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Electron resonance in the insulating spin glass Eu0.4Sr0.6 S
A. Deville, C. Arzoumanian, B. Gaillard, C. Blanchard, J.P. Jamet, H.
Maletta
To cite this version:
A. Deville, C. Arzoumanian, B. Gaillard, C. Blanchard, J.P. Jamet, et al.. Electron resonance in the insulating spin glass Eu0.4Sr0.6 S. Journal de Physique, 1981, 42 (12), pp.1641-1646.
�10.1051/jphys:0198100420120164100�. �jpa-00209361�
Electron resonance in the insulating spin glass Eu0.4Sr0.6S
A. Deville, C. Arzoumanian, B. Gaillard, C. Blanchard
Université de Provence, Département d’Electronique (*), Centre de St-Jérôme, 13397 Marseille Cedex 13, France J. P. Jamet
Laboratoire de Physique des Solides (**), Université Paris-Sud, 91405 Orsay, France and H. Maletta
Institut für Festkörperforschung, Kernforschungsanlage Jülich, 5170 Jülich, F.R.G.
(Reçu le 17 mars 1981, accepté le 11 août 1981)
Résumé. 2014 Nous avons étudié la résonance électronique de Eu2+ dans un échantillon monocristallin du verre
de spin isolant Eu0,4Sr0,6S entre 1,4 et 300 K. A haute température le modèle d’Anderson appliqué à la raie rétrécie
par échange fournit J1/k = 0,1 K entre les plus proches voisins Eu2+. Lorsqu’on abaisse la température, on observe
en dessous de 10 K un élargissement de la raie et un déplacement de son centre vers les champs faibles. Cependant
l’effet d’élargissement est moins prononcé en dessous de T = 2,3 K, valeur voisine de la valeur T g = 2,2 K obtenue
par extrapolation de mesures optiques. La raie reste lorentzienne même en dessous de la température de gel. Le
modèle de Salamon ne peut expliquer nos résultats expérimentaux. A 1,4 K, la dépendance en fréquence du champ
de résonance entre 9 et 9,6 GHz est assez bien décrite en supposant l’existence d’un champ interne Hi ~ 1 kG.
Abstract. 2014 The electron resonance on Eu2+ in a single crystal of the insulating spin glass Eu0.4Sr0.6S has been
studied between 1.4 and 300 K. Anderson’s treatment of the exchange-narrowed high temperature line gives J1/k = 0.1 K between n. n Eu2+. When lowering the temperature, a broadening of the line and a shift of its centre towards low fields are observed below 10 K. The broadening effect becomes less temperature dependent below
T = 2.3 K, which is close to the value Tg = 2.2 K extrapolated from optical measurements. The line remains Lorentzian even below the freezing temperature. Salamon’s model cannot explain our experimental results. At 1.4 K,
the frequency dependence of the resonance field between 9.0 and 9.6 GHz is fairly well described by assuming the
existence of an internal field Hi ~ 1 kG.
Classification
Physics Abstracts
75.30 - 76.90
1. Introduction. - The term spin glass first desi-
gnated magnetic alloys (CuMn, AuFe ... ) with a ran-
dom distribution of spins coupled by the long-range oscillating RKKY interaction. As it was known that the frustration effect associated with the existence of competing interactions played an essential role,
it was natural to think that insulating materials could also exhibit spin glass properties. EuxSr 1 - xS was the
first example of such materials and has been extensively
studied. Measurements made on powder samples [1]
indicate that, when x > 0.65 it is ferromagnetic at low
temperature (EuS is ferromagnetic, with Tc = 16.7 K)
(*) E.R.A. 375.
(**) L.A. 2.
[2], while for 0.13 x 0.65 (1) [1] one observes the
so-called spin glass phase. Its spin glass properties are thought to originate from the simultaneous existence of -the short-range ferromagnetic (Jj) and antif érro- magnetic (J2) exchange interactions between nearest and next-nearest neighbour Eu2+ ions respectively.
Although some progress has been made since the
pionering work by Owen et al. [4], the description of
the electron resonance of spin glass systems is still
largely phenomenological. We think that the study
e) Tholence has interpreted experimental results in dilute
EuXSrI _xS single crystals by supposing the existence of the spin glass phase for 0.05 x [3]. One of us (H. M.) has proposed to well distinguish between the spin glass phase and the superparamagnetic phase (0.13 x 0.65 and x 0.13 respectively, measured in
powder samples).
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198100420120164100
1642
of the resonance in EuxSr 1 - xS is promising, since complications associated with the presence of conduc- tion electrons are absent (the resonance line is not
distorted due to a small skin depth, and is not broa-
dened by spin-lattice relaxation even at 300 K since
Eu2+ is in a S state), and because it is possible to vary the europium concentration from the dilute case to the pure ferromagnetic EuS. This paper deals with the electron spin resonance of the rather concentrated
Euo.4Sro.6S spin glass. We describe the system and the
experimental conditions in sections 2 and 3 respec-
tively ; the experimental results are presented in
section 4 and discussed in section 5.
2. The systerm - EuS has the NaCI f.c.c. structure ; each europium is surrounded by 6 sulfur ions, 12 n.n
and 6 n.n.n europium ions, at 2.98, 4.21 and 5.96 À respectively. In EuxSr 1 - xS, Eu and Sr ions occupy
randomly the sites of the same f.c.c. sublattice.
E.P.R. studies of europium diluted in the diama-
gnetic host SrS indicate that in such compounds euro- pium is in the divalent state (4f’ ground configuration, 8S ground term, J = 7/2 ground multiplet). Europium
has two main natural isotopes : 1 s 1 Eu (natural occurrence and 15 3 Eu (natural occurrence
The ferromagnetism of EuS is attributed to the
predominance of the ferromagnetic interactions bet-
ween Eu2+ nearest neighbours. From a recent scatter- ing study in EuS by Bohn et al. [6], one knows that J 1 /k = 0.221 + 0.003 K, J 2/k= -O.lOO:tO.OO4 K.
The freezing-temperature Tg for the same crystalline sample Euo.4Sro.6S is 1.55 K determined from the
magnetization in the presence of a low-frequency vanishing magnetic field in the low-frequency limit [7] (2) ; Tg is frequency-dependent, and its value at 10 GHz extrapolated from optical measurements up to 10 MHz [7, 9] is 2.2 K.
3. Expérimentât conditions. - Measurements were
made on a Euo,4Sro.6S single crystal, at X-band, using
a superheterodyne single klystron spectrometer [10],
between 1.4 and 300 K. The sample was placed in a
small teflon holder inserted in a quartz tube; bet-
ween 1.4 and 4.2 K, the sample was placed in a cylin-
drical brass cavity (Qu ~ 20 000), inserted in a bath
cryostat and filled with liquid hélium ; the temperature
was measured with a GaAs diode and controlled by
pressure measurements. Experiments between 3.7 and 300 K were possible using a gas-flow cryostat (Oxford Instruments E.S.R. 9); the quartz tube and sample were then in a cylindrical cavity (Qu = 13 000) ;
the temperature was known from a thermocouple placed in the vicinity of the sample, and minor correc-
(2) it has been reported that in powder Euo.4Sro,6S, in the low-
frequency limit Tg = 1.92 K [8].
tions were eventually made using a GaAs diode
temporarly placed in the same conditions as the
sample. We recorded the derivative of the absorption y’(H ) ; the field was measured with a precision gauss- meter (Bell 660), and a control was made with DPPH.
Since the observed line had a large width, precise
determination of the linewidth required particular
care in the recording of the extrema of the absorption
derivative. We had first to eliminate two problems originating from the fact that we used a concentrated
sample, with a high angular momentum J value, at low temperature. Our first experiments clearly demonstrat- ed that for samples with an arbitrary shape, the line position and width became strongly anisotropic as the temperature was lowered. For instance, we obtained
for a given sample and two arbitrary orthogonal
directions AHpp = 940 G, Ho = 3 730 G and
respectively, at T = 10 K. We attributed this to the effect of dipolar forces phenomenologically described by the magnetization correction factor [11]. We
realized therefore a spherical sample (§§ - 0.8 mm)
and successfully observed that the line was then iso- tropic within experimental accuracy. In the second
place, at the lowest temperatures we observed that,
even with this small sphere, critical coupling of the cavity could lead to a distortion of the line ; we thus
partially detuned the cavity and controlled that this
detuning was always sufficient to avoid these dis- tortions.
4. Experimental results. - The resonance signal
consists of a single line : at room temperature the maximum of absorption was obtained for a value Ho corresponding to a ratio
Pr Ho
Pe Ho = 2.012 + 0.006, ,hereafter denoted g. The width between the extrema of the derivative was ~Hpp = 720 + 10 G. Neglecting
a slight asymmetry arQund Ho, the line can be consi-
dered as the derivative of a Lorentzian line, as shown
in figure 1, where we have plotted the reduced ampli-
1 d 1
Fig. 1. - Reduced amplitude
/ É’ versus
(H - HO) for Euo.4Sro.,,SYM Hpp/
(v = 9 280 MHz) at different températures, after the small correc-
tions described in section 4. Lorentzian (-) and Gaussian ( ----) lineshapes are drawn for comparison.
tude y’/yM versus 2(H - HO)IAHPP’ When the tempe-
rature was lowered, the line was observed to shift
towards low fields and simultaneously to broaden.
The temperature variation of (AHPP - I1Hpp(oo))
and Ho - where I1Hpp(oo) = 720 G is the room-
temperature width - are plotted in figures 2 and 3.
A question arose at the lowest temperatures because the r.f. field is linearly polarized and the line is broad ;
the experimental signal may then contain, in addition
to the main resonance signal induced by the left cir-
Fig. 2. - Temperature dependence of (àhpp - AHPP(oo» in log-
log plot, for Euo,4Sro.6S. AHpp(oo) = 720 G is the room temperature width (v = 9 280 MHz).
Fig. 3. - Temperature dependence of the resonance field Ho for Euo.4Sr,0.6S (v = 9 280 MHz).
cular component of the r.f. field (hereafter called the
true signal for brevity), a small contribution from the
right circular component. If meaningful results are
desired for the line position, width and shape, it is
necessary to determine the effect of this contribution.
We tried to obtain the true line from the experimental
one by subtracting the unwanted circular component.
This undesired contribution was guessed in two steps : the first point was to know the resonance frequency.
We will see later on that measurements of the reso- nance field at different frequencies below 7g are well
described by the relation hw = gPe(HO + Hi), where Ho is the applied field and H; an internal field. If the
magnetic field Ho is reversed, is the resonance field
- (Ho + Hi) or - (Ho - Hi) ? The answer does not
seem a priori obvious in a spin glass. In order to get an
unambiguous answer, we first recorded the resonance
spectrum from low to high fields, brought back the field to a low value, and changed its sign ; a new spectrum
was then made at the same temperature (1.4 K) and the
resonance field was found to be approximately
- (Ho + Hi). We then used the fact that
(d If) = 0, and made the assumption that dH H=o
= 0, and made the assumption that
the true line is symmetrical around Ho. We found
that the correction needed is rather small indeed : at 1.4 K, this correction leads to a 30 G broadening
and to a 20 G shift towards high fields ; for T > 3 K,
dHpp and Ho need no correction. In figure 1 we
have plotted the line obtained after subtraction of the unwanted resonance signal, for T = 1.4, 1.9, 2.2, 3 and 4.2 K : for H > Ho no correction was
needed and the line fits very well a Lorentzian at 1.4 K
as well as at 4.2 K ; for H Ho, figure 1 shows that
there remains a slight departure from the Lorentzian
shape ; it is difficult to say whether this departure is significant because of the way it was obtained ; how-
ever we can assert that for T Tg the line is certainly
far from Gaussian and we feel this is an important
feature.
We observed no memory effect in these experiments :
we first obtained the above results for Ho and AH by cooling the sample in zero field down to 4.2 K, record- ing the spectrum a number of times at 4.2 K, then cooling the sample in zero field down to 3.9 K, record- ing the spectrum at this temperature, and finally
reached 1.4 K after a number of such small temperature incréments ; in each cooling process zero-field was
achieved by compensating for the remanent field
of the magnet. In a second experiment the sample was
cooled from high temperature down to 1.4 K in a 6 000 G field, and we obtained strictly the same results
for Ho and AH as obtained in the zero-field cooling
process.
At 1.4 K, we made a determination of the variation of Ho versus the angular frequency w of the r.f. field around w° = 9.3 GHz, by measurements at about 9,
203C0
9.3 and 9.6 GHz. The results for Ho are plotted in
1644
Fig. 4. - Frequency dependence of the resonance field Ho at 1.4 K
for Euo.4Sro.rS in the 9 000-9 600 MHz frequency range.
figure 4, and can be described by the empirical relation
hm = gPe(HO + Hi), where Ho is the applied field,
g = 2.012 is the high temperature value of nw/Pe Ho,
and H; = 998 G. This result differs from that obtained for Cu Mn by Schultz et al. [19] who get
in an experiment where the sample was zero-field
cooled (Z.F.C.) to T Tg; it ressembles that obtained
by Monod and Berthier [20], who get a = 1, in an experiment where the Cu Mn sample was field cooled
(F.C.) to T « Tg. It is possible to understand our
results by noting that, in our experiments, T is never
far less than Tg. One can then think that we are in
a F.C. state even after Z.F.C. if one considers that, just below Tg, the field for resonance is sufficient to
immediately saturate the remanent magnetization (I.R.M. = T.R.M.) by an isothermal process. It would be of course of interest to make similar measurements at lower temperatures in order to test this interpre-
tation.
5. Discussion. - The previous experimental results suggest several comments. The first one concerns the
change of slope in the temperature variation of
(AHpp - AHPP(oo» (Fig. 2); the constancy of AHpp
between 200 and 300 K means that in this region we
are in the usual paramagnetic regime, and that we
observe the usual exchange-narrowed lineshape,
without any broadening due to spin-lattice relaxation,
which is not surprising since we deal with an S state ;
this justifies our choice for taking the room-tempe-
rature value of AH as AHPP(oo). The change of slope
of the linewidth at 2.3 K is significant : it cannot be an
artifact caused by a change of lineshape with tempe-
rature since the line remains Lorentzian, or caused by
the contribution of the line centred at - Ho, because
the corresponding shift is very weak even at 1.4 K.
We think that it reflects the freezing of the spins, and
this temperature of 2.3 K agrees well with the 2.2 K
Fig. 5. - Temperature variation of -
(v = 9 280 MHz).
value determined by extrapolation from optical mea-
surements (see section 2).
Although the most interesting region is the low- temperature one, it is useful to hrst discuss the origin
of the width AHpp(oo) at high-temperature. We first
determine what would be the linewidth if no exchange
were present (dipolar broadening) ; we can neglect the hyperfine interaction, which is negligible compared to
the dipolar coupling. The hamiltonian would then consist of the Zeeman and dipolar terms. We note
that since the Eu2+ concentration x is greater than o.l, the dipolar line should be Gaussian with a width
proportional to x1/2 [12] ; the linewidth will then be known if one knows its second moment M2 which
is easily determined using Van Vleck’s method [13].
In angular frequency units :
where 0 ik is the angle between the direction of the
applied field H and the vector rjk joining spin j to spin k. This result is established using the secular part of the dipolar term, which is necessary when the non-
secular part does not contribute to the linewidth
(if the non-secular part contributed, the second moment should be multiplied by the factor 10/3) [13].
Since the terms in (1) are proportional to I/r6, and
because there are twice as many n.n as n.n.n ions for a given Eu2+ ion, we can determine M2 by sum- ming up the contributions of the 12 n. n only. When H
is parallel to a [001] axis, we thus obtain :
where r is the distance between n.n ions. The width
between the extrema of the derivative of the absorp-
tion corresponding to dipolar coupling would then be
and for x = 0.4, (AHpp)diP = 2 660 G. The observed line is Lorentzian, with ANpp(oo) = 720 G, which
suggests a moderate narrowing by exchange.
We now consider the narrowing of the dipolar broadening using Anderson’s model [14]. The width
~03C9 of the exchange-narrowed absorption line, expres- sed in angular frequency units is approximately given by :
In this expression 03C9d = M2 ; We is related to the part M4 of the fourth moment which depends on the exchange coupling ; using the linewidth of the deriva- tive of the absorption line in field units, we obtain :
In our case úJe/Y = 2 840 G. Since we/y ~ Ho, we
consider that the non-secular part of the dipolar coupling contributes to the second moment [14];
its value and that of úJe have to be multiplied by 10/3 : úJe/Y = 9 460 G. We calculated M4 for HIII 001 |, considering the 12 n.n only; writing the exchange hamiltonian between to n.n - 2 JI Si Si
we finally obtain :
We finally find Jl/k = 0.1 K in fairly good agreement with results from Bohn et al. [6].
As the exchange energy is of the order of the Zeeman energy, the line must be isotropic [15] as experimen- tally observed. ,
We now discuss the low-temperature behaviour.
Since the line shifts and broadens while remaining nearly Lorentzian even at T Tg, the simplest phenomenological description for the beha-
viour of the transverse components M ± of the magne- tization uses the following modified Bloch equation :
where the first term describes the evolution in the free
spin case, and where T ± are complex quantities : I- ± = y ± iw ’; y is the half-width and co’ the shift of the resonance. The next step should then be to
change for instance the concentration in order to see
whether (7) is still valid and, if it is true, to see how y and 0)’ vary in order to relate them to microscopic
quantities. Salamon [16] claimed that it is possible
from electron resonance to establish, though indirectly,
the existence of a freezing of all the spins at a given temperature. We think it useful to discuss briefly
Salamon’s treatment : we first notice that, in the problem of ferromagnetism, Mori and Kawasaki [17]
established the following approximate relation for the Fourier components Mk (a = 0, ± ) of the magne- tization :
where w: is a real quantity which goes to zero with the exchange interaction, and rf the Fourier transform of a correlation function expressing the fact that the torque acting on the spins fluctuates around the
precessional motion. Salamon uses the fact that in a
spin glass the exchange interaction still commutes with the total spin, to assume that the treatment of
Mori and Kasawaki still holds, and he writes equa- tion (8) for the total magnetization M, supposing
that mi = 0; this leads therefore to equation (7), Ta having now a precise microscopic content : it is the Fourier transform of a correlation function. Salamon determines T « taking a correlation function of rectan-
gular shape (width = i). Under the condition
yHo i « 1, it can then be easily shown that the ratio of the linewidth over the shift, AHPP HO(oo) - HO(T)’o( T)’ , is proportional to 03C4-1 ; according to Salamon 03C4-1 - 0
when T --> Tg. The variation of this ratio for
Euo.4Sro.6S is given in figure 5. We observe that this
ratio does not go to zero when T --+ Tg ; one could
think that this comes from the fact that when T - Tg,
the condition yHo r « 1 is no longer verified ; this
however must be rejected since the experimental line
remains Lorentzian. We conclude that the disagree-
ment between Salamon’s model and our experimental
results stems from the fact that there really exists no justification for Salamon’s assumptions.
6. Conclusion. - The spin glass Euo,4Sro,6S has
been investigated by electron resonance between 300 and 1.4 K. At room-temperature the line is purely
Lorentzian and a simple calculation following Ander-
son’s model shows that the exchange energy is of the order of the Zeeman energy ; supposing a « 10/3
effect », we get J1/k = 0.1 K, in fairly good agreement with the usual value Jllk = 0.2 K taken for the
exchange integral in EuS.
On lowering the temperature, we observe below 10 K a broadening of the line, and a shift of its centre towards low fields. Moreover the rate of the linewidth variation with temperature decreases for T 2.3 K.
This temperature fairly well agrees with Tg = 2.2 K extrapolated from optical measurements. Such beha- viour has already been reported in manganese alu-
minosilicates [18]. It is noteworthy that the line remains
nearly Lorentzian even below Tg. This means that, the
