optical and magnetic properties of quasi one-dimensional dilute magnetic znmns and antiferromagnetic...

Phys. Status Solidi B 247, No. 10, 2522–2536 (2010) / DOI 10.1002/pssb.201046146 p s sb

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Optical and magnetic properties ofquasi one-dimensional dilute

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magnetic ZnMnS and antiferromagnetic MnS

Limei Chen*,1, Wolfram Heimbrodt1, Peter J. Klar2, Michael Froba3, Carsten Ronning4, andHans-Albrecht Krug von Nidda5

1Department of Physics and Material Sciences Center, Philipps-University of Marburg, Renthof 5, 35032 Marburg, Germany2 Institute of Experimental Physics I, Justus-Liebig University of Giessen, Heinrich-Buff Ring 16, 35392 Giessen, Germany3 Institute of Inorganic and Applied Chemistry, University of Hamburg, Martin-Luther-King-Platz 6, 20146 Hamburg, Germany4 Institute of Solid State Physics, Friedrich-Schiller University of Jena, 07737 Jena, Germany5 Institute of Physics, Center for Electronic Correlations and Magnetism, University of Augsburg, 86135 Augsburg, Germany

Received 30 March 2010, revised 8 July 2010, accepted 14 July 2010

Published online 6 September 2010

Keywords electron paramagnetic resonance, magnetic properties, magnetic semiconductors, nanowires, optical properties,photoluminescence

*Corresponding author: e-mail [email protected], Phone: þ49 6421 2821354, Fax: þ49 6421 2827036

We study the optical and magnetic properties of quasi one-

dimensional dilutemagnetic Zn1�xMnxS and antiferromagnetic

(AF) MnS as a function of size, Mn content x, and sample

morphology. On the one hand, we discuss the temporal

dynamics of the yellow Mn-related luminescence of the

samples under resonant excitation demonstrating that the non-

exponential behavior of the luminescence decay is an intrinsic

feature of such nanostructures and is strongly related to

interplay of the characteristic length scales such as the

extensions of the sample, the distance between killer centers,

and the distance between Mn ions. The transients of the Mn

related luminescence can quantitatively be described on the

basis of a modified Forster model accounting for killer center

statistics and reduced dimensionality. On the other hand, we

investigate the paramagnetic to AF phase transition of spherical

MnS nanostructures as a function of diameter. The phase

transition is gradually suppressed whilst the local magnetic

interactions such as the nearest neighbor and next-nearest

neighbor exchange constants remain unaltered, demonstrating

that the suppression of the magnetic order is driven by the

increasing surface to volume ratio leading to an effective

reduction of the numbers of nearest and next-nearest neighbors.

� 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction Howmuch the extension of a materialcan be reduced before losing its natural properties? ThisDemokrit’s question [1] has been debated formore than 2400years. For chemical properties, this limit is given by the radiiof atoms and molecules. Regarding electronic correlationsand magnetism, the question is still up-to-date becauseminiaturization in today’s electronics approaches dimen-sions where quantum effects become more and moreimportant. The aim of this work is to review the changes ofthe optical and magnetic properties of semiconductornanostructures such as nanowires or chain-like arrangementsof dot ensembles as a function of lateral diameter. Manyprocesses in semiconductors such as magnetic ordering,energy-transfer processes, spin-transfer processes, andcarrier-relaxation processes will be modified with respect

to bulk semiconductors in wire-like nanostructures becauseof the geometric restrictions.

In semiconductor structures these effects are usuallyreflected in the luminescence dynamics. Examples are inter-dot excitation-transfer in chain-like arrangements of dotensembles or excitation-transfer between transition-metalimpurities in II–VI nanowires. A change of such processesoccurs when the characteristic length scale of the problem islarger than the diameter of the wire or chain-like arrange-ment. The characteristic length scales involved stronglydepend on the type of process and can vary considerablybetween a few tens of nanometers and several hundrednanometers.

We have synthesized chain-like arrangements ofZnS:Mn as well as of MnS within mesoporous materials


Phys. Status Solidi B 247, No. 10 (2010) 2523

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with regular wire-like pore systems of diameters below10 nm. Furthermore, we have obtained Mn-doped ZnSnanowires and nanoribbons with diameters ranging fromseveral 10 nm to 1mm by CVD using vapour–liquid–solid(VLS) mechanism followed by dopant incorporation by ionimplantation. We will discuss in Section 3.1, the energy-transfer processes between a systemof localizedMn ions andthe so-called killer centers within Zn1�xMnxS dilutemagnetic semiconductor nanostructures and their impacton the transient behavior of the internal Mn 3d5 lumines-cence. In Section 3.2 we address the effect of size reductionon the magnetic ordering, i.e., on the paramagnetic (P) toantiferromagnetic (AF) phase transition, in MnS nanostruc-tures as well as on the dynamics of the Mn-related yellowemission.

2 Samples and experimental details2.1 Chain-like arrangements of dot ensembles

of ZnS:Mn and of MnS within mesoporous silica

2.1.1 Synthesis of the pristine mesoporousMCM-41 silica For the synthesis of the pristine MCM-41 silica, 0.25mol hexadecyl trimethylammonium bromide(C16TABr,Merck)were dissolved in 35molwater by stirringand heating to 65 8C. 0.2mol tetramethylammoniumhydroxide (TMAOH, 25% in water, Merck) and then 1molSiO2 (Cab-O-Sil, Riedel-de-Haen) were added. The mixturestatically heated to 150 8C for 24 h. After washing anddrying, the resultant was calcinated at 550 8C for 24 h andmesoporous silica of 3 nm pores is obtained [2].

2.1.2 Synthesis of pristine mesoporous SBA-15 silica For the synthesis of SBA-15 silica, 0.8 gPluronic1 P-123 were dissolved in 24 g of water and2.86 g of concentrated hydrochloric acid at 30 8C on a waterbath. After the addition of 1.6 g tetraethylorthosilicate(TEOS) the reaction mixture was stirred for 24 h at 30 8C.The resulting gel was then heated up to 80 8C for 24 h toobtain porous silica host with 6 nm pores and 140 8C for 24 hto obtain 9 nm pores. The resulting white powder waswashedwith deionizedwater and the surfactantwas removedby Soxleth extraction at 120 8C with a mixture of 97mlethanol and 3ml concentrated hydrochloric acid [2].

2.1.3 Incorporation of ZnMnS or MnS intomesoporous silica The impregnation procedure ofZnMnS was carried out by stirring 0.5 g of the porous hostmaterial (MCM-41 or SBA-15) in a 0.5M solution of zincacetate (Merck) and manganese acetate (Merck) with thedesired ratio of Zn/Mn for 10min. The dispersion wasseparated by centrifugation. The residue was dried invacuum and stored in a H2S atmosphere at 100 8C for 24 h.After impregnation/conversion cycle the samplewaswashedin deionized water.

The MnS spherical nanostructures were obtained in thesamemanner by incorporatingMn-acetate intoMCM-41 andSBA-15 type mesoporous silica matrices. Inside the pores

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the Mn-acetates were converted into b-MnS by treatmentwith H2S. Spherical b-MnS particles are then formed insidethe tube-like pores [2].

2.2 ZnS nanowires and nanoribbons dopedwith Mn and Ne fabricated by a VLS processfollowed by ion implantation

2.2.1 Synthesis of the ZnS nanowires CrystallineZnS wire- and belt-like structures with lateral sizes varyingover two orders of magnitude (50 nm to 10mm) have beensynthesized in a VLS process on (100) Si. The siliconsubstratewas coatedwith a 2 nm thick gold film. ZnS powderin a three-zone tube-furnace was evaporated and carried by aargon gas flow to the colder end of the tube where the growthof the nanowires took place. The size and the morphology ofthe nanostructures varies with the distance from the sourcematerial. The morphology and crystal structure of thesynthesized material was characterized by scanning electronmicroscopy (SEM), transmission electron microscopy(TEM), and X-ray diffraction (see Ref. [3] for details).

2.2.2 Ion implantation of Mn The ZnS parentstructures were ion-beam implanted with 55Mn, choosingdifferent ion fluences resulting in Mn concentrations varyingover six orders of magnitude from 4� 10�6 to 4.0%.We usedmultiple ion-energies ranging from 20 to 450 keV in order tocreate a box-like homogeneous distribution of the implantedions matching the lateral extensions of the nanowires andnanoribbons [4]. Post-implantation annealing procedureswereperformed under vacuum conditions at 600 8C for 30min inorder to remove the majority of the implantation defects.Electron spin resonance (ESR) measurements confirmed thattheMn ions are incorporated onZn lattice sites after annealing.

2.2.3 Co-implantation of Ne ions In order to proveour theory on the mechanism of Mn PL decay in ZnMnSwires, the samples were irradiated in a second implantationprocess with neon ions with ion energies ranging from 200 to20 keV at room temperature. The neon ions are notincorporated into the lattice but are diffused out so that thedefects remain in the lattice. This process increases thedefect concentration in the ZnMnSwire sample. Before neonimplantation, half of the surface of each specimen wascovered with an aluminum foil so that an area unaffected byneon implantation is preserved as a reference.

2.3 Optical and magnetic measurements Thephotoluminescence (PL) based optical measurements werecarried out at 10Kwith a specimen mounted in a contact-gasHe cryostat (Cryovac K 1104 C). For PL measurements,excitation lightwas provided either by aHeCd laser (325 nm;Kimmon IK series) or by a tunable tungsten lamp system setto 470 nm (bandwidth 5 nm, followed by a 0.32m mono-chromator ISA Triax 320). The PL signal was detected in therange from 500 to 700 nm. For PL excitation (PLE)measurements, the PL intensity was detected at 600 nm,


2524 L. Chen et al.: Optical and magnetic properties of dilute magnetic ZnMnS and antiferromagnetic MnSp

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varying the wavelength of the excitation light from 270 to580 nm using either the tungsten lamp system or a xenonlamp. The sample luminescence was detected using a 0.5mspectrometer (Zeiss) with a resolution better than 1 nmequipped with a GaAs photo multiplier (Hamamatsu).Optical absorption spectra were recorded in the temperaturerange from 10 to 200K using the tungsten lamp.

The time-resolved PL spectra for determining thetransients of the internal yellowMn2þ (4T1! 6A1) emissionhave been measured using the second or third harmonic of aNd-YAG laser (532 or 355 nm) with a pulse half-width ofabout 3.5 ns for excitation. The same low excitation densitywas used for all samples. We verified that the temporalbehavior of the internal Mn emission does not depend on theexcitation density in this regime, i.e., that no saturationeffects are present. The emission spectra at different delaytimes were recorded with an intensified charge-coupleddevice camera with a time resolution of 1.5 ns attached to asingle-grating monochromator. The spectra are taken withthe sample mounted in a cryostat at 10K.

The ESR studies were performed using a BrukerELEXSYS E500 cw-spectrometer at X-band frequency( f� 9.35GHz), equipped with a continuous He gas-flowcryostat (Oxford Instruments) covering a temperature rangebetween 4.2 and 300K. ESR measures the resonanceabsorption from the transverse magnetic microwave fieldas a function of the static magnetic field.

Magnetization measurements have been performed in acommercial superconducting quantum interference device(SQUID magnetometer; Quantum Design MPMS5) attemperatures between 2 and 300K.

3 Results and discussion3.1 Influence of reduced dimension on the

energy transfer process between Mn ions inZnMnS nanostructures The PL spectrum ofZn1�xMnxS alloys is dominated by the internal yellowMn2þ (3d5) PL band. The excited state (4T1) is an S¼ 3/2spin state whereas the ground state (6A1) is S¼ 5/2, thus thetransition is symmetry forbidden as well as spin-forbidden.However, the selection rules are partly lifted (e.g., due toreduction of the local symmetry, spin-orbital coupling, and s,p-d hybridization), nevertheless the intrinsic lifetime is stillvery long. For high quality-crystals with virtually no defectsother than the few Mn ions, the temporal PL decay behavioris found to be single exponential with a radiative lifetime ofabout 1.8ms [5]. In ZnS:Mn of comparable low Mn contentbut higher defect densities one observes a non-exponentialPL decay which is caused by an energy transfer from theexcitedMn ions to defect related killer centers whichmay beeither radiative or non-radiative centers. Furthermore, aconcentration quenching is known, meaning that thecharacteristic decay times decrease significantly from afew milliseconds to microseconds with increasing Mn-content x in bulk samples [6]. This is explained by migrationeffects of the excitation within the Mn subsystem yielding amore efficient transfer to the killer centers.


Despite several decades of intensive investigations, thephysical origin of the time behavior of the Mn internal PLdecay inMn-doped II–VI nanoparticles is still not clear. Onereason is that the various authors compare very different timewindows and even different excitation conditions. Oftenthe temporal behavior of the yellow Mn PL is crudelyapproximated by a bi-exponential decay. Furthermore, theexcitation conditions of the Mn system determine to someextent the observed decay behavior. A resonant opticalexcitation into the intrinsic intra-shell absorption of the Mn3d5 shell leads to a different situation than an excitation intothe band states of the ZnS host. In the latter case energytransfer from the band states into theMn-system,which takesplace within the first nanosecond after excitation, andtrapping of excitation by other deep defects, which in turnmay feed theMn-system at later times, may play a big role inthe observed PL behavior and lead to differences in the PLdecay curves obtained under different excitation conditions.Nevertheless, the general result remains, that the nanopar-ticles show a strong non-exponential PL decay whichbecomes continuously slower from the first nanosecond toseveral milliseconds, i.e., a time scale varying by almost fiveorders of magnitude. This decay behavior indicates that theexcitation of the Mn system can be relaxed via severalcompeting loss channels.

The explanations suggested so far for the changes of MnPL behavior compared to bulkmaterial cover awide range ofphenomena like enhanced s, p-d hybridization due toconfinement effects and a corresponding larger transitionprobability [7], surface effects resulting in enhanced non-radiative losses [8, 9], andmixing of 3d stateswith host statesvia exchange Coulomb interaction which weakens the spinselection rule and makes the Mn internal transition lessforbidden [10]. Godlewski et al. [11] proposed a mechanismbased on spin flip interactions between the Mn ions and freecarriers. Obviously, the importance of the different mech-anisms contributing to the PL behavior will vary signifi-cantly as time progresses after excitation. A drawback of allthese explanations is that they cannot explain simultaneouslythe fast component and the surviving slow component of thedecay curves.

The temporal PL behavior is determined by twocharacteristic length scales, i.e., the mean Mn–Mn distanceand the mean distance between Mn ions and killer centers.Both are lying typically in the nm range. Therefore, it isanticipated that artificial structuring on these length scaleswill affect the temporal behavior of the internal Mn2þ (3d5)PL due to geometrical restrictions.

We present a quantitative description of the temporalbehavior of ensembles of (Zn,Mn)S spherical nanoparticleswhich explains the non-exponential decay behavior as anintrinsic effect resulting from killer-center statistics withinthe ensemble [12]. In what follows we will show, that thenon-exponential decay behavior is an intrinsic effect of Mndoped ZnS nanostructures and can be tuned by the samplemorphology. We modified the original Forster model [13] tobe applicable for low dimensionality, i.e., one- and

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Energy (eV)2.0 2.5 3.5 4.0

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PLEPL4T1

4T2 4E,4A1 Eg

x=1%

x=5%

x=10%

x=20%

x=30%

Figure 2 (onlinecolorat:www.pss-b.com)PLandPLEspectraofaseries of Zn1�xMnxS nanospheres (6 nm) in mesoporous silica. Thespectra are taken at T¼ 10K.

two-dimensional (1D and 2D) [14]. If excitation transferbetween Mn ions and killer centers as well as migrationeffects between Mn ions are accounted for, and the correctdimensionality is used, one is able to describe the size andconcentration dependence of the decay curves of Zn1�xMnxSnanostructures, like wires and ribbons, from a few nanose-conds to several milliseconds.

3.1.1 Chain- l ike arrangements of dotensembles of ZnS:Mn

3.1.1.1 Structural properties To study nanoscale effects it isnecessary to precisely control the size of the nanoparticles. Anew family of host materials called M41S phases [15],provides ordered arrays of nanotubes with well defineddiameters between 3 and 12 nm – a range which is notaccessible using other techniques – and is ideally suited forthe incorporation of semiconductor guest materials. Itconsists of the large band-gap isolator SiO2, which servesas an electronic barrier material for the semiconductor. Inthis way, regular arrays of non-magnetic semiconductorquantum wires, including CdS [16], CdSe [17], GaAs [18],InP [19], Ge [20], and SiGe [21], have been successfullysynthesized. In general, the reduction of the dimension wasfound to modify their optical properties [22, 23] with respectto bulk material.

Figure 1a depicts the TEM image of the regular poresystem of a pristineMCM-41 structure, where the hexagonalsymmetry of the regular pore system is clearly visible, isdepicted. Figure 1b shows cross-section of the pore systemafter incorporation of the semiconductor. The nanosparticlesout of the semiconductor material can be discerned. It has tobe noted that the pore diameter poses a strict upper limit forthe diameter of the semiconductor nanosparticles. Thus, by acontrolled variation of the pore diameter of the silica host theupper limit for the nanosphere diameter of the correspondingdot ensemble can be tuned and varied. In an earlier paper [2]we studied the pore size distribution and could show that thedistribution is very narrow (aboutW 1 nm). The diameterfluctuations are smaller than the diameter steps of 3 nmwhichwe use for our studies here. This allows us to study sizeeffects systematically in particular, as usually the averageproperties of ensembles are mainly dominated by the

Figure 1 Transmission electron microscopy images: (a) top viewof a empty MCM-41 structure; (b) cut along the channels afterincorporation of the semiconductor material.

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members of the ensemble which are largest. The diametervalues given in what follows refer always to the porediameter and are in so far a measure of the maximum size ofthe particles in the pores.

3.1.1.2 Photoluminescence (PL) and PL excitation spectra Figure 2depicts the PL spectra and corresponding PLE spectra ofensembles of Zn1�xMnxS nanospheres within mesoporoussilica of different x. The yellow Mn luminescence bandcentered at about 2.1 eV dominates the PL spectrum. ThePLE spectra detected on the yellow Mn band show severalpronounced peaks below the band gap feature Eg at highenergies. These are commonly assigned to internal tran-sitionswithin theMn 3d5 shell from the excited S¼ 3/2 states4T1,

4T2,4E, and 4A1 to the S¼ 5/2 ground state 6A1. The

simultaneous observation of both, the band gap feature andfeatures due to internal Mn transitions, in the PLE spectrashows that the Mn system can be excited either directly viainternal Mn 3d5 absorption or indirectly via an energytransfer from the band states into the Mn 3d5 shell.

Figure 3 depicts normalized spectra in the range of theyellow Mn 3d5 PL band of an ensemble of 6 nmZn0.99Mn0.01S dots ensemble taken at different times afterthe excitation pulse. The time values in Fig. 3 correspond tothe center of the integrationwindow,whichwas 1ms long forall curves below 100ms, 10ms long for the curves between100ms and 1ms, and 100ms long for all curves taken at latertimes. The results shown for this specimen are typical for theentire series of Zn0.99Mn0.01S dot ensembles of different dotdiameter. The broad luminescence band centered at 2.1 eV ischaracteristic for the internal luminescence of Mn2R ionsincorporated on Zn sites. The set of normalized spectra inFig. 3 shows that the yellow band dominates the PL spectrumat all times, i.e., no change of energetic position or shape ofthe PL due to other underlying bands occurs. Therefore, themeasured PL decay behavior in the entire timewindowunderstudy (from about 50 ns to about 20ms) is due to the internal



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0.6 µs

5.6 µs

21 µs

100 µs

550 µs

1.0 ms

5.5 ms20 ms

Figure 3 NormalizedPL spectra from6 nmZn0.99Mn0.01S taken atdifferent times. The spectra are shifted vertically and the delay timesare indicated in the graph.

Mn emission. It is worth noting that the transient can bemeasured over more than four orders of magnitude inintensity, which is substantial for the following discussion.

3.1.1.3 Dependence on size The PL decay curves (shown bydifferent symbols) of 3, 6, 7, and 9 nm Zn0.99Mn0.01S dotensembles are shown in Fig. 4. All four decay curves show apronounced non-exponential behavior, a rather fast PL decaybetween 500 ns and 2000ms, followed by a significantlyslower decay at later times, which becomes almostexponential for t> 10ms. A clear trend is observed as afunction of particle size.

t (µs)

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τMn=4850 µsR0=4.85 nm

3nm 6nm 7nm 9nm

Figure 4 (online color at: www.pss-b.com) Luminescence decaycurve at 10K of the Zn0.99Mn0.01S dot ensembles with different dotdiametersafter resonantexcitation(symbols).Dashedandsolid linesare calculated using the real dot volumeand an effective dot volume,respectively.


The observed PL decay of all specimens is typical forZn1�xMnxS nanostructures. The data analysis can be basedon an ansatz of the PL decay derived by Forster for thegeneral case of an ensemble of excited molecules of type A,which can relax to their ground state either by radiativerecombination or by transferring their energy resonantly tomolecules of type B via a dipole–dipole mechanism [13]:

IðtÞI0

� �¼ exp � t

tMn

� �½Jðt;RgÞ�N

� exp � t

tMn

� �exp �

ffiffiffip

p NR30

R3g

ffiffiffiffiffiffiffiffit

tMn

r ! (1)

where

½Jðt;RgÞ�N ¼ 4p

V

ZRg

0

exp � R0

R

� �6t

tMn

!R2dR;

where tMn is the intrinsic lifetime of an isolated excited Mnion in the crystal, N is the number of killer centers in thecrystal, V¼ (4p/3)R3

g is the volume of the crystal correspond-ing to an average killer density Ckiller¼N/V, and V0¼ (4p/3)R3

0, where R0 is defined as the distance from the Mn ionwhere the rate of the dipole–dipole transfer of excitation to akiller center equals the intrinsic radiative decay rate of theisolated Mn ion. The approximation in Eq. (1) holds forRg!1 and N!1, i.e., a bulk-like volume V.

Spherical Zn0.99Mn0.01S dot ensembles of the diametersconsidered here consist of a few thousand atoms. Keeping inmind that the killer centers are a typical defect, andwill occurwith densities, e.g., of one defect per 1000 or 10 000 atoms oreven less, the number of defects N in the different dots of theensemble will fluctuate between none and a few, about anaverage valueN¼Ckiller�Vdot, whereVdot¼ (p/6)d3dot is thevolume of the spherical dot of diameter ddot. As can be seenfromEq. (1), the actual value ofNwill strongly determine thePL dynamics of a dot, e.g., single exponential decay forN¼ 0. The probability distribution for N is a binomialdistribution. As N is much smaller than the number of atomsper dot, the binomial distribution can be well approximatedby a Poisson’s distribution:

pðN; ~NÞ¼ expð� ~NÞ~NN

N!;

N¼ 0; . . . ; 1; Ckiller ¼~N

Vdot

:

(2)

The PL decay observed when measuring the ensemblecan be modeled to a first approximation as a weightedaverage of the individual dots [12]:

IðtÞI0

� �¼ exp � t

tMn

� �X1N¼0

pðN; ~NÞ

� exp �ffiffiffip

p NV0

Vsphere

ffiffiffiffiffiffiffiffit

tMn

r� �:

(3)

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τMn=4850µs, R0=4.85nmCKiller=1.075 x 1019cm-3

experimentbest fit by using parameter

fit by varying R0

fit by varying CKiller

9nm Zn0.99Mn0.01S dotsT=10K, 532nm excitation

bulk

Figure 5 (onlinecolorat:www.pss-b.com)Experimentaldata (fullcircles) fromPLdecay of 9 nmZnMnS (1%Mn) at 10Kand the bestfit curve (solid line), as well as the fit curves by varying eitherCkiller

(short dash lines) by (1.0� 0.2)� 1019 cm�3 or R0 (long dash lines)by 4.85 nm.

It should be noted that Eq. (3) depends on three
parameters only, i.e., Ckiller, tMn, and R0. We replace I0 byI (t¼ 0.6ms) to compare experiment and theory. Theintegrals J (t, ddot/2) need to be evaluated numerically.
The solid line in Fig. 5 shows the best fit of the theorydefined by Eq. (3) to the experimental PL decay data of the9 nm Zn0.99Mn0.01S dot ensemble. The following modelparameters were obtained: Ckiller¼ 1.075� 1019 cm�3,R0¼ 4.85 nm, and tMn¼ 4.85ms. The dash-dotted linesand the dashed lines show the sensitivity of the theory to thechoices of the model parameters R0 and Ckiller, respect-ively. A variation of R0 mainly shifts the point in timewhere the transition from ‘‘fast’’ to ‘‘slow’’ decay takesplace in the theoretical curve, whereas it hardly affects thedecay curve at very long times after the excitation. Incontrast, a variation of Ckiller mainly leads to a parallelvertical shift of the curves in the entire time window. Avariation of tMn changes the slope of the quasi-exponentialpart of the decay curve at longer times t > 5ms. Thedependence on the model parameters can be easilyunderstood from Eq. (3). The long-lived component ofthe PL of the dot ensemble originates from the dots of theensemble which do not contain killer centers, i.e., N¼ 0,and thus exhibits a mono-exponential decay, yielding theintrinsic Mn radiative lifetime tMn. The ratio between thedots without killer center and dots containing killercenters, which mainly leads to a parallel vertical shift ofthe decay curve, is determined by the average density ofkiller centers, Ckiller. The magnitude of R0 determines howmuch faster the dots containing killer centers decaycompared with those without killer centers.

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The actual values determined for Ckiller and R0 seemperfectly reasonable. Forster himself reported values of R0

between 5 and 8 nm in solutions ofmolecules [13]. The valuefor the killer density, although quite large for a defect densityin semiconductors, is nevertheless realistic, considering thatthe Zn1�xMnxS dots were synthesized inside mesoporoussilica matrices at a fairly low temperature, i.e., 100 -C.Furthermore, we have to take into account that Mn oninterstitial sites as well as Mn at the surface sense a differentcrystal field, and act therefore as quasi-killer centers withrespect to the analyzed yellow band arising from Mn ontetrahedral Zn sites. The value for the intrinsic Mn lifetimetMn¼ 4.85ms is almost a factor of 3 larger than the value of1.8ms reported for ZnS:Mn bulk crystals.

At first glance this might be surprising, but it becomesclear on considering the fact that the transition probability isproportional to the refractive index n of themedium in dipoleapproximation. The mean refractive index at about 580 nmof the Zn1�xMnxS nanoparticles embedded in the SiO2

mesoporous matrices is lowered almost by a comparablefactor with respect to that of bulk Zn1�xMnxS.

Figure 4 shows the decay curves for the entire series ofZn1�xMnxS dot ensembles of different diameters, exhibitingthe slowing down of the PL decay with decreasing dot size.The dashed lines correspond to calculations on the basis ofEq. (3), where the same three model parameters as for the9 nm specimenwere used, and the appropriate values for ddot,i.e., 3, 6, and 7 nm, respectively. The calculated curves showthe same behavior as the experiment, namely, a slowingdown with increasing dot size, but the dependence on dotdiameter is too strong compared with the experiment. Thismight be a hint for a somewhat higher killer concentration,which is plausible in the case of increasing surface-to-volume ratio. A very good fit for the entire series can beobtained by increasing the dot diameter compared to itsnominal value for the three samples with smaller dots, i.e.,using a larger effective dot volume, reflecting an excitationtransfer between the dots. Using the same values for R0, tMn,and Ckiller as before, one obtains effective diameters of 8.8,8.55, and 8.15 nm for the 7, 6, and 3 nm specimens,respectively. Especially for the smallest dots, an interdotcoupling between adjacent dots seems very likely, as thevalue for R0 is larger than the dot diameter.

3.1.1.4 Dependence on Mn concentration The different set ofsymbols in Fig. 6 show the PL transients of the yellowMnPLmeasured for a set of Zn1�xMnxS dot ensembles of differentx. The Mn concentrations are determined by the molar ratioof the zinc acetate and the manganese acetate during theimpregnation procedure. It is clearly seen that the PL decaybecomes faster with increasing x.

As we have already demonstrated that the temporal PLbehavior of ensembles of Zn0.99Mn0.01S nanospheres ofdifferent diameter d can be well described by a Forster-likemodel including killer center statistics (Eq. 3). Treatingdifferent Mn concentration x appears to be straightforward.One simply has the replace tMn under the square-root in



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101 τeff=4900µs

τeff=490µs

τeff=49µs

τeff=4.9µs

D=7nm τMn=4900µsCKiller=2.4 x 1019cm-3

1%5%10%20%30%

Figure 6 (online color at: www.pss-b.com) Transients of the yel-low Mn 3d5 luminescence band of ensembles of 7 nm Zn1�xMnxSnanospheres of different Mn content x synthesized within mesopo-rous silica. The lines are calculations according to Eq. (4) usingdifferent values of teff.

time (µs)

0 2000 4000 6000 8000 10000 12000 14000

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D = 7nm τMn= 4900µsτeff = τMn

1%, CKiller = 2.4x1019 cm-3

5%, CKiller = 3.6x1019 cm-3

10%, CKiller = 4.3x1019 cm-3

20%, CKiller = 4.5x1019 cm-3

30%, CKiller = 5.0x1019 cm-3

Figure 7 (online color at: www.pss-b.com) Measured and calcu-lated transients of the yellowMn 3d5 luminescence band of ensem-bles of 7 nm Zn1�xMnxS nanospheres of different Mn content xsynthesized within mesoporous silica. The lines are calculationsaccording toEq. (3)usingtMn¼ teff anddifferentvalues for thekillerdensity CKiller.

Eq. (3) by teff, yielding:

� 20

IðtÞI0

� �¼ exp � t

tMn

� �X1N¼0

pðN; ~NÞ

� exp �ffiffiffip

p NV0

Vsphere

ffiffiffiffiffiffiffit

teff

r� �;

(4)

where teff is smaller than tMn and accounts for the excitationmigration between Mn ions [6].

Calculations according to Eq. (4) are shown togetherwith the experimental data in Fig. 6. For teff¼ tMn¼ 4.9msone obtains a good agreement between the fitted curve andthe experimental data of the ZnMnS (1% Mn) nanosphereensemble with 7 nm diameter. The other curves arecalculated varying teff down to about 5ms, whilst keepingall other model parameters (Ckiller¼ 2.4� 1019 cm�3,tMn¼ 4.9ms, R0¼ 3.8 nm) constant.

No agreement between theory and experiment can beobtained for the Zn1�xMnxS nanosphere ensembles of higherx. This suggests that migration of excitation within the Mnsystem from an excitedMn ion via adjacent Mn ions to killercenters, which actually should facilitate the excitationtransfer from the Mn system to the killer centers, is of lessimportance than the direct excitation transfer from an excitedMn ion to a killer center by dipole–dipole interaction, i.e., theactual Forster mechanism.

What is the reason for this finding? A possibleexplanation is that hardly any interdot transfer of excitationtakes place and the ensemble is, to a first approximation,described as an ensemble of non-interacting nanospheres. Itis clear that within each of the nanospheres the direct Forstertransfer mechanism is dominant as the diameter d of the

10 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

nanospheres is comparable to 2R0 where, as pointed outabove, R0 is the distance from the Mn ion where the rate ofthe dipole–dipole transfer of excitation to a killer centerequals the intrinsic radiative decay rate of the isolated Mnion.

We will now try to identify the cause for the differencesbetween the observed transients of the Zn1�xMnxS nano-sphere ensembles of different x. It appears to be very likelythat the number of killer centers may increase with the Mnconcentration x. Therefore, we have calculated a set ofcurves according to Eq. (3), i.e., without accounting formigration of excitation within the Mn system, by varyingsolely the density of killer centers Ckiller. As can be seen inFig. 7 a good agreement between experiment and theory canbe obtained this way. We find that the killer density forx¼ 0.3 is about twice the value of that for x¼ 0.01. Theadditional killer centers at higher x are likely to be Mnrelated, e.g., caused by Mn ions at the surface of thenanospheres which will experience a different crystal fieldcompared to Mn ions in the bulk of the nanosphere.

3.1.2 ZnS nanowires and nanoribbons dopedwith Mn and Ne fabricated by a VLS processfollowed by ion implantation

3.1.2.1 Dependence on dimensionality Now, we focus on theeffects of sample geometry and will study the transients ofZn1�xMnxS nanostructures of different morphology, i.e.,nanowires and nanoribbons, of different sizes and Mncontents x.

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Figure 8 Scanning electron microscope images of the wire-like(left) and 2 ribbon-like (right) Zn1�xMnxS nanostructures. Thenanowires have typical diameters in the 100 nm range. The nano-ribbons have typically a thickness of about 50 nm and a width in therange of 10–25mm.

Figure 8 depicts SEM images of two different types ofZnS parent samples used for the ion implantation. The imageon the left shows ZnS nanowire structures whose typicaldiameters are in the 100 nm range. The nanostructuresdepicted in the image on the right are of a ribbon-like shapewith thicknesses of about 50 nm and widths in the range of10–25mm.

Figure 9 depicts normalized PL spectra in the spectralrange of the yellow Mn internal transition taken at differenttimes after the excitation pulse. The internal Mn2R yellowemission at 2.1 eV alone determines the PL decay at all timesafter excitation in the time window under discussion and themeasurements are done in the samemanner as for the ZnMnSdot ensembles.

To develop a general formula for the Forster-model validalso in the 1D and 2D case, we assume that the dipole–dipole

Energy (eV)

1.8 1.9 2.0 2.1 2.2 2.3

Nor

mal

ized

PL

inte

nsity

1µs

5µs

10µs

50µs

100µs

500µs

1ms

2ms

5ms

Figure 9 Normalized PL Spectra of a Zn0.96Mn0.04S ribbon-likesample recorded at different delay times after the excitation pulse.

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interaction is proportional to R�6 where R is the distancebetween the Mn ion and the killer center. R0 is a criticallength describing the strength of interaction and is defined asthe distance between the Mn ion and the killer center wherethe dipole–dipole transfer rate from the excitedMn ion to thekiller center equals the radiative decay rate of an isolatedMnion. A value ofR0¼ 4.85 nmwas determined by studying theMn internal PL decay of ZnS:Mn spherical particles withdiameters below 10 nm. We obtain for the transient I(t)/I0 ofthe Mn internal transition [14]:

Nor

mal

ized

PL

inte

nsity

0.

0

FiguZn1x¼mordesc

IðtÞI0

� �¼ exp � t

tMn

� �exp anDRD

0

t

teff

� �D=6 !

; (5)

where D¼ 3, 2, 1 is the dimensionality of the system, tMn isthe decay time of an isolated Mn2R ion in ZnS, n¼N/Rg isthe line density of killer centers. Rg is the sample extensionin one, two, or three dimensions, and a is a constant takingthe values 1.129, 1.354, and Hp in 1D, 2D, and 3-dimensional (3D), respectively. The parameter teffdescribes the effectiveness of the migration of the excitationwithin the Mn subsystem. For small Mn concentrationsteff¼ tMn. The higher the Mn concentration x the faster isthe energy migration and the smaller is teff.

Figure 10 shows the PL transients of two wire-like (opensymbols) and two ribbon-like (full symbols) Zn1�xMnxSnanostructures with a very low Mn-content x¼ 4� 10�6%(circles) and a higher concentration x¼ 3.2� 10�2%(squares). Two important observations can be made: (i) Forsamples of the same morphology, the decay of the higherconcentration sample is faster than that of lower x. The meanMn–Mn distance is about 200 nm for the low concentrationand about 10 nm for the higher concentration assuming a

Time (µs)

0 2000 4000 6000 80000001

.001

0.01

0.1

1 wires

ribbons

1D

2D

1.45D

1.52D

re 10 Fit of the decay curves of wire-like and ribbon-like

�xMnxS nanostructures with x¼ 3.2� 10�2% (squares) and4� 10�6%(circles)withamodifiedForstermodel.Theeffectivephologyofthesample isreflectedbythePLdecaybehaviorandisribed by the fractional dimensionality D of the model.



hys

ica ssp st

atu

s

solid

i b

Time (µs)0 2 4 6 8

Inte

nsity

10-5

10-4

10-3

10-2

10-1

100

1D

2D3D

Figure 11 Decay curves calculated with Eq. (5) in one (1D), two(2D), or three (3D) dimensional crystals. Assuming a small Mnconcentration we have set teff¼ tMn. The other parameters usedthroughout were R0¼ 4.85 nm, n¼ 0.45 nm�1, and tMn¼2.5ms.

random distribution of the Mn ions. This suggests that energytransfer between Mn ions occurs in the higher concentrationsample. (ii) The decay of the ribbon-like samples isconsiderably faster than that of the wire-like samples of thesame x. The reason for that becomes clear by fitting theexperimental data. The transients of the wire-like samples canbe fitted perfectly using Eq. (5) with D¼ 1, R0¼ 4.85 nm,tMn¼ 2.5ms, and n¼ 0.45 nm�1. For the low concentrationteff¼ tMn (full lines) but for the higher concentration (dashedlines) the fit yields teff¼ 1.2ms. This is a clear hint, thatenergy migration in the Mn subsystem takes place.

It is found that the wire-like nanostructures which have amean diameter of about 100 nmbehave like a 1D system.Thereason is the interplay of the lateral extension and meandistance between killer centers. The parametern¼ 0.45 nm�1 corresponds in 1D to a line density.Accounting for the diameter of the nanowire of 100 nm itcorresponds to volume density Ckiller� 1017 cm�3 which inturn corresponds to amean distance between killer centers ofabout 25 nm. Both lengths, wire diameter and mean distancebetween killer centers, are of the same order of magnitudeleading to a preferential transfer from Mn ions to killercenters along the wire axis.

The ribbon-like samples exhibit neither a pure 1D nor apure 2D character but an intermediate character correspond-ing to a ‘‘fractional dimension.’’ Such a fractional dimensioncan be defined within the model by a linear interpolation forthe dimensional parameterD and the parameter a. Fitting theexperimental data of the ribbon-like samples in this fashionwhilst keeping all other parameters fixed yieldsD¼ 1.45 forthe lower concentration and D¼ 1.52 for the higherconcentration. These values agree well with the fact, thatan energy transfer is possible in the ribbon-like samplesalong the ribbon axis as well as perpendicular to it in theribbon plane. Although the width of the ribbons is about 10–25 mm and thus considerably larger than the mean distancebetween killer centers. The observed decay is still notentirely 2D, i.e., sheet-like. It is worth noting, that the valueof 2.5ms for the intrinsic decay time tMn of an isolated Mnion is again significantly larger than the value of 1.8msestablished for isolated Mn2R ions in bulk crystals.

This finding is explained by the geometry of theexperiment and the mesoscopic sample morphology. Indipole approximation, the transition probability is pro-portional to the relative refractive index nr of the medium,i.e., tMn/ n�1

r . However, the typical lateral extensions of theZnS nanostructures are smaller than the excitation andemission wavelengths and, in addition, the nanostructuresare in vacuum during the measurement. Therefore, the lightinteracting with the sample experiences an effectiverefractive index neff with a value between nr¼ 3.5 of bulkZnS and 1 of vacuum. We found that the value tMn¼ 2.5msis suitable for all the Zn1�xMnxS nanostructures studiedindependent of Mn concentration x. This result is inconcordance with our explanation as experimental con-ditions and mesoscopic morphology are comparable for allspecimens.


The dependence of the transients on dimensionality isdemonstrated in Fig. 11 where decay curves are depicted forthe Forster-transfer in 3D, 2D, and 1D case calculatedaccording toEq. (5). The parameters n and tMnwere assumedto be the same in all three cases. It is seen that the non-exponential character increases and the decay becomesmuch slower on reducing the dimensionality. This is verifiedby the experimental results presented above. The twoobserved trends can be explained as follows: the reducedextensions in certain directions effectively increase therelative number of really isolated Mn ions, which cannottransfer the excitation to killer centers. In general, thetransients approach the exponential decay defined by theintrinsic Mn decay time at later times. This approach iscompleted at shorter times at lower dimensionality, i.e., inthe 1D curve in Fig. 11 the intrinsic lifetime of tMn¼ 2.5msused for the calculation is found at times >2ms whereas thetransients of the 2D and 3D case have not fully reached theintrinsic decay after 2ms.

3.1.2.2 Dependence on killer center concentration In order toperform additional tests of the modified Forster model fordifferent dimensionality used in the studies of the ZnMnSnanowires and nanoribbons, additional defects were intro-duced into the ZnMnSwire samples. TheMn-implanted ZnSwire sample (4� 10�3% Mn) was irradiated with neon ionsin a second implantation step with Ne fluences of3.14� 1013 cm�2. As neon ions are not incorporated intothe crystal lattice of ZnMnS, they only cause additionaldefects when diffusing through the sample.

Time-resolved and time integrated PL spectra of neon-implanted as well as the pristine ZnMnS samples weremeasured at 10K with laser excitation at 355 nm. The totalPL intensity of the neon-implanted sample is more than anorder of magnitude smaller. The non-exponential decaycurves of the internalMn2R yellow emission at 2.1 eVof bothsamples are shown in Fig. 12. It can be seen that, as expected,the Mn2R PL decay is considerably faster after neonimplantation. Fitting the results with themodel demonstrates

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Article

Time (µs)

0 2000 4000 6000 8000 10000

Nor

mal

ized

PL

inte

nsity

10-4

10-3

10-2

10-1

100without neon implantation with neon implantation

τMn =2.5msτMig =1.2ms α =1.129 R0=4.85nm

Figure 12 (online color at: www.pss-b.com)Measured and calcu-lated transients of the yellow Mn 3d5 luminescence band of a neonimplanted and a pristine Zn1�xMnxS wire-like nanostructures(x¼ 4� 10�3%), respectively. The lines are calculations accordingtoEq. (5)using thesameparameters as those inFig.10except the linedensity n.

that the change of the decay behavior can be reproduced bysimply increasing the line density n¼N/Rg of the killercenters (i.e. defects) 0.331–0.797 nm�1. All other fittingparameters are kept constant (see Section 3.1.2.1).

It is worth noting that the change in the line density byroughly a factor of 2 corresponds to a slight change of themean distance between killer centers by a factor of 1.25. Thisexplains why the dimensionality parameter D¼ 1 is notaffected although the decay becomes much faster.

3.2 Influence of reduced dimension on opticaland magnetic properties of MnS Miniaturization intoday’s electronics approaches dimensions where quantumeffects become more and more important. Experiments toswitch the state of a device by only one electron are inprogress. The additional use of the electron spin allows evenhigher efficiency. Therefore, investigations of magneticsemiconductors in strongly reduced dimensions are ofessential interest for spintronics. We have studied the P–AF phase transition of b-MnS incorporated within MCM-41silica nanopores, where we were able to exactly control thedimension in the range between 3 and 11 nm. Both opticalandmagnetic investigations have been carried out to analyzelocal interactions in the system. SQUID and electron Presonance studies reveal that in 3 nm pores no AF order isobserved down to 2K. By increasing the pore diameter up to11 nm, the AF transition at the Neel temperature TN� 100Kof bulk b-MnS is gradually recovered. PLE spectroscopyreveals that the nearest-neighbor coupling between the Mn-ions in all MnS nanostructures remains the same as in bulksuggesting that the suppression of the phase transition arisesdue to geometric restrictions alone.

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Ideal 1D and 2D systems of Heisenberg type, i.e.,characterized by isotropic interaction between the spins, donot develop any kind of long range magnetic order down tolowest temperatures. This so-called Mermin–Wagner theo-rem [24] was derived from spin-wave theory, showing thenumber of excited spin waves to diverge at finite tempera-tures in 1D and 2D Heisenberg magnets. This implies that aphase transition from the P state to the ordered state does notoccur. The Mermin–Wagner theorem is strictly valid forisotropic systems of ideal sheet or chain geometry only.

Real magnetic nanostructures usually exhibit finiteextensions in all three dimensions, e.g., quantum wires of afinite thickness and length or spherical dots ensemble of afinite diameter. And any anisotropy, e.g., induced by dipole–dipole interactions or spin-orbit coupling, may break thisstrong theorem, and a transition into a magnetically orderedstate becomes possible. As pointed out by Neel [25], atomsnear an interface have a different environment compared tobulk atoms, which gives additional contributions to themagnetic anisotropy. This may be especially relevant fornanostructures with large interfaces or surfaces. Forexample, there are some reports of the absence of a phasetransition from a P state to an ordered magnetic state for thinlayers of magnetic semiconductors such as MnSe [26–28].However, little is known about P–AF phase transitions innanoparticles of magnetic semiconductors.

Magnetism can be induced by substituting cations withmangetic transition metal ions in semiconductors. However,the influence of the dimension on long range magnetic ordercan be studied best by using the pure MnS system. MnSexists in three modifications of rock salt, zincblende andwurtzite type.We focus on to the wurtziteb-MnS, which canbe characterized as a hcp type III antiferromagnetwith aNeeltemperature of approximately TN� 100K and a Curie–Weiss temperature of u��930K. This system can beincorporated into the MCM-41 pores at moderate tempera-tures avoiding reactions with SiO2 walls and admixtures ofotherMnSmodifications. It is highly isotropic in the 3D case.Hence, the spin system can bewell described as aHeisenbergmagnet.

We will show that the incorporated material is really b-MnS of wurtzite type and how its optical and magneticproperties are influenced by the reduced dimension.

3.2.1 Mn internal transitions Optical spectro-scopic studies unambiguously prove that the nanostructuresare b-MnS. Figure 13 depicts the PL spectra of the MnSnanostructures of various diameters. The yellow emissionband centered at about 2.2 eV can be clearly detected. Itcorresponds to the Mn-internal transition between the firstexcited 4T1 and the

6A1 ground state of theMn 3d5-shell inb-MnS. The corresponding PLE spectra both show a series oftransitions which are typical for this MnS phase andcorrespond to the transitions from the 6A1(

6S) ground stateto the excited states 4T1(

4G), 4T2(4G), 4A1(

4G), 4E(4G), and4T2(

4D) (abbreviated as 4T�2) [29–31]. Furthermore, no

emission band situated in the red spectral region at 1.65 eV is



hys

ica ssp st

atu

s

solid

i b

Energy [eV]1.6 2.0 2.4 2.8 3.2

PL

inte

nsity

[arb

. uni

ts]

3nm

6nm

8nm

11nm

4T1

4T2 4A1,4E4T2*

β-MnS,

PL PLE

Figure 13 (online color at: www.pss-b.com) Comparison of PLand PLE results recorded at T¼ 10K of b-MnS nanoparticles ofdifferent diameters. The dashed lines mark the energies of theinternal Mn-transitions.

Temperature [K]

0 50 100 150 200

Ener

gy [e

V]

2.67

2.68

2.69

2.70

2.71

2.91

2.92

2.93

2.94

2.95

Energy [eV]

2.5 2.6 2.7 2.8 2.9

Abso

rptio

n [a

rb. u

nits

]

β-MnS 3nm

4T24A1,

4E 4T2*

TN(β-MnS bulk)

6A1 4A1,

4E

6A1 4T2

*

3nm

6nm

8nm

11nm

Figure 14 (online color at: www.pss-b.com) Left: Temperaturedependent absorption spectra obtained from 3 nm nanoparticles ofb-MnS in the temperature range from 10K (bottom spectrum) to200K (top spectrum). The dashed lines mark the energies of theinternal Mn-transitions. Right: Temperature dependence of the6A1! 4A1,

4E, and 6A1! 4T�2 transition deduced from the absorp-

tion spectra of the b-MnS nanoparticles of different diameters. TheNeel-temperature of bulk b-MnS is indicated.

detected which would be characteristic for a-MnS with thethermodynamically stable rocksalt structure. It shouldbe mentioned, that the charcteristic band would beobservable even in case of only a few a-MnS dots, since amost effective energy transfer fromb- toa-MnS takes place.

One more characteristic property of b-MnS is evidentfrom the temperature dependence of the internal transitionsderived from the optical absorption spectra depicted inFig. 14. The features of the Mn-internal transitions in thetemperature-dependent absorption spectra (illustrated for3 nm b-MnS nanoparticles in the left graph) show clearindications of an abrupt shift at a critical temperatureTcrit� 100K. The right graph of the figure summarizes theenergy shifts of the 6A1! 4A1,

4E, and 6A1! 4T�2 transitions

deduced from the absorption spectra of the b-MnSnanoparticles of different diameters. The critical tempera-ture Tcrit as well as the magnitude of the shift DE are veryclose to the Neel temperature TN and the shift of bulk b-MnSfor all nanostructures [31]. This is in good agreementwith earlier observations that in bulk wide-gap AFmanganese chalcogenides, a strong correlation existsbetween the energy positions of the Mn-internal transitionsand the magnetic phase transition from the P phase into theAF phase is observed [31–33].

This correlation of the energy relaxation of the variousMn 3d5-states can easily be derived in the framework of theHeisenberg-model for exchange coupled spins S

*

i, S*

j:

� 20

H ¼ �Xi;j

JijS*

iS*

j: (6)

Including only nearest-neighbor (nn) and next-nearestneighbor (nnn) interaction by Jnn and Jnnn, respectively, Jnnand Jnnn< 0, the relaxation E(T) induced by exchangeinteraction per Mn2þ ion is obtained in mean-field

10 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

approximation as:

EðTÞ¼ Hi¼1h i ¼ �Xj

J1j Sz1� �

Szj

D E

¼ � Sz1� �

JnnXj2nn

Szj

D Eþ Jnnn

Xj2nnn

Szj

D E" #:

(7)

As fluctuation effects are neglected in mean-fieldapproximation, one obtains E(Tcrit)¼ 0 and a complete AFspin ordering at T¼ 0K. Using the above equation atT¼ 0K, one has to sum over the given spin-up and spin-down states of the nn and nnn shells. For a Mn2þ ion in theground state (S¼ 5/2) this leads to:

Egrð0Þ ¼ ð4Jnn � 2JnnnÞS2: (8)

At sufficiently low excitation densities an excited(single) Mn2þ ion (S0 ¼ 3/2) can be assumed to be placedin an unchanged mean spin field of neighboring Mn2þ ions(S¼ 5/2). Therefore, one obtains for an excited state:

Eexð0Þ ¼ ð4Jexnn � 2JexnnnÞSS0; (9)

where JexnnðnÞ denotes the exchange interaction parametersbetween an excited Mn2þ ion and a nn or nnn Mn2þ ion in

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the ground state. The measured total spin-ordering-inducedshift of the various excitation peaks,

0

0

1

1

χ / (

10-6 m

3 /kg)

Figuencedete(leftline

www

DE ¼ ðEex � EgrÞT¼0 � ðEex � EgrÞT¼Tcrit;

is then given by:

DE¼ Eexð0Þ � Egrð0Þ� 4SðJnnS� 2JexnnS

0Þ;(10)

where the nnn interactions have been neglected forsimplicity. This equation indicates that the observed shiftof the Mn-internal transitions at Tcrit is to a firstapproximation determined by a local magnetic orderingeffect. In particular, a non-zero shift is still anticipated evenif nearest-neighbor coupling only is accounted for.

3.2.2 Change of magnetic properties with thereduction of size The fact that the shift of the internalMntransitions is observed in theMnS dot ensembles aswell as inbulk MnS, indicates that at least the local AF correlationsremain unchanged with respect to the bulk material.However, as we will see from SQUID and ESR measure-ments, that the long rangemagnetic order is strongly affectedby reducing the size of the nanostructures.

Figure 15 summarizes the temperature dependence ofthe magnetic susceptibilities for all pore diameters and bulkmaterial. Note that the mass susceptibility is shown, i.e., forthe nanoparticles its absolute value is not directly compar-able to bulk. The SiO2 contribution to the totalmass could notbe subtracted due to the unknown degree of filling. However,the Curie–Weiss temperatures can be derived because theyare not sensitive to the absolute susceptiblity.

All susceptibilities of the nanowires monotonouslyincrease with decreasing temperature and diverge onapproaching T¼ 0K. Only the bulk susceptibility exhibitsa weak anomaly at TN whereas no magnetic transition isnotable for the dot ensembles. As can be seen from the

0 100 200 300.0

.5

.0

.5

0 100 200 3000

5

10

3 nm6 nm8 nm11 nmbulk

T / K

TN

T / K

χ-1 /

(106 k

g / m

3 )

MnS

re 15 (onlinecolorat:www.pss-b.com)Temperaturedepend-of the magnetic mass susceptibility x of MnS nanostructuresrmined from magnetization at the magnetic field m0H¼ 0.1 Tgraph) and its inverse representation (right graph). The solids are fits curves by a sum of two Curie–Weiss laws (see text).

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inverse data, the susceptibilities do not followa singleCurie–Weiss law, x¼ cCW/(T� u), but can be well described by thesum of a Curie–Weiss and a Curie contribution, x¼ cC/T.Figure 18 depicts the obtained Curie–Weiss temperaturesand the relative portion of the Curie contribution dependenton the inverse pore diameter.

Starting from bulk (1/d¼ 0), the absolute value of theCurie–Weiss temperature u decreases linearly with 1/d downto 100K for d¼ 6 nm. At the same time, the Curiecontribution increases up to about 50%. Finally, ford¼ 3 nm, the Curie–Weiss law nearly meets the Curie law.Here, it is difficult to distinguish both contributionsunambigously.

To corroborate these results, we performed ESRinvestigations. In contrast to SQUID, ESR measurementsoperate locally on the magnetic ion and allow for a moreprecise study of the PM/AFM phase transition. For selectedsamples (3 nm, 11 nm, and bulk), the temperature depen-dence of the ESR signal is depicted in the left column ofFig. 16 as a contour plot. The bulk sample shows an abruptbreakdown of the signal on approaching the Neel tempera-ture from above, whereas no such anomaly is visible for thesample with a pore diameter of 3 nm. The ESR intensity ofthe 11 nm sample shows an intermediate behavior, itpartially breaks down near the bulk Neel temperature, but a

Figure 16 (online color at: www.pss-b.com) Left column: Tem-peraturedependent contourplot of theESRspectraofMnS(fromtopto bottom: 3 nm pores, 11 nm pores, bulk material). The signalamplitude is represented by color (increasing amplitude frommagenta, green, blue to red). Right column: Representative spectraat140K(datapoints).The solid lines indicate the twocomponentsofthe fit by Lorentz functions.



hys

ica ssp st

atu

s

solid

i b

Figure 18 (online color at: www.pss-b.com) Left axis: Curie–Weiss temperature (hexagons) of beta-MnS as a function of inversepore diameter. Right axis: Relative portion (stars) of Curie lawwith respect to total susceptibility, gained from SQUID (closed),and EPR (open symbols) data. Inset: Simulation of surface partS¼ 4p(d/2)3/3� 4p(d/2� rs)

3/3 of spherical particles with respectto their totalvolumeSþV¼ 4p(d/2)3/3,dependentontheirdiameterd. A surface thickness rs¼ 0.4 nm has been assumed (nearest neigh-bor distance).

30020010000

1

2

30020010000

100

200

300 3 nm 6 nm 8 nm 11 nm bulk

(I ESR /

arb.

uni

ts)-1

T / K

TN

µ 0∆H /

mT

T / K

MnSTN

Figure 17 (onlinecolorat:www.pss-b.com)EPRresultsofb-MnSnanoparticleswithdiametersof3,6,8,and11 nm.Leftgraph:Inversesusceptibility (inverse EPR intensity) as a function of temperature.The solid lines represent the high temperature Curie–Weiss law.Right graph: EPR linewidth as a function of temperature. The solidlines indicates the critical behavior of the bulk linewidth onapproaching TN as described in the text.

residual signal remains observable below that temperature.This clearly shows the advantage of ESR measurements inthis case: antiferromagnetically ordered spins do notcontribute to the signal due to the opening of a finiteexcitation gap in the spinwave spectrum. Therefore, ESR ismore sensitive to the phase transition than the staticsusceptibility.

The composition of the ESR spectra is shown in the rightcolumn of Fig. 16. All spectra are satisfactorily described bythe sum of two Lorentzian lines. Above TN, they can beroughly ascribed to the two contributions found in thesusceptiblity data before (see Fig. 18). The green line followsthe Curie–Weiss law whereas the red one belongs to theCurie contribution. This line does not show up a significantdependence of its linewidth (about 30mT) on temperatureand pore diameter. In contrast, the broad line strongly varieswith temperature and dimension. Its inverse intensity andlinewidth are shown in Fig. 17.

All inverse intensities have been normalized to the sameP moment, i.e., high temperature slope. The Curie–Weisstemperatures obtained from the linear fit correspond well tothose determined from the susceptibility measurements andare included in Fig. 18. On approaching TN from above, thebulk data diverge, indicating the long range AF order of thewhole sample. For 11 nm pores, still a distinct increase existsdue to the drop-out of the AF component in the ESR signal.But there is already a considerable Curie-like contributionbelow TN.With decreasing pore diameter, the anomaly at TNdiminishes and disappears completely for d¼ 3 nm.

A similar observation is gained from the linewidth data.In the bulk system, the linewidth diverges at TN due to thecorresponding decrease in the spin–spin relaxation time [34–37], which is correlated with the divergence of thecorrelation length. Assuming a dominant isotropicHeisenberg exchange and a weak (dipolar) coupling as


source of anisotropy, the temperature dependence of thecritical part of the linewidth is DH� (T� TN)

a. The criticalexponent is found to be a¼�1.1, which is in goodagreement with theoretical predictions [38]. It is indicatedby the solid red line. This divergence is partially visible in the11 nm pores as well, but becomes more and more smearedout with decreasing pore diameter. Finally, no indication forsuch a divergence is found for d¼ 3 nm.

At first glance, the observed decrease of theCurie–Weisstemperature and the suppression of the magnetic order seemto be in contradiction to the conservation of the exchangeparameter derived from optics above. To lift this paradoxon,we have to discuss the Curie–Weiss parameter in moredetail: it is given by the well-known connection [39, 40]:

u ¼ �2SðSþ 1Þ3kB

½Jnnznn þ Jnnnznnn�; (11)

where znn(n) and kB indicate the number of (next) nearestneighbors and Boltzmann’s constant, respectively. As thenearest neighbor exchange seems not to vary withnanostructure size, the numbers of nearest and next-nearestneighbors must. The only region for this to happen is thesurface of the nanoparticles. In Fig. 1, it was demonstratedthat the pore filling is not perfect: in majority, sphericalparticles of all sizes smaller than the pore diameter arepresent. The surface effect becomes more pronounced withdecreasing particle size due to the 1/d dependency of thesurface to volume ratio and, hence, reduces the largestpossible Curie–Weiss temperature. In total, a distribution ofparticle sizes with the sharp upper limit d can be assumed.This yields a distribution of Curie–Weiss temperaturesbetween a maximum absolute value jumax(d)j for the

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PL decay of MnS in silica framework

10K, 532nm laser excitation

Time (µs)0 200 400 600 800 1000

Nor

mal

ised

PL

inte

nsity

10-4

10-3

10-2

10-1

100

3 nm 5 nm

9 nm

11.6 nm

Figure 19 (online color at: www.pss-b.com) Measured transientsof the yellowMn3d5 luminescence bandofMnSdot ensembleswithdifferent sizes synthesized within mesoporous silica frameworks.

particles of size d and u� 0K for the smallest particles. Ourevaluation of the susceptibilities approximates this distri-bution in the easiest way by two Curie–Weiss laws. In thepresent case of an antiferromagnet, the small particlesdominate at low temperatures (Curie law) whereas thelargest particles gain weight with increasing T.

As one can see in Fig. 18, the relative portion of the Curiecontribution increases with decreasing pore diameter due tothe loss of particles with larger diameters. Additionally, neard¼ 6 nm, a step is visible in Curie contribution accompaniedby a kink in the Curie–Weiss parameter. Note that the Curiecontribution strongly varies for different batches of sampleswith 6 nm pores, i.e., in this regime, the system is verysensitive to slight changes in the pore diameter. This can beexplained via the ratio of surface volume (S) and total volume(SþV) which we plotted in the inset of Fig. 18, assumingspherical particles with a surface thickness of one nearest-neighbor distance (approximately 0.4 nm). Below 6 nm, thisratio increases strongly and changes fromavolumedominated(d> 8 nm) to a surface dominated behavior (d< 4 nm).

As far as ESR measurements are concerned, thisinterpretation is valid as well. Additionally, the long-rangeorder phase transition around the Neel temperature can befollowed with decreasing pore diameter in both intensity andlinewidth. The biggest particles inside the pore systemdominate the ESR signal only until they reach the AF state(because particles in the AF state do not contribute to theESR signal). As long as volume-dominated particlesare present, they give a divergent contribution to bothlinewidth and inverse intensity at the Neel temperature.However, their number decreases with pore diameter. As aconsequence, the corresponding anomalies become lesspronounced and do not shift.

Recapitulating the experimental results, magneticmeasurements indicate a gradual reduction of the Curie–Weiss temperatures and suppression of long range magneticorder with decreasing pore diameter. However, opticalmeasurements show that the short range exchange inter-actions in b-MnS are not affected by the reduced dimension.This means that the length scale of magnetic orderingdefining Tcrit is much smaller (less than a magnetic unit cell)than the length scales (several magnetic unit cells) of thelong-range magnetic order defining TN, which is detected intheESR experiment by the divergence of the spin-correlationlength. By controlled tuning of the pore diameter in the rangeof a few nanometers, we were able to determine dcrit� 6 nmas the critical diameter of MnS nanoparticles which isnecessary for the evolution of long-range magnetic order.This corresponds to approximately ten lattice constants.

3.2.3 Energy transfer within MnS dotensembles of different diameters Figure 19 depictsthe PL transients of the yellow Mn PL measured for a set ofMnS nanosphere ensembles of different sizes. It can beclearly seen that the PL decay of MnS spheres becomesslower with increasing pore diameter in contrast toZn1�xMnxS with x below 30% (see Section 3.1).

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The reason is not yet clear but there are two possibleexplanations. (i) The opposite PL decay behavior as afunction of size is related to the suppression of the P to AFphase transition with decreasing pore diameter. The analysisof the magnetic properties of the MnS dot ensembles yieldsthat the P to AF phase transition is indeed graduallysuppressed in this range of dot diameters, but with hardlyany change of the nearest neighbor and next-nearestneighbor exchange interactions. The Forster-like dipole–dipole energy transfer [13] between Mn ions is most likelynot the dominant process for excitation transport through theMnS system, but rather the Dexter exchange-type transfer[41]. The unchanged nn exchange interaction suggests,however, that the transfer mechanism should be the same forall samples. Therefore, it might be that the dependence of thetransient PL behavior on size is related to the gradualsuppression of the long-range order in the samples.(ii) Another reason could be a changed effective number of‘‘killer centers’’ in this case. Mn at the surface of particlessuffers an extremely changed ligandfield andmay act as non-radiative center. In case of Mn doped ZnS just a few centersmay appear at the surfece, whereas for MnS particles thiscould be an inherent source of PL quenching.

4 Conclusions We have shown that the transients ofthe internal 3d5 luminescence of (Zn,Mn)S nanowires aswellas (Zn,Mn)S spherical nanoparticles behave strongly non-exponentially. The non-exponential decay of the yellow Mnemission is an intrisic feature of the nanostructures. It arisesfrom an excitation transfer from the Mn ions to the so-calledkiller centers, i.e., non-radiative defects. The effectiveness ofexcitation transfer to the killer centers depends strongly onsample morphology. It can be suppressed partly innanostructures where the lateral geometric extensions arecomparable to the mean distance between killer centers. In



hys

ica ssp st

atu

s

solid

i b

this case, the transients can be well described by a Forstermodel taking into account the lower dimensionality of thesample. The excitation transfer between Mn ions and killercenters takes place either directly or via other Mn ions. Thelatter process becomes significant if the Mn content of thesample is increased such that the mean distance betweenadjacent Mn ions becomes comparable or even smaller thanthe mean distance between killer centers.

For (Zn,Mn)S dots ensembles, which are arranged quasione-dimensionally, we have shown that the decay behaviorof the internal 3d5 luminescence of ensembles ofZn0.99Mn0.01S quantum dots in the entire time slot from50 ns to 20ms can be well described by a modified Forstermodel accounting for killer center statistics within the dotensemble. We have also demonstrated that the transients ofthe Mn yellow luminescence in ensembles of Zn1�xMnxSnanospheres with diameters below 10 nm and Mn concen-trations x in the range of 1–30% differ significantly fromthose of corresponding Zn1�xMnxS bulk crystals. The reasonis that inter-dot transfer of excitation appears to be lesssignificant than intra-dot processes resulting in a stronginfluence of killer center statistics within the dot ensemble onthe PL dynamics leading effectively to a slowing down of thePL decay with decreasing dot diameter. The opposite isobserved in MnS dot ensembles of different size where theMn PL becomes faster with decreasing dot diameter. Thisseems to be related to the suppression of the P to AF phasetransition which gradually occurs between dot diameters of11 and 3 nm. The gradual suppression of the phase transitionis related to the reduction of the average number of nearestand next nearest neighbors due to the increasing surface tovolume ratio. The nearest neighbor and next-nearestneighbor exchange constants Jnn and Jnnn are not altered bythe reduction of the nanostructure size.

Acknowledgements We are greatful for the funding by theGerman Research Foundation (DFG) in the framework of thepriority program SPP 1165 ‘‘nanowires and nanotubes.’’ F. J.Brieler, D. Stichtenoch, T. Kurz, M. Dempel, and U. Kaiser haveinvolved in and contributed to the project.

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