Electronic transport in Eu1-xCaxB6

Article abstract of DOI:10.1103/PhysRevB.61.4174

We have measured the electrical resistivity, the magnetoresistance, the Hall effect, and the magnetization in varying temperature ranges between 0.3 and 300 K on single crystals of EuB₆, CaB₆, and Eu_0.8Ca_0.2B₆. The ferromagnetic phase transition of EuB₆, marked by a sharp peak in the temperature dependence of the electrical resistivity ρ(T) just below 16 K, is shown to be accompanied by a considerable increase of the effective charge carrier concentration n_eff. The overall features of the transport properties of Eu_0.8Ca_0.2B₆ are similar to those of EuB₆. A phase transition at 5.3 K has been established. However, the increase of n_eff across this phase transition by two orders of magnitude is much more pronounced than in pure EuB₆. 2000 The American Physical Society.

Full text of DOI:10.1103/PhysRevB.61.4174

PHYSICAL REVIEW B
VOLUME 61, NUMBER 6
1 FEBRUARY 2000-II
Electronic transport in Eu1ÀxCa B6
x
*
S. Paschen, D. Pushin, M. Schlatter, P. Vonlanthen, and H. R. Ott
Laboratorium f u¨ r Festk o¨ rperphysik, Eidgen o¨ ssische Technische Hochschule–H o¨ nggerberg, 8093 Z u¨ rich, Switzerland
D. P. Young and Z. Fisk
National High Magnetic Field Laboratory, Florida State University, 1800 East Paul Dirac Drive, Tallahassee, Florida 32306
͑
Received 7 July 1999; revised manuscript received 18 October 1999͒
We have measured the electrical resistivity, the magnetoresistance, the Hall effect, and the magnetization in
varying temperature ranges between 0.3 and 300 K on single crystals of EuB , CaB , and Eu0.8Ca0.2B . The
6
6
6
ferromagnetic phase transition of EuB , marked by a sharp peak in the temperature dependence of the electrical
6
resistivity ␳(T) just below 16 K, is shown to be accompanied by a considerable increase of the effective charge
carrier concentration neff . The overall features of the transport properties of Eu0.8Ca0.2B are similar to those
6
of EuB . A phase transition at 5.3 K has been established. However, the increase of n across this phase
6
eff
transition by two orders of magnitude is much more pronounced than in pure EuB6.
I. INTRODUCTION
are both divalent cations in the respective hexaborides, re-
It has been known for some time that the onset of mag-
placing Eu in EuB by Ca should have no sizeable effect on
6
netic order in EuB is accompanied by a large reduction of
the electrical resistivity. More recently, the previously sug-
the density of conduction electrons. Thus the charge-carrier
concentrations in EuB6 , CaB6, and Eu0.8Ca0.2B6 are all ex-
pected to be similar. What is, however, drastically altered
when replacing Eu in EuB6 by Ca is the regular array of
4f-electron moments.
6
1
gested ferromagnetic character of the ordered state has been
2
confirmed by neutron-scattering measurements. The same
experiments also confirmed that the aligned magnetic mo-
ments are due to the localized 4f electrons of the Eu2 ions
ϩ
and are of the expected magnitude of 7␮ /Eu ion. In the
paramagnetic state the temperature dependence of the elec-
B
II. SAMPLES AND EXPERIMENTAL METHODS
trical resistivity is of metallic character but the concentration
The single-crystalline EuB , CaB , and Eu Ca B
0.2 6
samples were prepared by solution growth from Al flux, us-
ing the appropriate amounts of the pure elements. Flux-
6
6
0.8
of itinerant charge carriers is known to be rather small.1
,3–7
It
is therefore not a priori clear whether the spontaneous align-
ment of the localized moments is simply due to the usual
Ruderman-Kittel-Kasuya-Yosida interaction or whether also
other coupling mechanisms might be of significance. A pos-
grown SrB samples have been shown to be of high struc-
6
1
1
tural and chemical quality. In addition to EuB , containing
6
the isotopes 10B and B in the ratio given by their natural
11
sible route to ferromagnetism in EuB was very recently pro-
6
abundance of approximately 1:4, we have also investigated
1
0
11
10
posed from a mean-field treatment including the effect of the
Eu B and Eu B samples containing only the isotopes
B
6
6
8
and 11B, respectively. By this approach we hoped to disen-
tangle some of the complicated features observed in conven-
bond-charge Coulomb repulsion by Hirsch. He argues that
in EuB , and possibly also in other metallic systems, ferro-
6
magnetism is driven by a band broadening or equivalently an
effective mass reduction, both occurring upon spin polariza-
tion. Hirsch takes the point of view that the giant shift of the
tional EuB samples with the natural mixture of B isopopes.
6
A non-negligible influence might be expected if polaronic
effects are important in the low-temperature behavior of
EuB6.
The electrical resistivity, the magnetoresistance, and the
Hall effect were measured by a standard low-frequency ac
technique in varying temperature ranges between 0.3 and
300 K and in magnetic fields of up to 70 kOe. The magne-
toresistance was measured in a transverse configuration, i.e.,
plasma edge observed in optical reflectivity measurements
9
on EuB by Degiorgi et al. is mainly due to an effective-
6
mass variation. In this contribution, however, we show by
temperature and magnetic-field dependent Hall-effect mea-
surements that in EuB a considerable change in the effective
6
charge-carrier concentration occurs upon spin polarization.
From these measurements and the data of Ref. 9 we give an
estimate for the variation of the effective mass across the
ferromagnetic phase transition.
ជ
the magnetic field H was applied perpendicular to the elec-
ជ
trical current I. For the Hall-effect measurements a standard
ជ
setup with the two Hall voltage contacts perpendicular to I
A completely different type of ferromagnetism has re-
1
0
ជ
cently been discovered in Ca1ϪxLa B . Here the ferromag-
and to H was used. In order to eliminate the misalignement
x
6
netic polarization is thought to be a manifestation of a new
ground state of the low-density ensemble of itinerant elec-
trons, which is amazingly stable up to temperatures of the
order of 1000 K. Therefore we have also investigated the
electrical transport properties of CaB and of Eu Ca B
voltage, the sample was, at each field setting, first measured
in an upright position, then turned by 180°, and subsequently
measured in a downward position. At each temperature a
sweep of the magnetic field was performed, stabilizing the
temperature with a capacitance thermometer. For EuB and
6
0.8
0.2
6
6
and compare them with the results on EuB . As Ca and Eu
Eu Ca B the electrical leads were contacted to the sample
6
0.8
0.2 6
0
163-1829/2000/61͑6͒/4174͑7͒/$15.00
PRB 61
4174
©2000 The American Physical Society

PRB 61
4175
ELECTRONIC TRANSPORT IN Eu1ϪxCa B
x
6
FIG. 1. Electrical resistivity ␳ vs temperature T for EuB
FIG. 2. Numerically calculated temperature derivative of the
6
1
0
11
samples 1 (Eu B ), 2 (Eu B ), and 3 (EuB ).
electrical resistivity ץ␳/ץT normalized to its maximum value as a
6
6
6
1
0
function of temperature T for the EuB samples 1 (Eu B ), 2
6
6
1
1
(
Eu B ), and 3 (EuB ). The solid lines are to guide the eye.
6 6
with silver epoxy, for CaB spring contacts were used. The
6
magnetic measurements were performed in a commercial su-
perconducting quantum interference device magnetometer in
the temperature range 1.9–300 K.
defined ͑12.4 K for sample 1, 12.5 K for sample 2, 12.8 K
for sample 3͒. The third maximum at T ϭ9.6 K is observed
3
9
,13
only for sample 2. Measurements of the specific heat
re-
vealed the occurence of two consecutive phase transitions in
III. EXPERIMENTAL RESULTS AND ANALYSIS
EuB . Our ␳(T) data show that the phase transition is even
6
more complicated and that the details at temperatures below
TC may be quite sample dependent. The Curie temperature
TC is, within 0.4 K, the same for all our samples. From these
data we have no unambiguous evidence for a B isotope ef-
fect on the ferromagnetic transition in EuB6.
Our results for the temperature dependence of the electri-
cal resistivity ␳(T) of the EuB samples are, in magnitude
6
and shape, very similar to those that have been published
1
,3–7,12,13
previously
and are displayed in Fig. 1. In the follow-
1
0
11
ing we refer to the samples Eu B , Eu B , and EuB as
6
6
6
We now turn to the electrical resistivity data of CaB and
6
sample 1, 2, and 3, respectively. It may be seen that the
general features of ␳(T) are the same for all three samples
but the absolute magnitudes of the resistivities are quite dif-
ferent. We have no obvious explanation for the latter fact.
Between room temperature and approximately 30 K, ␳ de-
creases as T decreases, a sign of common metallic behavior.
At lower temperatures ␳(T) increases, passes through a
cusplike maximum just below 16 K, and subsequently falls
Eu Ca B which are shown in Figs. 3 and 4, respectively.
0
.8
0.2 6
It may be seen that ␳ of CaB varies much less with tem-
6
perature than ␳ of EuB . Below room temperature ␳ of CaB6
6
decreases, reaching a minimum at 116 K. After a subsequent
increase it passes through a maximum at 53 K and again
through a further minimum at 10.8 K. Finally it increases
smoothly with decreasing temperature to 1.5 K. More pro-
nounced features of ␳(T) are recognized for Eu Ca B .
0
.8
0.2 6
off steeply to the lowest measured temperatures. Below 3 K,
2
The dominating sharp maximum at 5.3 K is preceded by a
shallow maximum at 208 K and a shallow minimum at 34 K.
The subsequent decrease of ␳(T) is intercepted by a mini-
mum at 2.5 K below which ␳(T) increases towards the low-
est measured temperatures. For comparison, Fig. 5 gives an
overview of the temperature dependences of the electrical
␳
(T) of all three samples is well described by ␳ϭ␳ ϩAT
0
with ␳ ϭ26.8, 15.1, and 40.3 ␮⍀ cm and Aϭ0.28, 0.08,
0
Ϫ2
and 0.24 ␮⍀ cm K for sample 1, 2, and 3, respectively.
The residual resistivity ␳ being the highest for the mixed-
0
isotopes sample may be related with enhanced disorder due
to the presence of both 1 B and B.
0
11
In Fig. 2 we carefully analyze ␳(T) of all three EuB6
samples in the temperature range between 7 and 17 K, by
plotting the numerically calculated derivative ץ␳/ץT as a
function of temperature. The passage through zero of ץ␳/ץT,
corresponding to the maximum of ␳(T), is followed by two
͑
samples 1 and 3͒ or even three ͑sample 2͒ maxima. The
temperatures at which ץ␳/ץT passes through zero are 15.6,
5.5, and 15.9 K for sample 1, 2, and 3, respectively. A
1
comparison with our temperature-dependent magnetic sus-
ceptibility measurements indicates that these temperatures
mark the onset of ferromagnetic order and thus have to be
identified with the Curie temperature T . The temperature of
C
the first maximum of ץ␳/ץT which we call T1 is, within
experimental uncertainty, the same for all three samples
͑14.9 K for samples 1 and 3, 14.8 K for sample 2͒, but the
temperature of the second maximum called T is less well
FIG. 3. Electrical resistivity ␳ vs temperature T for CaB6.
2

4176
S. PASCHEN et al.
PRB 61
FIG. 4. Electrical resistivity ␳ vs temperature T for Eu0.8Ca0.2B6.
The solid line is to guide the eye.
resistivities ␳(T), normalized to the room-temperature value,
of EuB sample 1, CaB , and Eu Ca B .
6
6
0.8
0.2 6
In Fig. 6 we replot the temperature dependence of the
electrical resistivity of the EuB sample 1 ͓Fig. 6͑a͔͒, and of
6
Eu Ca B ͓Fig. 6͑b͔͒, together with the magnetic suscep-
0
.8
0.2 6
tibilities ␹ of both samples. Just as for EuB the cusplike
6
feature of ␳(T) of Eu Ca B at 5.3 K is accompanied by a
0
.8
0.2 6
sharp increase of ␹ with decreasing temperature. This is a
clear indication that also Eu Ca B orders ferromagneti-
0
.8
0.2 6
cally, at a substantially reduced Curie temperature, however.
The saturation magnetization at 1.9 K is approximately 5 ␮B
per Eu ion, distinctly reduced if compared to approximately
7
␮ per Eu ion for EuB .
FIG. 6. Electrical resistivity ␳ and magnetic susceptibility ␹ in
SI units vs temperature T for EuB sample 1 (Eu B ) in ͑a͒ and for
6 6
Eu0.8Ca0.2B6in ͑b͒. The Curie temperatures TC are 15.6 and 5.3 K
for EuB6 and Eu0.8Ca0.2B6, respectively. The solid lines are to guide
the eye.
B
6
1
0
In the following we present our Hall effect measurements.
For pure EuB , low-temperature and low-field Hall-effect
data are available in the literature. The effective charge-
carrier concentration at 4.2 K that we have derived from our
Hall constant at 1 T agrees, within factors of 0.7 and 1.1,
with those derived from the low-field Hall constants of Refs.
6
5
,7
some representative data of the Hall resistivity ␳ ϭV d/I of
H
H
5
and 7, respectively. The field dependence of the Hall resis-
Eu Ca B , measured at fixed temperatures between 2 and
0
.8
0.2 6
tivity of EuB in magnetic fields up to 70 kOe, to be pre-
6
2
90 K, is plotted as a function of the magnetic induction B
sented below, has, to our knowledge, not yet been published.
The Hall effect shows the most spectacular features for
Eu Ca B and we shall present these data first. In Fig. 7
ϭ␮ H, where H is the external magnetic field and ␮ the
0
0
permeability of free space. VH is the Hall voltage, d the
0
.8
0.2 6
FIG. 5. Electrical resistivity ␳ normalized to the value at 288 K
FIG. 7. Hall resistivity ␳H of Eu0.8Ca0.2B6, measured at fixed
temperatures between 2 and 290 K, as a function of the magnetic
induction B. The solid lines are to guide the eye.
10
vs temperature T for EuB sample 1 (Eu B ) and for CaB and
6
6
6
Eu0.8Ca0.2B6.

PRB 61
4177
ELECTRONIC TRANSPORT IN Eu1ϪxCa B
x
6
FIG. 9. Effective charge-carrier concentration Ϫ1/(R e) of
FIG. 8. Effective charge-carrier concentration Ϫ1/(R e) of
H
H
1
0
EuB sample 1 (Eu B ) at different values of B between 1 and 7 T
Eu0.8Ca0.2B at different values of B between 1 and 7 T as a func-
6
6
6
as a function of temperature T. The Hall coefficient RH was calcu-
lated at each B value by R (B)ϭ␳ (B)/B. The dotted line indi-
tion of temperature T. The Hall coefficient RH was calculated at
each B value by R (B)ϭ␳ (B)/B. The dotted line indicates the
H
H
H
H
cates the Curie temperature determined from the position of the
maximum of ␳(T). The solid lines are to guide the eye.
Curie temperature determined from the position of the maximum of
(T). The solid lines are to guide the eye.
␳
negative slope of the 1-T curve coincides with the Curie
sample thickness, and I the applied current. Between 290 and
approximately 80 K, ␳H is a linear function of B up to B
ϭ7 T. At lower temperatures ␳H deviates from the linear
dependence at inductions B that decrease with decreasing
temperature. At 2 K, an almost linear dependence with a
slope whose absolute value is much smaller than at high
temperatures is recovered. Attempts to fit the highly nonlin-
temperature of Eu Ca B ͑dotted line in Fig. 8͒ indicates
0.8
0.2 6
that the drastic increase of the charge-carrier concentration is
directly related to the ferromagnetic phase transition.
The Hall effect of pure EuB6 is qualitatively similar to the
one of Eu Ca B , but the features described above are
0
.8
0.2 6
somewhat less pronounced in the case of EuB . In Fig. 9 we
6
ear ␳ (B) curves in the range between 2 and 80 K by either
plot Ϫ1/(R e), obtained as explained above, at fixed fields
H
H
a two band model or by considering the anomalous Hall
effect via our magnetization measurements on Eu Ca B
between 1 and 7 T as a function of temperature. The analogy
between the curves of Eu Ca B and EuB is not really
0
.8
0.2
6
0.8
0.2
6
6
in magnetic fields of up to 55 kOe, were not successful.
Neither of these considerations lead to an even qualitative
agreement between calculations and experiment. Therefore
obvious at first sight because the investigated temperature
range with respect to the Curie temperature is much less
extended for EuB , for which measurements only below 25
6
we suggest that the nonlinear ␳ (B) behavior results from a
magnetic-field-induced transition between a charge-carrier-
K have been made. Only the low-temperature tail of the
field-induced phase transition from a state with low charge-
carrier concentration at high temperatures to a state with high
charge-carrier concentration at low temperatures is experi-
mentally established. However, we speculate that at tempera-
H
poor state at high temperatures ͓linear ␳ (B) dependence
H
with a large absolute value of the slope͔ to a charge-carrier-
rich state ͓linear ␳ (B) dependence with a small absolute
H
value of the slope͔ at low temperatures. The temperature at
which this transition occurs increases with increasing applied
magnetic field. This is more clearly revealed by Fig. 8, where
tures well above the Curie temperature of EuB , all curves of
6
Fig. 9 will merge and assume a value somewhat smaller than
5ϫ1019 cm . Well below T , the ratio Ϫ1/(R e) tends to
Ϫ3
C
H
we plot Ϫ1/(R e) at different values of B between 1 and 7 T
decrease again, at least for external fields exceeding 3 T. For
Bϭ7 T the effective charge-carrier concentration assumes a
maximum at approximately 14 K and clearly decreases to-
wards lower temperatures. In smaller fields the position of
this maximum shifts to lower temperatures and the decrease
is less pronounced.
H
as a function of temperature. The Hall coefficient RH was
calculated at each B value by R (B)ϭ␳ (B)/B. The ratio
H
H
Ϫ1/(R e) may be interpreted as an effective charge-carrier
H
concentration. R is negative at all fields and at all tempera-
H
tures which implies that the charge carriers are predomi-
nantly electronlike. Above 80 K all curves in Fig. 8 fall on
The Hall-effect data of CaB is much easier to analyze.
6
top of each other, reflecting the linear variation of ␳ (B). At
The Hall resistivity ␳ (B) varies approximately linearly with
H
H
lower temperatures all Ϫ1/(R e) curves reveal a steep in-
B in the entire investigated temperature range between 1.9
H
crease over more than one order of magnitude. The tempera-
tures fixed by the largest slope of this increase range between
approximately 30 K for the curve at 7 T and approximately 5
K for the curve at 1 T. The effective electron concentration is
and 280 K. The slope of all ␳ (B) curves is negative, im-
H
plying predominant electron-type conduction. The corre-
sponding effective charge-carrier concentration reaches val-
ues between 1.8 and 2.4ϫ1019 cm . At 53 K, the
temperature where ␳(T) reaches a maximum, the electron
concentration increases slightly. This feature is reminescent
of those in ␳(T) and n(T) at the ferromagnetic phase tran-
sition in EuB and Eu Ca B .
Ϫ3
1
8
Ϫ3
approximately 8ϫ10 cm
above the transition and be-
tween 3 and 8ϫ10 cmϪ3 below the transition. The curve at
T reflects most closely the intrinsic ͑zero-field͒ behavior of
Eu Ca B . The fact that the temperature of the maximum
2
0
1
0
.8
0.2
6
6
0.8
0.2 6

4178
S. PASCHEN et al.
PRB 61
FIG. 10. Effective charge-carrier concentration per formula unit
neff determined from the Hall coefficient at 1 T of EuB sample 1
FIG. 12. Magnetoresistance MRϭ͓R(B)ϪR(0)͔/R(B) of
6
Eu0.8Ca0.2B at different B values between 1 and 7 T as a function of
6
10
(
Eu B ), CaB , and Eu0.8Ca0.2B as a function of temperature T.
temperature T. The dotted line indicates the Curie temperature de-
termined from the position of the maximum of ␳͑T͒. The solid lines
are to guide the eye.
6
6
6
The dotted lines indicate the positions where the respective ␳(T)
curves assume a maximum. The solid lines are to guide the eye.
An overview over the low-field Hall-effect data of all
three investigated samples, EuB , CaB , and Eu Ca B , is
given in Fig. 10 where we plot the effective charge-carrier
EuB sample 1 at different B values between 1 and 7 T as a
6
5,7,13
6
6
0.8
0.2
6
function of temperature. As previously reported,
the
high-temperature MR is negative, increasing in absolute
value with decreasing temperature. The maximum negative
MR of approximately 100% is reached at the Curie tempera-
concentration n ϭϪ1/͓R (Bϭ1 T)e] per formula unit as a
eff
H
function of temperature at 1 T. For the lattice constants we
1
3
14
used 4.1852 Å for EuB6, 4.146 Å for CaB6, and an inter-
polation between both values for Eu Ca B . For
ture of EuB . At lower temperatures the absolute value of the
6
0
.8
0.2
6
MR decreases, passes through zero, and reaches positive val-
ues as high as 700% at 7 T and 1.7 K.
Eu Ca B n increases most dramatically across the mag-
0
.8
0.2
6
eff
netic transition at 5.3 K ͑by two orders of magnitude͒ with
decreasing temperature. For EuB n increases by at least a
Above T , the magnetoresistances of EuB6 and
C
6
eff
Eu Ca B are qualitatively similar. As is shown in Fig. 12,
0
.8
0.2 6
factor of 2.3 and the transition temperature is considerably
above T the MR of Eu Ca B is, except for small posi-
C
0.8
0.2 6
higher. For CaB a slight increase of n may be identified
6
eff
tive values at small fields, negative and increases in absolute
between 200 and 30 K. The effective charge-carrier concen-
tration is, with less than 0.1 electron per formula unit at all
temperatures, rather low for all three materials. For
value with decreasing temperature. At T a maximum abso-
C
lute value of almost 100% is reached, just as for EuB . How-
6
ever, in contrast to the MR of EuB , the MR of Eu Ca B
6
0.8
0.2
6
Ϫ4
Eu Ca B we find, with less than 6ϫ10 charge carriers
0
.8
0.2 6
remains negative at temperatures well below TC .
per formula unit, an exceedingly low effective carrier con-
centration at high temperatures.
Finally, we present our magnetoresistance data. In Fig. 11
we plot the magnetoresistance MRϭ͓R(B)ϪR(0)͔/R(B) of
IV. DISCUSSION
The results of recent band-structure calculations by
Massida et al.15 suggest that the cubic hexaborides CaB and
6
EuB are semimetals, with a small band overlap at the X
6
point of the Brillouin zone. In a perfect semimetal the con-
centration of electrons in the conduction band is the same as
the concentration of holes in the valence band. The Hall
coefficient of such a system is only nonzero if the electron
and hole mobilities are not the same. The fact that we find a
negative Hall coefficient for all samples in the entire tem-
perature range indicates that the electrons are more mobile
than the holes. This is in agreement with the band structure
of Ref. 15 where, at the X point, the effective mass of the
charge carriers in the conduction band of both CaB and
6
EuB is smaller than the one of the holes in the valence band.
6
The effective charge-carrier concentration neff discussed in
the previous section is, in a perfect semimetal, related to the
real electron ͑or hole͒ concentration n by n ϭn(␮p
eff
FIG. 11. Magnetoresistance MRϭ͓R(B)ϪR(0)͔/R(B) of
ϩ␮ )/(␮ Ϫ␮ ), where ␮ and ␮ are the hole and electron
mobility, respectively. Thus the real electron concentrations
n
p
n
p
n
10
EuB sample 1 (Eu B ) at different B values between 1 and 7 T as
6
6
a function of temperature T. The solid lines are to guide the eye.
n in EuB , CaB , and Eu Ca B may even be smaller than
6
6
0.8
0.2 6

PRB 61
4179
ELECTRONIC TRANSPORT IN Eu1ϪxCa B
x
6
FIG. 14. Absolute value of the Hall mobility
͉
␮H
͉
of EuB6
FIG. 13. Temperature dependence of the effective mass ratio
1
0
1
0
sample 1 (Eu B ), CaB , and Eu0.8Ca B vs temperature T. The
m*/m (m ϭ mass of free electron͒ of EuB sample 1 ͑Eu B ͒
6 6 0.2 6
e
e
6
6
inset shows the temperature dependence of the ‘‘Hall’’ mean free
path ␭ of the same three samples obtained as explained in the text.
obtained by combining the effective charge-carrier concentration of
Fig. 10 with the temperature dependence of the plasma frequency
given by Degiorgi et al. ͑Ref. 9͒. The dots mark the data points and
the solid curve is obtained by a smooth interpolation between them.
around TC the Fermi surface is very sensitive to magnetic
fields. An appreciable decrease of the effective charge-carrier
concentration across the ͑zero-field͒ Curie temperature T is
C
the effective charge-carrier concentrations neff given in Fig.
deduced from the low-field Hall constant only. Higher fields
shift the decrease of the effective charge-carrier concentra-
tion to higher temperatures. In the case of Eu Ca B , the
1
0. Likewise, it cannot be excluded that ␮ and ␮ have a
p n
different temperature dependence which would affect the
way in which n is changed across the phase transition. How-
ever, this effect shall be neglected in the following estimate.
As mentioned in the introduction measurements of the
0
.8
0.2 6
temperature fixed by the largest slope of this decrease is
shifted from 5 K at 1 T to 30 K at 7 T. A similar sensitivity
is anticipated for EuB ͑cf. Fig. 9͒. Therefore we believe that
6
1
6
optical reflectivity of single-crystalline EuB ͑same sample
the above-mentioned high-field measurements cannot rule
out an appreciable modification to the Fermi-surface dimen-
sions with the onset of ferromagnetism.
6
as sample 3 of this study͒ revealed a large shift of the plasma
9
edge below T . The unscreened plasma frequency ␻ was
C
p
Ϫ1
shown to increase from approximately 2060 cm at 20 K to
approximately 4890 cm at 6 K. As pointed out by De-
giorgi et al. this shift suggests an increase of the itinerant
Combining the resistivity and the Hall-effect data we may
calculate both the low-field Hall mobility ␮ ϭR (Bϭ1
Ϫ1
H
H
9
2
T)/␳ and the ‘‘Hall’’ mean free path ␭ϭប(3␲ /
e ) ͓R (Bϭ1 T)] /␳, which we plot in Fig. 14 and in its
4
1/3
2/3
charge-carrier concentration, a reduction of their effective
H
mass, or a combination of the two. Combining the ␻ (T)
inset, respectively, as a function of temperature for EuB6
sample 1, CaB , and Eu Ca B . The absolute value of the
p
data of Ref. 9 with our low-field Hall-effect data of EuB ͑cf.
6
6
0.8
0.2 6
2
1/2
Fig. 10͒ using the relation ␻ ϭ(ne /⑀ m*)
with n
Hall mobility
Curie temperature of 15.6 K. Below TC ,
creases steeply by an order of magnitude and reaches values
as high as 2000 cm /V s at 1.5 K. For Eu Ca B ͉␮H͉
͉
␮H
͉
of EuB has a sharp minimum at the
p
0
6
ϭϪ1/͓R (Bϭ1 T)e] we can estimate the temperature de-
͉
␮H
͉
of EuB in-
H
6
pendence of the effective mass m*. ⑀ is the permittivity of
0
2
free space. In Fig. 13 we plot the ratio m*/m , where m is
e
e
0.8 0.2 6
the mass of a free electron, between 6 and 25 K, the tem-
passes over a broad maximum centered at 50 K from where
perature range where both ␻ and R (Bϭ1 T) have been
it falls by two orders of magnitude with decreasing tempera-
p
H
2
measured. With decreasing temperature m*/m first slightly
ture to 0.3 cm /V s at 1.6 K. Unlike in the case of EuB ,
e
6
increases and, between 17 and 9 K, drops by a factor of 3.5,
a substantial reduction. Thus, in addition to an increase of
the charge-carrier concentration, the effective mass of the
charge carriers is reduced in the course of the ferromagnetic
phase transition. As mentioned in the Introduction, Hirsch
proposed a model for EuB in which the entire shift of ␻
͉
␮H
͉
of Eu Ca B does not increase below T but instead
0.8
0.2
6
C
continues to drop. For CaB6
͉
␮H
͉
varies much less with tem-
perature. It passes over a maximum at 140 K and through a
shallow minimum at 30 K. With absolute values of the order
of 100 cm /V s in the entire temperature range the Hall mo-
bility of CaB6 lies inbetween the ones of EuB6 and
Eu Ca B . For all three samples the temperature depen-
2
6
p
8
can be explained by a shift of the effective mass. Our results
may thus serve to refine this model.
0
.8
0.2 6
dence of the ‘‘Hall’’ mean free path ␭ resembles that of
␮H . The ‘‘Hall’’ mean free path of Eu Ca B above T ,
being considerably shorter than the ones of EuB and CaB ,
Very recently, Aronson et al.16 reported on results of their
Shubnikov–de Haas and de Haas–van Alphen measurements
͉
͉
0.8
0.2
6
C
6
6
on a EuB single crystal. From the smooth temperature de-
might be due to the disorder introduced into the system by
6
pendences below 25 K of four fundamental frequencies, ex-
tracted from measurements at fields between 5 and 30 T,
Ca doping. It is somewhat surprising that ␭ of EuB below
6
T is much longer than ␭ of CaB . It should be kept in mind,
C
6
they conclude that the Fermi surface of EuB is essentially
unaffected by the onset of magnetism. Our Hall-effect mea-
surements, however, show that in the temperature range
however, that the Hall mobility and the ‘‘Hall’’ mean free
path are only effective parameters in a fictitious one band
model. In a perfect semimetal the Hall mobility is related to
6

4180
S. PASCHEN et al.
PRB 61
rate have been shown to be reduced upon spin polarization.
Thus the ferromagnetic phase transition of EuB6 has an ap-
preciable effect on all three fundamental parameters ͑carrier
concentration, mass, and scattering rate͒ and a serious com-
parison with any theoretical model cannot be made without
disentangling these effects.
the electron and hole mobilities by ␮ ϭ␮ Ϫ␮ , i.e., a
H
p
n
small absolute value of the Hall mobility ͑and a short
‘Hall’’ mean free path͒ can also be due to ␮ and ␮ being
‘
p
n
coincidentally very similar in magnitude. In view of this
likely complication we refrain from interpreting the overall
features of ␮ (T) in detail at this time. Nevertheless, the
H
increase of
͉
␮H
͉
below TC of EuB is, in part, due to the
In Eu0.8Ca0.2B6we have identified a ferromagnetic phase
transition at 5.3 K, accompanied by an increase of the effec-
tive charge-carrier concentration by as much as two orders of
magnitude. The carrier concentration at temperatures above
6
decrease of the effective mass ͑cf. Fig. 13͒ but, in addition,
there has to be a sizeable increase of the effective scattering
time ␶ϭm␮/e. Evidence for this has also been obtained
from an analysis of the optical conductivity data presented in
Ref. 9. This indicates that there must be a significant change
in the scattering mechanism for itinerant charge carriers in
Ϫ4
the phase transition is, with less than 6ϫ10 per formula
unit, extremely low for a metallic system. In particular, it
does not lie inbetween the carrier concentrations of EuB6 and
CaB6. Thus it appears to be extremely interesting to further
investigate Eu1ϪxCa B samples and systematically follow
EuB induced by the phase transition.
6
x
6
the evolution of the Curie temperature and the charge carrier
concentration upon Ca doping of EuB6.
V. CONCLUSIONS
We have shown that the ferromagnetic phase transition of
EuB at approximately 16 K is accompanied by a consider-
6
able increase of the effective charge-carrier concentration.
Part of the giant shift of the plasma frequency deduced from
optical reflectivity measurements is thus due to an increase
of the charge-carrier concentration upon spin polarization. In
addition, both the effective mass and the effective scattering
ACKNOWLEDGMENTS
9
We thank H. Thomas for technical assistance. This work
was financially supported by the Schweizerische National-
fonds zur F o¨ rderung der wissenschaftlichen Forschung.
1
1
0
1
*
Present address: MPI for Chemical Physics of Solids, N o¨ thnitzer
Str. 48, 01187 Dresden, Germany.
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