Magnetic properties of the itinerant metamagnetic system Co(S1-xSex)2 under high magnetic fields and high pressure

Article abstract of DOI:10.1103/PhysRevB.56.14019

The magnetization of the Co(S_1-x-Se_x)₂ system with 0≤x≤0.2 has been measured under high magnetic fields and high pressure. Ferromagnetic CoS₂ exhibits a second-order transition at T2=122 K. Substitution of 10% Se for S in CoS₂ reduces the Curie temperature to T_c.=27 K and the transition to first order. Co(S_1-xSe_x)₂ with 0.12≤x becomes an exchange-enhanced Pauli paramagnet. The itinerant metamagnetic transition has been observed in the paramagnet. Co(S_0.9Se_0.1)₂ also shows a transition just above T^c. Using the experimental data, the magnetic phase diagram of Co(S_1-xSe_x)₂ is determined. With increasing pressure, the Curie temperature of CoS₂ decreases and the ferromagnetic transition changes to first order at P≈0.4 GPa. In the pressure regime of the first-order transition P>0.4 GPa, the metamagnetic transition is observed just above T_c. In Co(S_0.9Se_0.1)₂, the ferromagnetism disappears at 0.25 GPa and paramagnetism appears. The observed magnetic properties and the magnetic phase diagram of Co(S_1-x.Se_x)₂ can be qualitatively described with a theory of the itinerant electron metamagnetism at finite temperatures.

Full text of DOI:10.1103/PhysRevB.56.14019

PHYSICAL REVIEW B
VOLUME 56, NUMBER 21
1 DECEMBER 1997-I
Magnetic properties of the itinerant metamagnetic system Co„S1؊xSe …
x 2
under high magnetic fields and high pressure
T. Goto,* Y. Shindo, and H. Takahashi
Institute for Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan
S. Ogawa
Faculty of Engineering, Tokyo Denki University, Kanda, Chiyoda-ku, Tokyo 101, Japan
͑
Received 20 February 1997͒
The magnetization of the Co(S1ϪxSex)2 system with 0рxр0.2 has been measured under high magnetic
fields and high pressure. Ferromagnetic CoS exhibits a second-order transition at T ϭ122 K. Substitution of
2
c
1
0% Se for S in CoS2 reduces the Curie temperature to T ϭ27 K and the transition to first order.
c
Co(S1ϪxSex)2 with 0.12рx becomes an exchange-enhanced Pauli paramagnet. The itinerant metamagnetic
transition has been observed in the paramagnet. Co͑S0.9Se ͒ also shows a transition just above T . Using the
0.1 2
c
experimental data, the magnetic phase diagram of Co(S1ϪxSe ) is determined. With increasing pressure, the
x
2
Curie temperature of CoS decreases and the ferromagnetic transition changes to first order at PϷ0.4 GPa. In
2
the pressure regime of the first-order transition PϾ0.4 GPa, the metamagnetic transition is observed just above
Tc . In Co͑S0.9Se ͒ , the ferromagnetism disappears at 0.25 GPa and paramagnetism appears. The observed
0.1 2
magnetic properties and the magnetic phase diagram of Co(S1ϪxSex)2 can be qualitatively described with a
theory of the itinerant electron metamagnetism at finite temperatures. ͓S0163-1829͑97͒06045-1͔
I. INTRODUCTION
structure consisting of Co atoms and chalcogen atom pairs. It
has been known from the electrical, magnetic, optical, and
9–21
Since itinerant electron metamagnetism, that is, the first-
order field-induced transition from the paramagnetic to the
ferromagnetic state in the itinerant electron system, was pre-
dicted to occur in a paramagnetic metal with a suitable en-
ergy dependence of the density-of-states ͑DOS͒ curve around
x-ray photoemission spectroscopy experiments1
that the
3d electrons arising from the Co atoms are in the low-spin
state. The 3d band is split into t2g and e subbands by a
crystalline field. The t2g band is completely filled with 3d
electrons. On the other hand, the e band is partially filled
g
g
1
2–5
6–11
the Fermi level, many theoretical
and experimental
with one 3d electron per Co atom. Therefore, the 3d elec-
studies have been made to elucidate it. Our group systemati-
cally studied the magnetization processes of various Co-
trons in the e band are responsible for the magnetic proper-
g
ties. The e states are hybridized with the antibonding p*
g
12
22
based pseudobinary compounds such as Y(Co Al ) ,
states arising from the chalcogen atom pairs. The hybrid-
1
Ϫx
x 2
1
3
14
Lu(Co1ϪxAl ) , Hf(Co1ϪxFe ) , and Lu(Co1ϪxGax)2
ization between the e and p* states in CoSe is stronger
x
2
x
2
g
2
͑Ref. 15͒ in magnetic fields up to 120 T and clearly observed
than that in CoS . In fact, recent band-structure calculations
2
the itinerant metamagnetic transitions in these compounds.
On the other hand, Adachi et al. found the metamagnetic
transitions in the paramagnetic Co(S1ϪxSex)2 com-
of CoS and CoSe indicate that the latter e band is wider
2
2
g
than the former one and the structures of both e bands are
g
very similar to each other.23 Therefore, the increase of the Se
concentration in Co(S1ϪxSe ) makes the bandwidth wider.
1
6,17
pounds.
We found that every metamagnetic compound has char-
x
2
CoS is an itinerant ferromagnet with a Curie temperature of
2
11
16,18
acteristics of a nearly ferromagnetic metal. The electronic
specific heat and magnetic susceptibility of the compound
are very large and the temperature dependence of the suscep-
tibility is anomalous: the susceptibility increases and then
decreases through a maximum value. This indicates that the
anomalous behavior of the susceptibility also originates from
the shape of the DOS curve. It should be noted that the
observed metamagnetic transitions appear with low critical
fields in the above paramagnetic pseudobinary systems that
are very close to their ferromagnetic instabilities and that the
critical field increases as the composition of the systems goes
away from the ferromagnetic region. This suggests that the
mechanism of the appearance of the metamagnetic transition
is closely related to that of the ferromagnetic instability.
Tcϭ122 K.
The Curie temperature is rapidly decreased
16,18
by the substitution of Se for S in CoS2.
The ferromag-
netic compound with xϭ0.05 and 0.1 near the disappearance
of ferromagnetism seems to show a first-order transition at
the Curie temperature.18 Co(S1ϪxSex)2 with xу0.12 be-
comes an exchange-enhanced Pauli paramagnet in which the
metamagnetic transition is induced by the application of high
magnetic fields.1
6,17
These results indicate that the
Co(S1ϪxSe ) system is one of the most suitable systems for
x
2
studying the relation between the ferromagnetic instability
and the appearance of the metamagnetic transition observed
in the itinerant metamagnetic systems.
The application of high pressure can finely increase the
bandwidth compared with the Se substitution. Thus, high
pressure is very useful for examining the detailed variations
of the magnetic properties due to the increase of the band-
18
The Co(S1ϪxSe ) system has the pyrite structure. This
x
2
structure is cubic and can be considered as an NaCl-like
0
163-1829/97/56͑21͒/14019͑10͒/$10.00 56
14 019
© 1997 The American Physical Society

14 020
T. GOTO, Y. SHINDO, H. TAKAHASHI, AND S. OGAWA
56
width. In this study, we have systematically studied the mag-
netization of the Co(S1ϪxSe ) system under high magnetic
x
2
24
25
fields and high pressure. Moriya and Yamada developed
a theory of the itinerant electron metamagnetism at finite
temperatures based on the spin-fluctuation model. Our ex-
perimental results are discussed with this theory.
II. EXPERIMENTAL PROCEDURE
Polycrystalline samples of CoS , CoSe , and their mixed
2
2
crystals have been prepared by a direct reaction of the con-
stituent elements in a vacuum at elevated temperature.18 We
also followed this method to prepare samples of
Co(S1ϪxSe ) with 0рxр0.3. We know from previous ex-
periments that the field and the temperature dependence of
the magnetization of a metamagnetic sample in the range
x
2
FIG. 1. Temperature variations of the magnetizations of CoS2
and Co͑S0.9Se ͒ measured in a magnetic field 0.5 T.
0.1 2
0
.1рxр0.2 are extremely sensitive to the local arrangement
locking screws and the clamp cylinder. Because the para-
magnetic susceptibility of a small amount of Ti almost com-
pensates the diamagnetic susceptibility of Cu, the suscepti-
26,27
of S and Se atoms around the Co atom.
to obtain the precise magnetization data of Co(S1ϪxSe ) to
Since we aimed
x
2
compare quantitatively their transition temperatures and
critical fields with the theory, we needed to have very good
homogeneous samples. In several trials of sample prepara-
tion, we found a small amount of selenium segregation and
condensations separately in an evacuated quartz tube when
the reaction temperature was high, above about 650 °C. This
suggests a deficiency in Se or a possible precipitation of
microcrystals of a Co-rich phase. On the other hand, the
reaction at a temperature below about 650 °C resulted in an
incomplete homogeneity of S and Se distribution, which
gives extremely broad ferromagnetic and metamagnetic tran-
sitions. We prepared the samples used in this study with the
following procedure. Cobalt metal of 99.9ϩ% purity in a
powdered form of about 50 ␮m size, sulfur lump of 99.999%
purity and selenium in a shot form of 99.999% purity were
mixed in stoichiometric proportions for a desired x value and
Ϫ9
bility of this alloy is extremely small, ϩ3ϫ10 emu/g at
Ϫ8
room temperature and ϩ5ϫ10 emu/g at 1.8 K. The in-
crease of the susceptibility at 1.8 K comes from some mag-
netic impurities. The strength of this material is nearly the
same as that of ordinary commercial BeCu containing ferro-
magnetic Co. The piston caps and pistons are made of high-
purity zirconia which shows diamagnetism with a suscepti-
Ϫ7
bility Ϫ1.7ϫ10 emu/g. The sample is compressed in a
Teflon cell filled with a liquid pressure medium, Flourinert,
in the clamp cylinder. The produced pressure at low tem-
peratures is calibrated by means of the Meissner effect of Pb
for which the pressure dependence of the superconducting
transition temperature is known to be highly accurate.28 The
high pressure clamp has been used for various magnetic
studies up to 1.3 GPa. In this pressure range, the plastic
deformation inside the clamp is found to be negligibly small.
Ϫ4
sealed in a quartz tube at a pressure less than 10 Torr. The
In this study, we measured the magnetizations of CoS and
2
total sample weight was about 4 g. As a preliminary reaction,
the sealed tube was heated in an electric furnace for two days
at 400 °C, two days at 450 °C, two days at 500 °C, and two
days at 550 °C and cooled in the furnace. After removal from
the tube, the sample was crushed into fine powder. The pow-
der was vacuum sealed again in a quartz tube and heated for
two days at 700 °C, four days at 750 °C, three days at
Co͑S Se ͒ under high pressure up to 0.8 GPa and high
0.9 0.1 2
magnetic field up to 9 T.
III. EXPERIMENTAL RESULTS
A. Magnetizations and susceptibilities
First we show in Fig. 1 the temperature dependence of the
700 °C, three days at 600 °C, and three days at 500 °C and
magnetization of CoS and Co͑S Se ͒ measured in a
cooled. The samples prepared as above were powdered for
magnetization measurements.
2
0.9 0.1 2
magnetic field of 0.5 T. CoS2 is a ferromagnet with a Curie
temperature Tcϭ122 K. The magnetization decreases more
rapidly in the vicinity of the Curie temperature than usual
ferromagnets, but the ferromagnetic transition is second or-
der. The magnetization does not depend on the cooling pro-
cess of the sample. In the case of Co͑S0.9Se0.1͒2, however,
the magnetization exhibits hysteresis around the Curie tem-
perature of about 30 K. This indicates that the substitution of
10% Se for S in CoS2 abruptly decreases the Curie tempera-
ture from 122 K to about 30 K and changes the type of the
ferromagnetic transition from the second order to the first-
order one. In the concentration region xу0.12, the
High magnetic fields up to 40 T were produced using a
wire-wound pulse magnet with a rise time of about 5 ms.
The sample magnetizations in pulsed high magnetic fields
were measured using a conventional induction method in the
temperature range between 4.2 and 200 K.
Magnetization measurements under high pressure and
high magnetic fields are very rare in spite of their importance
for magnetic studies. Recently, we made a magnetometer for
measuring precisely the magnetizations of weakly magnetic
materials under these conditions. We use an extraction
method with a nonmagnetic pressure clamp to detect sample
magnetizations in high magnetic fields up to 11 T produced
by a superconducting magnet. In order to reduce the magne-
tization background from the clamp, a high-purity TiCu alloy
including about 3 wt % Ti is employed as a material of the
16,18
Co(S1ϪxSe ) system becomes paramagnetic.
x
2
The temperature dependence of the susceptibility of
Co(S1ϪxSe ) with xϭ0.1–0.3 is shown in Fig. 2. The sus-
x
2
ceptibility was measured in a magnetic field, 0.5 T. In the

56
MAGNETIC PROPERTIES OF THE ITINERANT . . .
14 021
FIG. 3. Magnetization curves of the Co(S1ϪxSex)2 compounds
with 0рxр0.2 measured at 4.2 K in pulsed high magnetic fields up
to 32 T.
with increasing x. This value is consistent with the saturation
magnetizations of the ferromagnetic compounds with xϭ0
and 0.1.
We also measured the magnetization curves of all the
samples at various temperatures in pulsed high magnetic
fields up to 40 T. Figure 4 shows the magnetization curves of
ferromagnetic Co͑S Se ͒ at several temperatures between
FIG. 2. Temperature variations of the susceptibilities of the
Co(S1ϪxSe ) compounds with 0.1рxр0.3.
x
2
0.9 0.1 2
low-temperature region below 50 K, however, the suscepti-
bility is found to be increased by some ferromagnetic impu-
rities included in the sample. In order to eliminate the effect
of impurities as much as possible, we have determined the
susceptibility in this region from the slope of the magnetiza-
tion curve after the magnetization of the impurities saturated.
The inhomogeneous effect of the pseudobinary sample also
increases the susceptibility at low temperatures, especially in
the sample near the disappearance of ferromagnetism. There-
fore, the value of the susceptibility at low temperatures is
less reliable than that at high temperatures, TϾ50 K. A
sharp upturn of the susceptibility observed for xϭ0.1 origi-
nates from the appearance of the ferromagnetic state. All the
paramagnetic samples with more than 12% Se exhibit char-
acteristics of nearly ferromagnetic metals: the susceptibili-
ties have a broad maximum around 80 K. The maximum has
4
.2 and 100 K. This compound, whose ferromagnetic transi-
tion is first order, exhibits anomalous magnetic behavior in
the paramagnetic temperature region. We can see the rela-
tively sharp metamagnetic transition with hysteresis just
above the Curie temperature. With increasing temperature,
the first-order transition becomes broad accompanied with
the increase of the critical field and finally disappears. It
should be noted that CoS with the second-order ferromag-
2
netic transition has no metamagnetic transition in the para-
magnetic temperature region.
Figure 5 shows the magnetization curves of paramagnetic
Co͑S0.86Se0.14͒2 and Co͑S0.8Se0.2͒2 in the temperature region
from 4.2 to 140 K. The observed metamagnetic transition is
very sharp at low temperatures. With increasing temperature,
however, the transition becomes broad with the increase of
the critical field and finally disappears. This behavior is very
16,18
similar to that of ferromagnetic Co͑S Se ͒ in the para-
not been observed clearly in Co(S1ϪxSe ) .
The suscep-
0.9 0.1 2
x
2
magnetic temperature region.
tibility of ferromagnetic Co͑S Se ͒ seems to exhibit a
0.9 0.1 2
The average critical fields of Co(S1ϪxSex) with x
broad maximum just above the Curie temperature. Here we
define Tmax as the temperature at which the susceptibility
becomes maximum. The susceptibility at Tmax rapidly in-
creases with decreasing the concentration x.
2
ϭ0.1– 0.2 are summarized in Fig. 6͑a͒ as a function of the
B. Magnetizations in pulsed high magnetic fields
In order to examine the magnetic properties of the ground
states of the Co(S1ϪxSex)2 compounds, we measured the
magnetization curves for 4.2 K in pulsed high magnetic
fields up to 32 T. The results for xϭ0–0.2 are shown in Fig.
3. All the paramagnetic compounds with xу0.12 exhibit the
very sharp itinerant metamagnetic transitions to the ferro-
magnetic state compared with those observed by Adachi
1
7
et al. This suggests that the quality of the present samples
are very high. The average critical field of the transitions in
ascending and descending fields, B , increases linearly with
FIG. 4. Magnetization curves of Co͑S0.9Se ͒ at several tem-
c
0.1 2
x. The saturation magnetization above B decreases slightly
peratures.
c

14 022
T. GOTO, Y. SHINDO, H. TAKAHASHI, AND S. OGAWA
56
FIG. 5. Magnetization curves of Co͑S0.86Se
͒
and
0.14 2
Co͑S0.80Se ͒ at several temperatures.
0.20 2
square of temperature. The critical field shifts proportionally
2
to T and can be written in the low-temperature region T
Ͻ70 K as
FIG. 6. ͑a͒ Average critical fields of the Co(S1ϪxSex)2 com-
pounds with 0.1рxр0.2, B , as a function of the square of tem-
perature. ͑b͒ Estimated average critical fields at Tϭ0 K, Bc(0),
as a function of the concentration x.
c
2
B ͑x,T͒ϭB ͑x,0͒ϩ␣T .
͑1͒
c
c
Here B (x,0) is the average critical field at Tϭ0 K and ␣ is
c
ϭ0, but becomes first order at xϭ5 and 10%.16 The value of
Tc on the first-order phase boundary abruptly decreases with
2
constant. The T dependence has already been found in para-
magnetic Co-based Laves phase compounds.11–13,29 The fer-
romagnetic compound with xϭ0.1 and the paramagnetic
ones with xу0.12 have the same value of ␣ (Ͼ0). The
value of B (x,T) for ferromagnetic Co͑S Se ͒ should be-
increasing x. As described in discussion, the position of Tt
on the T line where the type of the ferromagnetic transition
c
c
0.9 0.1 2
come zero at the Curie temperature: B (0.1,T )ϭ0. From
c
c
this relation, we can correctly determine the equilibrium
value of T to be 27 K. Figure 6͑b͒ shows the estimated
c
average critical field at Tϭ0 K as a function of x. The criti-
cal field increases linearly with x. The critical concentration
xc at which the transition field becomes zero corresponds to
the disappearance of ferromagnetism. The critical concentra-
tion is estimated to be x ϭ0.11.
c
The critical temperature T for the disappearance of the
0
metamagnetic transition can be determined from the tem-
perature at which the hysteresis of the magnetization curve
disappears. As an example, Fig. 7 shows the difference be-
tween the critical fields in increasing and decreasing fields in
the sample with xϭ0.14. The difference ⌬Bc decreases
nearly linearly with temperature and becomes zero at T0 .
Using the observed values of the Curie and critical tem-
peratures T and T , we have determined the magnetic phase
c
0
FIG. 7. Difference between the critical fields ⌬Bc of
diagram of Co(S1ϪxSe ) in the x-T plane, which is shown
Co͑S0.86Se ͒ observed in increasing and decreasing fields. At a
x
2
0.14 2
in Fig. 8. The ferromagnetic transition is second order at x
temperature T , the metamagnetic transition disappears.
0

56
MAGNETIC PROPERTIES OF THE ITINERANT . . .
14 023
FIG. 8. Magnetic phase diagram of Co(S1ϪxSex)2 in the x-T
plane. Below the T line, ferromagnetism appears. With increasing
c
x, the type of the ferromagnetic transition is expected to change at
the point T on the T line, which corresponds to a concentration
t
c
xϭ1%. Between the T and T lines, the metamagnetic transition
c
0
occurs. The values of Tmax are also plotted, at which the suscepti-
bility becomes maximum.
changes from the second order to the first-order one can be
determined from the critical concentration x at which
t
Ϫ1
25
␹
(Tmax) ϭ0 is satisfied. The estimated critical concentra-
tion is x ϭ1%. Therefore, the second-order transition region
t
exists only in the vicinity of xϭ0. In the concentration re-
gion 1%ϽxϽ11%, however, the transition becomes first
order. The T0 line, on which the metamagnetic transition
FIG. 9. ͑a͒ Temperature dependence of the magnetization of
CoS2 measured in a magnetic field of 0.5 T at several pres-
25
disappears, is expected to merge into the T line at T .
c
t
Between the T and T0 lines, the metamagnetic transition
sures. ͑b͒ Magnetization of CoS around the Curie temperature
c
2
appears as shown in Fig. 8. For comparison, the values of
measured in a magnetic field of 0.1 T.
Tmax are also plotted in the x-T plane. The observed value of
Tmax is larger than that of T at the same concentration x.
ferromagnetic transition becomes first order, we have ob-
served the metamagnetic transition just above the Curie tem-
perature. As a typical example, we show the temperature
0
The T
Tt .
line is also expected to merge into the T line at
c
max
2
5
dependence of the magnetization curve of CoS at 0.77 GPa
2
in Fig. 10. As shown in the inset, the magnetization curve for
C. Magnetizations under static high field and high pressure
1
17 K clearly indicates the metamagnetic transition with
We measured the magnetizations of ferromagnetic CoS2
hysteresis. It should be noted that Co͑S Se ͒ with the
0.9
0.1 2
and Co͑S Se ͒ under static high magnetic field and high
0
.9 0.1 2
pressure. Figure 9͑a͒ shows the temperature dependence of
the magnetization of CoS in a magnetic field of 0.5 T at
2
various pressures. The magnetization was measured with in-
creasing temperature after zero-field cooling of the sample.
In the low-temperature region, the pressure effect on the
magnetization is small. In the vicinity of the Curie tempera-
ture, however, this effect is very large. In order to examine in
detail the magnetic behavior of CoS under high pressure
2
around the Curie temperature, we measured again the mag-
netization in a magnetic field of 0.1 T at various pressures.
Figure 9͑b͒ shows the magnetization around the Curie tem-
perature. With increasing pressure, the magnetization de-
creases more abruptly at the Curie temperature. This indi-
cates that the second-order ferromagnetic transition is
changed into the first-order one by the application of high
pressure PϾ0.4 GPa.
FIG. 10. The magnetization curves of CoS for 0.77 GPa around
2
At ambient pressure, CoS has no metamagnetic transition
above the Curie temperature. Under high pressure where the
the Curie temperature. The inset shows the magnetization curves on
a finer magnetic field scale.
2

14 024
T. GOTO, Y. SHINDO, H. TAKAHASHI, AND S. OGAWA
56
FIG. 12. Pressure dependence of the magnetization curve of
Co͑S0.9Se ͒ at Tϭ4.2 K.
0.1 2
magnetic properties by the application of high pressure is
almost the same as that due to the Se substitution ͑see Figs.
4 and 5͒.
FIG. 11. Magnetic phase diagram of CoS in the P-T plane. The
2
Curie temperature T above 1 GPa has been determined from the ac
The average critical fields of Co͑S Se ͒ at various
c
0.9 0.1 2
susceptibility measurements. Yomo’s data ͑Ref. 30͒ of T are also
c
pressures are summarized in Fig. 14͑a͒ as a function of the
plotted for comparison. The ferromagnetic transition is second or-
der below PϷ0.4 GPa and first order above this pressure. Between
the T and T lines, the metamagnetic transition appears.
square of temperature. The transition field under high pres-
2
sure also shifts proportionally to T at low temperatures and
c
0
can be written by
first-order ferromagnetic transition at ambient pressure also
2
B ͑P,T͒ϭB ͑P,0͒ϩ␣T .
͑2͒
exhibits the metamagnetic transition above T ͑see Fig. 4͒.
c
c
c
Figure 11 shows the magnetic phase diagram of CoS in
the P-T plane. The Curie temperature has been determined
from the magnetization measurements in the pressure region
2
Here B (P,0) is the average critical field for Pϭ0 GPa. In
c
the pressure region 0рPр0.77 GPa, ␣ (Ͼ0) is constant
and its value is equal to that of ␣ in Eq. ͑1͒. From both Eqs.
͑1͒ and ͑2͒, we consider that the value of ␣ for Co(S1ϪxSex)2
does not change in the pressure and concentration regions
Pр0.77 GPa and from the ac susceptibility measurements
above this region. The data of Yomo30 are also plotted for
comparison. It should be noted that the change of T around
c
0.4 GPa is anomalous: Tc decreases linearly with increas-
ing pressure in the low-pressure region 0рPр0.41 GPa, but
above 0.41 GPa it deviates remarkably from this liner rela-
tion. Above 1 GPa, T decreases more rapidly. The values of
c
T at Pϭ0.62 and 0.77 GPa are very close to that of T for
0
c
Pϭ0.41 GPa. We have observed the metamagnetic transi-
tion in the narrow temperature region between T0 and Tc
lines.
Co͑S Se ͒ is a ferromagnet near the disappearance of
0
.9 0.1 2
ferromagnetism and its pressure effect is expected to be very
large. In order to examine the change of the magnetic ground
state by the application of high pressure, we measured the
magnetization curves for 4.2 K at several pressures. The re-
sults are shown in Fig. 12. With increasing pressure, the
spontaneous magnetization abruptly decreases and the ferro-
magnetic compound becomes paramagnetic under pressures
higher than 0.21 GPa. In the paramagnetic pressure region,
the metamagnetic transition occurs. The magnetization after
the transition is nearly equal to the saturation magnetization
at Pϭ0 GPa in the pressure region 0рPр0.77 GPa.
We measured the temperature dependence of the magne-
tization curve of Co͑S Se ͒ at various pressures. Figure
0.9 0.1 2
13 shows the results for Pϭ0.21 and 0.77 GPa. The critical
field increases with increasing pressure and temperature. The
metamagnetic transition becomes broad with increasing tem-
perature. Comparing these results with the temperature de-
pendencies of the magnetization curves of Co(S1ϪxSe ) for
FIG. 13. Temperature dependence of the magnetization curve of
x
2
various concentration, we conclude that the change of the
Co͑S0.9Se0.1͒2 measured at Pϭ0.21 and 0.77 GPa.

56
MAGNETIC PROPERTIES OF THE ITINERANT . . .
14 025
FIG. 15. Theoretical magnetic phase diagram for aϾ0, bϽ0,
and cϾ0. The ferromagnetic transition is second order on the solid
2
5
28
5
28
Tc line (ac/b Ͻ ) and first order on the dotted Tc line (
2
3
Ͻac/b Ͻ 1 ). Between the T and T lines, the metamagnetic tran-
sition occurs. In the narrow region 28 Ͻac/b Ͻ , the transition
6
c
0
5
2
3
16
appears just above the first-order T line. The T line merges into
c
0
2
5
28
the T line at the point T corresponding to ac/b ϭ
.
c
t
tual materials can theoretically be evaluated using the fixed
31
spin-moment method of band calculations. Hathaway and
Cullen32 have actually estimated these coefficients for YCo2.
At a finite temperature T, the coefficients a, b, and c are
renormalized by thermal spin fluctuations and the equation
of state is rewritten as
FIG. 14. ͑a͒ Average critical fields of Co͑S0.9Se ͒ , B , for
various pressures as a function of the square of temperature. ͑b͒
0.1 2
c
Estimated average critical field for Tϭ0 K, B (0), as a function of
c
pressure. The critical pressure for the disappearance of ferromag-
netism is evaluated to be P ϭ0.25 GPa.
c
3
5
BϭA͑T͒MϩB͑T͒M ϩC͑T͒M ,
͑4͒
0
1
рPр0.77 GPa and 0.1рxр0.2 ͓see Fig. 6͑a͔͒. Figure
4͑b͒ shows the estimated average critical field for Tϭ0 K,
where A(T) is the inverse susceptibility at T. The coeffi-
cients A(T), B(T), and C(T) are functions of a, b, c, and
the mean-square local amplitude of thermally fluctuating mo-
ment ␰(T), which is proportional to T at low temperatures.
In the MY theory, the effects of zero-point spin fluctuations
B (P,0), as a function of pressure. The critical field in-
creases linearly with pressure. The critical pressure P at
which the transition field becomes zero is estimated to be
P ϭ0.25 GPa. This pressure corresponds to the disappear-
c
c
2
2
c
͑
quantum spin fluctuations͒ are completely neglected.
ance of ferromagnetism.
24
Moriya has determined the magnetic phase diagram of the
itinerant electron system with aϾ0, bϽ0, and cϾ0. The
negative value of b suggests that the density of states curve
has a positive curvature near the Fermi level. In the case of
ac/b Ͼ 1 , the ground state is paramagnetic. The condition
IV. DISCUSSION
1
A. Phase diagram and magnetic properties
in high magnetic fields
2
3
6
Moriya24 and Yamada25 have proposed a theory of the
for the occurrence of the metamagnetic transition at T
ϭ0 K is given by
itinerant metamagnetic transition at finite temperatures based
on the spin-fluctuation model. Here, we abbreviate this
theory as the MY theory. In order to use this theory for
analyzing our experimental results, we briefly introduce it.
The equation of state for an itinerant electron system is writ-
ten in the ground state as
3
ac
9
aϾ0, bϽ0, cϾ0, and
Ͻ
Ͻ
.
͑5͒
1
6
b2 20
2
3
6
For 0рac/b Ͻ 1 , the ground state becomes ferromagnetic.
Although the Stoner condition (aϽ0) is not satisfied in this
case, ferromagnetism appears. The large positive curvature
of the density of states curve near the Fermi level stabilizes
the ferromagnetism.
3
5
BϭaMϩbM ϩcM ,
͑3͒
where B is magnetic field, M the uniform magnetization, and
Ϫ1
a is the inverse susceptibility at Tϭ0 K, aϭ␹(0) . The
Figure 15 shows the theoretical phase diagram for aϾ0,
bϽ0, and cϾ0 in the vicinity of the disappearance of
coefficients a, b, and c are functions of the electronic den-
sity of states and its derivatives at the Fermi level. Here M
and ␹ are expressed in terms of ␮ /Co (ϭ␮ /f.u.) and
2
4
2
ferromagnetism. Because c␰(T) /͉b͉ increases proportion-
2
ally to T at low temperatures, the ordinate corresponds to
B
B
␮B /CoT, respectively. The coefficients a, b, and c for ac-
the temperature axis of the magnetic phase diagram of

14 026
T. GOTO, Y. SHINDO, H. TAKAHASHI, AND S. OGAWA
56
2
Co(S1ϪxSe ) indicated in Fig. 8. On the other hand, ac/b
x
2
increases linearly with x in the narrow region of x and there-
fore the abscissa is considered as the x axis. The phase tran-
sition between the paramagnetic and ferromagnetic states oc-
curs on the Tc line and the metamagnetic transition
disappears on the T line. Between the T and T lines, the
0
0
c
2
metamagnetic transition appears. With increasing ac/b , the
sign of B(T) in Eq. ͑4͒ changes from positive to negative on
the T line and B(T) becomes zero at the critical point T
where ac/b ϭ 2 is satisfied. Thus, the ferromagnetic transi-
tion is second order in the region 0рac/b Ͻ and first
c
t
2
5
8
2
5
28
5
2
3
16
order in the narrow region 28 Ͻac/b Ͻ . The T point on
t
the T line is considered as the tricritical point where the
c
type of the ferromagnetic transition changes. Moreover, the
FIG. 16. Inverse susceptibility of Co(S1ϪxSe ) at TϭT as a
max
function of the concentration x.
x
2
metamagnetic transition appears just above T in the narrow
c
region. The T line merges into the T line at T . The Curie
0
c
t
2
temperature T abruptly decreases with increasing ac/b in
c
ted the data as a function of x in Fig. 16. These data can well
be described by a simple relation,
5
2
3
16
the region 28 Ͻac/b Ͻ . This phase diagram well repro-
duces the experimental phase diagram of Co(S1ϪxSe ) in-
x
2
␹͑Tmax͒Ϫ1ϭ͑540xϪ5͒ ͓T͑␮ /Co͒Ϫ1͔.
͑8͒
dicated in Fig. 8. CoS with the second-order ferromag-
2
B
netic transition has no metamagnetic transition above Tc .
However, we have found that Co͑S Se ͒ exhibits the
first-order ferromagnetic transition and the metamagnetic
This relation can be deduced from Eq. ͑7͒ and the assump-
tion that the value of a increases linearly with x and those of
b and c are nearly constant in the concentration region 0.1
рxр0.3. The susceptibility ␹(Tmax) becomes infinite at x
ϭ0.01. This suggests that the type of the ferromagnetic tran-
sition changes at xϭ0.01. The Curie temperature for x
0.9 0.1 2
transition appears above T . This dramatic change of the
c
magnetic properties due to the substitution of only 10% Se
for S in CoS can be explained by considering that the value
2
2
5
28
of ac/b for CoS is slightly smaller than and increases to
a value between 2 and
2
5
8
3
16
ϭ0.01 corresponds to the point T in the phase diagram of
due to the Se substitution. The
t
Co(S1ϪxSe ) ͑see Fig. 8͒. Therefore, the Co(S Se ) sys-
rapid decrease of T in Co(S Se ) and the appearance of
x
2
1Ϫx
x 2
c
1Ϫx
x 2
2
5
28
tem satisfies ac/b ϭ at xϭ0.01.
the paramagnetic ground state with the metamagnetic transi-
tion in magnetic fields can also be explained using the theo-
retical phase diagram.
On the other hand, the critical field of the metamagnetic
2
transition near the disappearance of ferromagnetism (ac/b
3
According to the MY theory,25 the inverse susceptibility
is given by the relation
Х
) is given by
16
1
16
␰͑T͒2,
B ͑T͒ϭB ͑0͒ϩ
ͱ
͉
b
͉
/3c
͉
b
͉
͑9͒
c
c
␹Ϫ1͑T͒ϭaϩ b␰͑T͒ ϩ c␰͑T͒4.
5
3
2
35
9
͑6͒
b2 ac
3
3
B ͑0͒ϭ 4
ͱ
͉
b
͉
/3c
ͫ
Ϫ
ͬ
.
͑10͒
This relation indicates that the susceptibility for aϾ0, b
c
b2 16
c
5
2
9
20
Ͻ0, and cϾ0, and 28 Ͻac/b Ͻ increases and then de-
25
͓
Yamada’s expression for B (0) includes an error. ͔ Since
the values of b and c of Co(S1ϪxSe ) will be nearly con-
creases through
a
maximum value with increasing
c
2
5
temperature. Therefore, every paramagnetic system that
shows the metamagnetic transition has a broad maximum at
a temperature Tmax in the temperature dependence of the
susceptibility. The itinerant system with the first-order ferro-
magnetic transition also has a broad maximum in the para-
magnetic temperature region. These theoretical results are
consistent with the observed magnetic properties of
Co(S1ϪxSe ) .
x 2
stant in the narrow concentration region 0.1рxр0.2, the lin-
ear increase of Bc(0) with x mainly comes from the increase
Ϫ1
of aϭ␹(0)
͓see Figs. 6͑a͒, 6͑b͒, and Eq. ͑1͔͒. The ob-
2
served T dependence of Bc(T) originates from the thermal
2
2
spin fluctuation ␰(T) that increases proportionally to T at
low temperatures. The fact that ␣ in Eq. ͑1͒ does not depend
on x indicates that the thermal spin fluctuation in the ferro-
magnetic compound Co͑S0.9Se0.1͒2 above Tc is equal to that
in the paramagnetic compound with 0.12рxр0.2.
x
2
The inverse susceptibility at Tmax is written as
b2 ac
5
As described above, the magnetic phase diagram of
Co(S1ϪxSe ) , the susceptibility ␹(Tmax) and the critical
␹
͑Tmax͒Ϫ1
ϭ
ͩ
Ϫ
ͪ
.
͑7͒
b2 28
x
2
c
field B (x,T) can qualitatively elucidated with the MY
c
25
The temperature Tmax is always higher than T . This is
theory. Next, we try to evaluate the parameters a, b, and c
0
2
consistent with the experimental results of Co(S1ϪxSe ) , as
and the thermal spin fluctuations ␰(T) . Since the ferromag-
x
2
shown in Fig. 8. It should be noted that ␹(Tmax) becomes
netism of Co(S1ϪxSex)2 disappears at xϭ0.11, we have
ac/b ϭ 16 for xϭ0.11. We already obtain ac/b ϭ 28 for x
ϭ0.01 from Eq. ͑8͒. Therefore, we get
3
2
5
2
5
2
infinite at ac/b ϭ 2 , where the type of the ferromagnetic
8
transition changes and Tmax is equal to the Curie temperature
T corresponding to the point T . ͑The ferromagnetic region
c
t
2
3
ac
b2
is 0рac/b Ͻ .͒ In order to compare the experimental data
of ␹(Tmax
ϭ8.93ϫ10Ϫ2xϩ0.1777.
1
6
͑11͒
Ϫ1
)
with the theoretical relation ͑7͒, we have plot-

5
6
MAGNETIC PROPERTIES OF THE ITINERANT . . .
14 027
On the other hand, the concentration dependence of the criti-
cal field of Co(S1ϪxSex)2 for Tϭ0 K, which is shown in
Fig. 6͑b͒, is written as
netic transition. In the high-pressure experiments, we in-
creased the temperature of CoS after zero-field cooling.
2
Thus, the Curie temperature in the pressure region of the
first-order transition is observed to be higher than the equi-
B ͑x,0͒ϭ216xϪ23.8 ͓T͔.
͑12͒
c
librium value of T , as seen in the temperature dependence
c
of the magnetization of Co͑S Se ͒ indicated in Fig. 1. We
0.9 0.1 2
Using the relations ͑7͒, ͑8͒, ͑10͒, ͑11͒, and ͑12͒, we can
estimate the coefficients a, b, and c within the framework of
the MY theory as
consider that the second-order transition of CoS turns into
2
the first-order one at PϷ0.4 GPa, where the Curie tempera-
ture corresponds to the tricritical point T . The position of T
t
c
aϭ1.07ϫ10 ϩ5.4ϫ10 x ͓T ͑␮ /Co͒Ϫ1͔,
3
2
for CoS at 0 GPa exists on the second-order phase boundary
2
B
near T . This phase diagram can also be well reproduced by
t
bϭϪ7.1ϫ103 ͓T ͑␮ /Co͒Ϫ3͔,
the theoretical one shown in Fig. 15. Because the application
B
2
of high pressure increases the value of ac/b and shifts the
cϭ8.3ϫ103 ͓T ͑␮ /Co͒Ϫ5͔.
͑13͒
c
position of T to a point on the first-order phase boundary,
B
the metamagnetic transition appears just above T . These
c
In the Co(S1ϪxSe ) system, the second term of Eq. ͑9͒ is
x
2
facts indicate that CoS is a ferromagnet with a positive
2
2
experimentally expressed as ␣T
with ␣ϭ1.43
ϫ10 ͓T/K ͔. Using the values of a, b, and c, we obtain
the thermal spin fluctuation in Co(S1ϪxSe ) as
Ϫ1
value of aϭ␹(0) , which does not satisfy the Stoner con-
Ϫ3
2
dition.
x
2
The magnetic properties of ferromagnetic Co͑S Se ͒
0.9 0.1 2
with the first-order transition are drastically changed by the
application of high pressure. Although the Curie temperature
is T ϭ27 K at 0 GPa, the ferromagnetism disappears at P
ϭ0.25 GPa and paramagnetism appears at 0.25 GPa. In the
paramagnetic region PϾ0.25 GPa, the metamagnetic transi-
2
2
␰
͑T͒ ϭ6.1ϫ10Ϫ6T2 ͓͑␮ /Co͒ ͔.
͑14͒
B
At Tϭ100 K, the average local amplitude of the thermally
fluctuating moment reaches about 4 ͓␮ /Co͔.
The estimated values of a, b, c, and ␰(T) can quantita-
tively explain the experimental values of ␹(Tmax) and
B (x,T) and the phase boundaries at Tϭ0 K. However, we
have found that the value of ␹(0) (ϭa ) is much smaller
than the experimental one. In the case of Co͑S0.86Se ͒ , for
example, the susceptibility for Tϭ0 K is given by ␹(0)
Ϸ␹(Tmax)/16. As already described, the susceptibility mea-
sured at low temperatures is enlarged by the effects of mag-
netic impurities and sample inhomogeniety. The estimation
of the intrinsic value of ␹(0) from the experimental data is
difficult. However, the experimental value of ␹(0) in the
Co(S1ϪxSe ) system is obviously much larger than the cal-
culated one. This is because the effect of zero-point spin
fluctuations are completely neglected in the MY theory. We
consider that the value of ␹(0) obtained from Eq. ͑13͒ is
close to the one calculated from the density of state at the
Fermi level and the Stoner enhancement factor. The suscep-
tibility of Co(S1ϪxSe ) at Tϭ0 K will be enhanced by this
c
c
1
B
2
tion takes place even at Tϭ0 K. Using the values of T and
c
P , we can evaluate the pressure dependence of T to be
c
c
c
Ϫ1
dT /dPϭϪ108 K/GPa. This value is extremely large com-
c
pared with other itinerant ferromagnets. For example, the
0.14 2
value of dT /dP is Ϫ35 K/GPa for an Invar alloy Fe Ni
c
64 36
34
with a very large pressure effect of Tc . We can easily
understand such a large value of dT /dP using the theoret-
c
ical phase diagram. As shown in Fig. 15, the decrease of T
on the first-order phase boundary with increasing ac/b is
c
2
very large compared with that on the second-order phase
boundary. The critical field of Co͑S Se ͒ as a function of
0.9 0.1 2
x
2
temperature and pressure is given by Eq. ͑2͒. The first term is
written as
B ͑P,0͒ϭ4.25PϪ1.06 ͓T͔,
c
͑15͒
where P is expressed in terms of GPa. Equation ͑15͒ is very
similar to Eq. ͑12͒ for the concentration dependence of the
critical field at Tϭ0 K. This also suggests that both the ap-
plication of high pressure and the substitution of Se produce
x
2
33
effect. Recently, Takahashi and Sakai have proposed a new
model that the magnetization process of the itinerant electron
system exhibiting the metamagnetic transition is mainly
dominated by zero-point spin fluctuations in the ground state.
almost the same magnetic effects on CoS . Comparing both
2
equations we know that 1% Se substitution corresponds to a
pressure of 0.51 GPa. Since the critical concentration x of
c
B. Magnetic properties under static high fields
and high pressure
Co(S1ϪxSex)2 is estimated to be x ϭ0.11, the ferromag-
c
netism of CoS will disappear at P ϭ5.6 GPa.
2
c
As already described, CoS with the second-order ferro-
2
magnetic transition has no metamagnetic transition above
Tc , but the application of high pressure PϾ0.4 GPa changes
the ferromagnetic transition into the first-order one. We have
observed the metamagnetic transition just above the Curie
temperature at Pϭ0.62 and 0.77 GPa. These experimental
results are summarized in the P-T phase diagram shown in
V. CONCLUSION
CoS2 is a ferromagnet with the second-order transition at
Tcϭ122 K. The substitution of only 10% Se for S in CoS2
drastically reduces the Curie temperature to T ϭ27 K and
the transition becomes first order. Co(S1ϪxSe ) with 0.12
c
x
2
Fig. 11. The pressure dependence of T is anomalous above
рx becomes an exchange-enhanced Pauli paramagnet. The
temperature dependence of the susceptibility of ferromag-
netic Co͑S Se ͒ shows a broad maximum at a tempera-
ture Tmax in the paramagnetic temperature region, similarly
to the paramagnets. We have measured the magnetizations of
c
0
.4 GPa: the value of T decreases with increasing pressure,
c
but is remarkably higher than that expected from the data
below 0.4 GPa. This anomalous change originates from the
hysteresis of magnetization due to the first-order ferromag-
0.9 0.1 2

14 028
T. GOTO, Y. SHINDO, H. TAKAHASHI, AND S. OGAWA
56
pressure and the ferromagnetism disappears at 0.25 GPa. In
the paramagnetic pressure region, the clear metamagnetic
transition occurs. We have found that the application of high
pressure produces almost the same effects on the present
system as the Se substitution.
Co(S1ϪxSe ) with 0рxр0.2 in pulsed high magnetic fields
up to 40 T. The itinerant metamagnetic transitions have been
x
2
observed in the paramagnets. Co͑S Se ͒ also exhibits the
0.9 0.1 2
transition above T . The critical field of the transition in-
c
2
creases with increasing temperature as T . Using the experi-
We have analyzed the magnetization data using the MY
theory. The observed magnetic properties and the determined
mental data of T and the critical temperature T at which
c
0
the transition disappears, we have determined the magnetic
phase diagram in the x-T plane.
magnetic phase diagram of Co(S1ϪxSe ) can qualitatively
x
2
be elucidated with this theory. In order to explain these re-
sults quantitatively, however, the effects of zero-point spin
fluctuations must be included in the theory.
We have measured the magnetizations of ferromagnetic
CoS and Co͑S Se ͒ under static high magnetic fields and
2
0.9 0.1 2
high pressure. With increasing pressure, the Curie tempera-
ture of CoS decreases and the second-order ferromagnetic
2
transition changes into the first-order one at PϷ0.4 GPa. In
ACKNOWLEDGMENTS
the pressure regime of the first-order transition
P
Ͼ0.4 GPa, we have observed the metamagnetic transition
just above T . In the case of Co͑S Se ͒ , The Curie tem-
perature is drastically decreased by the application of high
The authors thank H. Yamada for useful discussions.
They also thank T. Harada for cooperative research in the
early stages of the study.
c
0.9 0.1 2
*
Author to whom correspondence should be sent; FAX: ϩ81-
478-5471; Electronic address: goto@mgl.issp.u-tokyo.ac.jp
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