetic resonance arises (120582 asymp400 nmndash450 nm) it can be seen that the dipolar contributions(1198861and 1198871) are dominant allowing the assumption of a dipole-

like sphereThe effective magnetic permeability of these semicon-

ductor nanoparticles has been obtained following the nextprocedure Using homemade computer routines the valueof the Mie coefficient 119887

1of the nanoparticle considering it

surrounded by the LC medium has been calculated Assum-ing that the spherical particle accomplishes the Rayleighapproximation at least in a wavelength range an effective

value of the magnetic permeability 120583119904 of the particle has

been deduced from expression (7) This value along with themagnetic permeability of LC host has been used to obtain theeffective magnetic permeability of the mixture by means ofthe effective medium theory (see (2)) The refractive indicesof liquid crystals have been obtained using the Cauchymodel[27ndash32] and the optical properties of the NPs materials havebeen derived from references [33ndash37]

3 Process and Results

In order to obtain a maximum magnetic response severalliquid crystals as well as semiconductor materials have beenconsidered All materials have been selected based on theavailability of data in the literature

In this sense analytical calculations considering 14 dif-ferent liquid crystals as host (5PCH E7 E44 MLC-6241-000MLC-6608 MLC-9200-000 MLC-9200-100 TL-216 5CBBL038 DNDA-OC3 UCF-35 UCF-N3b and W1825K) and8 materials as doping NPs (AlAs AlSb GaAs GaP InGaAsGaInP Si and TiO

2) have been carried out In the following

sections only results related to thosematerials that maximizethe effective magnetic permeability are shown

31 Magnetic Resonances of Nanoparticles Spectral Range Inthis section the optical behavior of an isolated nanoparticleembedded in a liquid crystal host is analyzed in order to checkthe appearance of a magnetic response and the spectral rangein which it remains

Considering each semiconductor material listed abovethe first four Mie coefficients (119886

1 1198862 1198871 1198872) have been cal-

culated Nanoparticles radius has been selected in the rangefrom 35 to 150 nm Although these nanoparticle sizes do notstrictly satisfy the Rayleigh criterion we have obtained thatthe dipolar character is dominant in the spectral range of


Table 1 Summary of themost important parameters of themagnetic resonances of semiconductor nanoparticles embedded in liquid crystalsOnly those cases presenting the most noticeable results have been included

Mixture Nanoparticle radius (nm) Ordinary Extraordinary1205820(nm) Δ120582 (nm) 120582

0(nm) Δ120582 (nm)

MLC6608 + AlAs 52 403 380ndash450 402 385ndash450MLC6608 + AlSb 59 546 498ndash600 546 504ndash600MLC6608 + GaAs 87 686 609ndash800 683 618ndash800MLC6608 + GaInP 78 576 553ndash690 574 555ndash700MLC6608 + GaP 50 464 430ndash500 463 437ndash510MLC6608 + InGaAs 75 626 596ndash740 625 605ndash770MLC6608 + Si 86 692 608ndash790 691 615ndash800MLC6608 + TiO

277 496 487ndash640 492 490ndash650

the magnetic resonance Nanoparticles have been consideredembedded in the liquid crystal under its extreme opticalconditions the ordinary and the extraordinary refractiveindices In addition although the calculations have beenmade for an isolated nanoparticle the low concentrationof NP in feasible experimental mixtures involves a lownanoparticle-nanoparticle interaction and their propertiesare close to those of the isolated case This analysis has beenmade in a global spectral range between 350 nm and 800 nmThe attention has been placed on the analysis of the coefficient1198871 which is related to a magnetic dipolar behavior All the

selected materials have a remarkable 1198871contribution in an

extended range of the visible spectrum Table 1 summarizesthe most important parameters derived from the simulationsalong with the LC host and NPs material These parametersare the wavelength at which the magnetic resonance ofthe nanoparticle is centered the spectral range where thedipolar term has predominance over the quadrupolar termsand the nanoparticle radius which maximizes the magneticresonance These data have been obtained considering theordinary and the extraordinary refractive indices of the liquidcrystal From Table 1 it can be seen that MLC6608 LC givesthemost remarkable results It will be seen in the next sectionthat despite the large list of LC analyzed only two of themoffer optimum results

32 Effective Magnetic Permeability of NPs Although nano-particle materials are not magnetic in the visible rangein previous sections it has been seen that NPs have aprominent magnetic response at a certain spectral rangeUnder the assumption of the dominant-dipolar behavior aneffective magnetic permeability can be deduced for thesenanoparticles As it was explained above this permeabilitycan be derived from the magnetic dipole term (119887

1) under the

Rayleigh approximation (7)In this work it has been obtained that the magnetic

response of semiconductor nanoparticles remains when theyare embedded in a liquid crystal presenting a nonunitaryeffective magnetic permeability at certain wavelengths rangeAs an example Figure 2 shows the effective magnetic per-meability of an AlSb nanoparticle of radius 58 nm embeddedin a W1825K liquid crystal host for both ordinary andextraordinary refractive indices of the LC As it can be seen

120583ord120583ext

0

1

2

3

4

Mag

netic

per

mea

bilit

y

500 600 700 800400

120582 (nm)

Figure 2 Magnetic permeability of an AlSb nanoparticle of 58 nmradius within the liquid crystal host W1825K

the effective magnetic permeability of the nanoparticle hasa resonant profile with positive and even negative valuesIn particular considering the simulation for the ordinaryrefractive index of the LC it presents a maximum positivevalue of 3758 at 621 nm and a minimum negative value ofminus0973 at 578 nm Another interesting feature of these resultsis the fact that the magnetic response of the semiconductornanoparticle can be tuned by changing the orientation ofLC molecules For the two possible extreme positions of LCmolecules an incident radiation ldquoseesrdquo the ordinary or theextraordinary refractive index of the LC respectively Thismagnetic anisotropy of the NP embedded in a LC can beclearly observed in Figure 2 where the effective magneticpermeability of the NP noticeably changes from the ordinaryto the extraordinary case As it can be seen the maximummagnetic anisotropy occurs in the wavelengths around themaximum absolute values of the permeability

The effective magnetic permeability of different nanopar-ticles embedded in a LC and the inducedmagnetic anisotropyhave been calculated The most remarkable results have beenobtained considering liquid crystals W1825K and MLC6608


Table 2 Maximum values of the effective magnetic permeability and magnetic anisotropy of an isolated nanoparticle made of differentsemiconductor materials (embedded in a W1825K LC host) for the ordinary and extraordinary cases Radius of each NP that maximizes thepermeability is also included

NP mixture 120583ordinary 120583extraordinary Δ120583max 119877max

AlAs 2451 1618 0833 52AlSb 3758 2297 1487 58GaAs 2482 1920 05828 85GaInP 2881 1958 0930 78GaP 2714 1760 0956 53InGaAs 1879 1603 0284 76Si 3001 2105 0931 70TiO2

2001 1439 0570 79

Table 3Minimumvalues of the nanoparticle permeability andmagnetic anisotropy of semiconductor nanoparticles (embedded in aW1825KLC host) for the ordinary and extraordinary cases Radius of each NP that minimizes the permeability is also included


AlAs 0246 0 816 0894 61AlSb minus0973 0423 1814 64GaAs minus0046 0593 0783 97GaInP minus0107 0785 1119 88GaP minus0087 0755 1117 58InGaAs 0250 0656 0456 90Si minus0423 0474 1193 78TiO2

0585 0991 0532 94

Table 2 shows the results for W1825K For each NP materialthe permeability and magnetic anisotropy shown in the tablehave been calculated with a nanoparticle size that maximizesthe permeability This value is also included in Table 2 Theprofile of the permeability function at both ordinary andextraordinary cases allows the appearance of a nonunitarymagnetic anisotropy in a range of incident wavelengths (seeFigure 2) In addition the magnetic anisotropy remains highin certain wavelengths range This is a key fact for practicaluse of the proposed system

Results shown in Table 2 consider maximum positivevalues of 120583

119904 Figure 2 also shows that there is magnetic

anisotropy considering the smallest values of the magneticpermeability of the nanoparticles with the same LC hostTable 3 shows the minimum effective magnetic permeabilityand the anisotropy that have been observed As in Table 2these values have been calculated with nanoparticle sizes thatminimize the permeability As it can be seen in some casesnegative values of 120583

119904can be achieved

As it can be seen in previous results the nanoparticlesize is one of the key parameters in the appearance ofmagnetic resonances Thus the dependence of the effectivepermeability with the NP size has been analyzed in order tofind the NP radius that maximizes 120583

119904value as it has been

observed in previous results Figure 3 shows the effectivepermeability (120583

119904) of the semiconductor NPs under study

embedded in different LCs as a function of theNP size Againalthough every combination of NP materialLC host listedabove has been considered only the most noticeable results

have been summarized The radius range has been selectedbetween 35 and 150 nm in order to ensure the appearance ofthemagnetic resonance in the visible range and to accomplishthe dipole-like criterion Both the ordinary (Figure 3(a)) andthe extraordinary (Figure 3(b)) refractive indices of the LChave been considered In both cases the same behavior can beobserved As it was expected there is an increase of 120583

119904as the

NP radius increases until it reaches a maximum valueThenit slowly decreases until a certainNP size at which the value of120583119904drops to a value of 1 (nomagnetic response)This behavior

is related to the evolution of the magnetic resonance of thenanoparticle When it arises its height increases as the NPsize increases until a maximum valueThen although the NPsize increases the magnetic resonance broadens producing adecrease of the height until it disappears

By comparing both figures (Figures 3(a) and 3(b)) it canbe seen that there are important changes in the values butnot in the profile of the permeability for a given NP-LCcombination The cases of Si and GaInP nanoparticles haveshown a remarkable difference at the maximum values ofpermeability thus they have a high magnetic anisotropy fora large range of values of the particle size (119877)

As it is also shown in Figure 3 the highest value of 120583119904

is achieved for an AlSb NP embedded in the liquid crystalMLC6608 with a value of 3779 while that considering aW1825K LC is 3758 both in the ordinary case As it canbe seen the results using both LCs are quite similar Otherinteresting NP materials having a pronounced peak of 120583

119904are

GaP and GaInP


12

16

20

24

28

32

36

40

Effec

tive m

agne

tic p

erm

eabi

lity

60 80 100 120 14040

Radius (nm)

Max 120583s AlSb + MLC6608

Max 120583s GaP + MLC6608

Max 120583s AlAs + MLC6608

Max 120583s Si + W1825K

Max 120583s GaInP + W1825KMax 120583s GaAs + W1825KMax 120583s TiO2 + MLC6608

Max 120583s InGaAs + W1825K

(a)

12

16

20

24

28

32

36

40

Effec

tive m

agne

tic p

erm

eabi

lity

60 80 100 120 14040

Radius (nm)




Max 120583s Si + W1825K



(b)

Figure 3 Evolution of the effective magnetic permeability (120583119904) of NPs embedded in a liquid crystal host as a function of the NP size when

the refractive index of the host is either the ordinary component (a) or the extraordinary one (b)

33 Effective Permeability of Mixtures The use of inclusionsin a LC host is a well-known technique either to change theproperties of the liquid crystal [38] or to actively controlthe optical properties of the NPs [17] In addition as it waspreviously mentioned the magnetism in liquid crystals is nota noticeable feature However in the previous section it isshowed that isolated semiconductor nanoparticles embeddedin a liquid crystal host can present magnetic properties Inthis sense this section is devoted to analyze the effectivemagnetic permeability (120583eff ) of a sample composed of a LCdoped with a certain concentration of these NPs While theeffective magnetic permeability (120583

119904) of an isolated NP has

been calculated previously the permeability of the LC (120583ℎ) is

equal to 1 in terms of relative permeability To perform thesecalculations the Maxwell-Garnett theory of effective indexpreviously explained has been used In order to maximizethe global magnetic response 120583eff has been calculated as afunction of both the size of the doping nanoparticle and itsconcentration in the volume of the mixture (f ) In addition120583eff has been calculated considering both the ordinary andextraordinary refractive indices of the LC in order to observeif a magnetic anisotropy is also possible in the mixture

The optimization of 120583eff regarding the two consideredparameters NP size and f shows that the nanoparticles radiusthatmaximize120583eff is very similar to that producingmaximumvalues of 120583

119904 with a slight variation in a range of 10 nm This

may occur as a result of the broadness in wavelength of 120583119904

function at the peak as it is observed in Figure 2Figure 4 shows the spectral profile of the function 120583eff

for the mixture W1825K LC doped with AlSb nanoparticlesand for both components ordinary and extraordinary Theradius of the nanoparticles and the volume fraction are63 nm and 5 respectively As it was expected this profile

OrdinaryExtraordinary

096

098

100

102

104

106

108

110

112

Effec

tive m

agne

tic p

erm

eabi

lity

800600 700500400

120582 (nm)

Figure 4 Effective magnetic permeability (120583eff ) of a composite ofW1825K LC doped with AlSb (119877 = 63 nm) NPs with a volumefraction of 5 as a function of the incident wavelength Both theordinary and the extraordinary components of the LC propertieshave been considered

is quite similar to that of the magnetic permeability of asingle NP However the low concentration of NPs results inthe fact that the magnitude of 120583eff is smaller than that ofan isolated nanoparticle In addition the spectral stabilityof the magnetic resonance of these nanoparticles producessmall values of themagnetic anisotropyHowever an effectivemagnetic anisotropy (Δ120583) can be clearly observed in themixture


100

101

102

103

104

105

106

107

108

109

110

111Eff

ectiv

e mag

netic

per

mea

bilit

y

001 002 003 004 005000

f

120583eff AlSb120583eff GaP120583eff AlAs

120583eff Si120583eff GaInP120583eff GaAs

120583eff TiO2

120583eff InGaAs

(a)

100

101

102

103

104

105

106

107

108

109

110

111

Effec

tive m

agne

tic p

erm

eabi

lity

001 002 003 004 005000

f



120583eff TiO2

120583eff InGaAs

(b)

Figure 5 Evolution of 120583eff as a function of the volume fraction for each mixture considering (a) the ordinary component or (b) theextraordinary component of W1825K LC

On the other hand the concentration of the nanoparticlesis also an important factor to manipulate the value of theeffective permeability of the mixture Simulations of themixture with a fixed NP radius and changing 119891 from 01to 5 have been made The fabrication of homogeneousNP-LC composites is not trivial in any case but it is verycomplex if the NPs concentration is larger than 5 [39] Inexperimental mixtures with high NP concentration there isa high probability of nanoparticles aggregation that woulddistort measures of the permeability Large values of 119891 mayalso disturb the formation of the LC phase Figure 5 showsthe global effective magnetic permeability of the mixture as afunction of the volume fraction for the ordinary (Figure 5(a))and extraordinary (Figure 5(b)) cases The dopants are NPsof semiconductor materials whose size produces a maximumvalue of 120583

119904 As it can be seen the value of 119891 producing a

maximum value of 120583eff is the maximum considered value of119891 This result is expected from (1) Thus the fabrication ofsamples with a high concentration of NPs is needed to obtainlarger magnetic behaviors in this kind of mixtures Despitethe low values by comparing both figures a detectablemagnetic anisotropy is observed Thus we can concludethat these composites would behave as magnetic anisotropicmetamaterials

4 Conclusions

While the dielectric anisotropy of liquid crystals is quiteinteresting for a large number of applications in several fieldsthese media do not have a remarkable magnetic responseOn the other hand interesting magnetic resonances arise inthe light scattering of high-refractive-index semiconductornanoparticles in the visible spectrum In this work the

magnetic properties of mixtures combining both media(LC doped with semiconductor nanoparticles) have beentheoretically studied

Light scattering resonances of semiconductor nano-spheres can be analyzed through the use of the Mie theoryBy analyzing the first four Mie coefficients it was observedthat around the magnetic resonances of these nanoparticlesthere is a clear predominance of the dipolar terms overthe quadrupolar ones This means that these nanoparticlesbehave as dipole-like spheres despite their real sizeThusMiecoefficients can be drastically simplified

Considering an isolated nanoparticle embedded in aLC the effective permeability of the nanoparticle underthe Rayleigh assumption has been deduced In this casea noticeable value of 120583 has been found showing that thepresence of the LC does not frustrate the appearance ofthese resonances In addition 120583 values change if ordinary orextraordinary refractive indices of the liquid crystal are usedThen there is an externally induced magnetic anisotropyin the NP Several semiconductor materials and LCs havebeen considered tomaximizemagnetic response In additionoptimum sizes of the nanoparticles have been calculated

On the other hand if the mixture composed of a liquidcrystal doped with these resonant nanoparticles in a certainvolume fraction is considered a new effective magneticpermeability of the mixture can be calculated using theMaxwell-Garnett effective medium theoryThus the mixtureis considered as an effective medium or a metamaterial Allanalyzed cases present a nonunitary permeability showing aneffective magnetism in the mixture However these valuesof 120583 are much smaller than those calculated for the isolatedparticlesThis fact is due to the contrast between the refractiveindex of the liquid crystal and that of the nanoparticle


besides the low concentration of NPs in the mixture Unfor-tunately high concentrations of nanoparticles in a liquidcrystal host cannot produce a stable and homogenous sampleHigh volume fraction of nanoparticles or devices with largesurfaces compared with NPs size can improve these resultsDespite the small values of the global effective permeabilityan appreciable magnetic anisotropy can be calculated inthese samples Thus a magnetic anisotropic media can beperformed by means of these composites This fact providesa new approach in the field of active magnetic devices andcan be useful for the improvement or even new designs ofthem For instance a new sensor could be tested and usedin significant potential applications like linear displacementand current sensing gyroscope devices or magnetic fielddetectors for technicalindustrial purposes Therefore infuture experimental works a small sampling of these sensorcapabilities will be presented

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work has been supported by Ministerio de Economıay Competitividad of Spain (Grants nos TEC2013-47342-C2-2-R TEC2012-38901-C02-01 and TEC2013-50138-EXP)and the RampD Program SINFOTON S2013MIT-2790 of theComunidad de Madrid Vicente Marzal acknowledges theMinisterio de Economıa y Competitividad for FPI grant

References

[1] M L Brongersma and P G Kik Eds Surface PlasmonNanophotonics Springer Dordrecht The Netherlands 2007

[2] F J Garcia-Vidal L Martın-Moreno and J B Pendry ldquoSurfaceswith holes in them new plasmonic metamaterialsrdquo Journal ofOptics A Pure and Applied Optics vol 7 no 2 pp S97ndashS1012005

[3] W Cai and V Shalaev Optical Metamaterials Springer NewYork NY USA 2010

[4] B Garcıa-Camara J F Algorri A Cuadrado et al ldquoAll-opticalnanometric switch based on the directional scattering of semi-conductor nanoparticlesrdquo The Journal of Physical Chemistry Cvol 119 no 33 pp 19558ndash19564 2015

[5] L De Sio G Klein S Serak et al ldquoAll-optical control oflocalized plasmonic resonance realized by photoalignment ofliquid crystalsrdquoThe Journal of Materials Chemistry C vol 1 no45 pp 7483ndash7487 2013

[6] A Alu and N Engheta ldquoEmission enhancement in a plasmonicwaveguide at cut-offrdquoMaterials vol 4 no 1 pp 141ndash152 2011

[7] S I Bozhevolnyi Plasmonic Nanoguides and Circuits PanStanford Publishing Pte Singapore 2009

[8] V N Smolyaninova I I Smolyaninova A V Kildishev andV M Shalaev ldquoBroadband transformation optics devicesrdquoMaterials vol 3 no 10 pp 4793ndash4810 2010

[9] V M Shalaev Ed Nanophotonics with Surface PlasmonsElsevier Amsterdam The Netherlands 1st edition 2007

[10] A Garcıa-Etxarri R Gomez-Medina L S Froufe-Perez et alldquoStrongmagnetic response of submicron Silicon particles in theinfraredrdquo Optics Express vol 19 no 6 pp 4815ndash4826 2011

[11] R Gomez-Medina B Garcıa-Camara I Suarez-Lacalle etal ldquoElectric and magnetic dipolar response of germaniumnanospheres interference effects scattering anisotropy andoptical forcesrdquo Journal of Nanophotonics vol 5 no 1 Article ID053512 2011

[12] K Vynck D Felbacq E Centeno A I Cabuz D Cassagneand B Guizal ldquoAll-dielectric rod-type metamaterials at opticalfrequenciesrdquo Physical Review Letters vol 102 no 13 Article ID133901 2009

[13] M Kerker D-S Wang and C L Giles ldquoElectromagneticscattering by magnetic spheresrdquo Journal of the Optical Societyof America vol 73 no 6 pp 765ndash767 1983

[14] JMGeffrin B Garcıa-Camara R Gomez-Medina et al ldquoMag-netic and electric coherence in forward- and back-scatteredelectromagnetic waves by a single dielectric subwavelengthsphererdquo Nature Communications vol 3 article 1171 2012

[15] C M Soukoulis T Koschny J Zhou M Kafesaki and EN Economou ldquoMagnetic response of split ring resonators atterahertz frequenciesrdquo Physica Status Solidi B vol 244 no 4pp 1181ndash1187 2007

[16] J N AnkerW P Hall O Lyandres N C Shah J Zhao and R PVan Duyne ldquoBiosensing with plasmonic nanosensorsrdquo NatureMaterials vol 7 no 6 pp 442ndash453 2008

[17] Y Zhang Q Liu H Mundoor Y Yuan and I I SmalyukhldquoMetal nanoparticle dispersion alignment and assembly innematic liquid crystals for applications in switchable plasmoniccolor filters and E-polarizersrdquoACS Nano vol 9 no 3 pp 3097ndash3108 2015

[18] D C Zografopoulos R Beccherelli A C Tasolamprou andE E Kriezis ldquoLiquid-crystal tunable waveguides for inte-grated plasmonic componentsrdquoPhotonics andNanostructuresmdashFundamentals and Applications vol 11 no 1 pp 73ndash84 2013

[19] W Dickson G A Wurtz P R Evans R J Pollard and A VZayats ldquoElectronically controlled surface plasmon dispersionand optical transmission through metallic hole arrays usingliquid crystalrdquo Nano Letters vol 8 no 1 pp 281ndash286 2008

[20] L De Sio G Klein S Serak et al ldquoAll-optical control oflocalized plasmonic resonance realized by photoalignment ofliquid crystalsrdquo Journal of Materials Chemistry C vol 1 no 45pp 7483ndash7487 2013

[21] L De Sio T Placido S Serak et al ldquoNano-localized heatingsource for photonics and plasmonicsrdquo Advanced Optical Mate-rials vol 1 no 12 pp 899ndash904 2013

[22] I Abdulhalim ldquoLiquid crystal active nanophotonics and plas-monics from science to devicesrdquo Journal of Nanophotonics vol6 no 1 Article ID 061001 2012

[23] Y J Liu G Y Si E S P Leong N Xiang A J Danner and J HTeng ldquoLight-driven plasmonic color filters by overlaying pho-toresponsive liquid crystals on gold annular aperture arraysrdquoAdvanced Materials vol 24 no 23 pp OP131ndashOP135 2012

[24] J S T Smalley Y Zhao A A Nawaz et al ldquoHigh contrast mod-ulation of plasmonic signals using nanoscale dual-frequencyliquid crystalsrdquo Optics Express vol 19 no 16 pp 15265ndash152742011

[25] R Ruppin ldquoEvaluation of extended Maxwell-Garnett theoriesrdquoOptics Communications vol 182 no 4 pp 273ndash279 2000

[26] C F Bohren and D R Huffman Absorption and Scattering ofLight by Small Particles JohnWileyamp SonsNewYorkNYUSA1983


[27] C-H Wen S Gauza J Li H Wang and S-T Wu ldquoHigh con-trast homeotropic alignment of difluorotolane liquid crystalsrdquoLiquid Crystals vol 32 no 5 pp 643ndash649 2005

[28] E Miszczyk Z Raszewski J Kdzierski et al ldquoInterferencemethod for determining dispersion of refractive indices ofliquid crystalsrdquoMolecular Crystals and Liquid Crystals vol 544pp 22ndash36 2011

[29] J Li and S-T Wu ldquoSelf-consistency of Vuks equations forliquid-crystal refractive indicesrdquo Journal of Applied Physics vol96 no 11 pp 6253ndash6258 2004

[30] S Kang S Nakajima Y Arakawa G-I Konishi and J Watan-abe ldquoLarge extraordinary refractive index in highly birefringentnematic liquid crystals of dinaphthyldiacetylene-based materi-alsrdquo Journal of Materials Chemistry C vol 1 no 27 pp 4222ndash4226 2013

[31] J Li G Baird Y-H LinH Ren and S-TWu ldquoRefractive-indexmatching between liquid crystals and photopolymersrdquo Journalof the Society for Information Display vol 13 no 12 pp 1017ndash1026 2005

[32] J Li C-H Wen S Gauza R Lu and S-T Wu ldquoRefractiveindices of liquid crystals for display applicationsrdquo Journal ofDisplay Technology vol 1 no 1 pp 51ndash61 2005

[33] E D Palik and G Ghosh Eds Handbook of Optical Constantsof Solids Academic Press San Diego Calif USA 1998

[34] S Zollner C Lin E Schonherr A Bohringer andM CardonaldquoThe dielectric function of AlSb from 14 to 58 eV determinedby spectroscopic ellipsometryrdquo Journal of Applied Physics vol66 no 1 pp 383ndash387 1989

[35] G E Jellison Jr ldquoOptical functions of GaAs GaP and Ge deter-mined by two-channel polarization modulation ellipsometryrdquoOptical Materials vol 1 no 3 pp 151ndash160 1992

[36] M Schubert V Gottschalch C M Herzinger H Yao P GSnyder and J A Woolam ldquoOptical constants of Ga x in 1minusx Plattice matched to GaAsrdquo Journal of Applied Physics vol 77 no7 pp 3416ndash3419 1995

[37] G E Jellison Jr ldquoOptical functions of silicon determinedby two-channel polarization modulation ellipsometryrdquo OpticalMaterials vol 1 no 1 pp 41ndash47 1992

[38] M Urbanski and J P F Lagerwall ldquoNanoparticles dispersedin liquid crystals impact on conductivity low-frequency relax-ation and electro-optical performancerdquo Journal of MaterialsChemistry C vol 4 no 16 pp 3485ndash3491 2016

[39] X Li C Yang Q Wang et al ldquoEnhanced birefringence formetallic nanoparticle doped liquid crystalsrdquo Optics Communi-cations vol 286 no 1 pp 224ndash227 2013

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


optical properties can be changed with real time control andreversibility capacity changing the resonant wavelength inthe same way This dynamic response is very interesting forapplications such as active polarizers [17] or new tools foractive photonic circuits [18]

Among all the active media used in plasmonic devicesliquid crystals are a good choice they have capacity to easilymodify their refractive index by electrical [19] optical [20]or thermal techniques [21] because of their high birefringenceand small elastic constants This control feature besides theirhigh compatibility with optoelectronic materials makes themthe perfect option as active dielectric media Liquid crystalproperties have also led to the development of a large varietyof photonic devices (modulators filters optical switches andso on) [22ndash24]

While liquid crystals have a remarkable dielectricanisotropy their magnetic properties in the visible range donot have a noticeable behavior In this sense this work isdevoted to analyze the magnetic properties of mixtures com-posed of a liquid crystal doped with semiconductor nanopar-ticles with magnetic resonances The magnetic permeabilityof the nanoparticles and the effective magnetic permeabilityof the mixture have been studied in a set of simulationsThe Maxwell-Garnett effective medium approach has beenconsidered in the calculus of the permeability [25] Searchinga noticeable magnetic anisotropy several liquid crystals andsemiconductor nanoparticles have been considered

2 Theory

The effective permeability 120583eff of mixtures composed of aliquid crystal (LC) doped with resonant nanoparticles (NPs)can be obtained through several effective medium approx-imations In particular a generalization of the Maxwell-Garnett Theory (MG) [25] has been considered in this workThis theory establishes that the effective dielectric function120598eff of a matrix with homogeneous spherical inclusions canbe expressed in terms of the optical properties of eachcomponent and the volume fraction of the inclusions (119891) [26]as follows

120598eff = 120598119898 [1 +3119891 ((120598 minus 120598

119898) (120598 + 2120598

119898))

1 minus 119891 ((120598 minus 120598119898) (120598 + 2120598

119898))] (1)

where 120598 and 120598119898are the dielectric permittivity of the inclusions

and the matrix material respectivelyDue to the symmetric nature of the electromagnetic

field an analogue expression can be derived for the effectivemagnetic permeability 120583eff

120583eff = 120583ℎ [1 +3119891 ((120583

119904minus 120583ℎ) (120583119904+ 2120583ℎ))

1 minus 119891 ((120583119904minus 120583ℎ) (120583119904+ 2120583ℎ))] (2)

where 120583ℎand 120583

119904are the magnetic permeability of the host

medium and the inclusion respectivelyIn this work a LC host medium with high-refractive-

index semiconductor nanoparticles as inclusions is consid-ered Selected NPs have both electric and magnetic reso-nances in the visible range although they are composed of

nonmagnetic materials (eg silicon and germanium) [11]Thus effective optical constants can also be derived for theindividual nanoparticles Focusing attention on the mag-netic properties the effective magnetic permeability of thesenanoparticles has been obtained through theMie theory [26]

The scattered electromagnetic field (119864119904 119867119904) of a spherical

particle (of radius 119877) made of a certain material embeddedin a homogeneous and isotropic media can be calculatedthrough theMie theory [26]This theory considers an expan-sion of the scattered fields in vector spherical harmonics(11987311989011198991198721199001119899 11987311990011198991198721198901119899

) when the sphere is radiated with anincident electromagnetic plane wave with wavelength 120582 andamplitude 119864

0

119864119904= 1198640

infin

sum

119899=1

1198941198992119899 + 1

119899 (119899 + 1)(1198941198861198991198731198901119899minus 1198871198991198721199001119899)

119867119904=119896

1205961205831198640

infin

sum

119899=1

1198941198992119899 + 1

119899 (119899 + 1)(1198941198871198991198731199001119899+ 1198861198991198721198901119899)

(3)

where 119896 is the wave vector and 120596 is the frequency of theincident field 120583 is themagnetic permeability of the surround-ing medium and 119886

119899 119887119899 are the so-called Mie coefficients

for the scattered field Applying the boundary conditionsbetween the sphere and the surrounding medium analyticalexpressions for these coefficients can be deduced [26]

119886119899=Ψ119899(119898119909)Ψ

1015840

119899(119909) minus Ψ

119899(119909)Ψ1015840

119899(119898119909)

Ψ119899(119898119909) 1205851015840

119899(119909) minus 120585

119899(119909)Ψ1015840119899(119898119909)

119887119899=Ψ119899(119898119909)Ψ

1015840

119899(119909) minus Ψ

119899(119909)Ψ1015840

119899(119898119909)

Ψ119899(119898119909) 1205851015840

119899(119909) minus 120585

119899(119909)Ψ1015840119899(119898119909)

(4)

Ψ119899and 120585

119899are the Riccati-Bessel functions and 119898 = 119899

119904119899

is the relative refractive index between the sphere (119899119904) and

the surrounding medium (119899) The factor is given by =119898120583119904 where 120583

119904is the magnetic permeability of the sphere

material The size parameter is 119909 which is given by therelation 119909 = 2120587119877119899120582 where 119877 is the radius of the sphereand 120582 the incident wavelength as was commented While 119886

119899

coefficients are related to the electric response of the system119887119899are usually related to the magnetic character In addition1198861and 1198871correspond to the dipolar behavior 119886

2and 1198872with

the quadrupolar one and so onThese complex expressions can be simplified under

certain assumptions for instance applying the Rayleighapproximation which is satisfied when

119909 ≪ 1

|119898| 119909 ≪ 1

(5)


450 500 550 600 650 700 750400

120582 (nm)

a1b1

a2b2

00

02

04

06

08

10M

ie co

effici

ents

(a)

450 500 550 600 650 700 750400

120582 (nm)

a1b1

a2b2

00

02

04

06

08

Mie

coeffi

cien

ts

(b)



1198861= minus11989421199093

3

120598 minus 1

120598 + 2 (6)

1198871= minus11989421199093

3

120583 minus 1

120583 + 2 (7)

119886119899asymp 119887119899asymp 0 119899 ge 2 (8)

















1 1198862 1198871 1198872) have been cal-





0(nm) Δ120582 (nm)


277 496 487ndash640 492 490ndash650





1) under the



120583ord120583ext

0

1

2

3

4

Mag

netic

per

mea

bilit

y

500 600 700 800400

120582 (nm)








2001 1439 0570 79




0585 0991 0532 94












119904as the






119904are

GaP and GaInP


12

16

20

24

28

32

36

40

Effec

tive m

agne

tic p

erm

eabi

lity

60 80 100 120 14040

Radius (nm)




Max 120583s Si + W1825K



(a)

12

16

20

24

28

32

36

40

Effec

tive m

agne

tic p

erm

eabi

lity

60 80 100 120 14040

Radius (nm)




Max 120583s Si + W1825K



(b)













096

098

100

102

104

106

108

110

112

Effec

tive m

agne

tic p

erm

eabi

lity

800600 700500400

120582 (nm)




100

101

102

103

104

105

106

107

108

109

110

111Eff

ectiv

e mag

netic

per

mea

bilit

y

001 002 003 004 005000

f



120583eff TiO2

120583eff InGaAs

(a)

100

101

102

103

104

105

106

107

108

109

110

111

Effec

tive m

agne

tic p

erm

eabi

lity

001 002 003 004 005000

f



120583eff TiO2

120583eff InGaAs

(b)





4 Conclusions








Competing Interests


Acknowledgments


References
















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




450 500 550 600 650 700 750400

120582 (nm)

a1b1

a2b2

00

02

04

06

08

10M

ie co

effici

ents

(a)

450 500 550 600 650 700 750400

120582 (nm)

a1b1

a2b2

00

02

04

06

08

Mie

coeffi

cien

ts

(b)



1198861= minus11989421199093

3

120598 minus 1

120598 + 2 (6)

1198871= minus11989421199093

3

120583 minus 1

120583 + 2 (7)

119886119899asymp 119887119899asymp 0 119899 ge 2 (8)

















1 1198862 1198871 1198872) have been cal-





0(nm) Δ120582 (nm)


277 496 487ndash640 492 490ndash650





1) under the



120583ord120583ext

0

1

2

3

4

Mag

netic

per

mea

bilit

y

500 600 700 800400

120582 (nm)








2001 1439 0570 79




0585 0991 0532 94












119904as the






119904are

GaP and GaInP


12

16

20

24

28

32

36

40

Effec

tive m

agne

tic p

erm

eabi

lity

60 80 100 120 14040

Radius (nm)




Max 120583s Si + W1825K



(a)

12

16

20

24

28

32

36

40

Effec

tive m

agne

tic p

erm

eabi

lity

60 80 100 120 14040

Radius (nm)




Max 120583s Si + W1825K



(b)













096

098

100

102

104

106

108

110

112

Effec

tive m

agne

tic p

erm

eabi

lity

800600 700500400

120582 (nm)




100

101

102

103

104

105

106

107

108

109

110

111Eff

ectiv

e mag

netic

per

mea

bilit

y

001 002 003 004 005000

f



120583eff TiO2

120583eff InGaAs

(a)

100

101

102

103

104

105

106

107

108

109

110

111

Effec

tive m

agne

tic p

erm

eabi

lity

001 002 003 004 005000

f



120583eff TiO2

120583eff InGaAs

(b)





4 Conclusions








Competing Interests


Acknowledgments


References
















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






0(nm) Δ120582 (nm)


277 496 487ndash640 492 490ndash650





1) under the



120583ord120583ext

0

1

2

3

4

Mag

netic

per

mea

bilit

y

500 600 700 800400

120582 (nm)








2001 1439 0570 79




0585 0991 0532 94












119904as the






119904are

GaP and GaInP


12

16

20

24

28

32

36

40

Effec

tive m

agne

tic p

erm

eabi

lity

60 80 100 120 14040

Radius (nm)




Max 120583s Si + W1825K



(a)

12

16

20

24

28

32

36

40

Effec

tive m

agne

tic p

erm

eabi

lity

60 80 100 120 14040

Radius (nm)




Max 120583s Si + W1825K



(b)













096

098

100

102

104

106

108

110

112

Effec

tive m

agne

tic p

erm

eabi

lity

800600 700500400

120582 (nm)




100

101

102

103

104

105

106

107

108

109

110

111Eff

ectiv

e mag

netic

per

mea

bilit

y

001 002 003 004 005000

f



120583eff TiO2

120583eff InGaAs

(a)

100

101

102

103

104

105

106

107

108

109

110

111

Effec

tive m

agne

tic p

erm

eabi

lity

001 002 003 004 005000

f



120583eff TiO2

120583eff InGaAs

(b)





4 Conclusions








Competing Interests


Acknowledgments


References
















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials







2001 1439 0570 79




0585 0991 0532 94












119904as the






119904are

GaP and GaInP


12

16

20

24

28

32

36

40

Effec

tive m

agne

tic p

erm

eabi

lity

60 80 100 120 14040

Radius (nm)




Max 120583s Si + W1825K



(a)

12

16

20

24

28

32

36

40

Effec

tive m

agne

tic p

erm

eabi

lity

60 80 100 120 14040

Radius (nm)




Max 120583s Si + W1825K



(b)













096

098

100

102

104

106

108

110

112

Effec

tive m

agne

tic p

erm

eabi

lity

800600 700500400

120582 (nm)




100

101

102

103

104

105

106

107

108

109

110

111Eff

ectiv

e mag

netic

per

mea

bilit

y

001 002 003 004 005000

f



120583eff TiO2

120583eff InGaAs

(a)

100

101

102

103

104

105

106

107

108

109

110

111

Effec

tive m

agne

tic p

erm

eabi

lity

001 002 003 004 005000

f



120583eff TiO2

120583eff InGaAs

(b)





4 Conclusions








Competing Interests


Acknowledgments


References
















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




12

16

20

24

28

32

36

40

Effec

tive m

agne

tic p

erm

eabi

lity

60 80 100 120 14040

Radius (nm)




Max 120583s Si + W1825K



(a)

12

16

20

24

28

32

36

40

Effec

tive m

agne

tic p

erm

eabi

lity

60 80 100 120 14040

Radius (nm)




Max 120583s Si + W1825K



(b)













096

098

100

102

104

106

108

110

112

Effec

tive m

agne

tic p

erm

eabi

lity

800600 700500400

120582 (nm)




100

101

102

103

104

105

106

107

108

109

110

111Eff

ectiv

e mag

netic

per

mea

bilit

y

001 002 003 004 005000

f



120583eff TiO2

120583eff InGaAs

(a)

100

101

102

103

104

105

106

107

108

109

110

111

Effec

tive m

agne

tic p

erm

eabi

lity

001 002 003 004 005000

f



120583eff TiO2

120583eff InGaAs

(b)





4 Conclusions








Competing Interests


Acknowledgments


References
















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




100

101

102

103

104

105

106

107

108

109

110

111Eff

ectiv

e mag

netic

per

mea

bilit

y

001 002 003 004 005000

f



120583eff TiO2

120583eff InGaAs

(a)

100

101

102

103

104

105

106

107

108

109

110

111

Effec

tive m

agne

tic p

erm

eabi

lity

001 002 003 004 005000

f



120583eff TiO2

120583eff InGaAs

(b)





4 Conclusions








Competing Interests


Acknowledgments


References
















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





Competing Interests


Acknowledgments


References
















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials
























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



research article induced magnetic anisotropy in liquid...

Documents