Neutron-scattering studies of a phase transition in the metamagnet FeBr2 under external magnetic fields

Article abstract of DOI:10.1103/PhysRevB.55.11466

Neutron-scattering experiments have been performed on the metamagnet FeBr₂ under external magnetic fields. We find an anomaly in the temperature (T) and magnetic-field (H) dependences of the intensity of the (2,0,1/2) antiferromagnetic Bragg scattering at the temperature T₁(H) at which an anomaly in specific heat has been observed in addition to the anomaly at the Neel temperature T_N(H). We argue that our results are consistent with the theoretical H-T phase diagram of a metamagnet in which the tricritical point decomposes into a critical end point and a bicritical end point. We locate the latter point at T_cr? 10.8 K and H_cr? 1.4 T in this compound.

Full text of DOI:10.1103/PhysRevB.55.11466

PHYSICAL REVIEW B
VOLUME 55, NUMBER 17
1 MAY 1997-I
Neutron-scattering studies of a phase transition in the metamagnet FeBr2
under external magnetic fields
K. Katsumata and H. Aruga Katori
The Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 351-01, Japan
S. M. Shapiro and G. Shirane
Physics Department, Brookhaven National Laboratory, Upton, New York 11973
͑Received 7 October 1996͒
Neutron-scattering experiments have been performed on the metamagnet FeBr2 under external magnetic
fields. We find an anomaly in the temperature (T) and magnetic-field (H) dependences of the intensity of the
͑2,0,1/2͒ antiferromagnetic Bragg scattering at the temperature T1(H) at which an anomaly in specific heat has
´
been observed in addition to the anomaly at the Neel temperature TN(H). We argue that our results are
consistent with the theoretical H-T phase diagram of a metamagnet in which the tricritical point decomposes
into a critical end point and a bicritical end point. We locate the latter point at TcrХ10.8 K and HcrХ1.4 T in
this compound. ͓S0163-1829͑97͒08317-3͔
I. INTRODUCTION
simple theory tells. The second-order line in FeBr2 shows a
maximum above Tt and makes an angle with the first-order
line at the multicritical point. This reminds us that the actual
phase diagram of FeBr2 is closer to the one shown in Fig.
1͑b͒.
Antiferromagnets with a strong uniaxial anisotropy ex-
hibit a phase transition from a state with very small net mo-
ment to the saturated paramagnetic state under an applied
magnetic field at low temperatures. This field-induced phase
transition ͑metamagnetic transition͒ has been studied for
more than 50 years.1 The magnetic-field–temperature (H-
T) phase diagram of a metamagnet is shown schematically in
Fig. 1͑a͒. The solid line represents a first-order transition and
the dotted one a second-order transition which meet at a
tricritical point ͑TCP͒. The existence of this H-T phase dia-
gram has been confirmed theoretically1 and a number of sub-
Recently, Azevedo et al.9 have found two new boundaries
in the H-T plane of FeBr2, one above and the other below
the second-order line. At these boundaries the temperature
and magnetic field dependences of the imaginary part (␹ )
Љ
of the ac susceptibility show an anomaly. These authors
claimed that the anomalies originate from noncritical spin
12
¨
fluctuations. The results of Mossbauer spectroscopy on
FeBr2 in external magnetic fields were interpreted based on
a model that the external magnetic field induces a transversal
precession of the moments on the down sublattice. Aruga
Katori et al.13 have measured the specific heat (Cp) of a
single crystal of FeBr2 under external magnetic fields. They
found two anomalies in Cp for 1.4 TрHр 2.9 T and
Tу4.9 K. The anomaly at the higher temperature represents
the transition from the paramagnetic to antiferromagnetic
phase. The anomaly at the lower temperature appears in the
stances exhibiting this phase diagram has been found.1,2
A
decomposition of TCP into a critical end point ͑CEP͒ and a
bicritical end point ͑BCEP͒, shown schematically in Fig.
1͑b͒, has been predicted by a mean-field theory3 and a Monte
Carlo simulation,4 when a further-neighbor interaction is in-
troduced in addition to the nearest-neighbor one in the
former case and when a single ion anisotropy term is in-
cluded in the latter case. On the other hand, a Monte Carlo
simulation5 on a three-dimensional Ising antiferromagnet
with next-nearest-neighbor interaction shows no evidence for
a decomposition of a TCP into a CEP and BCEP. The H-T
phase diagram shown in Fig. 1͑b͒ has attracted renewed the-
oretical interest6–8 in recent years motivated by the
discovery9 of a new boundary in the H-T plane of the meta-
magnet FeBr2.
The compound FeBr2 has the hexagonal CdI2 structure
and exhibits an antiferromagnetic ordering below 14.2 K. In
the ordered phase, spins in a c plane are parallel which are
aligned antiparallel with spins in the adjacent planes along
the c axis. The H-T phase diagram of FeBr2 has been deter-
mined from magnetic measurements.10,11 Qualitatively, the
experimental phase diagram is similar to the one shown in
Fig. 1͑a͒ with a TCP at Ttϭ4.6 K and Htϭ2.88 T. One
important thing to be noted here is that the first- and second-
order lines in FeBr2 do not meet smoothly at the TCP as the
FIG. 1. ͑a͒ Magnetic field (H) vs temperature (T) phase dia-
gram of a metamagnet. AF, antiferromagnetic phase; P, paramag-
netic phase; TCP, tricritical point. The solid line represents a first-
order transition and the dotted one a second-order transition. ͑b͒ A
decomposition of the TCP into a critical end point ͑CEP͒ and a
bicritical end point ͑BCEP͒ predicted by a mean-field theory.
0163-1829/97/55͑17͒/11466͑5͒/$10.00
55
11 466
© 1997 The American Physical Society

55
NEUTRON-SCATTERING STUDIES OF A PHASE . . .
11 467
FIG. 3. The magnetic field (H) vs temperature (T) phase dia-
gram of FeBr2 determined from the specific heat measurements
͑Ref. 13͒. The magnetic field is applied parallel to the easy axis
(c axis͒.
parallel alignment between the neighboring spins along the
c axis.
The electronic ground state of Fe2ϩ in FeBr2 is a triplet,
the lowest excited state lying ϳ100 cmϪ1 above it. Thus, the
effective Hamiltonian describing the low-temperature prop-
erties of FeBr2 is written as16
FIG. 2. Crystal structure of FeBr2.
form of a peak superposed on a broad shoulder, indicating
the occurrence of a phase transition at this boundary.
By Monte Carlo simulations, Selke and Dasgupta6 were
able to reproduce the two anomalies in the temperature de-
pendence of both dM/dT ͑the derivative of dc magnetization
with respect to temperature͒ and Cp in the applied magnetic
field observed in FeBr2. The physical origin of these anoma-
lies originates from the interplay of the effectively weak cou-
pling in the c plane and the coupling to several sites in ad-
jacent c planes.6,7 Starting from the infinite-dimensional
Hubbard model with uniaxial anisotropy, Held et al.8 have
obtained the H-T phase diagram schematically shown in Fig.
1͑b͒ which, they claim, is qualitatively very similar to the
experimental phase diagram of FeBr2.
ϭ
D
Sz͒2Ϫ2/3
͑
͕ ͖
i
͚
i
ϩ
Ϫ 2/␩͒J SzSzϪ2J SxSxϩSySy͒ , ͑1͒
͑ ͑
͖
ij ij
i j i j i j
͕
͚
iϾj
with Sϭ1. Here, D is the energy difference between the
doublet and singlet in the lowest triplet, Jij is the exchange
interaction constant, and ␩ is a constant describing the an-
isotropy in the exchange interactions. All the parameters in
Eq. ͑1͒ have been determined from the neutron inelastic scat-
tering study16 to be
In order to get a deeper understanding on the phase tran-
sition in FeBr2, we have performed neutron-scattering ex-
periments under applied magnetic fields. The neutron-
scattering technique has an advantage over the other ones in
that it measures directly the order parameter, thus providing
us with an important information on the phase transition.
The format of this paper is as follows. In Sec. II the mag-
netic properties of FeBr2 and relevant information are given.
The experimental details are given in Sec. III. The experi-
mental results are given in Sec. IV. The last section is de-
voted to a discussion.
2J1ϭ0.152 THz,
2J2ϭϪ0.051 THz,
2J ϭϪ0.06 THz,
͑2͒
Ј
DϭϪ0.22 THz,
␩ϭ0.78,
where J1 and J2 are the nearest- and next-nearest-neighbor
exchange interaction constants in the c plane, respectively,
and J is the exchange interaction constant between planes.
Ј
As one can recognize, the first term in Eq. ͑1͒ has the form of
a single-ion anisotropy with the easy axis along the z axis
which is taken to be parallel to the c axis of the crystal. The
II. PRELIMINARY DETAILS
The compound FeBr2 has the hexagonal CdI2 structure
(D33d) shown in Fig. 2. The structure consists of Fe2ϩ layers
which are sandwiched by two BrϪ bilayers along the c axis.
The lattice constants at room temperature are aϭ3.772
value of D is larger than that of J and this is the reason why
Ј
FeBr2 exhibits a metamagnetic transition.
Figure 3 shows the H-T phase diagram of FeBr2 deter-
mined from the specific heat measurements.13 In zero field,
Å and cϭ6.223 Å. From a specific heat measurement,14
a
´
magnetic ordering occurs at 14.2 K in zero field. The mag-
netic structure determined from neutron scattering15 is such
that spins in the c plane are parallel to each other with anti-
only one sharp anomaly in Cp was found at the Neel tem-
perature (TN) of 14.2 K being consistent with the previous
work.14 As H increases, TN decreases. For 1.4 TрHр 2.9 T,

11 468
KATSUMATA, ARUGA KATORI, SHAPIRO, AND SHIRANE
55
another anomaly in Cp appears in the form of a peak super-
posed on a broad shoulder. The peak becomes sharp with the
increase of the magnetic field up to 2.9 T, which shows the
existence of a new phase boundary. Below 1.4 T, it was
unable to resolve the two anomalies. The H-T phase diagram
shown in Fig. 3 is quantitatively the same as the one deter-
mined from the magnetic measurements.9
III. EXPERIMENTAL DETAILS
The single crystal of FeBr2 was grown by the Bridgman
technique. The powders of FeBr2 were obtained by a direct
reaction of Fe ͑Johnson Matthey, Specpure͒ with HBr gas
͑Matheson, 99.8%͒. After the reaction, the powders were
packed into a quartz ampoule and heated up to 800 °C under
a stream of HBr gas for a further purification. The dimen-
sions of the single crystal used in this experiment were about
10 mmϫ15 mmϫ3 mm. The crystal consisted of a few do-
mains.
FIG. 4. Peak intensity at ͑2,0,1/2͒ vs temperature for different
magnetic fields.
The neutron-scattering experiments were carried out on
the H4M triple-axis spectrometer at the High Flux Beam
Reactor of the Brookhaven National Laboratory. The hori-
linearly on T/TN(H) above 2.25 T. These results suggest that
we have another phase transition in addition to the one at
TN(H) in the high-field region: If we had only one phase
transition, all the data points measured in different fields
should lie on a universal curve when the temperature is
scaled with TN(H).
zontal collimator sequence was 20 -40 -S-20 -80 . A pyro-
Ј
Ј
Ј
Ј
lytic graphite filter after the sample was used to eliminate
higher-order beams. The phase diagram discussed above cor-
responds to the field applied along the c axis. Because of the
antiparallel arrangement between neighboring spins along
the c axis, the magnetic reflections all contain half integer
Miller indices lϭ͑2nϩ1͒/2 (n an integer͒. The crystal is
mounted in a flow cryostat inside a vertical superconducting
magnet. In order to study the magnetic reflections with the
field applied along the c axis, the crystal is tilted by ϳ4°
about the ͓110͔ direction within the cryomagnet, and so the
c axis makes an angle of ϳ4° with respect to the field di-
rection. This slight tilting of the c axis does not alter the
H-T phase diagram because the component of H parallel to
the c axis is ϳHcos4°ϭ0.998H. This orientation allows us
to study the ͑2,0,1/2͒ magnetic Bragg peak as well as the
orthogonal ͑1,1,0͒ nuclear peak.
We show, in Fig. 7, I͑2,0,1/2͒ versus T scaled by the
temperature T (H)͔ at which an anomaly in specific heat
͓
1
has been observed13 for Hϭ1.75 T, 2.25 T, and 2.50 T. We
see that the data points fall on a universal curve at low tem-
peratures T/T1(H)Ͻ1. On the other hand, they are not on a
universal curve at high temperatures T/T1(H)Ͼ1.
Figure 8 shows I͑2,0,1/2͒ versus H measured at the des-
ignated temperatures. Here, we subtracted the intensity at
Tϭ20 K as the background. In Fig. 9 is shown I͑2,0,1/2͒ as
a function of H scaled by the critical field H(T )͔ at which
͓
1
an anomaly in Cp has been observed. The data points ob-
served at low fields H/H(T1)Ͻ1 fall on a universal curve.
The data at high fields H/H(T1)Ͼ1, on the other hand, are
not on a universal curve.
IV. EXPERIMENTAL RESULTS
Figure 4 shows the temperature dependence of the inten-
sity (I) of the ͑2,0,1/2͒ antiferromagnetic Bragg scattering
for different magnetic fields. Since the linewidth of the
͑2,0,1/2͒ scattering does not depend much on T nor H as
shown in Fig. 5, we plot in Fig. 4 the peak intensity. The
width is almost resolution limited. It is evident that the ex-
ternal field changes drastically the temperature dependence
of the intensity.
In order to see the effects of magnetic fields on the tem-
perature dependence of I͑2,0,1/2͒ more clearly, we plot in
Fig. 6, I͑2,0,1/2͒ as a function of T scaled by the respective
´
Neel temperature T (H)͔ in applied magnetic fields ob-
͓
N
tained from the specific heat measurement.13 At low fields
(Hр1.0 T͒ the temperature dependence of I͑2,0,1/2͒ shows
the behavior typical of an antiferromagnet in which I de-
pends on the square of the sublattice magnetization. At high
fields (HϾ1.50 T͒, however, the data do not lie on the typi-
cal curve below about T/TN(H)ϭ0.95 and I depends almost
FIG. 5. Linewidth ͑full width at half maximum͒ vs magnetic
field of the ͑2,0,1/2͒ magnetic Bragg peak measured along the
h 0 1/2 direction at several temperatures. The widths were ob-
͓
͔
tained by Gaussian fits to the data.

55
NEUTRON-SCATTERING STUDIES OF A PHASE . . .
11 469
FIG. 8. Peak intensity at ͑2,0,1/2͒ vs magnetic field applied
along the c axis for different temperatures.
TT and TH in the H-T phase diagram, which emerge from the
bicritical end point. At TT the temperature dependence of
dM/dT shows an anomaly for fixed H. On the other hand,
the field dependence of dM/dH shows an anomaly at TH for
fixed T. Also, the field dependence of the staggered magne-
tization exhibits an anomaly at TH .7 The results of the mag-
FIG. 6. Peak intensity at ͑2,0,1/2͒ vs reduced temperature
´
T/TN(H). Here, TN(H) represents the Neel temperature in respec-
tive magnetic field determined from the specific heat measurements
͑Fig. 3͒.
V. DISCUSSION AND CONCLUSIONS
netic measurements9 show that the anomaly in ␹ ͑and prob-
Љ
ably an anomaly in dM/dT) occurs at T1(H) in Fig. 3 at
which an anomaly in Cp has also been observed. Figure 9
shows that an anomaly in the staggered magnetization, which
is proportional to the square root of I͑2,0,1/2͒, appears at
H(T1) or, equivalently, at T1(H). These facts indicate that
either the lines TT and TH merge into the line T1(H) in Fig.
3 or they are absent in FeBr2.
Based on the former idea, the line T1(H) is not a true
phase transition line but represents the positions at which
noncritical spin fluctuations occur.9 However, a sharp
anomaly in Cp has been observed at T1(H) in high fields,13
indicating the occurrence of a phase transition at this bound-
ary. Based on the latter idea, we see close similarity of the
From Fig. 6, we see that all the data measured in different
fields lie on a universal curve above about T/TN(H)ϭ0.95.
This means that the character of the transition from the para-
magnetic to antiferromagnetic phase does not change with
H. The transition which is of second order occurs at the
phase boundary denoted by TN(H) in Fig. 3.
From Fig. 7, we see that I͑2,0,1/2͒ measured at the des-
ignated fields changes with temperature in two steps indicat-
ing the existence of a boundary around T/T1(H)ϭ1. Figure
9 gives further evidence for the existence of the boundary at
H(T1) or equivalently at T1(H) where the intensity changes
abruptly.
Selke7 has predicted from the mean-field calculation on a
simple cubic Ising model that there exist two lines called
FIG. 9. Reduced peak intensity at ͑2,0,1/2͒ vs reduced magnetic
field H/H(T1) for the designated temperatures. Here, I(Hϭ0͒ is the
peak intensity at ͑2,0,1/2͒ measured in zero field and H(T1) is the
magnetic field giving an anomaly in specific heat at T1 ͑Fig. 3͒.
FIG. 7. Peak intensity at ͑2,0,1/2͒ vs reduced temperature
T/T1(H). Here, T1(H) is the temperature at which an anomaly in
specific heat has been observed ͑Fig. 3͒.

11 470
KATSUMATA, ARUGA KATORI, SHAPIRO, AND SHIRANE
55
experimental H-T phase diagram shown in Fig. 3 to the the-
oretical one shown in Fig. 1͑b͒.
above considerations, we conclude that the experimental H-
T phase diagram of FeBr2 is close to the one shown sche-
matically in Fig. 1͑b͒. We tentatively locate the bicritical end
point at TcrХ 10.8 K and HcrХ 1.4 T based on the H-T
phase diagram shown in Fig. 3.
In conclusion, we have studied the magnetic phase tran-
sition in the metamagnet FeBr2 under external magnetic
fields by the neutron-scattering technique. We find an
anomaly in the temperature dependence of the intensity of
the ͑2, 0, 1/2͒ antiferromagnetic Bragg scattering at T1(H) in
addition to that at TN(H). We conclude that the H-T phase
diagram is close to the one shown schematically in Fig. 1͑b͒
with a BCEP located at TcrХ 10.8 K and HcrХ 1.4 T.
We call the layers with positive magnetic moments ͑//
H) the ϩ layers and the ones with negative moments the
Ϫ layers. In zero field, the magnetization (mϩ) in the ϩ
layers and that in the Ϫ layers (mϪ) are oppositely directed
and their magnitudes are equal. For finite H, in the AF I
phase of Fig. 1͑b͒, mϩϾmϪ yet they are oppositely directed.
On the other hand, in the AF II phase, mϩÞmϪ and they are
parallel.7 In the region HϽHcr , where Hcr is the BCEP field,
the transition between the AF I and AF II phases is continu-
ous. This is consistent with the result shown in Fig. 6 in
which only one anomaly in the temperature dependence of
I͑2,0,1/2͒ has been observed at TN(H) below about 1.5 T.
This is also consistent with the fact that only one anomaly in
Cp has been observed below about 1.4 T.13 At high fields
(HϾHcr), the transition from the AF I to AF II phase is
expected to be of first order. Experimentally, no jump in
sublattice magnetization is observed at T1(H) as shown in
Fig. 7. This is probably due to demagnetization effects which
give rise to a region where the AF I and AF II phases coexist.
A sharper change in the sublattice magnetization is observed
at H(T1) when measurement is done under fixed tempera-
tures ͑Fig. 9͒. This is understandable from the curvature of
the T1(H) line in Fig. 3. The coexistence region is narrower
along the H direction than along the T direction. From the
ACKNOWLEDGMENTS
This work was partially supported by the U.S.-Japan Co-
operative Program on Neutron Scattering operated by the
U.S. Department of Energy and the Japanese Ministry of
Education, Science, Sports and Culture, by the Special Co-
ordination Funds of the Science and Technology Agency of
the Japanese Government, and by the NEDO International
Joint Research Grant. Work at Brookhaven National Labora-
tory was carried out under Contract No. DE-AC02-
76CH00016, Division of Materials Science, U.S. DOE.
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