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Submitted on 1 Jan 1979
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Magnetic phase diagram of CeSb for a field applied along a < 111 > direction
P. Burlet, J. Rossat-Mignod, H. Bartholin, O. Vogt
To cite this version:
P. Burlet, J. Rossat-Mignod, H. Bartholin, O. Vogt. Magnetic phase diagram of CeSb for a field applied along a < 111 > direction. Journal de Physique, 1979, 40 (1), pp.47-50.
�10.1051/jphys:0197900400104700�. �jpa-00208883�
Magnetic phase diagram of CeSb for a
field applied along a 111 > direction
P. Burlet, J. Rossat-Mignod
Laboratoire de Diffraction Neutronique, Département de Recherche Fondamentale, Centre d’Etudes Nucléaires, 85 X, 38041 Grenoble cedex, France.
H. Bartholin
Laboratoire Louis Néel et Service National des Champs Intenses, Centre National de la Recherche Scientifique,
166 X, 38042 Grenoble cedex, France.
and O. Vogt
Laboratorium für Festkörperphysik, Eidgenössische Technische Hochschule, CH-8093 Zurich, Switzerland.
(Reçu le 10 juillet 1978, accepté le 14 septembre 1978)
Resume. 2014 Nous avons déterminé le diagramme de phase de CeSb pour un champ magnétique appliqué selon
une direction 111 > au moyen d’expériences d’aimantation et de diffraction neutronique.
Ces résultats confirment ceux obtenus précédemment pour un champ magnétique appliqué selon une direc- tion 100 > qui ont montré l’existence d’un ordre magnétique tout à fait original décrit par l’empilement de plans (100) ferromagnétiques et de plans ne contenant aucune aimantation.
Abstract. 2014 The magnetic phase diagram of CeSb for a magnetic field applied along a 111 > direction has been determined by means of magnetization and neutron diffraction experiments. The results confirm those obtained previously [1] for a magnetic field applied along a 100 > direction which have established the existence of a quite original magnetic ordering consisting in sequences of ferromagnetic and non magnetized (100) planes.
Classification Physics Abstracts
61.12 - 75.25 - 75.50 C
1. Introduction. - In a previous paper [1] ] the magnetic phase diagram of CeSb was determined by
neutron diffraction experiments with a magnetic field applied along a fourfold axis of the f.c.c. structure.
The magnetic structures of the different phases consist
in square wave structures. The wave vector k = [o, o, k]
takes only rational
values 2n n + 1
2 indicating that then+ _ 1
magnetic cell is commensurate with the lattice.
A strong anisotropy confines the magnetic moments along the k-vector, i.e. a fourfold axis. All the magnetic
structures can be generated by a periodic stacking of ferromagnetic planes with a magnetization parallel Mi or antiparallel MI to the applied field and non
magnetized planes P called paramagnetic planes.
Three types of magnetic structures have been distin-
guished :
- the antiferro-paramagnetic structures (AFP) generated by the two types of ferromagnetic planes
and by paramagnetic planes, as for example the
magnetic structure + 0 - + 0 - [k = (0, 0, 2/3)]
observed just below TN in zero magnetic field ; .
- the antiferro-ferromagnetic structures (AFF)
which contains only ferromagnetic planes, as for example the + + - + + - structure which was deter- mined at low temperature with an applied field ;
- the ferro-paramagnetic structures (FP) generated by ferromagnetic planes Mi and paramagnetic planes.
The most simple example corresponds to the magnetic
structure + + 00 + + 00.
A simple thermodynamic model was used to deter-
mine the magnetic entropy of the paramagnetic planes, the value per cerium ion is S/k = In 2 where
k is the Boltzmann constant.
The problem in this compound is to explain the origin of the large anisotropy and the nature of the planes which have no magnetization. What kind of interactions can stabilize such structures ?
In this paper, magnetic and neutron diffraction measurements performed with a magnetic field applied along a 111 > direction are discussed.
LE JOURNAL DE PHYSIQUE. - T. 40, N° 1, JANVIER 1979
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0197900400104700
48
2. Magnetic measurements. - Magnetization mea-
surements have been performed in static magnetic
fields up to 150 k0e at low temperature as described in [1], at the Service National des Champs Intenses (Grenoble). The field was applied along a ( 111 > axis.
Excepted at 4.2 K, the measurements were done at constant temperature and in decreasing field.
Fig. 1. - Magnetization measured at T = 4.2 K for a magnetic
field applied along a 111 ) direction. The field was decreased from + 150 k0e to - 150 k0e and increased from - 150 k0e to + 150 kOe.
The magnetization measured at T = 4.2 K (Fig. 1)
and the phase diagram (Fig. 2) are characteristic of a
large anisotropy. The ratio of saturated magnetizations
M[ 111
and of the critical fieldsH c[111]
are equal toM[001 ] H,,[l 11] ]
the cosine of the angle between 001 ) and 111 >
directions. Thus the magnetic moments are confined along a 001 ) direction while a large magnetic field
is applied along a 111 ) direction. Moreover as in [2],
a remanent magnetization is observed which disap-
pears at about TN/2 (Fig. 3) and above T = 9 K, the critical fields vary strongly with the temperature because of the existence of magnetic structures containing non magnetized planes. In order to verify
if such planes still exists when a magnetic field is applied along a 111 ) direction we have performed
neutron diffraction experiments.
3. Neutron diffraction results. - The crystal and
the neutron diffraction spectrometer described in [1]
have been used. The [111] axis was put vertical and
parallel to the magnetic field. Taking into account
the misorientation of the crystal, the angle between
the [111] axis and the magnetic field was about one
degree and then Hx > Hy and HZ (Fig. 4). The [111]
reflection was measured to obtain the value of the
ferromagnetic component. The wave vector was determined by scanning the reciprocal lattice along 100 > directions.
Fig. 2. - (H, T) magnetic phase diagram determined by magne- tization experiments for a magnetic field applied along a 111 )
direction. Only the main transition lines are represented. The circles
correspond to the experimental points obtained in decreasing field
and the full lines represent the phase diagram for an applied field along a 100 ) direction where the critical field values have been
multiplied by J3.
Fig. 3. - Thermal variation of the rémanent magnetization in increasing temperature for H = 0. The sample was saturated at
T = 4.2 K by a magnetic field applied along a 111 > direction.
The amplitude values of the harmonics were deduced from the superlattice reflection intensities.
When the field is applied along a ( 111 > direction,
the observed phases are the same as those determined with a field applied along a 100 > direction [1].
In figure 5 we report only the high temperature part of the phase diagram obtained with increasing tempe-
Fig. 4. - Orientation of the magnetic field with respect to the crystal
axes.
rature. With decreasing temperature the same phase diagram is observed except for some hysteresis effects.
When a ferromagnetic component exists, the crystal
has a single domain configuration Kx because of the misorientation of one degree which favours the x-
direction.
If the critical field values determined in [1] ] are multiplied by /3- we can see in figure 5 that the 111 >
and 100 > phase diagrams are quite similar, the
critical field values and the slopes of transition lines
are comparable. This result is in agreement with
magnetization measurements and characteristic of a
very large anisotropy even at high temperatures.
For the FP phases, the analysis of the wave vector
value show that to reach the phase k = 1/2 closer
values than k = 6/11 are possible such as 8/15, ...
and near TN, before the FP phase k = 6/11, a FP phase corresponding to k = 4/7 has been observed.
These results confirm the value k
= 2n n + 1
and thesequence
already observed in [1] when the magnetic field
increases.
In order to precise the nature of the FP phases when
a magnetic field is applied along a 111 > direction
we have investigated in detail the most simple one,
the FP phase corresponding to k = 1 /2. The integrated
intensities of the superlattice reflections measured at T = 14.3 K and H = 35 kûe are reported in table I.
We can deduce that the amplitude of the k = 1/2
Fourier component is Ak = (1.41 + 0.07) ,uB.
Fig. 5. - Magnetic phase diagram of CeSb determined by neutron diffraction experiments in increasing temperature, for a magnetic field applied along a ( 111 > direction (5a) and a 100 > direction (5b). In order to have a direct comparison between the two phase diagrams the magnetic field scale has been divided by J3 for the ( 111 > phase diagram.
50
Table I. - Intensities in mbarn/Ce3 + of the super- lattice reflections corresponding to the FP phase
k = 1/2 for a field of 35 kOe applied along a 111 )
direction at T = 14.3 K.
The ferromagnetic component has been determined
by measuring the weak nuclear reflections [111] and
[311] ; its value is Ao = (1.0 ± 0.05) MB. Therefore,
as the crystal is in a single Kx-domain state, there are ( 100) ferromagnetic planes and in these successive ( 100) planes the moments lie along the [100] direction with
a value given by
The phase IF cannot be determined by neutron
diffraction measurements, but it can take only the
value ± n/4 and the moment value is :
This result corresponds to the FP-structure + + 00 + + 00 with the magnetic moment in the ferromagnetic planes practically equal to the moment
value 2.14 JlB of the cerium free ion.
Any other choice for W gives a magnetic moment
which would exceed the free ion value 2.14 /lB’ such
a solution is impossible and must be excluded. There- fore the combination of the Fourier components k = [0, 0, 0] and k = [1/2, 0, 0] lead to the conclusion that the magnetic ordering corresponds to the FP-
structure + + 00 + + 00 [1]. In the ferromagnetic
(100) planes the moments lie along the [100]-direction
with a value close to the free-ion one ; whereas in the other ( 100)-planes there is no magnetic moment along
the [100]-direction. The problem is to know if these planes are non magnetized planes or if they contain magnetic moments which are confined within the (100) plane. From the magnetization and the neutron results
we can say that the magnetic order in these planes
cannot be ferromagnetic and it must propagate along
the [100]-direction with a wave vector kx = 1/2.
Therefore such magnetic order must give rise to
Fourier components k = [1/2, ky, A-J. However scans performed along the symmetry directions [1/2, 0, k], [1/2, k, 0], [1/2, k, k] have evidenced no superlattice reflection, indicating that any simple antiferromagnetic ordering exists in theses planes. These results lead to the same conclusion as that deduced from [1] : the magnetic ordering consists in a stacking sequence + + 00 + + 00 of ferromagnetic and non magnetized layers along the 100 > direction. This fact is rather
surprising because when a magnetic field is applied along a 111 > direction, it has a large component in the non magnetized layers which would polarize
the cerium moments. Therefore, these planes must
not be considered as disordered but rather as non
magnetized planes. This non magnetic state may be the result of an antiquadrupolar coupling.
4. Conclusion. - Magnetization and neutron dif-
fraction experiments performed on a CeSb single crystal with a magnetic applied along a ( 111 >
direction are in complete agreement with the previous
results [1] obtained when the magnetic field is applied along a 001 > direction. The comparison of the magnetic phase diagrams corroborates the existence of a large anisotropy which confines the moment along
a fourfold axis whatever the field direction. The existence of magnetic structures described by sand-
wiches of ferromagnetic and non magnetized planes pointed out in [1] is confirmed by the observation of no
ordering while a large magnetic field component exists in these planes.
References
[1] ROSSAT-MIGNOD, J., BURLET, P., VILLAIN, J., BARTHOLIN, H.,
WANG TCHENG-Si, FLORENCE, D. and VOGT, O., Phys.
Rev. B 16 (1977) 440.
[2] BARTHOLIN, H., FLORENCE, D., WANG TCHENG-SI and VOGT, O., CeBi : Phys. Status Solidi A 24 (1974) 631; CeSb : 29 (1975) 275.
For more detailed references see reference [1].
