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arXiv:1101.4770v1 [cond-mat.str-el] 25 Jan 2011
Nature of magnetic order in YbInNi4
T. Willers,1N. Hollmann,1S. Wirth,2H. Kierspel,1A. Bianchi,3Z. Fisk,4and A. Severing1
1Institute of Physics II, University of Cologne, Z¨ulpicher Straße 77, D-50937 Cologne, Germany
2Max Planck Institute CPfS, N¨othnizer Straße 40, 01187 Dresden, Germany
3D´epartement de Physique and Regroupement Qu´eb´ecois sur les Mat´eriaux de Pointe,
Universit´ede Montr´eal, Montr´eal, Quebec H3C 3J7, Canada
4University of California, Irvine, CA, USA
(Dated: January 26, 2011)
We have measured field and temperature dependent magnetization of YbInNi4to elucidate the
nature of the magnetic transition at 3 K. For small fields we find magnetic order as previously
reported. In contrast to former reports, however, our high resolution magnetization measurements
down to 500 mK indicate dominating antiferromagnetic exchange interactions. We discuss the
presence of geometrical frustration.
PACS numbers: 71.27.+a, 75.30.Cr
I. INTRODUCTION
YbInNi4forms in the same cubic C15b structure
as YbXCu4where Xstands for In, Ag, Au, or Pd.
YbInCu4exhibits an isostructural first order valence
transition as function of temperature,1YbAgCu4is a
heavy Fermion or Kondo compound and does not ex-
hibit magnetic order at ambient pressure analogous
to YbInCu4.1,2 In YbAuCu4, YbPdCu4, and YbInNi4
Yb is trivalent3,4 over the entire temperature range
and orders magnetically at 0.6, 0.8, and 3 K, respec-
tively. First reports hinted towards antiferromagnetism
in YbAuCu4and YbPdCu4,2and ferromagnetism in
YbInNi4.5Neutron diffraction data have confirmed anti-
ferromagnetism in YbAuCu4while YbPdCu4was found
to be ferromagnetic.3
The noncentrosymmetric cubic C15b (AuBe5)
structure6of YbInNi4is shown in Fig. 1. The Yb and
In ions reside on distinct face-centered-cubic sublattices
displaced by (1
4,1
4,1
4) along the unit cell diagonal and
FIG. 1: (color online) Unit cell of YbInNi4.
are surrounded by space-filling Ni tetrahedra. As a
result the tetrahedra formed by the magnetic Yb ions
are alternately intercalated with Ni tetrahedra (light
yellow tetrahedra in Fig. 1) or filled with In ions (dark
pink tetrahedra in Fig. 1). In this cubic structure the
crystal field (CEF) splits the 8-fold degenerate J=7/2
Hund’s rule ground state of Yb3+ into two doublets (Γ6
and Γ7) and one quartet (Γ8). There had been a debate
concerning the ground state wave function,5,6 but recent
spectroscopic results came to the conclusion that the
ground state must be the Γ8quartet7,8 despite the fact
that specific heat finds only an entropy of Rln 2 at the
ordering transition.5
In an extensive study of transport and thermodynamic
measurements on YbInNi4, Sarrao et al. find ferromag-
netism arising at 3 K.5The isothermal magnetization
data indicate a ferromagnetic transition when cooling
down from 5 to 2 K, but even at 2 K no hysteresis has
been reported. At a field of 1 T the magnetization is only
weakly saturated and barely recovers half of the theoret-
ically predicted ordered moments deduced from each of
the possible CEF ground states. Magnetic order at 3 K is
confirmed by a drop in the resistivity and a sharp peak
in the specific heat. The ordering peak in the specific
heat disappears when applying a 10 T field and a broad
hump shows at slightly higher temperatures which was
interpreted as a smearing out of the ordering transition
towards higher temperatures, suggesting ferromagnetic
order. In this work we present field and temperature de-
pendent magnetization data down to 500 mK. While the
data of Sarrao et al. are in agreement with our findings,
we present additional and complementary measurements
that provide more insight into the nature of magnetism
of YbInNi4.
II. EXPERIMENTAL DETAILS
Single crystals of YbInNi4were grown by flux growth.
X-ray diffraction pattern confirm the absence of impu-
rity phases and the existence of the 200 reflection in the
2
0 50 100 150 200 250 300
0
20
40
60
80
100
120
140
experimental data
Curie-Weiss fit
1/ (mole / emu)
T (K)
B||(100) = 1 T (zfc)
FIG. 2: (color online) SQUID: Inverse susceptibility versus
temperature measured with an applied field of 1 T along
(100). The solid line is a Curie-Weiss fit to the data for
T>50 K.
diffraction pattern verifies the C15b structure where Yb
and In ions are located on distinct sublattices. Isother-
mal magnetization measurements in fields up to 5 T and
temperatures down to 2 K were performed using a vibrat-
ing sample magnetometer (VSM) in a physical property
measurement system (PPMS) by Quantum Design. The
temperature dependent iso-field magnetization was mea-
sured with a superconducting quantum interference de-
vice (SQUID) magnetometer. After degaussing at 300 K,
the sample was cooled down to 2 K in zero field and then
the magnetization curves were measured for increasing
external fields, starting with the smallest field of 5 mT.
The field was applied along (100) and (110). Static mag-
netic susceptibility data from 2 to 300 K were measured
after zero-field-cooling with the VSM (for 100 mT and
1 T applied field, not shown here) and with the SQUID
(for 10 mT and 1 T applied field). Isothermal magneti-
zation at 500 mK was measured in another SQUID mag-
netometer using a 3He cryostat. Care was taken in an
effort to minimize the remanent field of the supercon-
ducting magnet.
III. RESULTS
Figure 2 shows the inverse susceptibility from 2 to
300 K measured with an applied field of 1 T after cooling
in zero field in the SQUID. This curve agrees well with
our VSM data (not shown here) and previous results.5,9
From a Curie-Weiss (CW) fit to 1/χfor T >50 K we
obtain ΘCW ≈-19 K and an effective magnetic moment
of 4.3 µB(nearly the free ion value of 4.5 µB). Sarrao et
al. and Yabuta et al. reported ΘC W = -8.2 and -12.4 K
as well as µef f = 4.1 and 4.6 µBfrom their susceptibility
data, respectively.5,9 It should be noted that ΘCW and
µeff depend on the temperature range considered within
the CW fit.
0 1 2 3 4 5
0
5000
10000
0.00
0.50
1.00
1.50
2.00
100K
50K
25K
300K
10K
5K
4K
3K
M (emu G / mole)
B (T)
BII(100) 2K
M (
B
/ f.u.)
FIG. 3: (color online) VSM: Isothermal magnetization as a
function of field at various temperatures.
-1.0 -0.5 0.0 0.5 1.0
-5000
0
5000
-1.0 -0.5 0.0 0.5 1.0
-1.00
-0.50
0.00
0.50
1.00
-0.10 -0.05 0.00 0.05 0.10
-4000
0
4000
T = 500 mK
M (emu G / mole)
T = 500 mK
M ( / f.u.)
B (T)
B (T)
M (emu G / mol)
FIG. 4: SQUID with He3insert: Isothermal magnetization
for the complete field loop from zero field to 1 T, -1 T, and
back to 1 T recorded at 500 mK. For fields between -20 mT
and 20 mT the data were recorded in steps of 20 µT.
Figure 3 shows the isothermal magnetization data of
YbInNi4at several temperatures between 2 and 300 K
and for fields up to 5 T along the crystallographic (100)
direction. For all temperatures the magnetization still in-
creases monotonically up to 5 T, i.e. it is far away from
saturation. Below 4 K the onset of a magnetic transi-
tion becomes obvious and below 3 K the systems ap-
pears magnetically ordered. Field loops were measured
for 2, 3, and 4 K, i.e. just above and within the mag-
netically ordered state, but a ferromagnetic hysteresis
was not observed within the accuracy of this experiment.
Data taken with the field parallel to (111) show the same
behavior with only a minor anisotropy at higher fields
(not shown here). In order to investigate the magnetic
order in more detail, another isothermal magnetization
measurement was performed at even lower temperature
(500 mK), i.e. well inside the ordered phase. Figure 4
3
0 2 4 6 8 10 12 14 16 18 20 22
0
2000
4000
6000
8000
10000
0.00
0.50
1.00
1.50
2 3 4
0
200
400
600
800
1000
M (emu G / mole)
T (K)
B||(100)
B||(110)
5mT
10mT
50mT
0.1T
1T
2T
3T
4T
M (
B
/ f.u.)
5T
M (emu G / mole)
T (K)
B = 5 mT
FIG. 5: (color online) Temperature magnetization along (100)
and (110) for various external fields applied. The inset shows
the low temperature behavior of the 5 mT curve in detail.
shows the field loop from zero field to 1 T, -1 T, and back
to 1 T. For fields between -20 and +20 mT the data were
recorded in steps of 20 µT. As is obvious from the inset
to Fig. 4 there is no sign of hysteresis or coercivity within
the experimental accuracy of 10 µT.
In Fig. 5 the temperature dependent magnetization be-
tween 2 and 20 K is plotted for various fields and two
different field directions. For the smallest external field
of 5 mT ordering sets in at 3 K. Below 3 K, i.e. once the
moments are ordered, the magnetization retains a con-
stant, temperature independent value. Moreover, there is
an anisotropy in the ordered phase such that the moment
for Bk(100) is smaller than for Bk(110), with µor d = 0.12
and 0.16 µB/f.u., respectively. Increasing the applied
field to 10 mT leads to an increase of the ordered mo-
ments by a factor of two. The ordering temperature and
the anisotropy of the saturated moment at low temper-
ature remain the same. For external fields larger than
50 mT the transition into magnetic order becomes broad-
ened and the magnetization keeps increasing upon low-
ering the temperature. In addition, the anisotropy has
vanished in external fields of 50 and 100 mT. In agree-
ment with the isothermal magnetization data the mo-
ment increases for larger external fields. Interestingly,
the anisotropy is reversed for external fields larger than
0.1 T, i.e. the moment along Bk(100) becomes larger
than for Bk(110).
IV. DISCUSSION
There is good agreement with the data presented above
and the isothermal and iso-field magnetization data of
Ref. 5 within the temperature and field range where both
data sets overlap. In the present study more emphasis
was put on low field and low temperature measurements
in order to elucidate the nature of the ordered state. We
summarize our observations: 1) For small external fields
there is magnetic order with a constant iso-field magneti-
zation below 3 K. 2) The ordered moment increases from
5 to 10 mT, but for larger fields the order is subdued and
iso-field magnetization keeps increasing even below 3 K.
3) The ordered moment found in the iso-field data is very
small. 4) There is no ferromagnetic hysteresis. 5) The
anisotropies in the low-field ordered state and the high-
field non-ordered state are reversed. 6) The isothermal
magnetization is still not saturated at 5 T.
Before discussing in detail the magnetization data, it is
essential to recollect the crystal-field scheme of YbInNi4
because its total splitting is small. According to inelas-
tic neutron data the first excited crystal-field state is at
3 meV and the second one at 4 meV.6,7 Therefore, for
applied fields of ≥1 T intermixing of ground and excited
state wave functions takes place. At high enough fields,
this intermixing is the dominating effect for the lack of
saturation in the isothermal magnetization data with in-
creasing field: The larger the applied field, the more in-
termixing takes place, and the larger is the magnetic mo-
ment which contributes. Ionic full multiplet calculations
based on the crystal-field scheme show that saturation
as function of field may be reached above 40 T which
is in agreement with high field experiments by Sarrao
et al..5Simulations find also that the anisotropy of the
crystal-field ground states induces the anisotropy in the
iso-field data for fields larger than 100 mT. The observed
anisotropy is compatible with a Γ6or a Γ8state, but
not with a Γ7. The same simulations confirm that fields
smaller than 100 mT are too weak to cause a noteworthy
intermixing so that only these low field measurements
are representative for the magnetism of the CEF ground
state.
The onset of magnetic order below 3 K is in agreement
with zero field specific heat and resistivity data shown
in Ref. 5. However, in case of ferromagnetic ordering all
possible CEF ground states would yield a ordered mo-
ment that is at least ten times larger than the observed
value for applied fields of 5 and 10 mT. This very small
constant moment below 3 K and the increase of the lat-
ter with increasing field cannot be explained by ferromag-
netic domain effects because it contradicts the absence of
hysteresis in the isothermal magnetization data (Fig. 4).
The increase of the ordered moment at 10 mT exter-
nal field can also not be explained with intermixing of
higher lying CEF states (see above). For external fields
of ≥50 mT the magnetic order is subdued, i.e. there is no
longer a constant magnetic moment observed when cool-
ing down to 2 K. This is in strong contradiction to con-
ventional ferromagnets, where the application of a high
external field favors ordering such that saturation takes
already place at higher temperature and intermixing of
higher lying crystal-field states only lead to an increase
of the ordered moment. Furthermore, conventional fer-
romagnetism can also not explain that the anisotropy of
the high-field and the low field state are reversed. To
summarize, the observations 2)-5) listed above exclude
4
conventional ferromagnetism. In the specific heat data5
the sharp peak seen at 3 K in zero-field disappears in a
10 T field. Instead, a broad hump appears. This was
interpreted as a smearing out of the ordering tempera-
ture with increasing field and hence, taken as a sign for
ferromagnetism. However, the data above show that for
10 T magnetic order has disappeared so that the hump in
the high field data should rather be interpreted in terms
of crystal-field effects, which are of course different with
respect to zero field due to intermixing of states when a
large field is applied.
The assumption of a canted antiferromagnetic ordered
state can explain the observations above. In the range of
5 to 10 mT the resulting effective moment is aligned along
the external field. It would also explain the small size of
the ordered moment. A field of only 50 mT overcomes the
antiferromagnetic exchange, so that a more paramagnetic
response is observed for larger external fields. Hence we
conclude that YbInNi4orders in a weak, possibly canted
antiferromagnetic structure.
At first sight it seems surprising that a simple cubic
structure leads to a non-trivial ordered state. A possible
explanation might be in the crystallographic fcc (C15b)
structure of YbInNi4where the magnetic Yb ions form
two subnetworks of corner sharing tetrahedra (see Fig.1)
so that simple next nearest neighbor antiferromagnetic
interactions will give rise to frustration. For the isostruc-
tural compounds RInCu4, R = Gd, Dy, Ho, and Er strong
signs of antiferromagnetic geometrical frustration were
found.10 The frustration parameter f=−ΘC W /TN,
which is defined as the ratio of the negative Curie-Weiss
temperature ΘC W and the ordering temperature TN,
gives a measure of the degree of frustration. Materials
with f > 10 are considered to be strongly and materials
with f≈3 are considered to be moderately frustrated.11
From susceptibility measurements in Ref. 9 and 5 and
our high temperature susceptibility data we calculate a
frustration parameter between 3 and 6 for YbInNi4, i.e.
YbInNi4is a moderately frustrated system. Frustration
works against magnetic order and might therefore explain
why the order observed in YbInNi4is weak and not sim-
ple. A non-trivial antiferromagnetic structure has indeed
been observed in the isostructural compound YbAuCu4
which also orders antiferromagnetically. YbAuCu4shows
similar isothermal magnetization behavior as YbInNi4,
characterized by a metamagnetic transition at 1 T and
the absence of hysteresis. The magnetic structure has
been determined with neutron diffraction and it turns
out to be an incommensurate antiferromagnetic spiral
structure.3Here too, frustration might be important. Fi-
nally we want to note that frustration will lead to finite
entropy at low temperatures, implying that there is resid-
ual entropy in YbInNi4even below the ordering transi-
tion at 3 K. This could be a possible explanation for why
at the ordering transition an entropy less than Rln 2 is
liberated although the CEF ground state is most likely a
Γ8quartet.7,8
V. SUMMARY
We have presented field and temperature dependent
magnetization data on YbInNi4down to 500 mK, and
exclude that magnetic order is due to conventional fer-
romagnetic interactions, because 1) hysteresis is absent
in the ordered state, 2) the iso-field data show a satu-
rated ordered moment only for weak external fields, and
3) the magnetic anisotropies reverse with increasing field.
Therefore, ordering must be predominantly of antiferro-
magnetic nature. A canted antiferromagnetic state, i.e.
a phenomenologically weak ferromagnet, could explain
the observations. Simple next nearest neighbor antifer-
romagnetic interactions will give rise to moderate geo-
metrical frustration, possibly resulting in a non-trivial
ordered state.
Acknowledgments
Full multiplet calculations to accompany the experi-
mental analysis were performed using the CrystalField-
Theory package for Mathematica written by Maurits W.
Haverkort. We gratefully acknowledge Thomas Lorenz
and Martin Rotter for fruitful discussions and Susanne
Heijligen and Christoph Klausnitzer for experimental
support. T.W. and N.H. are partially supported by
the Bonn-Cologne Graduate School of Physics and As-
tronomy. Z.F. acknowledges support through U.S. Na-
tional Science Foundation under Grant No. NSF-DMR-
0801253.
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