# The phase transition in the localized ferromagnet EuO probed by $_{µ}$SR 

S. J. Blundell, 1, ∗ T. Lancaster, 1 F. L. Pratt, 2 P. J. Baker, 1,2 W. Hayes, 1 J.-P. Ansermet, 3 and A. Comment 3 

$^{1}$Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom 

$^{2}$ISIS Muon Facility, ISIS, Chilton, Oxon. OX11 OQX, United Kingdom 

$^{3}$Institut de Physique de la Mati`ere Condens´ee, Ecole Polytechnique, F´ed´erale de Lausanne, CH-1015 Lausanne-EPFL, Switzerland 

(Dated: September 4, 2018) 

We report results of muon spin rotation measurements performed on the ferromagnetic semicon- ductor 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. 

Europium oxide (EuO) crystallises in the rock-salt structure and is a ferromagnetic semiconductor with a Curie temperature ( T$_{C}$ ) of 69 K [1]. It shows a colossal magnetoresistance effect in its Eu-rich form [2, 3] and the associated metal-insulator transition has been linked to the formation of bound magnetic polarons [4]. It is the only magnetic binary oxide known to be thermody- namically stable in contact with silicon [5], and this, to- gether with a nearly 100% spin polarization of mobile electrons for carrier concentrations below half filling of the conduction band [6, 7], means that it is thought to be highly relevant for spintronic applications [8]. The magnetic moments of the Eu 2+ (4f $^{7}$, $^{8}$S$_{7}$$_{/}$$_{2}$ ) ions result from 4f charge density which is nearly completely local- ized inside the filled 5s $^{2}$5p6 shells and there is negligible overlap. This makes EuO an excellent approximation to a Heisenberg ferromagnet [9], although there is evidence of some momentum dependence in the exchange inter- actions [10]. The ferromagnetic interactions are due to an indirect exchange mediated by electrons in anion va- lence bands [11], specifically virtual excitations of oxygen valence band p electrons into empty Eu 2+ (5d) conduc- tion bands and exchange interaction of the d electron (p hole) with the localized 4f electrons. EuO is one of a family of isostructural europium chalcogenides EuX with X=O, S, Se and Te. As the size of the chalcogen increases from O to Te, the lattice parameter a increases across the series: 5.14 ˚ A in EuO, 5.97 ˚ A in EuS, 6.20 ˚ A in EuSe and 6.60 ˚ A in EuTe [12]. Only EuO and EuS are ferro- magnets and both the nearest-neighbor and next-nearest- neighbour exchange constants are larger in EuO com- pared to EuS [9, 13]. In EuO, the saturation magnetiza- tion M$_{s}$ is given by gJµ$_{B}$ (4 /a $^{3}$), yielding µ$_{0}$M$_{s}$ = 2 . 40 T (using gJ = 7). 

Neutron studies of EuO are significantly hindered by the strong absorption of neutrons by Eu, though the use of a thin-slab geometry and use of $^{153}$Eu (which has the smaller absorption cross section of the two naturally oc- curring isotopes) has allowed a detailed study to be per- formed [9]. Nevertheless, a technique such as muon-spin rotation ( µ SR) avoids these difficulties entirely, and in contrast to NMR there is no electric field gradient or 

quadrupolar contribution to the observed muon response, simplifying the analysis. In this paper we present the re- sults of µ SR experiments to study the magnetic order and the fluctuations in samples of EuO and use the results to compare with theoretical predictions [14–16]. 

Our µ SR experiments were carried out using the GPS instrument at the Swiss Muon Source (S µ S), Paul Scher- rer Institute (PSI) in Switzerland. In our µ SR exper- iment, spin polarised positive muons ( µ $^{+}$, momentum 28 MeV /c ) were implanted into small crystals of EuO. The muons stop quickly (in < 10 − 9 s), without signif- icant loss of spin-polarization. The observed quantity is then the time evolution of the average muon spin polarization P$_{z}$ ( t ), which can be detected by counting emitted decay positrons forward (f) and backward (b) of the initial muon spin direction; this is possible due to the asymmetric nature of the muon decay [17, 18], which takes place in a mean time of 2 . 2 µ s. In our experiments positrons are detected by using scintilla- tion counters placed in front of and behind the sam- ple. We record the number of positrons detected by for- ward ( N$_{f}$ ) and backward ( N$_{b}$ ) counters as a function of time and calculate the asymmetry function, G$_{z}$ ( t ), using G$_{z}$ ( t ) = [ N$_{f}$ ( t ) − α$_{exp}$N$_{b}$ ( t )] / [ N$_{f}$ ( t ) + α$_{exp}$N$_{b}$ ( t )], where α$_{exp}$ is an experimental calibration constant and differs from unity due to non-uniform detector efficiency. The quantity G$_{z}$ ( t ) is then proportional to P$_{z}$ ( t ). 

Raw data for EuO at two temperatures, one slightly higher and one much lower than T$_{C}$ , are shown in Fig. 1(a). These demonstrate that spin relaxation above T$_{C}$ changes to a damped coherent oscillation below T$_{C}$ . If the experiment is repeated with a sample of EuO in which 0.6% of the Eu ions are replaced with Gd, an almost iden- tical result is obtained [Fig. 1(b)] although the damping rate of the oscillations in the ordered state is noticeably larger (by about a factor of two). This level of Gd dop- ing is known to introduce a static magnetic inhomogene- ity [19]. The frequency of the oscillations in both cases increases rapidly on cooling below T$_{C}$ , see Fig. 1(c,d,e), approaching ≈ 30 MHz at zero temperature. The Fast Fourier transform data in Fig. 1(c) demonstrate that only a single precession frequency is observed. The tempera- 

