Raman scattering in EuSe and EuTe near magnetic phase transitions

Journal of Magnetism and Magnetic Materials 11 (1979) 403-407 © North-Holland Publishing Company

RAMAN SCATTERING IN EuSe AND EuTe NEAR MAGNETIC PHASE TRANSITIONS * S.A. SAFRAN * t , G. DRESSELHAUS *, R.P. SILBERSTEIN ** and B. LAX *:~ Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Received 4 August 1978; in revised form 20 September 1978 The ordering and fluetnations of the spins in the magnetic semiconductors EuSe and EuTe are correlated with the selection rules and intensities of inelastic light scattering from one phonon-one spin excitations in these materials. Calculations of the Raman line shape in EuSe are presented for T >> Te and T ~ Te. 1. Introduction

line (magnetically ordered) spectra. In section 3, we calculate the broadline line shape for EuSe for both T > > T c and T ~. T e near the paramagnetic to foursublattice transition. The evolution of spectrum from a single peaked to a double peaked structure as T approaches Te from above, is discussed in terms of spin fluctuations. The theoretical predictions for the broadline line shape and the sharp line selection rules are compared with experiment. Section 4 focuses on the low temperature spectrum of EuTe. The magnetic field dependence of the Raman spectra for EuTe near the spin flop to paramagnetic transition is predicted to be sensitive to the change in the order parameter critical exponent # [9,10], due to the changes in the effective dimensionality of the system near T = 0 [11, 12].

The europium chalcogenides EuSe and EuTe are magnetic semiconductors that exhibit a wide variety of magnetic phases. Due to the near cancellation of the first- and second neighbor exchange constants, EuSe is a metamagnet which has one-, two-, three-, and four- sublattice phases [1 ]. EuTe is a two-sublattice antiferromagnet which undergoes magnetic field induced transitions to spin-flopped and aligned paramagnetic phases. Recent Raman scattering experiments on these materials have shown that their phonon spectra, which are forbidden in first order, are magnetic phase dependent [2-6]. In the paramagnetic phase, a broad spectral line has been observed with a full width (Av ~ 30 cm -1) spanning the entire LO branch. As magnetic ordering occurs, this "broadline" due to spin-disorder scattering [2-7] is quenched, and sharp lines (Av ~< 0.6 cm - I ) are observed [2,3,5]. In this paper, we analyze the temperature and magnetic field dependence of the Raman intensities in the neighborhood of the magnetic phase transitions of EuSe and EuTe, in terms of the one phonon-one spin Raman mechanism presented in refs. [4,7,8]. Section 2 reviews the theory for the Raman scattering intensity for both the broadline (paramagnetic) and sharp

2. Raman intensity The Raman scattering mechanism which has recently been established for one-phonon scattering in the europium chalcogenides [4,7,8] involves an incident photon of energy hcoi which virtually excites the electronic system from the 4f 7 ground state to the 4P s 5d excited state. The excited electrons (or excitons) interact with both the LO phonons and with the spins through the large (~.0.6 eV) spin-orbit coupling in this excited electronic state. Finally, the electrons return to their ground state, emitting a photon of energy hcos. In the dipole approximation, the Raman intensity for this one phonon-one spin process, is proportional to c$(6o) [10]:

* This work was supported by NSF grant DMB 7302473A01. * Francis Bitter National Magnet Laboratory, supported by the National Science Foundation. :~Physics Department. ** Center for Materials Science and Engineering and Department of Electrical Engineering and Computer Science.

c5(co) = cJ B(co) + ci s(CO), 403

(la)

S.A. Safran et aL ] Raman scattering in FuSe and EuTe

404

where ~B(60) = ~ fis.ioo'(q, 60i) /=LO oo'q

X (S"~r(--q,O) S'd(q, 60 -- 60i(q))),

(lb)

and ~S(w) = , ~ .

,fislod(q wi)(So(q))

Li,t/o,OO ]=LO

× (So,(--q)) 6(q - qo) 6(w - wj(q)).

(Ic)

In eq. (1), ci s and c5s refer to the broadline (spin disorder) and sharp line (spin order) spectra respectively. Here we have considered only the Stokes scattering process, with kBT < < h60LO, so that the phonon population factor is neglected. The photon energy loss is h60 = h(6oi - COs),while fisjod(q, 600 is a form factor, proportional to the square of the wave vector-dependent Raman tensor [10]. The indices i and s refer to the incident and scattered photons with polarization vectors, e i and e s, / refers to the phonon branch, and o, o' label the x, y, z components of the Fourier transforms of the spin operators, So(q). For the NaC1 structure, a symmetry analysis [10] of the f o r m factor indicates that near q = O,fisioo,(q, 600 is proportional to q2 for all i, s, ] and o. On the other hand, near the L point (qL = n/a(1, 1, 1)) the form factor is a maximum for all choices of e i and e s except for the polarization combination that transforms as F~ [13]. The te.rm marked cJa in eq. (la) arises from spin fluctuations (S'o = So - (So)) and is proportional to the two-spin correlation function. The term c.is in eq. (la) is proportional to the square of the staggered magnetization No = (So(qo)), and gives rise to a sharp line at the phonon energy corresponding to wave vector q0, where (S(qo)) is nonzero in the ordered magnetic phase. For example, in the two sublattice antiferromagnetic phases of EuSe and EuTe, qo = qL while in the four-sublattice phase of EuSe, qo = qL/2.

3. EuSe - Raman line shape

At high temperatures, where the two spin correlation function is q independent, the Raman spectra of~ all four europium chalcogenides consists of a broad

line peaked at coLO(qL) [14], consistent with our theory [10]. However, near T¢, the Raman spectrum should be influenced not only by the form factor which has a maximum at qL, but also by the q = qL/2 component of the two spin correlation function, since near phase transitions, the spin fluctuations of wave vector qL/2 are large. For ferromagnets, such as EuO and EuS, the Raman tensor vanishes at q = 0, and thus there are no dramatic changes in the spectrum near Tc [15]. On the other hand, for EuSe at H = 0 and T near Te for the paramagnetic to four-sublattice transition at 4.6 K, large spin fluctuations occur at qL]2. Since the Raman tensor is nonzero at that wave vector, a shift in the peak of the broadline from qL to qL/2 is expected. We have calculated the Raman line shape for the broad line in EuSe for both T > > Tc and T ~ T¢ using both the quasi-elastic and mean field approximations for the two-spin correlation function [16]:

(So(q, O) So(-q, co)) ~ (r/rc) X { ( T - T c ) I T e + [J(qo)-J(q)]lJ(qo)} -~ ~(60), (2a)

J(q) = ~ exp(iq • R) J(R).

(2b)

R

In eq. (2b) the sum over R runs over nearest and next nearest neighbors with exchange constants Jx = 0.1 67 K and J2 = -0.158 K [17]. The form factor ofeq. (1) is taken from the results of ref. [10], while phonon dispersion curves for the LO branch have a simple tight binding form as given in ref. [7]. We note that 60LO(0) = 182 cm -1, 60LO(qL) = 153 cm -1 as given by experiment [5], while the tight binding model yields 60LO(qL/2) = 169 cm -1 . In actual calculations, the delta function of eq. (2a) was taken to be a Lorentzian with a full width of 2 cm -1 , representing the phonon lifetime. Since wave vectors near qo are weighted heavily in the form factor, the frequency dependence of the spectrum is governed by the LO phonon dispersion and life time, rather than by the spin excitation lifetimes which tend to zero as q approaches qo- (This is not the case for the ferromagnets EuO and EuS, see ref. [71.) The results of these calculations are shown in fig. 1 where the Raman broadline intensity is plotted as a function of co. At high temperatures, the line shape resembles that of EuS [4,7], with a peak at WLO(qL)

S.A. Safran et aL /Raman scattering in EuSe and Eu Te

405

i

3

T=TcTc~~~Tc =4.6K .~_~,D

\;

//\

'

2

T:fK

i

~ o [ r a

0

2

4 T (K)

AF-Tr ~40

I.TK

I

160

(crn-j)

180

169

Fig. 1. Raman broad line intensity (arbitrary units) vs. to (Raman shift in cm -1) for EuS¢, calculated using eq. (2). The calculated curves are for room temperature (paramagnetic phase) and for T = Tc = 4.6 K. The peak at 167 cm -1 is due to spin fluctuations of wave vector qL/2. The inset shows the pertinent experimental results, displaced vertically for clarity (see ref. [3]).

and a width comparable to the dispersion of the LO phonon branch. However, at Tc, the spin fluctuations with wave vectors near q0 increase, giving rise to a new peak in the spectrum at o~LO(qL/2). The intensity of the peak at coLO(qL) also increases, since there are also large fluctuations near qL (associated with the two-sublattice phase, almost degenerate in energy with the four-sublattice phase). These calculations have been performed using the mean field forms for the correlation functions. Although both Raman [15] and M6ssbauer [18] data indicate that the transition at 4.6 K is first order, the qualitative agreement between theory (which assumed a second-order transition) and experiment as shown is fig. 1 indicates the presence of large fluctuations at the spin ordering wave vector qL/2. The larger intensity predicted by the mean field calculation, is due to the assumption of a second-order transition with large spin fluctuations at both qL and qL/2. The sharp feature observed in the Raman spectrum at coLO(qL) for T > T c [19] supports the assumption of additional spin fluctuations at qL. Below the transition, the broadline is partially quenched and sharp lines corresponding to coLO(qL/2 ) (four sublattice = AF-I), wLO(2qL/3) (three sublatrice = Ferri), and ~LO(qL) (two sublattice = AF-II), are observed as shown in fig. 2. The assignment of

\

Ferri

176

AF-I

~

I

I

120

140

I I

I

160 180 Roman shift (cm"~)

14.2 K 200

Fig. 2. Observed zero-field Raman spectra in EuSe for right angle scattering. The Raman frequencies are indicated for the four sublattice antiferromagnetic phase (4.2 K), the three sublattiee ferrimagnetic phase (2 K), and the two sublattiee antfferromagnetic phase (1.7 K). These frequencies correspond to WLO(qL/2), COLO(2qlJ3) and COLO(qL) respectively, in agreement with the one-phonon-one-spin mechanism (see refs. [3,7]). The magnetic phase diagram of EuSe is shown in the inset. For a discussion of the experimental details see ref. [ 3 ].

these lines [3] is in agreement with the predictions of the one phonon-one spin mechanism (see table 3 of ref. [7]). In contrast to the linear spin Raman mechanism, a Raman process quadratic in the spin would give rise to a sharp line at ¢OLo(qL) in the foursublattice phase, and a sharp line at W[,o(0 ) in the two-sublattice phase. These lines have not been observed, indicating that the one-spin mechanism is dominant.

406

S.A. Safran et al. / Raman scattering in EuSe and EuTe

Eq. ( l c ) indicates that the intensities o f these sharp lines are proportional to the square of the staggered magnetization. Thus, the sharp line intensity can be used to measure directly the temperature and magnetic field dependence o f the order parameter in all the magnetic phases of EuSe. Of particular interest would be the determination of the first or second order nature o f the phase transitions for T < 4.6 K and H > 0, since there is as yet no theory which accurately accounts for the complete phase diagram of EuSe.

4. EuTe - sharp line spectrum In contrast to the situation in EuSe, the low temperature (T < T N = 9.6) Raman spectrum of EuTe is complex and has been found difficult to interpret. Only the spectra reported in ref. [5] have been interpreted as containing a sharp line at ~LO(qL) in the (H = 0) two-sublattice phase of EuTe. In zero field, the temperature dependence of this sharp line can be used to infer the first- or second-order nature of the phase transition at Tar, as was done for EuSe [15]. In addition to probing the H = 0 effects, the sharp line Raman intensity of EuTe can be used to measure the staggered magnetization near the (second order) spin flop to paramagnetic transition which occurs at H = He(T). In particular, near He(T), N varies as (Hc~(T) - H2) ~ [10]. Recent renormalization group calculations have shown that there are three regions o f interest each having different value for/3(d, n) : (i) for T ~ 0, quantum effects which introduce time dependence in the spin operators predict/3 = /3mean field = 1 [12], and the Raman intensity should therefore be a linear function o f H2; (ii) for T - ~ T N and H = 0 (neglecting anisotropy),/3 =/3(d = 3, n = 3) = 0.38 [11]; (iii) for 0 < T < TN,/3 =/3(d = 3, n = 2) = 0.36 [9], since near the spin flop to paramagnetic transition only two components of the spin show critical fluctuations (neglecting anisotropy). Thus, the sharp line intensity should be sensitive to the changes in the dimensionality as reflected in the values of/3 in these regions as well as to the crossover effects which arise as one goes from region to region. EuTe is o f special interest in this regard, in that an experimentally accessible value of Hc(0) occurs at 72 kG. The predictions of quantum crossover from/3 = ½ at T = 0

to/3 = 0.36 near Hc(T) can therefore be tested by measurements of the sharp line in EuTe. In conclusion, we have shown that the Raman excited LO phonons are a useful probe of spin ordering and fluctuations in the europium chalcogenides. A single one p h o n o n - o n e spin mechanism accounts for b o t h the broadline and sharp line spectra observed in the magnetic phases of the europium chalcogenides.

Acknowledgement The authors wish to acknowledge Prof. M.S. Dresselhaus for many useful comments and suggestions.

References [1] R. Griessen, M. Landor and H.R. Ott, Solid State Commun. 9 (1971) 2219. [2] R.P. Silberstein, L.E. Schmutz, V.J. Tekippe, M.S. Dresselhaus and R.L. Aggarwal, Solid State Commun. 18 (1976) 1173. [3] R.P. Silberstein, V.J. Tekippe and M.S. Dresselhaus, Phys. Rev. B16 (1977) 2728. [4] R. Merlin, R. Zeyher and G. Giintherodt, Phys. Rev. Lett. 39 (1977) 1215. [5] G. Giintherodt, Proc. 13th Int. Conf. Physics Semiconductors, ed. G.F.G. Fumi (Tipografia, Marves, Italy, 1977) p. 291. [6] A. Schelgel and P. Wachter, Solid State Commun. 13 (1973) 1865. [7] S.A. Safran, G. Dresselhaus and B. Lax, Phys. Rev. B16 (1977) 2749. [8] Y. Ousaka, O. Sakai and M. Tachiki, Solid State Commun. 23 (1977) 589; O. Sakai and M. Tachiki, J. Phys. Chem. Solids 39 (1978) 269. [9] S.K. Ma, Modern Theory of Critical Phenomena, (Benjamin, Reading, MA, 1976). [10] S.A. Safran, Ph.D. thesis, MIT, January 1978. [11] M.E. Fisher, AIP Conf. Proc. 24 (1975) 273. [12] J.A. Hertz, Phys. Rev. B14 (1976) 1165. [13] An analysis of the Raman tensor under the combined operations of time reversal and Hermitian conjugation shows that only the antisymmetric (eix eys - eyiesx ) components of the Raman tensor are expected to be nonzero for the one phonon-one spin process in the limit that the phonon energy is neglected (off resonance) (see also refs. [4,8,10]). This is in contrast to our previous results of ref. [7] where only the time reversal symmetry of the Raman tensor was considered. [14] P. Griinberg, G. Giintherodt, A. Frey and W. Kress, Physica 89B (1977) 225.

S.A. Safran et al. /Raman scattering in EuSe and Eu Te

[ 15] The temperature dependence of the broad line intensity in these materials is discussed in ref. [10] and in S.A. Safran, R.P. Silberstein, G. Dresselhaus and B. Lax, Solid State Commun., to be published. [16] W. Marshall and R.D. Lowde, Rep. P~og. Phys. 31 (1971) 705.

407

[17] L. Passel, D.W. Dietrich and J. Als-Nielsen, Phy~ Rev. B14 (1976) 4897. [18] G. Petzich and T. Kasuya, Solid State Commun. 8 (1970) 1625. [19] R.P. Sflberstein, J. Magn. Magn. Mat. 11 (1979).