INSTITUTE OF PHYSICS PUBLISHING

JOURNAL OF PHYSICS: CONDENSED MATTER

J. Phys.: Condens. Matter 15 (2003) 2811–2823

PII: S0953-8984(03)59274-8

Magnetic anisotropy of pure and doped YbInCu4
compounds at ambient and high pressures
N V Mushnikov1,2,4 , T Goto1, E V Rozenfeld2 , K Yoshimura3 , W Zhang3 ,M Yamada1 and H Kageyama1
1 Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa,
Chiba 277-8581, Japan
2 Institute of Metal Physics, Kovalevskaya 18, 620219 Ekaterinburg, Russia
3 Department of Chemistry, Graduate School of Science, Kyoto University,
Kyoto 606-8502, Japan

E-mail: mushnikov@imp.uran.ru

Received 5 February 2003
Published 22 April 2003
Online at stacks.iop.org/JPhysCM/15/2811
Abstract
The susceptibility and high-field magnetization of single-crystalline
Yb1−x Yx InCu4 (x = 0, 0.2 and 0.3) samples have been measured for different
field orientations at ambient and high pressures. The compounds with x = 0
and 0.2 undergo a first-order valence transition from the intermediate-valence
state to the trivalent state on increasing either temperature or magnetic field.
The magnetization and susceptibility of these compounds have appreciableanisotropy in both states. The magnetic phase diagram of Yb1−x Yx InCu4
determined at ambient pressure is also anisotropic, which is explained by the
crystal-field calculations for the free Yb ion in the high-temperature phase.
Moreover, the low-temperature magnetization process for x = 0.2 and 0.3
has been measured in low fields under high pressure; it shows anisotropic
ferromagnetic ordering.

1. Introduction
Ytterbium compounds display a variety of magnetic transitions because of the instability off 13 electronic configuration of Yb3+ . Since the energy states of the trivalent f 13 and divalent
f 14 configurations are very close, a mixed-valence state is frequently realized in Yb-based
compounds [1]. A small change produced in the local environment around the Yb ion will
modify its electronic state and the physical properties of the compounds.
The YbInCu4 compound has the cubic C15b-type crystal structure and undergoes a firstorder temperature-induced isostructural valence phase transition at ambient pressure [2, 3].
Above the critical temperature Tv ∼ 40 K the Yb ion is trivalent and the compound exhibits a4

Address for correspondence: Institute of Metal Physics, Kovalevskaya Street 18, 620219 Ekaterinburg, Russia.

0953-8984/03/172811+13$30.00© 2003 IOP Publishing Ltd

Printed in the UK

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N V Mushnikov et al

Curie–Weiss susceptibility. The valence of the Yb ion decreases suddenly by ∼ 0.1 at Tv ; thisaccompanies a lattice constant increase of 0.15% [4–6]. In spite of the small change in thevalence, both the susceptibility and the electrical resistivity decrease substantially and a Pauliparamagnetic (Fermi-liquid) state is realized below Tv. The application of a high magnetic fielddestabilizes the mixed-valence state: a metamagnetic-like field-induced valence transition to
the trivalent state is observed at a critical field Bv [7, 8].
The valence transition of YbInCu4 is easily affected by either applying high pressure or
alloying. The pressure effect on the critical temperature Tv was studied by means of resistivity,
magnetic susceptibility and thermal expansion measurements [2, 3, 9, 10]. The value of Tv isfound to decrease on applying pressure; dTv /d P ∼ −20 K GPa−1 . This is consistent with thestabilization of the high-temperature trivalent state of Yb having smaller size. The pressure
effect on the critical field Bv is reported to also be negative; d Bv /d P ∼ −10 T GPa−1 [11].
With proper alloying on the Yb or the In site, on the other hand, both the critical temperatureand field are increased or decreased simultaneously [3, 4, 12]. In the case of substitutionof Y for Yb, the valence transition shifts to the low-temperature low-field region [3, 11–13].
Although the mixed-valence state of the parent YbInCu4 survives even at 2.5 GPa [14], thatof Yb0.8 Y0.2 InCu4 disappears under high pressure of above 1 GPa and the trivalent state exists
over the entire temperature range [11]. It should be noted that a weakly ferromagnetic statewith a magnetic moment of 0.05 µ B /Yb appears below 1.7 K at 1.2 GPa [15].
The formation of the low-temperature Fermi-liquid state in YbInCu4 derives fromthe interaction between f electrons of Yb in the mixed-valence state and conduction-band
electrons [16]. As a first approach, the Anderson single-impurity model is applied to clarify
the low-temperature behaviour of a periodic lattice of magnetic Yb ions [1]. The Bethe ansatz
solution to the Coqblin–Schrieffer model (the Anderson single-impurity Hamiltonian in the
Kondo limit) describes quantitatively the physical properties of some Yb compounds having
a continuous valence transition with temperature [1, 17, 18]. In order to explain the firstorder transition in YbInCu4 within the framework of the Anderson model, the electron–latticecoupling and the Coulomb repulsion between the f- and conduction-band electrons were taken
into account [16]. Since this model does not include the interaction of the f electrons withthe crystal electric field, the magnetic behaviour deduced is completely isotropic. On theother hand, the importance of anisotropic interactions in the magnetism of Kondo systems
has been pointed out [19–21]. The J = 7/2 ground state multiplet of an Yb3+ ion in a
cubic crystal field is split into a 6 doublet, a 7 doublet and a 8 quartet [22]. The splitting
causes anisotropy of the paramagnetic susceptibility. However, the effect of the crystal electricfield on the high-temperature susceptibility is expected to be very small since the splitting is
modest (total splitting  = 44 K [23]). In the Coqblin–Schrieffer model the crystal field
results in the occurrence of anisotropic coupling between conduction and 4f electrons at low
temperatures [24]. Recently, the magnetic phase diagram of YbInCu4 was studied theoretically,
considering crystal-field effects [25]. It was shown that the calculated phase diagram in the
B–T plane has some anisotropy with respect to the direction of an external magnetic field
applied to the cubic lattice.
The valence transition in YbInCu4 is extremely sensitive to small variation in the
stoichiometry and site disorder [26]. Therefore, many of the studies were performed using
single-crystalline samples, which, as a rule, were more homogeneous and showed a sharpertransition than polycrystals [3, 11]. However, the orientation of the samples was notdetermined, since the anisotropy of the physical properties was expected to be very small. In thepresent study we have measured the magnetic susceptibility and the high-field magnetization
curve of Yb1−x Yx InCu4 with x = 0, 0.2 and 0.3 at ambient and high pressures using oriented
single crystals to examine the crystal-field effects in the magnetization and field-induced

Magnetic anisotropy of pure and doped YbInCu4 compounds at ambient and high pressures

2813

valence transition. Moreover, we have carefully measured the low-field magnetization processof Yb1−x Yx InCu4 with x = 0.2 and 0.3 under high pressure to study the anisotropy of theferromagnetic ordering found by Mitsuda et al [15].
2. Experimental details
Single crystals of pure and substituted YbInCu4 compounds were grown from an In–Cu
flux [26, 27]. Polycrystalline samples were first prepared by arc-melting of the starting elements
mixed in a one-to-one ratio of Yb1−x Yx InCu4 to InCu2 in an argon atmosphere. The ingot was
crushed into a powder, placed in an alumina crucible and then sealed in an evacuated quartz
tube. Subsequently the powder sample was heated to 1000 ◦ C and cooled very slowly to800 ◦ C, at which point the flux was separated from single crystals. Single-crystalline samples
were oriented using an x-ray Laue diffractometer with a Polaroid camera. Two parallel faces
were ground perpendicular to each of the [001], [11̄0] and [111] axes of the cubic crystals. The
oriented samples have the shape of a right-angle prism with a volume of ∼2.5 mm3 . Hereafter
we denote the principal axes as [100], [110] and [111], respectively.
The magnetic susceptibility was measured using a Quantum Design SQUID magnetometerat ambient pressure in the temperature range 5–200 K in a magnetic field 0.5 T. The
magnetization under pressure was measured with an extraction-type magnetometer in magnetic
fields up to 9 T produced by a superconducting magnet. Hydrostatic high pressure was applied
to the sample up to 1.3 GPa using a non-magnetic clamp pressure cell made of a CuTi alloy.
The oriented sample inside the cell was placed in a Teflon capsule filled with a liquid pressure
medium, Fluorinert. A He3 cryostat was used to cool the sample together with the pressure cell
down to 0.6 K. The details of the measurement system are described in [28]. The high-fieldmagnetization curve was measured by an induction method in pulsed magnetic fields up to
42 T with a pulse duration time of ∼20 ms. The shape of the magnetization curve for bulk
single crystals coincides with that for powdered samples of the same compositions, ensuringthat the eddy current effect is negligibly small. The uncertainties in the absolute value of the
field and magnetization are 0.5 and 2%, respectively, while the uncertainties due to the changeof the sample orientation are ±0.1 T and ±0.02 µ B /Yb.
3. Experimental results
The magnetic susceptibility of YbInCu4 has been measured previously by many researchers(see, e.g., [3]). For homogeneous samples, two temperature ranges of distinct behaviour
were observed. Above the temperature of the valence transition Tv , the susceptibility obeys aCurie–Weiss behaviour with a very small negative paramagnetic Curie temperature θ . Below
Tv the sample is characterized by considerably lower Pauli-paramagnetic susceptibility, which
is nearly temperature independent. Figure 1(a) shows the temperature dependence of themagnetic susceptibility χ of a YbInCu4 single crystal measured with a SQUID magnetometerin a magnetic field of 0.5 T applied along main crystallographic directions with increasing
temperature. The single crystal exhibits a very sharp valence transition at Tv = 43 K. Although
the transition temperature does not depend on the direction of the applied magnetic field, thevalues of the susceptibility along the three axes are slightly different. As clearly seen fromthe inset in figure 1(a), the susceptibility in the low-temperature mixed-valence state is largest
for the [100] axis and smallest for the [110] axis. In the case of the high-temperature trivalentstate, the difference is somewhat smaller, but the same tendency is observed.
The temperature dependence of the inverse susceptibility χ −1 (T ) shown in figure 1(b) isalmost linear above Tv . The observed differences in the slope of χ −1 (T ) for different directions

2814

N V Mushnikov et al-63

χ (10 m /mol)

T (K)
[100]
[111]
[110]

a)
-1

6

3

-1

χ (10 (m /mol) )

χ

T (K)

b)

Figure 1. Temperature dependences of the molar susceptibility (a) and inverse molar susceptibility(b) of single-crystal YbInCu4 measured for different crystallographic directions. The insets show
two parts of the curves on a larger scale.

imply that both the paramagnetic Curie temperature θ and the effective magnetic moment µe f f
are anisotropic. Since the linear fits of the χ −1 (T ) dependence for different temperature
ranges give slightly different slopes, the absolute values of θ and µe f f are determined with theaccuracy ±0.5 K and ±0.1 µ B /Yb, respectively. At the same time, the uncertainties in therelative changes of the parameters with the sample orientation are estimated to be ±0.02 K
and ±0.01 µ B /Yb. The values of θ and µe f f determined from the linear fit of χ −1 (T ) in thetemperature range 50–200 K are listed in table 1. The difference between the paramagnetic
Curie temperatures for the [100] and [110] directions amounts to ∼2 K, which is quite large
for cubic samples. The values of µe f f determined in the present study are found to be slightly
lower than the free Yb3+ ion value 4.54 µ B . Observation of a slightly lower value of µe f f
was also reported in [7, 27]. One of the possible reasons for this is the crystal-electric-field
effect. The susceptibility of 4f ions is usually affected by the crystal field. Another reason isMagnetic anisotropy of pure and doped YbInCu4 compounds at ambient and high pressures

2815

Table 1. Summary of the magnetic parameters of YbInCu4 for different field orientations.
Field orientationsfor 4.2 K (T)aMeasured Bv
Calculated Bv for 5 K (T)Measured M for 4.2 K and 40 T (µ B /Yb)
Calculated M for 8 K and 40 T (µ B /Yb)
Estimated θ (K)Estimated µef f (µ B /Yb)

[100]

[110]

[111]

32.9
31.3
3.35
3.91
−2.05
4.15

34.3
34.0
3.21
3.78
−0.05
4.09

33.1
32.9
3.30
3.86
−1.91
4.15

a Averaged for field-up and field-down branches of the magnetization curve.

the deviation of the valence of the Yb ion in the high-temperature state from 3+. According
to LIII x-ray absorption spectroscopy, the valence of Yb above Tv is estimated to be 2.93 [18]or 2.9 [4]. If the estimated value is correct, however, the high-temperature phase is also amixed-valence state and the susceptibility is modified considerably by valence fluctuations.
We believe that the valence of the Yb ion is 3+ in the high-temperature state. In terms of the
Kondo impurity model, the reduction of µe f f is caused by the Kondo interaction.
According to the isotropic models of the valence transition in YbInCu4 , there are two
characteristic energy scales [16]. In the high-temperature phase T > Tv , the localized
f electrons of Yb interact weakly with the conduction-band electrons. The thermodynamic
properties of this state are described with the Kondo temperature TK ∼ 25 K [27]. The
value of TK can be estimated by fitting the effective moment determined experimentally tothe prediction of the J = 7/2 Kondo model. In the low-temperature phase T < Tv , a Fermiliquid state is realized, in which the f- and conduction-band states are strongly hybridized. A
different Kondo energy scale T0 determines the low-temperature thermodynamic properties.
The zero-temperature susceptibility χ(0) is proportional to 1/T0 [17, 29]:
N A ν(ν 2 − 1)g 2J µ2B,(1)24πk B T0
where N A is the Avogadro number, ν = 2 J + 1 is the degeneracy of the ground state, g J is
the Landé factor. For YbInCu4 , the T0 -value amounts to 430–540 K [11, 27]. The difference
between the T0 -values determined from the present susceptibility data for different axes does
not exceed 7%. Hence, isotropic models are not so bad for describing the valence transitionin YbInCu4.
Figure 2 shows the high-field magnetization curves measured at 4.2 K along different
directions of single-crystalline YbInCu4 . The magnetization curve for each direction indicatesa sharp valence transition with hysteresis above 30 T. The magnetization M for the [110]direction is smallest in both the low- and high-field states, while the critical field is highest.
The critical field Bv was attributed to the field of a maximum of the derivative dM/d B. The
average value of the critical fields was determined from the field-up and field-down branches ofthe magnetization curve, as listed for the three principal axes in table 1. The observed anisotropyof Bv is in agreement with the magnetic phase diagram recently calculated by Dzero [25] on thebasis of a simple assumption that the free energy of the low-temperature state is a constant, by
taking into account crystal-field effects for the free Yb ion. According to the calculation [25],anisotropies of Bv and M exist, although anisotropy of Tv is absent in a weak field. The
value of Bv at low temperatures is largest for the [110] direction and the anisotropy of Bv isof the order of 2 T. These results are consistent with our experimental values of Bv at 4.2 K.
However, the calculations indicate that Bv and the magnetization M for the [100] direction
have an intermediate value. (The values of Bv and M for the [111] direction are smallest andlargest, respectively.) These results are inconsistent with the experimental data.
χ(0) =

2816

N V Mushnikov et al

.

.

.

.

Figure 2. High-field magnetization curves of YbInCu4 measured for different crystallographic
axes at 4.2 K. Inset: a part of the curve on a larger scale. Arrows indicate the field sequence.

At high temperatures above Tv the anisotropy of M becomes very small. The high-fieldmagnetization curves measured at 50 K along the three principal directions coincide within
the accuracy of our high-field magnetometer.
Since the anisotropy of the magnetization curves increases with decreasing temperature,
we also studied two Y-substituted single crystals, where the valence transitions are shifted to
the low-temperature region. The substitution of non-magnetic Y, La and Lu for magnetic rareearth atoms weakly affects the crystal electric field and, as a rule, does not change the type ofthe magnetic anisotropy. Figure 3 shows the temperature dependence of the susceptibility ofsingle-crystalline Yb0.8 Y0.2 InCu4 and Yb0.7 Y0.3 InCu4 measured at ambient and high pressuresin a magnetic field of 0.5 T. The critical temperature of the valence transition in Yb0.8 Y0.2 InCu4
is Tv ∼ 21 K. Zhang et al [11] found that the critical temperature of Yb0.8 Y0.2 InCu4 isdecreased together with the critical field by applying pressure and the mixed-valence statecompletely disappears at 1.3 GPa. On the other hand, the present Yb0.7 Y0.3 InCu4 sample
retains the trivalent state down to 0.6 K even at ambient pressure. The magnitude of thesusceptibility in the trivalent state of the two compounds at ambient pressure is largest forthe [100] direction and smallest for the [110] direction, although the difference is very small(open symbols in figure 3(b)). This indicates that the substituted compounds at ambientpressure show qualitatively the same anisotropy as the parent YbInCu4 .
We found that external hydrostatic pressure produces completely different effects on theanisotropy of the magnetic susceptibility for the two Y-substituted compounds. The anisotropyof Yb0.8 Y0.2 InCu4 is enhanced by applying a high pressure of 1.0 GPa, but the type of theanisotropy remains unchanged (closed symbols in figure 3(a)). In the case of Yb0.7 Y0.3 InCu4 ,an external pressure of 1.2 GPa enhances the susceptibility along the [111] direction andMagnetic anisotropy of pure and doped YbInCu4 compounds at ambient and high pressures

2817

a)

b)

Figure 3. Temperature dependences of the molar susceptibility of Yb0.8 Y0.2 InCu4 (a) andYb0.7 Y0.3 InCu4 (b) single crystals measured along different crystallographic axes for ambientpressure (open symbols) and for 1.2 GPa (closed symbols).

suppresses that along the [100] direction (closed symbols in figure 3(b)). However, this isvalid only for a low-field region.
Figure 4 shows the magnetization curves of the two Y-substituted compounds
Yb0.8 Y0.2 InCu4 and Yb0.7 Y0.3 InCu4 for 0.6 K under a high pressure of 1.0 or 1.2 GPain steady magnetic fields up to 9 T. The first-order field-induced valence transition isconsiderably broadened for Yb0.8 Y0.2 InCu4 in comparison with that for the pure YbInCu4
compound. Perhaps the broadening comes from inhomogeneous distribution of the substituent.
Y-substituted YbInCu4 samples always show a broadened valence transition [11–13]. In
the high-field region above 5 T, the magnitude of M, for both compounds, is largest forthe [100] direction and smallest for the [110] direction, in agreement with the anisotropy of the2818

N V Mushnikov et al

.
.
.

[100]
[111]
[110]

µ

.
.
a)

.
b)

.
.
.

.
.

M (µB/Yb)
.
.

B (T)
.

.

.

.

.

.

.

Figure 4. Magnetization curves of Yb0.8 Y0.2 InCu4 for 1 GPa (a) and Yb0.7 Y0.3 InCu4 for
1.2 GPa (b) measured along different crystallographic axes at 0.6 K. Inset: a part of the curveon a larger scale.

susceptibility measured at ambient pressure (figure 3(a)). It is clear also that the anisotropy of
Bv of the order of 1 T persists in Yb0.8 Y0.2 InCu4 under high pressure (see also figure 2).
The magnetization curves of Yb0.7 Y0.3 InCu4 at 0.6 K are typical of paramagnets both atambient pressure (not shown) and at 1.2 GPa (figure 4(b)). However, they are quite different
from the simple paramagnetic magnetization curve for free Yb3+ ions, which is given by the
Brillouin function with J = 7/2. This function indicates that the magnetization easily saturates
to 4 µ B /Yb ion in a magnetic field of ∼3–4 T for such a very low temperature. Thus, both the
Kondo interaction and the crystal-field effect should be considered together with the RKKY
interaction to explain the magnetization curve of Yb0.7 Y0.3 InCu4 at low temperatures.
The observed anisotropy of the magnetization of Yb0.7 Y0.3 InCu4 under pressure in highmagnetic fields above 5 T is qualitatively the same as that of the other samples studied:the magnetization is largest for the [100] direction and smallest for the [110] direction.
In magnetic fields below 5 T the situation changes: the magnetization of Yb0.7 Y0.3 InCu4

Magnetic anisotropy of pure and doped YbInCu4 compounds at ambient and high pressures

2819

.
.
[100]

.

[111]
[110]

.

µ

.
.
a)
.
.
.
b)
.
.
.
.

.

.

.

.

.

Figure 5. Low-field hysteresis loops of Yb0.8 Y0.2 InCu4 for 1.3 GPa (a) and Yb0.7 Y0.3 InCu4 for
1.2 GPa (b) measured along different crystallographic axes at 0.6 K.

becomes largest along the [111] direction, while it is smallest along the [100] direction (seethe inset in figure 4(b)).
The paramagnetic Curie temperature θ of YbInCu4 is negative as shown in table 1. This
indicates that the interaction between Yb3+ ions is antiferromagnetic. Svechkarev et al [30]found that the pressure derivative dθ/d P is positive. They estimated a latent interaction in
YbInCu4 by plotting the value of θ against the de Gennes factor for a series of heavy rare-earth
RInCu4 compounds. The estimated interaction is positive. They expected that a ferromagnetic
ordering might appear after the disappearance of the mixed-valence state under high pressure
due to the latent positive interaction. Recently, a weakly ferromagnetic ordering was foundin a single-crystalline sample of Yb0.8 Y0.2 InCu4 under high pressure, P  0.8 GPa [15].
Figure 5 shows the low-temperature magnetization processes of Yb0.8 Y0.2 InCu4 for 1.3 GPa
and Yb0.7 Y0.3 InCu4 for 1.2 GPa. In the Yb0.8 Y0.2 InCu4 sample, weak ferromagnetism isabsent up to 1 GPa, but is clearly seen at 1.3 GPa, where the low-temperature mixed-valence
state is completely suppressed. The weak ferromagnetic states for the two compounds have

2820

N V Mushnikov et al

appreciable magnetic anisotropy. The remnant magnetization is largest for the [111] direction,
while the coercivity is smallest for the [100] direction. The hysteresis loop becomes smallerwith increasing temperature. For Yb0.8 Y0.2 InCu4 at 1.3 GPa the hysteresis disappears at 2.4 K
simultaneously for all of the directions and the magnetization is almost proportional to themagnetic field. Yb0.7 Y0.3 InCu4 at 1.2 GPa has a lower Curie temperature: the hysteresis has
already completely disappeared at 1.8 K.
4. Discussion
The origin of the observed magnetic anisotropy of YbInCu4 is the interaction of the anisotropic
4f orbitals of Yb3+ ions with the crystal electric field produced by the surrounding ions of the
cubic lattice. We calculate theoretically the critical field of the valence transition and themagnetization curve for different directions of the cubic cell, taking an approach similar tothat in [25].
The transition line of the magnetic phase diagram in the B–T plane can be determinedfrom the condition that the free energies FL and FH of low-temperature and high-temperaturephases are equal to each other:
FL (T, B) = FH (T, B).

(2)

Since the characteristic energy of the low-temperature mixed-valence state of YbInCu4 isvery high (T0 ∼ 500 K), we can assume after the authors of [25, 31] that the free energy of themixed-valence state does not depend on temperature and magnetic field: FL (T, B) = constant.
The constant value can be determined using the condition FL (Tv , 0) = FH (Tv , 0). On the other
hand, the trivalent Yb3+ is treated as a free ion. FH (T, B) is given by

 
Ĥ
FH (T, B) = −T ln(Q),.
(3)
Q = Tr exp −T
Here and below, the temperature T is expressed in units of energy. In (3) Ĥ stands for the
Hamiltonian of an Yb3+ ion ( J = 7/2, g J = 8/7) in a cubic crystal field, which is written interms of operator equivalents [22, 32]:Ĥ = B0 + B40 (O40 + 5O44 ) + B60 (O60 − 21O64 ) − B M,(4)
where the magnetization is given by



Ĥ
g J µB
Tr J exp −
.
(5)
M=
Q
T
According to the inelastic neutron scattering study [23], in the high-temperature phaseT > 45 K the excited 6 and 7 states are located at E 6 = 3.2 meV and E 7 = 3.8 meVrespectively above the ground state quartet 8 (we assume E 8 = 0). Using these values, thecrystal-electric-field parameters B0 , B40 and B60 are expressed as
E6 + E7
7E 6 − 9E 7
−5E 6 − 3E 7
B0 =
,
B40 =
,
B60 =
.
(6)
4
15 840332 640
We calculated the magnetic phase diagram in the B–T plane using a standard procedure of
diagonalization of the Hamiltonian. The results are shown in figure 6. The phase boundarylines for the three principal directions of the crystal coincide each other at high temperatures(T > 0.8Tv ), but they are clearly separated at low temperatures. The calculated results givethe largest critical field for the [110] axis and the smallest field for the [100] axis, in agreementwith the experimental results (figure 2). Moreover, the calculated values of Bv are very close to
the experimental ones (see table 1), although no fitting parameters were used in the calculation.

Magnetic anisotropy of pure and doped YbInCu4 compounds at ambient and high pressures

2821

Figure 6. The calculated magnetic phase diagram of YbInCu4 in the B–T plane.

This indicates that the simple free Yb ion approach developed by Dzero et al [25, 31] describes
well the anisotropic behaviour of the field-induced transition in YbInCu4 .
However, it should be noted that the magnetic phase diagram reported in [25] differsfrom that given in the present paper, although the starting formulae are exactly the same. The
wrong results given by [25] are caused by some technical errors appearing in the process of
calculation.
Figure 7 shows the magnetization curves of the trivalent state calculated at 8 K by taking
into account the crystal-field effects. In magnetic fields around 40 T, the magnetization islargest for the [100] axis and smallest for the [110] axis, in agreement with the experimental
magnetization curves above the critical field (figure 2). The calculated magnetization ishigher by about 15% than the experimental one. The possible reasons for the difference
have already been discussed above. However, the order of the magnetization values calculated
for the different directions is consistent with that determined experimentally (see table 1).
The difference between the magnetizations of the trivalent state calculated for the [110] and[111] directions becomes very small in the low-field region below 10 T. This corresponds
to the magnetization curves of Yb0.8 Y0.2 InCu4 measured at a high pressure of 1.2 GPa(figure 4(b)). However, the experimental value of the magnetization measured for the [111]direction becomes largest below 3 T. (The direction of easy magnetization above 5 T is the[100] axis.) This cannot be explained by the present theoretical model. It should be notedthat the Yb0.8 Y0.2 InCu4 compound for 0.6 K exhibits an anisotropic ferromagnetic ordering(figure 5(a)). The magnetization in the low-field region is enhanced especially for the [111]direction; this is accompanied by the ferromagnetic ordering produced under high pressure.
Perhaps the anisotropic mixing between the ground 8 state and the conduction electronstate will determine the anisotropy of the ferromagnetic ordering and the low-temperaturesusceptibility.
As described above, the magnetic anisotropy observed in the trivalent state and the phase
diagram can be explained very well by the crystal-electric-field calculation on the assumption

2822

N V Mushnikov et al

Figure 7. Calculated magnetization curves of YbInCu4 at 8 K for different directions. The verticallines correspond to the calculated critical field of the valence transition. In the low-field region,
the mixed-valence state with low susceptibility is realized. The magnetization curves are depicted
tentatively by thick straight lines with a small slope. (The magnetization curves in the trivalent state
are shown with fine lines.) In the high-field region, the trivalent state is induced. The magnetization
curves of the state are shown by thick lines.

that the free energy of the low-temperature phase is a constant. This indicates that the anisotropy
in the trivalent state is caused by the interaction between the Yb 4f electrons and the crystal
electric field. The same type of anisotropy is observed in the low-temperature susceptibilityof YbInCu4 (figure 1), in which a coherent Kondo state is formed. Maekawa et al [20]studied the crystal-field effects in the Kondo state in cubic crystals. It was shown that theexchange interaction between 4f and conduction electrons is strongly renormalized at low
temperatures. The renormalization of the exchange interaction causes an anomalous shift anddamping of the crystal-field levels. Since the crystal electric field determines the anisotropy ofthe magnetic susceptibility, the anisotropy may be depressed by the Kondo effect. However, we
can clearly find a difference in susceptibility between different directions in the mixed-valence
state (figure 1). Perhaps the crystal-field effect is non-negligible in the mixed-valence state,since the valence of Yb is still not far from 3+. Moreover, the crystal field may result in theoccurrence of anisotropic coupling between conduction and 4f electrons [24], which causes
anisotropy of the susceptibility.
5. Conclusions
In summary, we have measured the magnetic susceptibility and the high-field magnetization
curve of single-crystalline Yb1−x Yx InCu4 with x = 0, 0.2 and 0.3 along the principal
crystallographic directions of the cubic lattice at ambient and high pressures. YbInCu4
and Yb0.8 Y0.2 InCu4 exhibit temperature- and field-induced valence transitions. We havefound appreciable anisotropy in the susceptibility, high-field magnetization, effective moment,
paramagnetic Curie temperature and critical field of the valence transition. We have calculated

Magnetic anisotropy of pure and doped YbInCu4 compounds at ambient and high pressures2823

the magnetization curve and the magnetic phase diagram in the B–T plane using the model ofa phase transition between the free Yb3+ paramagnetic state in a cubic crystal electric field andthe low-temperature state with constant free energy. The calculated results agree well withthe experimental data of the susceptibility and high-field magnetization in the trivalent state
and with the phase diagram. Moreover, we have measured the low-temperature magnetization
process for Yb0.8 Y0.2 InCu4 and Yb0.7 Y0.3 InCu4 in low fields under high pressure and observed
anisotropic ferromagnetic ordering.
Acknowledgment
This work was supported by a Grant-in-Aid for Scientific Research on Priority Areas (B) from
the Ministry of Education, Culture, Sports, Science and Technology of Japan. The stay of
NVM at ISSP was also supported by this Ministry.
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