Magnetic Field and Pressure Phase Diagrams of Uranium Heavy-Fermion Compound U$_2$Zn$_{17}$

0.87 MB·English

by  Naoyuki Tateiwa

Typeset with jpsj3.cls <ver.1.1> Full Paper
Magnetic Field and Pressure Phase Diagrams of
Uranium Heavy-Fermion Compound U Zn ∗
2 17
Naoyuki TATEIWA1†, Shugo IKEDA1,2, Yoshinori HAGA1, Tatsuma D. MATSUDA1, Etsuji YAMAMOTO1,
Kiyohiro SUGIYAMA3, Masayuki HAGIWARA4, Koichi KINDO5, and Yoshichika O¯NUKI1,3
1Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195
2Graduate School of Material Science, University of Hyogo, Kamigori, Hyogo 678-1297
3Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043
1 4KYOKUGEN, Osaka University, Toyonaka, Osaka 560-8531
1 5Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581
0
2
We have performed magnetization measurements at high magnetic fields of up to 53 T
n
on single crystals of a uranium heavy-fermion compound U Zn grown by the Bridgman
a 2 17
J method.IntheantiferromagneticstatebelowtheN´eeltemperatureTN=9.7K,ametamagnetic
5 transition isfoundatHc ≃32Tforthefieldalongthe[11¯20]direction (a-axis).Themagnetic
phase diagram for thefield along the[11¯20] direction is given.Themagnetization curveshows
] a nonlinear increase at Hm ≃ 35 T in the paramagnetic state above TN up to a characteristic
el temperatureTχmax wherethemagneticsusceptibilityorelectricalresistivityshowsamaximum
- value. This metamagnetic behavior of the magnetization at Hm is discussed in comparison
r
with themetamagnetic magnetism of theheavy-fermion superconductorsUPt ,URu Si , and
t 3 2 2
s UPd Al . We have also carried out high-pressure resistivity measurement on U Zn using
. 2 3 2 17
t a diamond anvil cell up to 8.7 GPa. Noble gas argon was used as a pressure-transmitting
a
mediumtoensureagoodhydrostaticenvironment.TheN´eeltemperatureT isalmostpressure-
m N
independent up to 4.7 GPa and starts to increase in the higher-pressure region. The pressure
- dependencesofthecoefficientoftheT2termintheelectricalresistivityA,theantiferromagnetic
d
n gap ∆, and the characteristic temperature Tρmax are discussed. It is found that the effect of
o pressure on the electronic states in U2Zn17 is weak compared with those in the other heavy
c fermion compounds.
[

KEYWORDS: U Zn , magnetic phasediagram, pressure phasediagram
1 2 17
v
9
1. Introduction the magnetic ordering temperature T varies as a
7 mag
8 Uraniumintermetalliccompoundsexhibituniqueelec- function of |Jcf|D(εF),4) where |Jcf| is a magnitude of
0 tronicstatessuchasmagneticorderings,heavyfermions, the magnetic exchange interactionbetween the localized
1. and anisotropic superconductivity.1–3) These proper- moment and the conduction electron spin, and D(εF)
0 ties are basically derived from the competition between is the electronic density of states at the Fermi energy
1 the Ruderman-Kittel-Kasuya-Yosida (RKKY) interac- εF. The pressure-induced superconductivity was discov-
1 tionandthehybridization(Kondo)effect.Theformerin- ered around Pc in some cerium antiferromagnetic com-
:
v teractionenhancesthelong-rangemagneticorder,where pounds such as CeCu2Si2, CeRh2Si2, CePd2Si2, CeIn3,
Xi 5f electronswithmagneticmomentsaretreatedaslocal- and CeRhIn5.5–8) On the other hand, pressure exper-
izedelectronsandtheindirect5f-5f interactionismedi- iments on uranium compounds are small in number,
r
a atedbythespinpolarizationoftheconductionelectrons. andmoreover,thepressureeffectinuraniumcompounds
On the other hand, the latter effect quenches the mag- seems to be small compared with that in cerium com-
netic moments of the localized 5f electrons by the spin pounds of which the critical pressures Pc are usually
polarization of the conduction electrons, leading to an below 10 GPa. The pressure-induced superconductivity
extremely large density of states, called heavy fermions. wasonlyobservedbelowPc oftheferromagneticstatein
The application of pressure is a useful experimental UGe2 and UIr.9–12)
method for controlling the magnetic RKKY interaction In this study, we focus on the uranium heavy-fermion
and hydridization effect. As pressure is applied to some antiferromagnet U2Zn17 and studied its electrical and
compounds with magnetic orderings, the magnetic or- magnetic properties at a high magnetic field and a
dering temperature Tmag decreases and becomes zero at high pressure. U2Zn17 crystalizes in the rhombohedral
a critical pressure Pc: Tmag→0 at P→Pc, where the Th2Zn17-typestructure(spacegroupR¯3m).13,14)Atam-
pressure-induced superconductivity or non-Fermi liquid bientpressure,U2Zn17 showsantiferromagneticordering
behavior appears. The pressure dependence of the mag- ata N´eeltemperatureTN = 9.7K withanorderedmag-
netic ordering temperature Tmag in cerium compounds netic moment µord = 0.8 µB/U.15,16) The ordered mo-
is basically explained by the Doniach model, in which mentissubstantiallybelowtheparamagneticmomentof
3.15µ /Udeducedfromthehigh-temperaturemagnetic
B
susceptibilitymeasurementonasinglecrystalsample.17)
∗J.Phys.Soc.Jpn.80014706(2011).
†E-mailaddress:[email protected]
1
2 J.Phys.Soc.Jpn. FullPaper AuthorName
The specific heat coefficient C/T shows a large value of
about500mJ/K2·molUaboveT butisreducedtoabout
N
γ = 200 mJ/K2·mol at T ≪ T .13) These results reveal
N
the heavy-fermion nature of an itinerant-5f electronic
stateinU Zn .Aprevioushigh-pressureexperimenton
2 17
U Zn showedthattheantiferromagneticorderingtem-
2 17
perature T increases slightly with increasing pressure
N
from T = 9.70 K at 1 bar to 9.85 K at 1.72 GPa.18,19)
N
Inthisstudy,wehavemeasuredthemagnetizationunder
high magnetic field, as well as performed the resistivity
measurementunder high pressuresof up to 9 GPa using
a diamond anvil cell.
2. Experimental Methods
Asingle-crystalsampleofU Zn wasobtainedbythe
2 17
Bridgman method with a W crucible sealed with argon
gas. The crucible was kept at 950-1050 ◦C for 12 h and
then cooled down slowly at a constant rate. The crystal
structurewasinvestigatedbysingle-crystalX-raydiffrac-
tion techniques using an imaging plate (IP) area detec-
tor(RigakuCorporation)withMoKαradiationatroom
temperature.
The electrical resistivity at both ambient and high
pressures was measured by the four-probe DC method
in the temperature range from 2 to 300 K. The mag-
neticsusceptibilityandmagnetizationweremeasuredus-
ing a commercial superconducting quantum interference
device(SQUID)magnetometerinthetemperaturerange
from 2 to 300 K. The high-field magnetizationwas mea-
Fig. 1. (Coloronline)CrystalstructureinU2Zn17.
sured by the standard pick-up coil method at the High-
Magnetic-Field Laboratory, KYOKUGEN, Osaka Uni-
versity, using a long-pulse magnet with a pulse duration temperature.Inthefollowing,thepressuredeterminedat
of 20 ms. 4.2 K will be shown.
For the high-pressure study, a small sample was cut
3. Results and Discussion
andpolishedto180×50×20µm3.Fourgold-wires10µm
indiameterwerebondedtothesampleusingsilverpaste. 3.1 Crystal structure of U Zn
2 17
We useda diamondanvilcellofthe DunstanandSpain- Figure 1(a) and 1(b) show the crystal structure of
type.20,21) The sampleand smallruby chips wereplaced U Zn .CrystallographicparametersforU Zn atroom
2 17 2 17
in a sample hole 400 µm in diameter of a stainless-steel temperature is shown in Table I. The lattice parame-
gasketinDAC.Theculet-sizeofthediamondsis800µm. ters are a =8.9830(4)˚A and c = 13.1800(9) ˚A at room
Theelectrodesareinsulatedfromthemetalgasketusing temperature. The crystallographic parameters are con-
amixture ofAl O powderandstycast1266.20–23) Fora sistent with the previous study within experimental er-
2 3
pressure-transmittingmedium,weusedthenoblegasar- ror.31) It is noted that the atomic coordinates in Table
gon (Ar), which is known to provide a good hydrostatic I are standardized using STRUCTURE TIDY.32) The
condition up to 10 GPa at room temperature.24,25) We unit cell shown in Fig. 1 (a) containing 6 formula units
confirmedthatargonisalsoappropriateasthe pressure- (114 atoms) appears complicated. To illustrate the lo-
transmitting medium in the cryogenicexperiment under cal environment around the uranium site, we picked up
high pressure.26) Argon can be liquefied at 87 K. It was neighboring Zn atoms, as shown in Fig. 1(b). The ura-
loadedintothesamplechamberofDACusingapurpose- niumsitehas19Znneighbors,forminganearlyspherical
built cryogenic device. The pressure was determined by cage, with an open space toward the other uranium site
the ruby fluorescence method at room temperature and connectedtothenextZncage.Thecenterofmassofthe
4.2 K.27–29) We used the hydrostatic ruby pressure scale unit consisting of 2 U and 32 Zn atoms shown in Fig.
obtained by Zha et al.30) Some ruby chips with a di- 1(b)islocatedat(0,0,1/2)andequivalentpositions.The
ameter less than 5 µm are placed in the sample cham- magneticmomentsoftheUionsinthe cage,lyinginthe
ber.Note thatthe pressuredoesnotchangesignificantly (0001)plane,areantiferromagneticallycoupledintheor-
duringthe coolingprocessforthe presentDAC.The dif- deredstate belowT .15,16) The directionofthe moment
N
ference between the pressure at 4.2 and 300 K is less in the basal plane is not determined.
than 5%. This is different from the other types of dia-
mondanvilcells where the pressureat low temperatures
isusuallyabout1GPahigherorlowerthanthatatroom
J.Phys.Soc.Jpn. FullPaper AuthorName 3
TapbelreatIu.reCirnystthaellohgerxaapghoincalpaserattminegte(rsspafocreUgr2oZunp17Ra¯3tmr)owomithtelamt-- (a) U Zn T T
2 17 N cmax
ticeparameters a=8.9830(4)˚A andc=13.1800(9) ˚A.Thecon- [1120]
ventionalunweightedandweightedagreementfactorsofR1 and U) 10 [1010]
wR2 are7.9and19%,respectively. -
l
o
m
Atom Site x y z Beq (˚A2) u/
Zn(1) 18h 0.4956(3) 0.50438(16) 0.1526(2) 0.76(6) m
Zn(2) 18f 0.2965(3) 0 0 0.86(6) e3 5
Zn(3) 9d 1/2 0 1/2 0.70(7) 0-
Zn(4) 6c 0 0 0.0999(4) 0.80(8) (1 H // [0001]
U 6c 0 0 0.33611(10) 0.51(5) c
0
1 10 100
3.2 Resistivity and magnetic susceptibility at 1 bar
Temperature (K)
Figure 2 shows the logarithmic-scale of the tempera-
turedependencesoftheelectricalresistivityρforthecur-
(b)
rentsalongthe J k [11¯20](a-axis)and[0001](c-axis)di- U Zn H // [0001]
rections.Thevaluesoftheresidualresistivityratio(RRR 300 2 17
= ρRT/ρ0) are 75 for J k [11¯20] and 81 for J k [0001],
where ρRT and ρ0 are the resistivity at room tempera- u)
m
ture and the residual resistivity, respectively, indicating 200
e [1120]
a comparably high quality of the present samples. The U/
- [1010]
resistivity ρ increases with decreasing temperature with ol
m
a broad maximum at Tρmax = 18.7 and 23.5 K for J k ( 100
[11¯20] and [0001], respectively. The resistivity shows a c
/
sharpkinkattheN´eeltemperatureT =9.65Kandde- 1
N
creases steeply with decreasing temperature. We define
0
TNasthepeakpositioninthetemperaturedependenceof 0 100 200 300
d2ρ/dT2. The overall feature of the temperature depen-
Temperature (K)
denceoftheresistivityisroughlyconsistentwiththatre-
portedinapreviousstudyusingapolycrystalsample.13)
Thus far, the temperature dependence of the resistivity
using a single crystal sample was reported only for J k
Fig. 3. (Color online)Temperature dependences of (a) the mag-
[0001].33) The resistivity ρ for J k [11¯20] is found to be netic susceptibility χ and (b) the inverse susceptibility 1/χ for
approximately half as small as that for J k [0001]above themagneticfields along[11¯20],[10¯10],and[0001] directionsin
T . U2Zn17.
N
Figure3(a)showsthe logarithmic-scaleofthetemper-
ature dependences of the magnetic susceptibility χ for the magnetic fields along the [11¯20], [10¯10], and [0001]
directions.ThemagneticsusceptibilitiesχforH k[11¯20]
and [10¯10] have broad maxima at T ≃ 17 K, which
150 χmax
T is close to T at which the resistivity shows a maxi-
U Zn TN r max J // [0001] mum. T ρmoraxT corresponds to the characteristic
2 17 χmax ρmax
temperature T0 of the electronic state in U2Zn17. The
100 susceptibility χ shows a sharp kink at the antiferromag-
netic transition temperature T = 9.8 K and decreases
m) N
W(cid:215)c [ 1120] steTephleyibnevleorwseTmN.agnetic susceptibility 1/χ follows the
m
r ( 50 Curie-Weiss law above 40 K for H k [11¯20] and [10¯10],
and above 100 K for H k [0001], as shown in Fig. 3(b).
The effective paramagneticmoments µ and the Curie-
eff
Weiss temperatures Θ are = 3.19 µ /U and - 91 K for
B
0 H k [11¯20], 3.15 µ /U and -87 K for H k [10¯10] , and
1 10 100 B
2.99 µ /U and Θ = -109 K for H k [0001], respectively.
Temperature (K) B
Thesevaluesofµ forH k[11¯20]and[10¯10]areroughly
eff
similar to the values for a free U ion value of 3.6 µ /U
B
in the 5f2 and 5f3 configurations.
Fig. 2. (Coloronline)Temperaturedependences oftheelectrical The anisotropy of χ for three axes becomes smaller
resistivity at 1 bar for currents along J k [11¯20] and [0001] di- withdecreasingtemperatureintheantiferromagneticor-
rectionsinU2Zn17. deredstatebelowT .Inparticular,thereisnosignificant
N
4 J.Phys.Soc.Jpn. FullPaper AuthorName
U Zn
1.0 2 17 (a) 20 K
U Zn
2 17 14
H // [1120]
H // [1120] 12
U) 11
/B ) 9.2
n (m unit 8.2
atio 0.5 arb. 7.2
z (
agneti [0001] ation 41..23
M z
eti
n
g
0.0 a
0 20 40 60 M
Magnetic field (T)
0.5 µ /U
B
Fig. 4. (Coloronline)Magnetizationcurvesinthemagneticfield 0 20 40 60
along[11¯20]and[10¯10]directionsat1.3KinU2Zn17. Magnetic field (T)
U Zn H // [1120]
(b) 2 17
differencebetweenthetemperaturedependencesofχfor
H k [11¯20] and [10¯10] perpendicular to the [0001] direc- 20 K
tion. A previous work has shown the magnetic suscep-
14
tibilities for the fields parallel and perpendicular to the
[0001]direction.17) Theresultisbasicallyconsistentwith 12
) H
theresultofthepresentwork.Inthepresentstudy,itwas nit m 11
clarifiedthatthereisnoanisotropyofχinsidethe(0001) u
b.
planeevenbelowTN.Itisnotedthatthevalueofthecrit- ar 9.2
(
ical exponent of the magnetic Bragg intensity β (= 0.36 H
±0.02)inthe neutronscatteringexperimentforU Zn d 8.2
2 17 /
M
is between those expected for three-dimensional Heisen-
d 7.2
berg (β = 0.367) and XY (β = 0.345) magnets.16,34)
The anisotropy of the antiferromagnetic state is weak in 4.2
H
U Zn . c
2 17
1.3
3.3 High-magnetic-field experiment 0 20 40 60
Figure 4 shows the magnetization curves for the field Magnetic field (T)
along the [11¯20] and [10¯10] directions at 1.3 K. There is
nostronganisotropyinthe magnetizationprocessesata
low magneticfield. The magnetizationfor H k [11¯20]in- Fig. 5. (Color online) (a) Magnetization curves at various tem-
creases approximately linearly with increasing magnetic peratures and (b) differential magnetization curves for the field
field and shows a metamagnetic transition at H = 33 alongthe[11¯20]directioninU2Zn17.
c
T. With further increasing field, the magnetization in-
creasesmonotonicallyandamountsto1.1µB/Uat50T. K. At 11, 12, and 14 K, the slope of the magnetization
The present value is larger than the antiferromagnetic
curves shows another metamagnetic behavior at H . In
m
ordered moment (0.8 µ ), indicating the itinerant band
B fact, there appear broad peaks at Hm in the dM/dH
magnetismof5f electronsinU2Zn17.Themagnetization curves at these temperatures, as shown in Fig. 5 (b). At
forH k[0001]increaseslinearlyasafunctionofmagnetic
20 K, the magnetization increases linearly.
fieldandstartstodeviateupwardfromabout42T.This Figure 6 shows the magnetic phase diagram for H k
resultsuggeststhatthemetamagnetictransitionalsoex- [11¯20]. The data obtained from the high-field magneti-
ists for H k [0001] at a magnetic field higher than 52 T,
zation measurement are shown by open circles and dia-
the highest magnetic field in the present study. monds. The field dependences of T and T , deter-
N χmax
Figure 5 (a) shows the magnetization curves in the
mined by the SQUID magnetization measurement, are
magnetic field along the [11¯20] direction at various tem-
shown by open squares and triangles, respectively. The
peratures. The corresponding field derivatives of the metamagnetic transition field H in the antiferromag-
c
magnetization curve, dM/dH, are shown in Fig. 5 (b).
netic order state decreases from 32.5 T at 1.3 K to 27.8
The metamagnetic transitionat Hc becomes broad with T at 9.2 K. A curve connecting the Hc data seems to
increasingtemperatureupto9.2K,justbelowT =9.65
N
J.Phys.Soc.Jpn. FullPaper AuthorName 5
the electrical resistivity has a maximum. The metam-
U2Zn17 agnetic behavior appears at H , where the relation of
H m
m k T ≃ µ H is realized by applying magnetic field,
H // [1120] B χmax B c
T) Hc as shown in Fig. 7. The relation of Tχmax = 17 K and
d ( Hm = 32 T in U2Zn17 is shownin the Fig. 7 by a closed
el circle, approximately consistent with this relation.
c fi Variousmicroscopictheoreticalstudies havebeenper-
eti AF
n formed on the metamagnetic behavior of the magneti-
g
a
M zation in heavy-fermion compounds. Miyake and Ku-
T ramoto have calculated the magnetization process us-
T χmax
N
ing a semi-phenomenological model called the duality
model of heavy fermions on the periodic Anderson lat-
tice model.38,39) Inthe model, the metamagneticbehav-
Temperature (K) ior takesplace whenthe secondderivativeof the density
of states is positive and the coupling between itinerant
and localized parts of f electrons is large.From a differ-
Fig. 6. (Coloronline)MagneticphasediagramofU2Zn17 forthe
fieldalongthe[11¯20]direction.Solidanddottedlinesareaguide ent point of view, it was proposed that the anisotropy
totheeyes. ofthehybridizationmatrixelementyieldsthecharacter-
istic shape of the density of states that plays a major
role in the metamagnetism.40,41) Ohkawa and cowork-
ers clarified the spin-lattice effect cooperating with the
100
ferromagneticexchangeinteractioncausesthemetamag-
neticbehaviors.42–44) Althoughafinalconsensushasnot
U Zn
2 17 been established yet, the metamagnetic behavior in the
USn URu Si heavy-fermion system is one of the important issues in
3 2 2
f-electron magnetism. We hope that the present obser-
T) 10 UPt3UPd2Al3 vation in U2Zn17 stimulates future studies on the issue.
(
m
H 3.4 High-pressure experiment
CeRu Si
2 2 Figure8(a)showsthelogarithmictemperaturedepen-
denceoftheelectricalresistivityρinthecurrentparallel
to the [11¯20] direction under high pressures. The resis-
CeCu
6 tivity at room temperature increases slightly with in-
1
creasingpressure.ThecharacteristictemperatureT ,
ρmax
1 10 100 where the resistivityshows a maximum,is shifted to the
higher temperature side with increasing pressure. T
Tc (K) ρmax
max is 27.6 K at 8.7 GPa.
To clarify the behavior of the resistivity ρ around the
magnetic ordering temperature T , we show the low-
Fig. 7. (Coloronline)MetamagneticanomalyfieldsHmofseveral N
heavy-fermioncompounds, showninlogarithmicscale.Aclosed temperatureresistivityinFig.8(b),wheretheN´eeltem-
circlecorrespondstothatinthecaseofU2Zn17. perature TN is shown by an arrow. The pressure depen-
dence of T is shown in Fig. 9. The N´eel temperature
N
T isalmostpressure-independentupto4.7GPa.Above
reachthephaseboundaryofT below7T.Itseemsthat N
N the pressure, T starts to increase with increasing pres-
the metamagnetic behavior at H in the paramagnetic N
m sure. T is 12.2 K at 8.7 GPa. A characteristic feature
stateappearsinthe temperature regionbetweenT and N
N is that the sign of dT /dT changes at approximately 5
T . N
χmax GPa. The present result is roughly consistent with that
We suggest that the metamagnetic behavior at H
m of the previous study up to 1.7 GPa.18,19)
in the paramagnetic state of U Zn is similar to those
2 17 The resistivitybelow T is analyzedusing the antifer-
observed for heavy-fermion compounds such as UPt , N
3 romagnetic magnon model described as
URu Si , and UPd Al below T , where the mag-
2 2 2 3 χmax
netic susceptibility shows a maximum.35–37) It is basi- ρ=ρ +AT2+BT(1+ 2T)exp(−∆), (1)
0
cally supposed that the behavior is associated with the ∆ T
change of the hybridization effect between conduction where the third term corresponds to the contribution of
electrons with a wide energy band and almost localized the electron scattering by an antiferromagnetic magnon
f-electrons.1) Almost localized f-electrons become itin- withanenergygap∆,whichwasusedinthe analysesof
erant with decreasing temperature through the many- URu Si andCePd Si .45,46) Afitofthe resistivitydata
2 2 2 2
bodyeffect.Thecrossoverfromlocalizedtoitinerantoc- is shownbysolidlines inFig.8(b).The pressuredepen-
curs at a characteristic temperature T0, corresponding dences of the obtained parameters A and ∆ are shown
to Tχmax or Tρmax, where the magnetic susceptibility or in Fig. 10 (a). A decreases simply with increasing pres-
6 J.Phys.Soc.Jpn. FullPaper AuthorName
(a) 15
U Zn Trmax 8.7 GPa U2Zn17
2 17 7.1
J // [1120] 4.7
2.5 K) 10 T
m) 50 1.4 e ( N
c r
Æ W atu
(mr mper 5

e
T
0
1 10 100 0
0 5 10
Temperature (K)
Pressure (GPa)
(b) 80
T
70 U Zn N 1 bar
60 2 17 1.4 GPa
50 J // [1120] 2.5 Fig. 9. (Coloronline)Pressuredependence oftheN´eeltempera-
tureTN inU2Zn17.
40 4.7
7.1
30
m) 20 8.7 (a) 0.8
c
Æ W 10 U2Zn17 30
(m 0
r 2)
- 1 00 K 20
- 2 00 cm/ 0.4 K)
- 3 00 Æ W 1 (D0
m
- 4 00 (A
- 5 00 0.0 0
0 10 20 (b) 30
Temperature (K)
T
rmax
K) 20
e (
ur
Fig. 8. (Color online) (a)Temperature dependences of the elec- at
tricalresistivityρand(b)low-temperatureresistivityatseveral per 10
m
pressuresinU2Zn17. e
T
0
0 5 10
sure, from 0.35 µΩ·cm/K2 at 1 bar to 0.14 µΩ·cm/K2. Pressure (GPa)
The corresponding γ values are estimated as 190 and
120 mJ/K2·mol at 1 bar and 8.7 GPa, respectively, us-
ingtheKadowaki-Woodsrelation(A/γ2 =1.0×10−5).47)
The estimatedγ at1 baris consistentwiththe observed Fig. 10. (Coloronline)Pressuredependencesof(a)thecoefficient
of T2 term of the resistivity A(left side) and the antiferromag-
value of about ≃ 200 mJ/K2·molU. It is suggested that
neticgap∆(rightside),and(b) thecharacteristictemperature
γ decreases with increasing pressure. ∆ increases mono- TρmaxwheretheresistivityρshowsamaximumvalueinU2Zn17.
tonically from 19 K at 1 bar to 33 K at 8.7 GPa, indi-
cating thatthe antiferromagneticstate is enhanced with
increasing pressure. possibility that the slight change in the pressure depen-
Very recently, Sidorov, et al. performed the resistiv- dencesofAand∆atapproximately3GPashowninFig.
ity and ac heat capacity measurements on U Zn up 10 (a) is due to the appearance of the pressure-induced
2 17
to 5.5 GPa.48) The reported pressure dependence of T new magnetic phase revealed by our work.
N
is roughly consistent with that observed in the present Figure10(b)showsthepressuredependenceofTρmax.
study. In the study, two successive magnetic transitions This characteristic temperature Tρmax varies linearly as
wereobservedinthepressurerangeof2.64-3.25GPa.It a function of pressure, shown as a solid straight line in
was concluded that the antiferromagnetic ground state the Fig. 10(b). The pressurederivative of∂Tρmax/∂P is
changes to a new antiferromagnetic phase at approxi- 1.0K/GPa.NotedthatTρmax correspondstothecharac-
mately2.4GPa.Sincewehavenotinvestigatedthepres- teristictemperatureT0 oftheelectronicstateinU2Zn17.
sure dependence of TN in detail at approximately this The Gru¨neisen parameter ΓT0 for T0 is written as fol-
pressure,the change of the magnetic ground state is not
discussed within the present data. We only mention the
J.Phys.Soc.Jpn. FullPaper AuthorName 7
On the other hand, the magnetic orderedstate does not
seem to be easily destroyed by high pressure. A much
higher pressure far above 10 GPa seems to be needed to
suppress the magnetic ordered state.
We compare the pressure effect on the antiferromag-
netic state in U Zn with the cerium antiferromagnetic
2 17
compoundsCeIn andCeRhIn whosebulkmoduliof67
3 5
and 78, respectively, are close to that of U Zn .56,57)
2 17
0
T Both CeIn and CeRhIn order antiferromagneticallyat
3 5
T =10 K and 3.8 K, respectively, at ambient pressure.
N
Underhighpressure,theantiferromagneticorderingtem-
perature T becomes 0 K at critical pressures P of 2.1
N c
and 2.5 GPa,respectively, and the ground state changes
into the superconducting one at approximately P . The
c
magnetic to non-magnetic transition takes place below
3 GPa in both compounds whose compressibility β (=
1/B) is similar to that of U Zn . On the other hand,
2 17
theantiferromagneticorderedstateinU Zn isnoteas-
2 17
ily destroyed, but is stabilized under high pressures of
up to 9 GPa. The pressure effect on the antiferromag-
netic phase as well as on the paramagnetic electronic
Fig. 11. (Color online) Gru¨neisen parameter ΓT0 vs linear heat
capacity coefficient γ for several cerium and uranium com- state in U2Zn17 is thus highly different from those of
pounds.19,50,51) Theboldlineisaguidetotheeye. theheavy-fermionceriumcompoundsdescribedbasically
by the Doniach model for the Kondo lattice. The weak
pressure effect on T may be ascribed to the itinerant
lows: N
character of the 5f electrons in U Zn , as discussed
2 17
Γ =−∂lnT0 =B 1 ∂T0, (2) in uranium monochalcogenides UX(X=Te, Se, S).58–61)
T0 ∂lnV T0 ∂P The pressure dependence of the Curie temperature TC
where B is the bulk modulus, estimated to be 83 GPa inuraniummonochalcogenidesdeviatesfromthatinthe
at297KforU Zn byultrasoundmeasurement.49) The Doniach model, but is explained by the spin fluctuation
2 17
Gru¨neisen parameter Γ is 4.6 in U Zn . This value theory of an itinerant 5f electron system based on the
T0 2 17
is small compared with those of heavy-fermion com- Hubbardmodel.62,63)Inthetheory,thepressure-induced
pounds,wheretheGru¨neisenparameterisusuallyabout increaseinthe hydridizationbetween5f andconduction
one or two orders of magnitude larger than those of or- electronsstrengthenstheexchangeinteractionJ between
dinary metals.19,50,51) For example, the Gru¨neisen pa- uraniumions,butitalsodecreasesthe5f spectralweight
rameters for the characteristic temperature T of the (magnetic moment) atthe uraniumsite.The modelpre-
0
heavy-fermionsuperconductorsCeCu Si ,UBe ,UPt , dicts a much more gradual demagnetization of the itin-
2 2 13 3
and URu Si are 22, 103, 76, and 19, respectively.19,50) erant magnetic system under higher pressure than the
2 2
In Fig. 11, we plot the relations of the Gru¨neisen pa- Doniach picture. The present weak pressure dependence
rameter ΓT0 and the electronic specific heat coefficient ofTN inU2Zn17mayreflecttheitinerantcharacterofthe
γ for several cerium and uranium heavy-fermion com- 5f electronsinthecompound,whichisdifferentfromthe
pounds.19,50–52) Theoretically, the γ value correlates 4f electronsysteminceriumcompounds.Itisinteresting
with the Gru¨neisen parameter enhanced by the many- to note high-pressure studies of the well-known heavy-
body effect in the Kondo lattice system.53,54) It is sup- fermion antiferromagnet UCu5 where the antiferromag-
posedthatthe Gru¨neisenparameterofU2Zn17 isunusu- netic phasetransitiontakesplaceatTN =15.9K.Itwas
ally small when the large γ value is taken into account. revealedthattheN´eeltemperatureTN ofUCu5 increases
The Gru¨neisen parameter Γ for A in the resistivity is with increasing pressure very gradually at a rate of 0.33
A
estimated as 2.5 in the low-pressure region. This value K/GPa and that the magnetic phase exists even at 13
is also small compared with those of UBe and UPt , GPa.64,65) It is suggested that the pressure response of
13 3
where the values of Γ are 17 and 61, respectively.19) uranium heavy fermion compounds with the antiferro-
A
These small values of the Gru¨neisen parameters suggest magnetic ground state generally differs from that of the
that the electronic state in U Zn is not so sensitive to 4f electron system in cerium compounds.
2 17
thechangeofthelatticeparameterscomparedwiththose
4. Conclusions
of the other heavy-fermioncompounds with the order of
γ = 100 mJ/K2·mol. We have performed a high-field magnetization exper-
It is interesting to note that the antiferromagnetic iment as well as a high-pressure experiment on single
stateinU2Zn17isverysensitivetoasmallamountofsub- crystals of U2Zn17 grown by the Bridgman method. We
stitution on the Zn site.55) The antiferromagnetic tran- alsomeasuredtheelectricalresistivityandmagneticsus-
sitiontemperature T is stronglydepressedto below 1.5 ceptibilityatambientpressure.Theexperimentalresults
N
K with the substitution of only 2% Cu on the Zn site. are summarized as follows:
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