Electron localization into magnetic polaron in EuS

Electron Localization into Magnetic Polaron in EuS V.G. Storchak a,∗ , O.E. Parfenov a , J.H. Brewer b , P.L. Russo b , S.L. Stubbs b , R.L. Lichti d , D.G. Eshchenko c , E. Morenzoni c , S.P. Cottrell e , J.S. Lord e , T.G. Aminov f , V.P. Zlomanov g , A.A. Vinokurov g , R.L. Kallaher h and S. von Moln´ar h a Russian

Research Centre “Kurchatov Institute”, Kurchatov Sq. 1, Moscow 123182, Russia of Physics and Astronomy, University of British Columbia, Vancouver, B.C., Canada V6T 1Z1 c Paul Scherrer Institute, CH-5232, Villigen, Switzerland d Department of Physics, Texas Tech University, Lubbock, Texas 79409-1051, USA e ISIS Facility, Rutherford Appleton Laboratory, Oxfordshire OX11 OQX, UK f Institute for General and Inorganic Chemistry, Moscow 119991, Russia g Department of Chemistry, Moscow State University, Moscow 119991, Russia h Florida State University, The Center for Materials Research and Technology, Tallahassee, Florida 32306, USA b Department

Abstract Recently the spin of the electron has become the focus of a new direction in electronics — semiconductor spintronics — which utilizes mechanisms of strong mutual influence of magnetic and electrical properties in magnetic semiconductors. These mechanisms are still a matter of considerable debate, however, all of them involve a concept of magnetic polaron - a microscopic cloud of magnetization made of several neighboring magnetic ions and a carrier(s) - which determines most of the electrical, magnetic and optical properties of the material. Although a great number of experiments indicate the existence of magnetic polaron in magnetic semiconductors and related materials it has eluded direct observation until now. Using the positive muon as both a donor centre and a local magnetic probe, we have been able to generate and detect the magnetic polaron and determine its size in the magnetic semiconductor EuS. Key words: magnetic semiconductor, magnetic polaron, exchange interaction

1. Introduction From the earliest transistor to the microprocessor in a modern computer, electronic devices have employed the transport of electric charges. In order to enhance the multifunctionality of devices (for example, carrying out processing and data storage within the same chip), researchers have tried to exploit another property of the electron — its spin — which can also carry information. However, the semiconductors currently used in integrated circuits, such as Si, Ge and GaAs, are non-magnetic, in which the carrier energy is almost independent of the spin direction. In contrast, in magnetic semiconductors (MS), the exchange interaction gives rise to pronounced spin-related phenomena. Magnetic semiconductors are of fundamental interest because they provide optimal conditions for the formation of a new type of quasiparticle — magnetic polaron (MP) conduction electrons “autolocalized” in an atomic-scale unsta∗ Tel: 7-495-1967356, Fax: 7-495-1969133, email: [email protected] Preprint submitted to Elsevier

ble phase region which stabilizes by electron localization (e.g., as a ferromagnetic (FM) “droplet” in an antiferromagnetic (AFM) or paramagnetic (PM) “sea”) [1]. The MP concept has become the basis for any discussion concerning the physical properties of MS and related materials. For a recent review see [2]. Although the overwhelming consensus leaves very little doubt about the existence of the MP, its direct observation remains a formidable challenge. Nevertheless, it is important to know its microscopic characteristics (binding energy, size or magnetic moment) and to control them if possible, as they determine the electrical and optical properties of the materials used as working media for prospective spintronics devices. In order to find a way to detect the magnetic polaron directly, one has to appreciate the conditions for its formation: Formation of an MP bound to a corresponding donor combines the long range Coulomb interaction with the exchange coupling J to ensure localization of an electron with effective mass m∗ so that the change in the free energy 8 September 2008

∆F =

~2 a3 e2 −J 3 − ∗ 2 2m R R εR

2. Experimental

(1)

Time-differential µ+ SR experiments were performed on the M15 surface muon channel at TRIUMF using the HiTime apparatus. In order to get rid of demagnetization effects in applied magnetic fields [12] we used a ball-shaped EuS powder sample 7 mm in diameter. In zero magnetic field (ZF) we detected oscillations of the muon spin in the FM state. An important point here is that there is only one line (a single frequency) in the µ+ SR spectra, which indicates that all muons occupy equivalent positions in EuS lattice.

has a minimum as a function of R - the radius of the electron confinement. In order to compensate for the increase in the electron kinetic energy due to localization [first term in Eq.(1)] one needs an insulating matrix with low ε (to ensure a strong, unscreened Coulomb interaction) and a heavy electron which exhibits strong exchange coupling J. The exchange contribution to the localization amounts to a difference between the PM order of the host and the enhanced (FM) order in the MP. In an external magnetic field H, all Eu ions develop a net magnetization increasing towards low temperature; this reduces the energy advantage afforded by the exchange coupling, rendering the MP unstable at high H and low T . Therefore one has to search for the MP at high enough T that its mediated exchange contribution [the second term in Eq.(1)] is dominant. The requirement of an insulating host can be met in pure EuS, which has a large enough energy gap (1.6 eV) to ensure exponentially low free electronic states even at room temperature. One can then inject a low concentration of free carriers into the empty conduction band from the ionization track of a high energy µ+ which may then (after stopping) act as a centre for electron localization to form the MP. In a typical muon spin relaxation (µ+ SR) experiment, each incoming 4 MeV muon creates an ionization track of electrons and ions liberated during the µ+ thermalization process. Experiments in insulating [3,4] and semiconducting [5–9] media have shown that the muon thermalizes very close (10−6 -10−5 cm) to some of its ionization track products. Thus one of the excess electrons generated in the end of the track can be captured by the thermalized muon to form a muonium atom. In semiconductors, this phenomenon of “delayed muonium formation” produces a model system with which to study electron capture by and release from the donor centre (positive muon) [9] in the extremely dilute limit: Mu (a neutral donor) is typically found at low temperatures, while a diamagnetic bare µ+ state (an ionized donor) is observed at higher temperatures [10]. In semiconductors, two sets of quite different Mu states are so far known to coexist with diamagnetic state(s): deep (∼ 0.2 eV or higher) Mu states with the hyperfine constants of A ∼ (0.1 − 0.5)Avac (Avac = 4463 MHz is the hyperfine constant for Mu in vacuum) and shallow (∼ 0.01 eV, A ∼ 10−4 Avac ) Mu states [11]. In magnetic semiconductors, the second term in Eq. (1) may cause formation of a Mu bound state with an electron wave function more compact than in a typical Mu shallow donor state: the long-range Coulomb interaction ensures initial electron capture while the short-range exchange interaction provides further localization via formation of MP bound to the muon. Transverse magnetic field µ+ SR techniques provide a reliable way to detect the MP thus formed and to determine its spectroscopic characteristics.

Fig. 1. Local magnetic field Bµ at the muon in three different EuS samples under zero applied field (ZF). Squares: polycrystalline EuS spherical sample used in high magnetic field measurements to follow. Circles and triangles are polycrystalline disk-shaped EuS samples from different sources.

The internal magnetic field (Bµ ∼ 0.3 T , see Figure 1) thus measured at the muon in EuS at low temperature is typical of those measured by µ+ SR in other FM materials [12,13], which suggests that the muon occupies an interstitial position in EuS. By analogy with other materials with NaCl structure, we assume this position to be tetrahedral [12,13], having 4 Eu ions as nearest neighbours. The ZF muon precession signal disappears above the FM transition (Tc ≈ 17 K) which is consistent with the disappearance of long-range FM order. In transverse magnetic field (TF) with H ≫ Bµ , low temperature measurements again detect a single line broadened due to interaction with Eu magnetic moments; this is the case both below and above Tc , up to ∼ 100 K. At higher temperatures, however, the muon precession spectra split into three distinct lines (see Fig. 1). Evolution of these signals with temperature is presented in Figure 2. We claim that the central line is the signal from bare muons which avoid electron capture, and that the two satellite lines represent muons that managed to capture and localize electrons. Relative changes in the amplitudes of these lines reflect the magnetic nature of electron localization: at higher mag2

100 times less than that of a deep Mu state and about 100 times larger than that of a shallow Mu state. Thus its electron wave function is significantly more compact than in a shallow state but considerably more dilated than in a deep state. The relevant hyperfine interaction scales as 1/R3 , where R is the characteristic Bohr radius of the corresponding 1s wave function. We find R ≈ 0.3 nm, which is about 6 times larger than the Bohr radius of Mu (or H) in vacuum and about 10 times smaller than that of a typical shallow state. In conclusion, using the positive muon as a donor centre we have detected an individual MP bound to the muon in EuS. The characteristic radius of this MP at T = 90 K is R ≈ 0.3 nm which is consistent with MP composed of the 4 saturated nearest Eu ions. 4. Acknowlegments

Fig. 2. Fourier transform of the muon spin precession signal in EuS an external magnetic field of 5 T at different temperatures.

This work was supported by the Kurchatov Institute, the Canadian Institute for Advanced Research, the Natural Sciences and Engineering Research Council of Canada and the Royal Society of London.

netic field increased magnetization diminishes the magnetic term in the free energy [see Eq. (1)], making it too small to compensate for the increase in electron kinetic energy due to localization. Accordingly, the amplitude of the central line is increased with respect to that of satellite lines when the magnetic field is increased from 1 T to 7 T. This behaviour is in marked contrast with that of Mu in non-magnetic semiconductors, where it disappears at high temperature [10,9]. The difference is again because in magnetic semiconductors the electron is strongly coupled to a number of magnetic ions. This coupling is much greater than either the hyperfine interaction or the Zeeman splitting. The muon sees a mean field proportional to the hyperfine coupling A and to the PM magnetization of the host. Then within the mean field approximation, at low magnetic field and high temperature the splitting between the satellites can be expressed as ( ) g µB B ∆ν = A (S + 1) . (2) 3kB T

References [1] E.L. Nagaev, Colossal Magnetoresistance and Phase Separation, in Magnetic Semiconductors (London: Imperial College Press, 2002). [2] S. von Moln´ ar and P.A. Stampe, Magnetic Polarons in Handbook of Magnetism and Advanced Magnetic Materials edited by Helmut Kronmueller and Stuart Parkin. Volume 5: Spintronics and Magnetoelectronics (John Wiley & Sons, Ltd., 2007). [3] V.G. Storchak, J.H. Brewer and G.D. Morris, Phys. Rev. Lett. 75 (1995) 2384. [4] V.G. Storchak, D.G. Eschenko, J.H. Brewer et al., Phys. Rev. Lett. 85 (2000) 166. [5] V.G. Storchak et al., Phys. Rev. Lett. 78 (1997) 2835. [6] D.G. Eshchenko, V.G. Storchak, J.H. Brewer and R.L. Lichti, Phys. Rev. Lett. 89 (2002) 226601. [7] V.G. Storchak, D.G. Eshchenko, R.L. Lichti and J.H. Brewer, Phys. Rev. B67 (2003) 121201. [8] D.G. Eshchenko, V.G. Storchak, S.P. Cottrell and S.F.J. Cox, Phys. Rev. B68 (2003) 073201. [9] V.G. Storchak, D.G. Eshchenko and J.H. Brewer, J. Phys.: Condensed Matter 16 (2004) 4761. [10] B.D. Patterson, Rev. Mod. Phys. 60 (1988) 69. [11] J.M. Gil et al., Phys. Rev. B64 (2001) 075205. [12] A. Schenck, Muon Spin Rotation: Principles and Applications in Solid State Physics (Adam Hilger, Bristol, 1986). [13] J.H. Brewer, Muon Spin Rotation/Relaxation/Resonance, in Encyclopedia of Applied Physics 11, 23 (VCH Publishers, New York, 1994).

In high fields (though not high enough to decouple the electron and ions spins) the satellite frequency splitting saturate at the value of A. This result seems to be model independent, as it is the same as for any known Mu state with A ≪ Avac at B ≫ A/γµ in non-magnetic semiconductors: both the deep MuBC state and the shallow Mu state exhibit satellite lines separated by ± 12 A from the central diamagnetic line [10,11]. Although we failed to reach saturation in ∆ν at room temperature, we found it at T = 90 K above 5 T. From these measurements we determine A = 37 ± 3 MHz. 3. Discussions This Mu state is fundamentally different from any previously studied isotropic Mu state found in insulators or semiconductors: its hyperfine constant is found to be about 3