We report results of muon spin rotation measurements performed on the
ferromagnetic semiconductor EuO, which is one of the best approximations to a
localized ferromagnet. We argue that implanted muons are sensitive to the
internal field primarily through a combination of hyperfine and Lorentz fields.
The temperature dependences of the internal field and the relaxation rate have
been measured and are compared with previous theoretical predictions.Comment: 4 pages, 4 figure

Ansermet, J. -P.

Baker, P. J.

Blundell, S. J.

Comment, A.

Hayes, W.

Lancaster, T.

Pratt, F. L.

English

arXiv

We report results of muon-spin-rotation measurements performed on the ferromagnetic semiconductor EuO, which is one of the best approximations to a localized ferromagnet. We argue that implanted muons are sensitive to the internal field primarily through a combination of hyperfine and Lorentz fields. The temperature dependences of the internal field and the relaxation rate have been measured and are compared with previous theoretical predictions. © 2010 The American Physical Society

Blundell, Stephen

Lancaster, Tom

Pratt, FL

Baker, PJ

Hayes, W

Ansermet, J-P

Comment, A

Oxford University Research Archive

Phase transition in the localized ferromagnet EuO probed by mu SR

ORA - Oxford University Research Archive

Blundell S

Lancaster T

Pratt F

Baker P

Hayes W

Ansermet J

Comment A

ePubs: the open archive for STFC research publications

Phase transition in the localised ferromagnet EuO probed by muSR

S. J. Blundell

T. Lancaster

F. L. Pratt

P. J. Baker

W. Hayes

J.-P. Ansermet

A. Comment

Crossref

Phase transition in the localized ferromagnet EuO probed by
                    
                      
                        μ

We report results of muon-spin-rotation measurements performed on the ferromagnetic semiconductor EuO, which is one of the best approximations to a localized ferromagnet. We argue that implanted muons are sensitive to the internal field primarily through a combination of hyperfine and Lorentz fields. The temperature dependences of the internal field and the relaxation rate have been measured and are compared with previous theoretical predictions

Ansermet, J.-P.

Comment, Arnaud

Infoscience - École polytechnique fédérale de Lausanne

Phase transition in the localized ferromagnet EuO probed by SRS. J. Blundell,1,* T. Lancaster,1 F. L. Pratt,2 P. J. Baker,1,2 W. Hayes,1 J.-P. Ansermet,3 and A. Comment31Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom2ISIS Muon Facility, ISIS, Chilton, Oxon OX11 OQX, United Kingdom3Institut de Physique de la Matière Condensée, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, SwitzerlandReceived 25 February 2010; published 31 March 2010We report results of muon-spin-rotation measurements performed on the ferromagnetic semiconductor EuO,which is one of the best approximations to a localized ferromagnet. We argue that implanted muons aresensitive to the internal field primarily through a combination of hyperfine and Lorentz fields. The temperaturedependences of the internal field and the relaxation rate have been measured and are compared with previoustheoretical predictions.DOI: 10.1103/PhysRevB.81.092407 PACS numbers: 75.50.Dd, 75.40.s, 75.50.Pp, 76.75.iEuropium oxide EuO crystallizes in the rocksalt struc-ture and is a ferromagnetic semiconductor with a Curie tem-perature TC of 69 K.1 It shows a colossal magnetoresis-tance effect in its Eu-rich form2,3 and the associated metal-insulator transition has been linked to the formation of boundmagnetic polarons.4 It is the only magnetic binary oxideknown to be thermodynamically stable in contact withsilicon,5 and this, together with a nearly 100% spin polariza-tion of mobile electrons for carrier concentrations below halffilling of the conduction band,6,7 means that it is thought tobe highly relevant for spintronic applications.8 The magneticmoments of the Eu2+ 4f7 , 8S7/2 ions result from 4f chargedensity which is nearly completely localized inside the filled5s25p6 shells and there is negligible overlap. This makesEuO an excellent approximation to a Heisenbergferromagnet,9 although there is evidence of some momentumdependence in the exchange interactions.10 The ferromag-netic interactions are due to an indirect exchange mediatedby electrons in anion valence bands,11 specifically virtual ex-citations of oxygen valence band p electrons into empty Eu2+5d conduction bands and exchange interaction of the delectron p hole with the localized 4f electrons. EuO is oneof a family of isostructural europium chalcogenides EuXwith X=O, S, Se, and Te. As the size of the chalcogen in-creases from O to Te, the lattice parameter a increases acrossthe series: 5.14 Å in EuO, 5.97 Å in EuS, 6.20 Å in EuSe,and 6.60 Å in EuTe.12 Only EuO and EuS are ferromagnetsand both the nearest-neighbor and next-nearest-neighbor ex-change constants are larger in EuO compared to EuS.9,13 InEuO, the saturation magnetization Ms is given bygJB4 /a3, yielding 0Ms=2.40 T using gJ=7.Neutron studies of EuO are significantly hindered by thestrong absorption of neutrons by Eu, though the use of athin-slab geometry and use of 153Eu which has the smallerabsorption cross section of the two naturally occurring iso-topes has allowed a detailed study to be performed.9 Never-theless, a technique such as muon-spin-rotation SRavoids these difficulties entirely, and in contrast to NMRthere is no electric field gradient or quadrupolar contributionto the observed muon response, simplifying the analysis. Inthis Brief Report we present the results of SR experimentsto study the magnetic order and the fluctuations in samplesof EuO and use the results to compare with theoreticalpredictions.14–16Our SR experiments were carried out using the GPSinstrument at the Swiss Muon Source SS, Paul ScherrerInstitute PSI in Switzerland. In our SR experiment, spin-polarized positive muons +, momentum 28 MeV /c wereimplanted into small crystals of EuO. The muons stopquickly in 10−9 s, without significant loss of spin polar-ization. The observed quantity is then the time evolution ofthe average muon-spin polarization Pzt, which can be de-tected by counting emitted decay positrons forward f andbackward b of the initial muon-spin direction; this is pos-sible due to the asymmetric nature of the muon decay,17,18which takes place in a mean time of 2.2 s. In our experi-ments positrons are detected by using scintillation countersplaced in front of and behind the sample. We record thenumber of positrons detected by forward Nf and backwardNb counters as a function of time and calculate the asym-metry function, Gzt, using Gzt= Nft−expNbt / Nft+expNbt, where exp is an experimental calibration con-stant and differs from unity due to nonuniform detector effi-ciency. The quantity Gzt is then proportional to Pzt.Raw data for EuO at two temperatures, one slightly higherand one much lower than TC, are shown in Fig. 1a. Thesedemonstrate that spin relaxation above TC changes to adamped coherent oscillation below TC. If the experiment isrepeated with a sample of EuO in which 0.6% of the Eu ionsare replaced with Gd, an almost identical result is obtainedFig. 1b although the damping rate of the oscillations inthe ordered state is noticeably larger by about a factor of 2.This level of Gd doping is known to introduce a static mag-netic inhomogeneity.19 The frequency of the oscillations inboth cases increases rapidly on cooling below TC, see Figs.1c–1e, approaching 30 MHz at zero temperature. Thefast Fourier transform FFT data in Fig. 1c demonstratethat only a single precession frequency is observed. The tem-perature dependence of the precession frequency in the Gd-doped sample is almost identical to that in the pure sample,demonstrating that the order parameter is following the in-trinsic magnetism in the EuO host and is relatively insensi-tive to low levels of doping. In fact, at the 0.6% level of Gddoping, 93% of the Eu ions have their full complement 12of nearest-neighbor Eu ions, with most of the remaining Euions having only one of those nearest neighbors replaced byGd. For both samples, the relaxation rate of the oscillatorycomponent rises as T approaches TC from below and thePHYSICAL REVIEW B 81, 092407 20101098-0121/2010/819/0924074 ©2010 The American Physical Society092407-1low-temperature relaxation rate of the Gd-doped sample islarger than that of the pure sampleThe muon spin precesses around a local magnetic field,B with a frequency =  /2B, where  /2=135.5 MHz T−1. This local field B0.22 T at T=0 isa sum of various terms, including the Lorentz field BL, thehyperfine field Bhf, the demagnetizing field Bdemag, and thedipolar field Bdip. The latter quantity is a function of themuon site r and can be written asBdip r = iDi	rmi	, 1a sum over the magnetic ions in the crystal; the magneticmoment of the ith ion is mi. In Eq. 1, Di	r is the dipolartensor given by Di	r=04Ri33RiRi	Ri2−	, where RiRix,Riy,Riz=r−ri. The behavior of this tensor is domi-nated by the arrangement of the nearest-neighbor magneticions and leads to a nonzero local magnetic field for almost allpossible muon sites.20 On electrostatic grounds, the likelymuon site in EuO is at the 141414 position see Fig. 2a,equidistant from four Eu cations and four oxygen anions asfound in other systems with the NaCl structure, see, e.g.,Ref. 21. Because of the magnetic anisotropy,22 the easy axisfor the Eu moments is along the 	111 set of directions andfor this moment alignment the 141414 position is a point atwhich the dipolar magnetic field actually vanishes. The valueof Bdip has been calculated for the case in which the muon isdisplaced from the 141414 site and its position is allowed tovary along the 111 direction, see Fig. 2b. The dipolar fieldvanishes at both 141414 muon site and121212 oxygen site andincreases sharply as the site moves away from these specialpositions of high symmetry. The two curves show the casesin which the muon displacement is the same or a differentchoice of 	111 direction. In the former case, the dipolar fieldat the muon site is parallel to the moment direction; in thelatter case for which there are three possibilities, it liesalong one of the crystallographic axes and its amplitude isreduced by a factor of 3. Thus if the muon site is displacedfrom the 141414 position toward a particular oxygen anion, thenthere would be a contribution to the dipole field resulting in........................................................................................................................................................................................................................................................... .... .... ... ........... ................................................................................................................................................................................................. . .. ...........TFIG. 1. Color online a Raw SR data for EuO. Above TC at70 K, Pzt relaxes. An oscillating signal develops below TC datashown for 1.5 K. b The same for Eu0.994Gd0.006O. c Plot show-ing FFT of the muon data for EuO as a function of temperature. Thesingle precession frequency which follows the order parameter isclearly visible. d The extracted precession frequency for EuO as afunction of temperature. e The same experiment repeated forEu0.994Gd0.006O. The line through the data in d and e is identicalfor the two samples and is a best fit of the data to the phenomeno-logical function T=01− T /TC	, producing 1.5, 	0.4. A more reliable extraction of the critical exponent 	, focus-ing only on the critical regime, is given later in the Brief Report.FIG. 2. Color online a Muon site in EuO. The crystal struc-ture for one eighth of the unit cell is shown the side of the cube isa /2. b Calculated dipole field along the 	111 axes in EuO. Themuon is located at  and the Eu moments are all aligned along111 solid black line or one of 1¯11, 11¯1, or 111¯ dashed redline.BRIEF REPORTS PHYSICAL REVIEW B 81, 092407 2010092407-2two precession frequencies with a ratio of 3, and with am-plitudes in a 3:1 ratio. Since only a single frequency is ob-served, we conclude that the muon site is indeed at the 141414position in which the dipolar field is zero, so that the ob-served local field B=0.22 T at T=0 is due to a sum of theLorentz field BL=0M /3=0.80 T at T=0, Bdemag and Bhf.Since the sample is polycrystalline and multidomain, we ne-glect Bdemag and deduce that the hyperfine field Bhf0 an-tiparallel to the magnetization, as found for EuS,23 and takesthe value Bhf=−BLB, and so either −0.58 or −1.02 T. Forboth samples, the amplitude of the oscillatory component isreduced from the full value at low temperature see Figs. 1aand 1b, but recovers on warming toward TC, so a fractionof muons may implant in some additional state which depo-larizes the muon very rapidly.We note that a recent experiment24 on SmS has shownevidence for the formation of a bound magnetic polaron con-sisting of an electron around the implanted muon, in whichthe electron localization is stabilized by exchange energy.This occurs in the paramagnetic state in which a ferromag-netic droplet is localized in the paramagnetic host. A similareffect has been noted in EuS Ref. 25 although the largermagnetization ensures it occurs at temperatures TC Ref.26 and the same will be true in EuO in which the magneti-zation is even larger. Therefore such a muon-related polaronis not relevant for EuO in the studied temperature regime.The temperature dependence of the precession frequencyfor both EuO and Eu0.994Gd0.006O was followed near TC andthe results are plotted in Fig. 3. The fitted values of TC andthe critical exponent 	 are similar in each case, though thevalue of 	 is quite sensitive to the precise value taken for TC.Due to the difficulty in stabilizing the temperature better than10 mK, we do not believe that the difference between thetwo values of 	 is significant. They are both close to 0.36–0.37 obtained using neutron scattering27 and 0.38 obtainedfrom a second-order  expansion for the Heisenberg ferro-magnet with dipolar interactions.28Above TC, we observe simple exponential relaxationFigs. 1a and 1b with a relaxation rate . For zero-fieldrelaxation of muons initially polarized parallel to z,  can bewritten in terms of field-field correlation functions using =22 − dt	Bx0Bxt+ 	By0Byt.18 When each Eu spincomponent fluctuates, it produces a field fluctuation via theresulting modulation of the dipolar and hyperfine couplings.Our measurements of the zero-field relaxation rate for theEuO sample are plotted in Fig. 4 a less complete set of datafor the Gd-doped sample is also shown. There is a small risein  as the temperature is lowered toward TC but apart fromthis  remains just below 2 MHz for both samples acrossthe entire range studied.These results can be compared with calculations on a lo-calized Heisenberg ferromagnet which have been performedwith EuO in mind15,16 Fig. 4. The theory of Lovesey andEngdahl15 includes only the dipolar coupling and has beenevaluated for temperatures above 1.3TC, assuming a muonsite of 141414 . Though underestimating the observed experi-mental values, this theory does remarkably well in providinga good estimate of the size of , the discrepancy perhapsbeing due to neglecting the hyperfine contribution. It isknown that critical fluctuations enhance the role of the hy-perfine coupling over the dipole coupling14 because Bdip=0at the muon site in the ordered state and the peak in thesusceptibility is at k=0. Nevertheless, when the dipolar cal-culation is extended into the critical regime just above, andvery close to, TC it predicts a divergence in  which is notobserved. An earlier mode-coupling approach16 also predictsa very sharp increase in  on cooling to TC from about 0.3 Kabove it; this is also not observed in our data. It is possiblethat the absence of a divergence results from an interferencebetween the dipolar and contact interactions of the + spinwith the magnetic critical fluctuations.29 However, anotherpossibility results from magnetic polarons this time not in-volving the muon but intrinsic to EuO Ref. 12. Magneticpolaron formation has been detected using Ramanscattering30 in a narrow range 20 K above TC. It may bethat the formation of magnetic polarons modifies the relax-ation in this regime from that which would be expected fromtheory, perhaps by providing an additional relaxation channelfor the muon which masks the critical slowing down pre-dicted by the theory and hence the absence of the divergencein . We note that a similar absence of a divergence in  isFIG. 3. Precession frequency extracted from SR data as afunction of temperature close to TC for a EuO and bEu0.994Gd0.006O..........T/Tc − 1T (K)Lovesey and EngdahlMode couplingFIG. 4. Color online Relaxation rate as a function of tempera-ture in the paramagnetic regime for pure EuO solid circles and bEu0.994Gd0.006O dots. The predicted relaxation rates for TTCaccording to Ref. 15 numerical calculation: thick solid line, purple;critical regime using experimental values of correlation length:thick dashed line, purple and Ref. 16 dotted line, blue are alsoshown.BRIEF REPORTS PHYSICAL REVIEW B 81, 092407 2010092407-3observed in EuB6 Ref. 31 in which magnetic polarons havebeen found.30In conclusion, we have identified the muon site in EuOand estimated the hyperfine field. Our results confirm long-range order which is relatively insensitive to low doping ofGd. The measured  in the paramagnetic state agrees quitewell with the theory of Lovesey and Engdahl, but the avail-able theories fail in the critical regime, possibly due to mag-netic polaron formation.We thank EPSRC U.K. for financial support and AlexAmato for experimental assistance. Part of this work wasperformed at the Swiss Muon Source, Paul Scherrer Institute,Villigen, Switzerland.*s.blundell@physics.ox.ac.uk1 B. T. Matthias, R. M. Bozorth, and J. H. van Vleck, Phys. Rev.Lett. 7, 160 1961.2 Y. Shapira, S. Foner, and T. B. Reed, Phys. Rev. B 8, 22991973.3 P. Sinjukow and W. Nolting, Phys. Rev. B 68, 125107 2003.4 J. B. Torrance, M. W. Shafer, and T. R. McGuire, Phys. Rev.Lett. 29, 1168 1972.5 K. J. Hubbard and D. G. Schlom, J. Mater. Res. 11, 2757 1996.6 K. Sattler and H. C. Siegmann, Phys. Rev. Lett. 29, 1565 1972.7 P. G. Steeneken, L. H. Tjeng, I. Elfimov, G. A. Sawatzky,G. Ghiringhelli, N. B. Brookes, and D.-J. Huang, Phys. Rev.Lett. 88, 047201 2002.8 A. Schmehl et al., Nature Mater. 6, 882 2007.9 O. W. Dietrich, J. Als-Nielsen, and L. Passell, Phys. Rev. B 14,4923 1976; J. Als-Nielsen, O. W. Dietrich, and L. Passell, ibid.14, 4908 1976; L. Passell, O. W. Dietrich, and J. Als-Nielsen,ibid. 14, 4897 1976.10 H. Miyazaki, T. Ito, H. J. Im, S. Yagi, M. Kato, K. Soda, andS. Kimura, Phys. Rev. Lett. 102, 227203 2009.11 V.-C. Lee and L. Liu, Phys. Rev. B 30, 2026 1984.12 A. Mauger and C. Godart, Phys. Rep. 141, 51 1986.13 H. G. Bohn, W. Zinn, B. Dorner, and A. Kollmar, Phys. Rev. B22, 5447 1980.14 S. W. Lovesey, E. B. Karlsson, and K. N. Trohidou, J. Phys.:Condens. Matter 4, 2043 1992; S. W. Lovesey, K. N. Trohi-dou, and E. B. Karlsson, ibid. 4, 2061 1992.15 S. W. Lovesey and E. Engdahl, J. Phys.: Condens. Matter 7, 7691995.16 A. Yaouanc, P. Dalmas de Réotier, and E. Frey, Phys. Rev. B 47,796 1993.17 S. F. J. Cox, J. Phys. C 20, 3187 1987; S. J. Blundell, Con-temp. Phys. 40, 175 1999.18 P. Dalmas de Réotier and A. Yaouanc, J. Phys.: Condens. Matter9, 9113 1997.19 A. Comment, J.-P. Ansermet, C. P. Slichter, H. Rho, C. S. Snow,and S. L. Cooper, Phys. Rev. B 72, 014428 2005.20 S. J. Blundell, Physica B 404, 581 2009.21 K. Aggarwal, L. Asch, F. N. Gygax, O. Hartmann, G. M.Kalvius, A. Kratzer, F. J. Litterst, K. Mattenberger, A. Schenck,and O. Vogt, Hyperfine Interact. 51, 935 1989.22 A. Kasuya and M. Tachiki, Phys. Rev. B 8, 5298 1973.23 D. G. Eshchenko, V. G. Storchak, E. Morenzoni, and D. An-dreica, Physica B 404, 903 2009.24 V. G. Storchak, J. H. Brewer, D. J. Arseneau, S. L. Stubbs, O. E.Parfenov, D. G. Eshchenko, E. Morenzoni, and T. G. Aminov,Phys. Rev. B 79, 193205 2009.25 V. G. Storchak et al., Phys. Rev. B 80, 235203 2009.26 V. G. Storchak et al., Physica B 404, 899 2009.27 J. Als-Nielsen, O. W. Dietrich, W. Kunnmann, and L. Passell,Phys. Rev. Lett. 27, 741 1971.28 A. D. Bruce and A. Aharony, Phys. Rev. B 10, 2078 1974.29 V. Yu. Yushankhai, Hyperfine Interact. 50, 775 1989.30 C. S. Snow, S. L. Cooper, D. P. Young, Z. Fisk, A. Comment,and J.-P. Ansermet, Phys. Rev. B 64, 174412 2001.31 M. L. Brooks, T. Lancaster, S. J. Blundell, W. Hayes, F. L. Prattand Z. Fisk, Phys. Rev. B 70, 020401R 2004.BRIEF REPORTS PHYSICAL REVIEW B 81, 092407 2010092407-4

The phase transition in the localized ferromagnet EuO probed by muSR

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