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Thermal dependence of the longitudinal spin fluctuations in YMn2
J. Deportes, B. Ouladdiaf, K.R.A. Ziebeck
To cite this version:
J. Deportes, B. Ouladdiaf, K.R.A. Ziebeck. Thermal dependence of the longitudinal spin fluctuations in YMn2. Journal de Physique, 1987, 48 (6), pp.1029-1034. �10.1051/jphys:019870048060102900�.
�jpa-00210510�
Thermal dependence of the longitudinal spin fluctuations in YMn2
J. Deportes (*), B. Ouladdiaf (*) and K. R. A. Ziebeck (**)
(*) Laboratoire Louis-Néel, C.N.R.S., 166 X, 38042 Grenoble Cedex, France (**) Institut Laue-Langevin, 156 X, 38042 Grenoble Cedex, France
(Reçu le 19 dgcembre 1986, accepté le 17 février 1987)
Résumé. 2014 En dessous de 100 K, le composé YMn2 s’ordonne antiferromagnétiquement avec une structure hélimagnétique à longue période. La transition à l’état paramagnétique est du premier ordre accompagnée
d’une importante réduction de volume de 5 %. Au-dessus de TN, la susceptibilité magnétique croît avec la température. La substitution de Mn par 10 % d’Al supprime la transition du premier ordre et la variation
thermique de la susceptibilité devient de type Curie-Weiss. L’anomalie de volume observée à TN a été associée à la disparition du moment magnétique du manganèse et les propriétés dans l’état paramagnétique sont
caractérisées par de fortes fluctuations longitudinales. Les propriétés magnétiques du composé Y(Mn0,9Al0,1)2 correspondent à celles d’un système localisé. La diffusion paramagnétique de neutrons polarisés en fonction de
la température jusqu’a 300 K a été étudiée sur les deux composés, en utilisant la technique d’analyse de polarisation. Les résultats obtenus montrent que le composé YMn2 présente une diffusion paramagnétique large et renforcée autour des vecteurs de diffusion correspondant aux raies antiferromagnétiques de l’ état
ordonné. L’amplitude de la diffusion, c’est-à-dire la composante longitudinale des fluctuations, augmente avec la température. Le composé YMn2 représente un excellent système pour étudier l’antiferromagnétisme
itinérant. Dans le cas du composé Y (Mn0,9Al0,1)2 la diffusion paramagnétique devient large et décroît quand la température croît: comportement analogue à celui d’un système localisé.
Abstract. 2014 Below 100 K, YMn2 orders antiferromagnetically with a long period spiral structure. The transition to the paramagnetic state is first order accompanied by a 5 % reduction in volume. Above
TN the uniform susceptibility increases with temperature. The addition of 10 % Al suppresses the transition temperature and the susceptibility becomes Curie-Weiss. On the basis of bulk measurements it has been
proposed that the volume change in YMn2 is associated with the collapse of the Mn moment and that the
paramagnetic properties are characterized by strong longitudinal spin fluctuations. The magnetic properties of Y(Mn0.9Al0.1)2 are believed to be of a local nature. Using polarized neutrons and polarization analysis the paramagnetic scattering from the two compounds has been investigated as a function of temperature up to 300 K. The results obtained on YMn2 reveal substantial scattering at all temperatures which remains strongly
enhanced about the staggered antiferromagnetic wave vector. Moreover the amplitude of the long wavelength components of the spin fluctuations increases with increasing temperature. Therefore YMn2 represents an excellent system for studying itinerant antiferromagnetism. In the case of Y(Mn0.9Al0.1)2 the enhanced scattering becomes weaker as the temperature is raised as expected for local behaviour.
Classification
Physics Abstracts
75.20
1. Introduction.
The importance of spin fluctuations in characterizing
the thermal properties of transition metal paramag-
nets has recently attracted considerable attention. In
general transverse fluctuations (angular variation of the magnetization density) drive the order-disorder transition. Although this is similar to Heisenberg systems in which the moments are localized detailed differences occur for itinerant magnets. These differ-
ences are revealed in the magnitude, wavevector and
energy dependence of the spin density-spin density
correlation function (S (0, t ). S(q, t». In the case
of weak itinerant magnets (small moments and low ordering temperatures) longitudinal (amplitude)
fluctuations are expected to characterize the thermal
properties in the paramagnetic phase. As the wave
functions are delocalized mode-mode coupling [1]
enhances the long wavelength components of the spin fluctuations. This is not surprising, since in the ground state collective excitations occur only in a
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019870048060102900
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small part of the Brillouin zone around the centre.
The relative importance of the one electron excita- tons depends on the nature of the band structure
and in particular on the bandwidth. Moriya [2] has
shown that if the mean square local amplitude of the spin fluctuations (S2 ) increases approximately linearly with temperature then the susceptibility
above T, follows a Curie-Weiss law. This then leads to a natural explanation of the Rhodes-Wohlfarth ratio in which the paramagnetic moment A p obtained
from the Curie constant is, in the case of weak itinerant magnets, larger than the ground state
value. Magneto-volume effects also provide informa-
tion regarding the importance of spin fluctuations since a longitudinal component produces an expan- sion of the lattice above Tc. However the most direct
technique for establishing the presence and import-
ance of spin fluctuations is provided by neutron scattering which enables the spatial and temporal dependence of ( S (0, t ) . S (q, t ) ) to be established.
If polarized neutrons and polarization analysis are
used the paramagnetic scattering can be placed on
an absolute scale and a qualitative comparison with theory made. Neutron measurements on a wide range of transition metals and compounds have
confirmed that the long wavelength spin fluctuations spectrum is enhanced [3]. In the case of MnSi [4]
and «Mn [5] the presence of amplitude fluctuations
increasing with temperature have also been ident- ified. Presented here are the results of a polarized
neutron study of the spin fluctuations in an antifer-
romagnetic system Y (Mnl - xAlx)2 which as a func-
tion of Al content changes from itinerant to localized
behaviour.
2. Physical properties.
Below 100 K, the cubic Laves phase compound YMn2 orders helimagnetically with a complex spin arrangement which has a very long period of modu-
lation (400 A) [6]. The moment per manganese atom is 2.7 ¡.LB at 4 K. The transition at the Neel tempera-
ture is first order with a large temperature hysteresis
of 20 K accompanied by a giant volume change of
about 5 % [7]. Above TN the magnetic susceptibility
increases with temperature and the thermal expan- sion coefficient is strongly enhanced [8]. These prop- erties are consistent with itinerant electron magnet- ism in which the large reduction in volume at
TN is associated with a collapse of the Mn
moments [9]. The substitution of manganese by
aluminum suppresses the Neel temperature and the spontaneous volume magnetostriction disappears for
x > 0.1 whereas the paramagnetic susceptibility be-
comes Curie-Weiss. On the basis of N.M.R.
measurements at 1.4 K Shiga [10] concluded that the
Mn moment remained constant with Al content.
Polarized neutron measurements have been carried out on a pure sample of Mn2Y and a sample
containing 10 % Al for which the bulk measurements indicate different behaviour.
3. Polarized neutron measurements.
The paramagnetic scattering was determined using polarized neutrons and polarization analysis avail-
able on the D5 triple axis spectrometer which is
situated on the hot source at the H.F.R. in Grenoble.
Details of the experimental arrangement were simi- lar to those reported previously [11]. The final wavelength was fixed at 0.84 A (112 meV) and the
energy resolution of the spectrometer, determined using a vanadium sample, was ± 28 meV which is approximately three times the observed Neel tem-
perature of YMn2. The powder samples of vol-
ume 10 cc were sealed in an aluminium can which
were attached to the second stage of a Displex closed cycle refrigerator. A clean measurement of the
paramagnet scattering was obtained by determining
the difference of the spin flip count obtained with the incident neutrons polarization parallel and per-
pendicular to the scattering vector. In the case of YMn2 measurements were made at 120, 200 and 300 K and for Y (MIlo.9Alo.l)z at 10, 200 and 300 K.
At each temperature a Bragg scan was carried out using the non spin-flip count (Fig. 1). The para-
magnetic scattering was placed on an absolute scale by normalization using the (111) nuclear Bragg intensity. An effective moment u per manganese
Fig. 1. - The powder diffraction pattern obtained at 300 K for YMn2l using 0.84 A neutrons.
atom was obtained by integrating the observed scattering throughout a volume defined by an inverse
atomic radius i.e. Qo = / 6 ?T B 1/3
where ,03A9 is the atomic radius i.e. 60 = 6 7T 2 )111 Q where d2 is the
atomic volume, namely
where
where f (Q) is the Mn2 + form factor and A is the energy resolution of the spectrometer, A = +
28 meV. However owing to the limited data below
1.5 A-1 it was decided also to Fourier transform the data and carry out a real space integration of the
moment as a function of radial distance.
where p (r) is the magnetization density at r.
This analysis produced a moment at a radius
corresponding to essentially half the Mn-Mn separ- ation which was in agreement with the value ob- tained from the reciprocal space integration.
4. Results.
4.1 YMn2. - Bragg scans carried out at all three temperatures confirmed that the specimen was single phase and had the Laves phase MgCU2 structure with
a = 7.681 A. The paramagnetic scattering was deter-
mined at different wave vectors between 0.2 A-1
and 3 A-1 remote from any nuclear Bragg peaks.
For these measurements the spectrometer was set in the elastic positions with a window of ± 28 meV (Fig. 2). In the forward direction the observed level of scattering was low in agreement with observed uniform susceptibility. At finite wavevectors the
scattering was strongly peaked at positions corre- sponding to antiferromagnetic Bragg peaks below TN.
On raising the temperature to 200 K (- 2 TN) the scattering remained strongly enhanced around the
same wave-vector. On warming to 300 K (- 3 TN )
the enhanced scattering around the antiferromagne-
tic wave vector was found to increase significantly
with temperature. The correlation length which is
related to the width (F.W.H.H.) of the enhanced
scattering cannot be determined unambiguously
Fig. 2. - The wave vector dependence of the paramagne- >
tic scattering from YMn2(M2(Q) f 2(Q)) observed at
120 K, 200 K and 300 K.
1032
since a powder sample was used and the scattering
from several magnetic zones overlap.
4.2 Y(Mno.9Alo.l)z. - The single phase nature of
the compound was confirmed by carrying out Bragg
scans at 10, 200 and 300 K. At 10 K the paramagnetic scattering was found to be extremely enhanced at
1.14 A-’ and 1.8 A-’ (Fig. 3). The wave vectors correspond to the positions in the pure compound YMn2 at which the first two antiferromagnetic peaks
are observed below 100 K. Although the peaks in
the spin flip count are extremely intense they are quite broad and correspond to strong correlations
over finite distance e.g. clustering. On the basis of
these data subsequent powder diffractions measure- ments using a high flux unpolarized beam and a
multidetector revealed two very weak peaks. As the temperature was raised to 120 K the two peaks in spin flip scattering became less pronounced with the
enhanced paramagnetic response merging into single peak. On warming to 300 K the scattering became globally peaked around the wave vector 1.55 A-1
but the magnitude had decreased. As the level of enhanced scattering located around the zone centre
decreased with increasing temperature the scattering
at large wavevector out the zone boundary increased.
5. Discussion.
It has been suggested [9] that the large volume change observed in YMn2 at the Neel temperature (100 K) arises from the collapse of the Mn moment.
Current theories [12] concerning magneto-volume
effects e.g. invar are based on the importance of the amplitude of the moment and associated fluc-
Fig. 3. - The wave vector dependence of the paramagne- tic scattering from Y(Mno9Aloi)2 observed at 10 K, 200 K
and 300 K.
tuations. In this manner it is possible to account for
why certain magnets expand or contract on becoming paramagnetic i.e. nickel and iron. However in these
cases the observed volume changes at Tc are
~ 0.2 % much smaller than the 5 % change observed
in YMn2. It is not clear at present, what change in
the size of moment is necessary to produce the
observed volume changes in 3d metallic magnets.
The uncertainty arises from the definiton of a
moment in the paramagnetic phase which is not unambiguous owing primarily to the relative import-
ance given to the quantum fluctuations. In systems such as NiS the situation is more transparent. It has
been suggested by Mott [13] that the first order transition at 210 K from antiferromagnetism to para-
magnetism with an accompanying volume change
arises from a total collapse of the Ni moment
1.7 AB- Paramagnetic scattering measurements on
NiS using polarized neutrons and polarization analysis did not reveal significant intensity thus confirming Mott’s suggestion [14]. Similar measure-
ments on the chemically disordered invar compound Fe3Pt [15] revealed substantial scattering indicating
that only a small moment change is necessary to
produce the observed volume anomaly. The present study on YMn2 also revealed substantial scattering corresponding to a moment per Mn atom of
1.7 u B above TN indicating that the majority of the
moment persists into the paramagnetic phase. Con-
siderable scattering was also observed in the
Y (MIlo.9Alo.l )2 system in which the antiferromagnetic phase had been suppressed by the addition of aluminum. Although the wave vector dependence of
the scattering observed in the two materials YMn2
and Y (MIlo.9Alo.l)2 are similar i.e. enhancement of the long wavelength components of the spin fluctua-
tions about the staggered wave vectors, the thermal variation of the scattering is significantly different.
The thermal variation of the paramagnetic scatter- ing in Y(Mno9Alo 1)2 is consistent with that expected
for a local moment sytem. Although the addition of aluminum suppresses long range antiferromagnetic
order the response observed at low temperatures i.e.
10 K is strongly enhanced consistent with incipient antiferromagnetism. As the temperature is raised the spatial correlations become weaker (Fig. 3) as expected for increased thermal disorder of the spin system. The enhanced scattering decreases with a
corresponding small increase of the low level back
ground thus leading to an amplitude per Mn atom
essentially independent of temperature. The value obtained for the amplitude of the Mn moment i.e.
2.5 ± 0.3 /L B is close to the ground state value.
In the case of Mn2Y, the amplitude of the long wavelength components of the spin fluctuations increase with temperature (Fig. 2), resulting in a
moment per Mn atom which also increases slightly (Table I). Since the long wavelength components of
Table I. - A summary of the principal results obtained
from the paramagnetic neutron scattering measure-
ments for YMn2l
the spin fluctuations occupy only a small volume in
phase space a substantial increase in the amplitude is required to significantly affect the moment i.e. given by equation (2). The thermal increase of the long wavelength components of the spin fluctuations is a
signature of itinerant behaviour. The radial depen-
dence of the scattering observed in YMn2 is shown in
figure 4 for the three temperatures at which the
measurements were made.
The thermal variation of the amplitude of the spin density is of central importance to current theories of finite temperature magnetism. In the case of weak
itinerant magnets (small moments and low transition temperatures) the amplitude of the long wavelength
thermal spin fluctuations are expected to dominate
the thermal properties above Tc. Formally the equal
time correlation function (M_q Mq)o from which
the moment is derived is defined as :
Although it is not possible experimentally to perform this integration in systems comprising
atomic or local moments it is generally sufficient to
integrate up to an energy corresponding to ± 2 kTc
to obtain (M2) . The majority of the weight, in fact,
lies within an energy range ± kTc. For Heisenberg magnets the region of thermal fluctuations is well
separated in energy from the single particle spectrum and all spin fluctuations with wave vectors through-
out the zone participate to the response. The sum
rule L M2(Q) then yields g2,U2 S(S+ 1). This is
Q
not the case for metallic magnets in which the magnetic electrons participate in the Fermi surface.
For such materials the thermal and single particle
Fig. 4. - The radial dependence of the observed para-
magnetic moment M2(r) at 120 K, 200 K and 300 K from YMn2.
spectra overlap in some part of the zone in a manner
dependent upon the band structure. If the exchange splitting of the bands persists above the transition temperature then a small region in E - q space may exist around the zone centre, which is free from single particle excitations ; it is in this region that spin waves may be expected to propagate below TN and the paramagnetic response within the thermal energy range to be enhanced above TN. At large
wave vectors in the zone the correlation function is sensitive to on site fluctuations with a characteristic time scale given by the bandwidth, which is typically
several eV. Consequently the response in this region
is suppressed in the thermal energy range. If the
exchange splitting goes to zero at T, t e single
particle excitations will occupy the entire zone and extend down to zero energy. Under such circumst-
ances the long wavelength fluctuations are also affected by the band degrees of freedom. Since there is no distinct separation between the thermal and
single particle spectrum there is no sum rule for
y M2(q ), except on integration over the bandwidth
q
which yields 1/2 (1/2 + 1 ). Consequently the concept of a moment above TN is not without ambiguity. The ambiguity may be further examplified with reference
to a localized system which has a singlet ground
state. If the excited state is not thermally populated
and the neutron energy transfer insufficient to excite the state then the response will be zero. However if the energy transfer is equal or greater than the
separation in energy of the excited state a moment can be derived. When the integration is confined to
the thermal energy range and the temperature raised
so that the excited state becomes populated then the
observed response would increase with temperature suggesting an increase in the amplitude of the
moment. In such systems the scattering would occur throughout the zone.
Such behaviour is distinct from that expected and
observed in itinerant magnets in which the delocali- zation of the wavefunctions gives rise to an enhance-
ment of the long wavelength spin fluctuations.
Modem theories of metallic magnetism at finite temperature are primarily concerned with the ther- mal part of the spin fluctuation spectrum. Whilst it is
formally difficult to derive a unique expression for a
thermal moment it is also difficult to extract exper-
imentally the thermal part of spin fluctuations from the total spectrum. At low temperatures the Bose factor suppresses the thermal part of the response and only the neutron energy loss part of the spectrum
can be determined
where the first term represents the zero point motion
and the second term the thermal fluctuations. For an
