Physica B 249—251 (1998) 624—627

Magnetic trap for excitons

P.C.M. Christianen!,*, F. Piazza!, J.G.S. Lok!, J.C. Maan!, W. van der Vleuten"

! Research Institute for Materials, High Field Magnet Laboratory, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, Netherlands" COBRA Interuniversity Research Institute, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands

Abstract

High in-plane magnetic field gradients are used to control the lateral motion of excitons in an InGaAs quantum well.The gradients, as large as 6.104 T/m, are produced by positioning a thin magnetized stripe of dysprosium on top of thequantum well. By measuring the exciton photoluminescence energy and intensity, spatially resolved with lm resolution,it is shown that the diamagnetic excitons are forced to regions of low magnetic field, because of the interaction of theirmagnetic moment with the inhomogeneous field. These results show the possibility to magnetically confine excitons toa limited region of space, which opens the way for the realization of the first magnetic trap in solids. ( 1998 ElsevierScience B.V. All rights reserved.

Keywords: Magnetic trap; Excitons; Photoluminescence

1. Introduction

Spatially inhomogeneous magnetic fields havefrequently been used for spatial confinement of allkinds of species, varying from atoms, molecules,and plasmas to biological systems. In particular,the observation of Bose—Einstein condensation ofmagnetically trapped rubidium atoms has attractedenormous research interest [1], and recently it hasbeen demonstrated that living creatures, such asfrogs and grasshoppers, also can be trapped insidehuge magnetic field gradients [2]. In all these cases,the underlying trapping mechanism stems from themagnetic field dependence of the free energy of the

*Corresponding author. Fax: #31 24 3652440; e-mail:peterc@sci.kun.nl.

object under study. For example, if this energyincreases with field (diamagnetism) the object tendsto move to regions of low field, since it experiencesa magnetic force F equal to M+B, the object’smagnetization times the field gradient.

So far a magnetic trap in solid state material hasnever been realized, in spite of the unique physicalproperties arising when magnetic barriers are usedfor confinement. For instance, electrons and holesin semiconductors will be driven to the same regionof space, irrespective of their opposite charges, be-cause their energies both increase linearly withfield. Moreover, the motion of a neutral particle,like a bound electron—hole pair (exciton), which hasa diamagnetic response, can be controlled by mag-netic field gradients, and not by the commonly usedelectric fields, which act on the charged particles

0921-4526/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved.PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 2 7 3 - 7

only. In order to realize a magnetic trap in solids,the magnetic field needs to be varied on a distancecomparable to some characteristic length scale,which for particles in semiconductor heterostruc-tures is typically about 1 lm. This paper describeshow to produce such field gradients by positioninga thin magnetized Dysprosium (Dy) stripe on top ofa semiconductor quantum well (QW), and how tomeasure this gradient with the use of photo-luminescence (PL) spectroscopy. Finally, the feasi-bility of a magnet trap is demonstrated by theparticular dependence of the PL intensity on themagnetic field gradient, which shows that excitonsare indeed pushed towards low-field regions.

2. Experimental geometry

The experimental geometry is shown in Fig. 1.A 25 lm thick polycrystalline Dy film, held bya copper (Cu) holder, was positioned on top ofa semiconductor heterostructure, containing an8 nm In

0.2Ga

0.8As/GaAs QW at 0.07 lm below its

surface. The sample was mounted on an x—ymicrometric translation stage with the GaAs sub-strate upwards, put inside a 17 T Bitter Magnet andcooled down to 4 K. All measurements were per-formed in a background magnetic field of 7 T, di-rected perpendicular to the QW plane, whichsaturated the magnetic polarizability of the Dy toa value of about 2.5 T. A laser beam was focused toa 1 lm spot in the QW plane, using a 10] micro-scope objective, through the GaAs substrate, whichis possible because GaAs has a larger band gapthan an In

0.2Ga

0.8As QW. PL and photolumines-

cence excitation (PLE) spectra were measured asa function of the position with respect to the Dystripe.

3. Experimental results

3.1. Determination of the magnetic field gradient

Typical PLE spectra, recorded in 5 lm steps anddetected on the heavy-hole (hh) exciton emission,are displayed in Fig. 2. For clarity, the position ofthe Dy stripe is indicated by the shaded region.

Fig. 1. Schematic representation of the experimental geometry.

Fig. 2. PLE spectra as function of the position on the sample.The position of the Dy stripe is indicated by the shaded region.The spectra were recorded in steps of 5 lm and are verticallyshifted for clarity.

The spectra show the typical magneto-excitontransitions (hh—1s, —2s, —3s) [3], which clearly shiftto higher energies when measured nearby or on topof the Dy stripe, as a result of the local maximum inmagnetic field, given by the sum of the backgroundfield and the field of the magnetized stripe. Thisspatial dependence of the energy shift is nicely re-produced when it is measured at different positionsalong the Dy stripe. Furthermore, the shift is not

P.C.M. Christianen et al. / Physica B 249—251 (1998) 624—627 625

observed in the absence of the background mag-netic field, and therefore, it is not related to anykind of spatial inhomogeneity in the sample, whichmight arise from, for instance, internal strain orimperfect growth.

To convert the energy shift to the local value ofthe magnetic field, the precise field dependence ofthe exciton transition energies was measured ona position far from the Dy stripe, where the localfield equals the background field. The resultingmagnetic field profile (symbols in Fig. 3) revealsthat on top of the Dy stripe an enhancement aslarge as 0.8 T was reached. In Fig. 3, this enhance-ment is compared with a numerical evaluation ofthe magnetic field component perpendicular to theQW, generated by an uniformly magnetized film of25 lm thickness with a magnetic polarizability of2.4 T (solid curve). The calculations describeproperly the experimental results provided the dis-tance between the QW and the Dy was taken to be20 lm, which is far more than the expected min-imum distance (0.07 lm). This discrepancy is prob-

Fig. 3. Experimentally determined magnetic field profile asfunction of the position with respect to the Dy stripe (symbols),whose center corresponds to 0 lm. The solid curve is the cal-culated field of a 25 lm thick uniformly magnetized (2.4 T) stripeat a 20 lm distance.

ably caused by the difference in thermal expansioncoefficients of the Dy and the Cu holder (Fig. 1),which means that during cooling down the Dy isexpelled from the sample surface. Obviously, thisimplies that by eliminating this thermal effect,a three times larger field enhancement (2.4 T) canbe achieved. In this situation, the field profile willalso be much more rectangular [4], leading to evenhigher field gradients.

3.2. Exciton motion in magnetic field gradients

After the realization of the high magnetic fieldgradients described above, its influence on the ex-citon motion was studied by the systematic invest-igation of the PL intensity as a function of position.In case excitons are driven out of a region where thegradient, and therefore the magnetic force, is high,the integrated PL intensity emitted from this regionis expected to be smaller than that from the sur-rounding regions. In this experiment, light of850 nm was focused (through the substrate) toa 1 lm spot in the QW. The PL was measuredthrough a small pinhole in a confocal geometry [5],which ensured that light emitted from outside thephoto-excited region was rejected, leading to 1 lmresolution both in excitation and detection. Typicalresults of the spatial-dependent integrated PLintensity are shown by the symbols in Fig. 4, meas-ured in a field profile similar to the one presented inFig. 3. It is clear that the PL intensity stronglydepends on position, and is found to be inverselyproportional to the field gradient, which can beexplained as follows. The PL intensity is propor-tional to the exciton recombination rate (whichdoes not depend on magnetic field), multiplied bythe exciton density in the probed region. The ex-citon density is of course reduced by diffusion,which however is not expected to depend much onmagnetic field (between 7 and 7.8 T), and definitelynot on the gradient as observed in Fig. 4. Thereforethis particular spatial dependence of the PL inten-sity proves unambiguously that the excitons arepushed out of the photo-excited region by the mag-netic force which is proportional to the magneticfield gradient. The strength of this force is illus-trated by the fact that at the point of maximum

626 P.C.M. Christianen et al. / Physica B 249—251 (1998) 624—627

Fig. 4. Integrated PL intensity as function of the position withrespect to the Dy stripe (symbols). The solid curve was cal-culated using a model described in the text.

gradient the PL intensity is reduced to only 40% ofits value far from the stripe.

To quantify the effect of the magnetic field gradi-ent on the exciton motion and therefore the PLintensity, a simple model is used assuming that thePL signal originates from excitons which are notforced to move away by the gradient. Diffusion isneglected since in first order it simply reduces thedensity by a fixed factor independent of magneticfield. According to this model the PL intensity isgiven by a/(b#DFD), where a is proportional to theexcitation power times the recombination prob-ability, b is proportional to the recombinationprobability times the inverse of the mobility andF is the magnetic force. By calculating F from theexperimental magnetic field profile, and using a andb as fit parameters, the result of this model (solidcurve in Fig. 4) reproduces the data reasonablywell, which confirms that the magnetic force is ableto drive excitons to selected regions of space.

4. Discussion and conclusion

The excitons move in a classical potential, in-duced by the spatially varying field, which is ent-irely determined by their magnetism. They aredriven to the point of minimum energy (lowestfield), which can be described in terms of a magneticforce. To be confined to such a minimum, thisminimum should be surrounded by regions of high-er potential (higher field), and furthermore, the ex-citons should dissipate their energy by, for instance,interacting with the lattice. In this process, theexchange of energy from the center of mass tointernal motion of an exciton is of uppermost im-portance. This exchange is, however, not trivial ina magnetic field, and in itself is an interestingresearch topic. Altogether, regardless of the actualdissipation mechanism, to obtain an efficientconfinement the kinetic energy of the excitonsshould be smaller than the energy differenceimposed by the field difference *B. For themaximum possible *B in the present experimentalgeometry (2.4 T) this energy barrier is equal toabout 1.5 meV (deduced from the field dependenceof the hh—1s transition), which is more than 15times larger than k

B¹ at 1 K. Therefore, we con-

clude that a magnetic trap for excitons is feasible:excitons can be confined to a limited region ofspace, at elevated densities and low temperatures,a situation which is favorable for studying excitoncondensation.

References

[1] M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman,E.A. Cornell, Science 269 (1995) 198.

[2] M.V. Berry, A.K. Geim, Eur. J. Phys. 18 (1997) 307.[3] J.C. Maan, in: Butcher et al. (Eds.), The Physics of Low-

Dimensional Semiconductor Structures, Plenum Press,New York, 1993, p. 333.

[4] A. Matulis, F.M. Peeters, P. Vasilopoulos, Phys. Rev. Lett.72 (1994) 1518.

[5] T. Wilson (Ed.), Confocal Microscopy, Academic Press,New York, 1990.

P.C.M. Christianen et al. / Physica B 249—251 (1998) 624—627 627