Exotic (anti)ferromagnetism in single crystals of Pr6Ni2Si3

1.1 MB·English

by  Y. Janssen

Exotic (anti)ferromagnetism in single crystals of Pr Ni Si
6 2 3
Y. Janssen,∗ K. W. Dennis, R. Prozorov, P. C. Canfield, and R. W. McCallum
Ames Laboratory DOE and Department of Physics and Astronomy, Iowa State University,Ames,IA 50011,USA
(Dated: February 5, 2008)
The ternary intermetallic compound Pr Ni Si , is a member of a structure series of compounds
6 2 3
based on a triangular structure where the number of Pr atoms in the prism cross section can be
systematicallyvaried. Pr Ni Si containstwodistinctPrlatticesiteswhichresultincomplexinter-
6 2 3
actions between the magnetic ions. Extensive measurements of specific heat and magnetization on
singlecrystalsamplesindicatethatPr Ni Si orderswithbothaferromagnetandanantiferromag-
6 2 3
netcomponent, withorderingtemperaturesof39.6Kand∼32K,respectively. Theferromagnetic
component // c-axis is accompanied by a large hysteresis, and the antiferromagnetic component,
8
⊥ c-axis is accompanied by a spin-flop-type transition. More detailed measurements, of the vector
0
magnetization,indicatethattheferromagneticandtheantiferromagneticorderappearindependent
0
of each other. These results not only clarify the behavior of Pr Ni Si itself, but also of the other
2 6 2 3
members of the structure series, Pr Ni Si and Pr Ni Si .
5 2 3 15 7 10
n
a PACSnumbers: 75.50.-y,75.30.Gw,75.10.-b
J

7
1 I. INTRODUCTION

]
i A magnetic system with magnetic moments on non-
c
equivalent crystallographic sites may be difficult to ana-
s
- lyze experimentally. Different site symmetries and in-
l
r teratomic spacings can produce magnetic interactions
t
m with different signs or strengths as well as different crys-
tallineelectricfieldsplittingsandevenvalencies. If,how-
.
t ever, the considered magnetic system forms part of a se-
a
m ries, similarities in magnetic properties of the members
may lead to a greater understanding of the properties of
- Pr1 Ni
d all members. Rare-earth intermetallic compounds often
n form natural series, because, due to the chemical simi-
Pr2 Si
o larity of rare earths, a particular rare earth can be re-
c
placedforanother, andtheresultingmagneticsystemat-
[
ics can be appreciated (See e.g. Ref.1). Another type of

1 series that may be considered is the structure series. In
v a structure series, structural features are systematically FIG. 1: Schematic drawing2 of the Ce6Ni2Si3-type unit cell
4 repeated, which may help in understanding the physical of Pr6Ni2Si3.
0
properties of members of such series.
7
2 In 1984, Parth´e and Chabot3 reviewed the crystal
. structures of ternary rare-earth (R) transition metal (T)
1
silicide and boride (M) compounds. At that time, about tionsissmall. Inaddition, thelowconcentrationofboth
0
8 80 different compositions were known. A number of the rare earth and transition metal ions is expected to re-
0 R-T-Mcompoundscanbeclassifiedaspartofastructure sultinweakmagneticinteractionsandloworderingtem-
: series. The majority of these structural series consist of peratures. On the contrary, the latter series consists of
v
layeredstructures,andtheorganizationofthelayersdis- roughly 50 % rare-earth and, moreover, there are differ-
i
X tinguishesmembers. However,therearealsoatleasttwo entRlocalenvironments,seee.g.Ref.4,5. Furthermore,
r R-T-M structure series where the basic building block is both the n=3 and the n=4 members are known to or-
a
a triangular prism. These prisms may be assembled into der magnetically4,5,6,7.
largerprismsinageometricprogressionwhereeachmem- InhexagonalPr Ni Si ,withspacegroupP63/m,the
6 2 3
ber of this progression represents a unique crystal struc- Pr ions occupy two independent low-symmetry 6h sites,
turewithaspecificratioofrareearthtotransitionmetal denotedasPr1andPr2inFig.1. Thecrystal3 structures
atoms. The two known series of this type are described oftheothermembersofthestructureseries,respectively
by the formulae R1n(n+1)T3(n2+1)M2n2+1, with as n=2 Pr5Ni2Si3 andPr15Ni7Si10,havethesamespacegroupas
2
member UCo Si and R Ni Si , Pr Ni Si . In Pr Ni Si , Pr ions occupy 3 independent
5 3 (n+2)(n+1) n(n−1)+2 n(n+1) 6 2 3 5 2 3
with as n = 2 member the title compound Pr Ni Si 6h sites and one 2d site. In Pr Ni Si , Pr ions occupy
6 2 3 15 7 10
(Fig. 1). In the former series there is only a single 5 independent 6h sites. Both Pr Ni Si and Pr Ni Si
5 2 3 15 7 10
rare earth site so the potential for competing interac- have Pr ions occupying sites comparable to Pr1 and Pr2
2
in Fig 1. growth was determined to be between ∼ 1000◦C and
Results from polycrystalline samples, for Pr Ni Si ∼ 880◦C. The starting elements were sealed in a 3-cap
5 2 3
(n = 3), or more accurately5 Pr Ni Si , and for Tacrucible11,thatwassealedinanevacuatedquartzam-
5 1.9 3
Pr Ni Si (n=4)indicatethatbothcompoundsorder poule. Theampoulewasinitiallyheatedupto∼1200◦C,
15 7 10
ferromagnetically4, at ∼ 50 K, and at ∼ 60 K, respec- to ensure a well-homogenized alloy, cooled to 1000◦C at
tively. For both Pr Ni Si and Pr Ni Si the specific ∼50◦C/h,andthencooleddownto880◦Cat3◦C/h. The
5 2 3 15 7 10
heat shows, besides the anomaly due to the Curie tem- ampoule was taken out of the furnace, inverted and cen-
perature,another,weaker,anomaly,at∼27Kandat∼33 trifuged, resulting in a separation of crystals from an ex-
K, respectively. For both these compounds, at temper- cess liquid. Crystals have a hexagonal-prismatic growth
atures below the low-temperature specific-heat anomaly, habit with faces parallel to the [001] crystallographic di-
the magnetization isotherms show the development of a rection,andnormaltothe[110]direction13. Thecrystals
significantcoercivity. Moreover, thereoccursevidenceof were up to 10 mm long, and had effective diameters of
metamagnetic-like transitions close to 3 T for Pr Ni Si up to 1 mm. A photograph of a Pr Ni Si crystal is
5 2 3 6 2 3
at 5 K, and close to 4 T for Pr Ni Si at 5 K. displayed in Fig. 2.
15 7 10
In this paper, we report on the magnetic properties of
solution-grown, single-crystalline Pr Ni Si , the n = 2
6 2 3
member of the aforementioned structure series. Results For initial characterization, we measured a powder x-
of specific heat, and of extensive anisotropic magneti- ray diffraction pattern on finely ground crystals from
zation measurements are presented. Moreover, measure- thegrowthyieldwithaRigakuMiniflex+diffractometer
mentsofthemagnetizationvectorhavebeenusedtoclar- employing Cu-Ka radiation. The pattern was analyzed
ify the low-temperature magnetic order, which following with Rietica14, using a Le Bail-type15 refinement, and it
crystallographic nomenclature8 appears to be ’exotic’. was indexed according to the space group P63/m, with
Finally, the results are discussed within the systemat- lattice parameters a = 11.96(2) ˚A and c = 4.27(1) ˚A.
ics seen also for the n = 3 and n = 4 members of the Theseresultsareconsistentwiththoseforisostructural16
series. Ce6Ni2Si3,whichhassomewhatlargerlatticeparameters
(a=12.11 ˚A, and c=4.32 ˚A), consistent with lanthanide
contraction.
II. EXPERIMENTAL
Specific heat was determined in a Quantum Design
physical property measurement system (QD-PPMS) at
temperatures between 2 K and 70 K. Magnetization
measurements were performed using Quantum Design
magnetic property measurement system magnetometers
(QD-MPMS), in magnetic fields up to 5 T, and at tem-
peraturesbetween5Kand300K.Formostoftheexper-
iments described below, only the magnetization compo-
nent parallel to the applied field was measured for sam-
ples aligned with the applied field parallel and perpen-
dicular to the hexagonal c-axis. To investigate a possi-
ble in-plane magnetic anisotropy the sample was aligned
withthefieldperpendiculartothec-axis,androtatedby
means of a horizontal-axis rotator around the c-axis.
Generally, a magnetization vector can be decomposed
intothreeperpendicularvectorcomponents. Wecandis-
tinguishalongitudinalcomponent,alongtheappliedfield
FIG.2: Photographofaself-fluxgrowncrystalofPr Ni Si ,
6 2 3 direction, here called M , and transverse components in
on a background with a mm-scale. The crystal axis is the c L
the plane perpendicular to the applied field, here called
axis, and a [110] facet is facing the reader.
M andM . WeusedaQD-MPMS-5system,whichwas
X Y
equipped with both a conventional longitudinal pick-up-
coil system and a transverse pick-up-coil system. Since
Single crystals of Pr Ni Si were grown out of a themagnetometerisequippedwithonesingletransverse
6 2 3
high-temperature ternary solution9,10,11. An initial al- pick-up-coil system, we used the vertical-axis sample ro-
loy composition and a useful temperature range for tatortodetermineboththeM andtheM components
X Y
growthweredeterminedbymeansofcombinedDTAand of magnetization. For these vector measurements, the
growthexperiments12. Theinitialalloycompositionused sample was aligned with the unique c-axis at an angle of
was Pr Ni Si , and the useful temperature range for about 60 degrees with the applied field direction.
60 25 15
3
tribution per Pr ion C was obtained by subtracting
M
250
thislatticecontributionfromthemeasuredspecificheat.
a Pr Ni Si
6 2 3 Notice that, besides the peak near 40 K, also a shoul-
Specific heat
der with a maximum around 30 K can be observed. The
200
temperature-dependent magnetic entropy S , estimated
M
by integrating C /T up to 70 K and displayed in the
) M
1
-K 150 inset of Fig. 3 b, saturates at a value close to Rln2 at
1
-ol 40K,andthenremainsapproximatelyconstantupto70
m K. This indicates that, averaged over the two crystallo-
J.
( 100 graphicallydistinctPrions,apairofwell-isolatedsinglet
P
C states, or a doublet ground state, is responsible for the
magnetic order in this compound.
50
0 250
0 10 20 30 40 50 60 70
5
20 T (K) // c-axis
200
b
18 1.0 4 c-axis poly.
3 )
- m
1146 R ln 2) 0.5 /f.u.)B3 150 mol.cPr
-1K) 12 S (M M ( 2 // c-axis 100-1 (
-1 Pr 10
ol 0.0
m 8 0 10 20 30 40 50 60 70 1 50
J. T (K)
C (M 6 c-ax is
4 0 0
0 100 200 300
2
T (K)
0
0 10 20 30 40 50 60 70
T (K)
FIG. 4: (Color online) Closed circles, left axis: Pr Ni Si
6 2 3
temperature-dependent magnetization measured in 0.01 T,
bothforH //c-axis(top)andforH ⊥c-axis(bottom). Open
circles,rightaxis: temperature-dependentinversedifferential
FIG.3: (Coloronline)aZero-fieldspecificheatCp asafunc- susceptibility determined for H // c-axis (bottom) and H ⊥
tionoftemperature,alsoincludedisanestimateofthelattice c-axis (top) together with polycrystalline average χ−1 (cen-
specific heat. The mean-field-like with an onset near T = 40 ter).
KisclosetotheCurietemperature. bMagneticspecificheat
perPrionobtainedfroma. Notetheshoulderbetween30-35
K. The inset shows the estimated magnetic entropy to reach
values close to Rln2 at the ordering temperature. Fig.4 shows temperature-dependent magnetization
measured upon cooling in a field of 0.01 T applied both
parallel and perpendicular to the c-axis. Two features
are immediately obvious: the magnetization parallel to
thec-axisindicatesaferromagneticcomponent//c-axis
III. RESULTS
below ∼ 40 K, and the magnetization ⊥ c-axis is much
smaller than the magnetization parallel to the c-axis, es-
Temperature-dependent specific heat is presented in pecially below 40 K, which indicates that the magnetic
Fig. 3a. It will be shown below that Pr Ni Si orders anisotropy in this compound is very large and favors the
6 2 3
ferromagnetically. Then an onset criterion17 for a peak moments to align themselves parallel to the c-axis.
in specific heat can be used. The peak in specific heat Temperature-dependent magnetization for both these
shows an onset temperature close to 40 K. A lattice con- samplealignmentswasdeterminedinvariousfieldsupto
tribution to specific heat, also shown, was estimated ac- 5 T. From these it was found that above 50 K the mag-
cording to the Debye model, and we obtained a Debye netization for both alignments increases linearly with in-
temperature of Θ ≈ 165 K. An electronic contribution creasing fields, thus a differential magnetic susceptibility
D
wasignored. Anestimate,Fig.3b,forthemagneticcon- χ = ∆M couldbedetermined. Apolycrystallineaver-
diff ∆H
4

agewasobtainedbyaveragingχ//c-axisandχ⊥c-axis
0.08
according to χ =(χ +2χ )/3.
avg // ⊥ Pr Ni Si
Fig.4 also shows the inverted temperature-dependent 0.07 1.00 6 2 3
H // c-axis
differential magnetic susceptibilities // c-axis, ⊥ c-axis
and polycrystalline average. All three are linear, though 0.06 R0.98
not parallel, with temperature above 100 K, thus can be
described by a Curie-Weiss law. The effective moments 0.05 0.96 T = 39 K
calculated for χavg, χ//, and χ⊥ equal 3.35 µB/Pr, 3.50 3u) 39 T 4(0K) 41
µ /Pr,and3.26µ /Pr,whichareareallnottoofarfrom m 0.04
thBe theoretical freeB-ion value for Pr (3.58 µ ), thus indi- (e
B 3 0.03 T = 39.4 K
catingthatthemagnetisminPr Ni Si isdeterminedby M
6 2 3 T = 39.6 K
Pr local magnetic moments. However, the fact that the 0.02 T = 39.8 K
calculatedeffectivemomentsaredifferentforthedifferent T = 40 K
crystallographic directions is an indication of a substan- 0.01
tial crystal-field splitting of the 2J+1 levels of the Pr-4f T = 41 K
0.00
shell,whichisstillnoticableatroomtemperature. Weiss 0 100 200 300 400 500 600
temperatures Θ of 41 K, 53 K, and 33 K were found for
H (Oe)
Θ , Θ , and Θ , respectively, positive values which 0.14
avg // ⊥
are reasonably close to TC, and which indicate (mainly) T = 39 K
ferromagnetic interactions between the Pr moments. 0.12
0.10
T = 39.4 K
A. H // c-axis
T = 39.6 K
) 0.08
2
The Curie temperature for the onset of ferromagnetic mu T = 39.8 K
order // c-axis can be determined from Arrott plots18. 2 (e 0.06 T = 40 K
Fig.5showssuchplotsforPr Ni Si ,obtainedfrommag- M
6 2 3
0.04
netization isotherms H // c-axis in fields up to 500 Oe.
In Arrott’s original paper18, plots of M3 vs H are used T = 41 K
ratherthanthemoreconventionalM2 vsH/M. Accord- 0.02
ing to Arrott’s criterion, precisely at T , the magnetic
C
susceptibility χ tends to infinity, causing terms of M3 to 0.00
0 500 1000 1500 2000 2500 3000 3500 4000
bedominantatlowenoughH. Inotherwords,theCurie
H/M (Oe/emu)
temperature is at that temperature where H-dependent
M3 is exactly linear starting at H = 0. A criterion for
the linearity of a fit line is given by the regression fac-
tor R, which ranges between 0 and 1, where 1 indicates
FIG.5: (Coloronline)Pr Ni Si ArrottplotsforH //c-axis.
a perfect line. The top panel of Fig. 5 shows M3 vs H 6 2 3
The upper panel shows field (H) dependent magnetization
taken at temperatures between 39 K and 40 K, and the (M3)forrepresentativetemperatures. TheinsetshowstheT-
inset to that panel shows the temperature-dependent R dependentregressionfactorRforalinearfitthroughM3(T),
ofsuchlinearfits. FromthistheCurietemperatureisde- indicating the Curie temperature T =39.6(1) K. The lower
C
termined as T =39.6 (1) K. This value agrees very well panelshowsconventionalArrottplots,ofM2 vs. H/M ofthe
C
with the above obtained value for the onset of the spe- same data sets.
cific heat peak. For completeness, a more conventional
Arrott plot of M2 vs H/M is displayed in the bottom
panel of Fig. 5. As expected, the curve taken at 39.6
K extrapolated to zero M2 is closest to intercepting the
H/M axis. propagationfieldHP atwhichtheexternalfieldisableto
detachthenarrowwallsfromthepinningsites. Athigher
Hysteretic behavior of Pr Ni Si at 1.8 K for H //
6 2 3
fields the walls are removed from the crystal. Upon de-
c-axis is shown in Fig. 6. These results were obtained
creasing the fields from 1 T into the region of negative
by cooling the aligned crystal in zero field and measur-
fields, reversed domains and domain walls can nucleate
ing first the virgin magnetization curve. The observed
but the movement of these walls is impeded by the pin-
presence of high coercivity in conjunction with the small
ningsitessothatthereverseddomainscannotgrow. This
slopeofthevirgincurvecanbetakenasasignatureofthe
presence of narrow domain walls19,20,21,22,23. Such nar- becomes possible again only for negative fields equal in
magnitudetoH ,causingtheabsolutevalueofthecoer-
row walls can be strongly pinned by magnetic obstacles P
cive field to be equal to the propagation field, H =H .
ofatomicdimensions. Thestrongincreaseofthemagne- C P
tization on the virgin curve at H = 0.45 T marks the Becauseofthestronghysteresis,thespontaneousmag-
P
5

10 0.5
8 Pr6Ni2Si3 Pr6Ni2Si3
H // c-axis H // c-axis
6 10 0.4 30
4 8
/f.u.)B 02 M (/f.u.)B246 15 K6 K 4 K 3 K1.8 K H (T)C0.3 -1-1 H (T)c20
M ( -2 0 00.2 010
0.0 0.1 0.2 0.3 0.4
-4
0H (T)
-6 0.1 0
0 2 4 6 8 10 12 14 16
-8 T (K)
-10 0.0
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 0 5 10 15 20 25 30 35 40
0H (T) T (K)
FIG.6: (Coloronline)Pr6Ni2Si3 zero-field-cooledmagnetiza- FIG. 7: (Color online) Pr6Ni2Si3 temperature-dependent co-
tion loop for H // c-axis at 1.8 K. The inset shows the de- ercive field for H // c-axis. The line is obtained as descibed
velopmentofvirginmagnetizationwithtemperature,demon- in the text.
strating the coercive behavior.
T−1, and α(T)=0.37(9)+0.079(6)T, leading to a zero-
netization M at 1.8 K can directly be obtained from
S temperature H of 0.71 T. The dotted line in the main
this Figure. It equals about 8.5 µ /f.u., amounting to C
B Fig. 7 was calculated using these values.
about 1.4 µ /Pr ion, which is much lower than the free-
B
SinceM Sisconstantbelow15K,M isnotexpecting
ion value of 3.2 µ /Pr, which may be related to strong S
B
tocontributetovariationsofα(T)below15K.Therefore,
crystal-electric field effects and the low point symmetry
thevariationsinαbelow15Khavetobeproportionalto
of both Pr-crystallographic sites.
thevariationsof1/γ2,theinvertedproductoftheaverage
The temperature dependence of the coercive field is
exchangeenergyandtheaverageanisotropyenergy. Both
demonstrated in the inset of Fig. 6, which shows virgin
the exchange energy and the anisotropy energy may be
M(H) at different temperatures below 15 K. Note that
expected to decrease with increasing temperature, lead-
besideshavingadifferentcoercivefieldthesecurvesover-
ing to α growing with increasing temperature.
lap, so M is almost temperature independent below 15
S
K.
Measurements at various temperatures below T indi-
C
cate the same behavior as at 1.8 K, but with a strongly B. H ⊥ c-axis
temperature-dependent H Fig. 7 shows temperature-
C
dependent H . According to a model proposed by Bar-
C Fig.8showstemperature-dependentmagnetizationfor
baraandUehara22,thetemperaturedependenceofcoer-
H⊥ c-axis measured, with temperature decreasing, in
civity can be described as:
various fields up to 5 T. In 0.01, 1 and 2 T, the mag-
netization shows a maximum, which appears close to 32
H−1(T)=H (0)−1+αT, (1) K, for 0.01 T and 1 T, and close to 27 K for 2 T. In
C C 3 T and higher, no maximum is observed. Such behav-
where α is proportional to the spontaneous magneti- ior, a maximum in temperature-dependent magnetiza-
zation divided by the domain-wall energy, α ∝ M /γ2. tion, which shifts to lower temperature with increasing
S
γ2 in turn is proportional to the product of the average field strengths, is common in antiferromagnets24. Note
exchangeenergyandtheaverageanisotropyenergy. The also that the maximum in the 0.01 T curve occurs at a
inset of Fig. 7 shows temperature-dependent H C−1 at temperature close to the 32 K shoulder in specific heat.
temperatures between 1.8 K and 15 K. A very good fit Field-dependent magnetization isotherms for H⊥ c-
to this line is given by a second-order polynomial, and axisattemperaturesbetween5Kand45Kareshownin
when comparing to Eq. 1, this means that α is linearly Fig. 9. At 5 K, starting in zero field, the magnetization
dependent on T. Values found are: H (0)−1 = 1.4(3) startsatzeroandfirstincreasesweaklyandlinearlywith
C
6
which ends close to 3 T, above which the magnetization
continues to increase linearly with increasing field, at a
slope similar to the slope in low field. As temperature
Pr Ni Si m 0H = increases, this process becomes less pronounced, result-
8 m H6 ^ 2 c-3axis 10 mT ing in a weakly s-shaped magnetization at 30 K, and a
1 T
0 featurelessmagnetizationat35Kandhigher. Alsothese
2 T
3 T results are consistent with the magnetization of a simple
0.035
6 4 T antiferromagnet,andthemagnetizationprocesscouldbe
0.030
u.) 0.025 5 T interpreted as due to a spin flop24.
/f.B 4 0.020
0.015
m(
M 0.010
5 T
0.005 8
3.4 T
2 0.000
0 100 200 300
2.95 T
7
8 7.620
0
0 50 100 150 200 250 300 6 6 3.4 T
7.615
T (K)
4

0.765 0.5 T
5 2 0.760
u.) 0 0.755
FfoIrGH.8⊥: (cC-oalxoirsomnelianseu)rTedeminpveararitouurse-fideelpdesnudpenttom5aTg.neNtoiztaettiohne /f.B 4 0 m 02H (T)4 0 1002 003020.5 T
m(
maxima for 0.01 (≈ 32 K), 1 (≈ 32 K, and 2 T (≈ 27 K. M
3
2 2.05 T
1.6 T
10 1
0.5 T
9 Pr Ni Si 5 K
8 6 2 3
7 H ^ c-axis 10 K 0
6 15 K 0 50 100 150 200 250 300 350 400
5 20 K
Hor. rotator angle (deg.)
4
25 K
3
u.) 2 30 K
/f.B01 35 K FtiIoGn,.m10e:asuPrre6dNai2tS5i3Kh,oirnizvoanrtiaolu-asnfigeleldsde(pHen⊥decn-taxmisa)gunpettioza5-
mM ( 00 40 K T. The left inset shows all data as a function of H, superim-
posed on a denser dataset measured at zero angle. The right
0
45 K
0 insetshowsazoominofthe0.5Tdata(bottom)andthe3.4
0 T data (top).
0
0
0
0 1 2 3 4 5 6
m H (T) To determine magnetic anisotropy in the plane per-
0 pendicular to the c-axis we more precisely measured
the magnetization at 5 K for the field ⊥ c-axis with
a horizontal rotator, rotating the sample around the c-
axis. In a hexagonal system with a very strong in-plane
FIG. 9: (Color online) Field-dependent magnetization of
anisotropy, the in-plane magnetization may vary by as
Pr Ni Si atvarioustemperaturesmeasuredwithH ⊥c-axis.
6 2 3 much as 1−cos30◦ ∼ 15%. Fig. 10 shows the magneti-
For clarity, the curves have been shifted by 1 µ /f.u. with
B
zationinvariousfieldsupto5T,measuredathorizontal
respect to one another.
rotator angles between 0 and 360◦. For all chosen field
strengths, the variation in magnetization is smaller that
the symbols used for the figure. The in-plane anisotropy
of Pr Ni Si in fields up to 5 T is thus very small, which
6 2 3
increasing field. Close to 2 T, the magnetization starts is exemplified in the left inset, by plotting all thus mea-
to increase much faster with increasing field, a process sured magnetization values on a more densely measured
7
field-dependent magnetization curve, measured at zero
angle. Strongly zoomed in, see right inset of Fig. 10, PrNiSi
eg˙t˙he magnetization at 0.5 T shows a very weak and 12 10 H =6 02 3 M
foldvariation,withanamplitudeofvariationofabout0.1 8 (cooled in 5 T) T
%. Thisvariationdisappearsinhigherfields: thezoomed 6 M
in angular dependent magnetization measured in 3.4 T 4 L
shows no such variation. This 12 fold variation may be 2
related to the two crystallographically distinct magnetic /f.u.)B 0
Pr sites in the unit cell of Pr6Ni2Si3. mM ( -2
-4
-6
C. H applied at 60◦ from the c-axis -1-08 -MT
0 50 100 150 200 250 300 350
Rotator position (°)
The crystal was mounted and centered in a straw
such that the applied field H made an angle of ≈ 60◦
with the c-axis. The very weak in-plane anisotropy,
Fig. 10, made it clear that no particular attention to
FIG.11: Pr Ni Si zero-fieldmagnetization,measuredat5K
the planar direction closest to the applied field was nec- 6 2 3
both parallel to the applied field H (M ) and perpendicular
essary, which is not true if the in-plane anisotropy is L
to it (M ) as a function of (vertical) rotator position. This
strong25. Thesample wasthencooled inanappliedfield T
was measured on a field-cooled sample which was mounted
of 5 T from room temperature to 5 K, at which tem- with its c-axis at an angle of approx. 60 degrees with H.
perature the field was removed. Vertical-rotator angle-
dependent zero-field magnetization measured both par-
allel (longitudinal magnetization M ) and perpendicu-
L
lar to H (transverse magnetization M ) are shown in
T
Fig. 11. Whereas the measured ML is vertical-angle in- 14
dependent, M is determined as the amplitude of the PrNiSi at 5 K
T 12 6 2 3
measured transverse magnetization cosine. We thus find
for M a value of ≈ 7.5µ /f.u. and for M 3.8 µ /f.u.
T B L B 10
|M|
Theangleofthemagneticmomentwiththeappliedfield
iwsitghivetnhebyantgalne−a1tMMwTLh=ich63t◦h,ewchriycshtaisl ianxigsoowdasagmreoeumnteendt /f.u.)B 68 M
in the sample holder. The size of the moment vector mM ( L
(cid:112)
|M| = M2+M2 = 8.4µ /f.u. is in excellent agree- 4
L T B M
ment with the magnetization moment found at 5 K for T
2
H // c-axis.
Field-dependent magnetization was determined by 0
0 1 2 3 4 5
measuring both M and M at 5 K in various H up
L T m H (T)
to5T.M wasdeterminedintheconventionalway. Full 0
L
rotations of the vertical rotator, similar to the measure-
ment shown in Fig. 11, were made to determine M .
T
In this way, we verified that the magnetic moment does
FIG.12: Pr Ni Si field-dependentmagnetization,measured
6 2 3
not rotate in the plane perpendicular to the magnetic at5Kbothparallel(M )andperpendicular(M )totheap-
L T
field, which was a distinct possibility25. The results plied field, resulting in a vector-summed magnetization |M|.
are shown in Fig 12. As expected, M increases uni-
L
formly with increasing H, and the spin-flop-like transi-
tion starts close to 2.5 T, a field some 15% (=1/sin 60◦)
higher than for the measurement shown in Fig. 9. At
the same time, M decreases uniformly with increasing small, linear increase with increasing field strenghts up
T
fields, which generally indicates a rotation of the mag- to ∼ 2.5 T, and increases even further during the spin-
netic moment towards H. The spin-flop-like transition flop-like transition, up to about 3.5 T, above which it
for this magnetization-vector component mimics the one further increases slightly and linearly. This anomalous
for M , but as a stronger decrease rather than an in- change in length of the magnetization vector is an im-
L
crease. The amount by which the magnetization vector mediate indication that the metamagnetic spin-flop-like
decreasesforM duetothespin-flop-liketransitionmay transition for H ⊥ c-axis is not due to a simple rotation
T
seem small compared to the increase observed for M . of the magnetization vector25.
L
This is clarified examining the total magnetization, the The lower panel of Fig. 13 shows the measured field-
vector sum |M|, also shown in Fig. 12. |M| shows a dependent magnetization vector with the field applied
8

lowing proposed nomenclature8. As described below, it
maywellbethattheferromagneticordermainlyinvolves
PPrrNNiiSSii aatt 55 KK
1100 66 22 33 one of the two Pr sites, and the antiferromagnetic or-
der the other. In our view, two magnetic phase transi-
88 HH //// cc--aaxxiiss tions may be discerned, possibly with different propaga-
HH^^ ^^^^^^ cc--aaxxiiss
tionvectors,q=0fortheferromagneticorderandanother
u.)u.) 66 one for the antiferomagnetic order. The first transition
mmM (/f.M (/f.BB 44 MM c-axisc-axis omcacgunrsetaictaTllyC /=/3c9-.a6xiKs,,wwihthereaPspromntoamneenotussomrdaegrnefetrizrao--
tionsubstantiallylowerthanthetheoretical free-ionmo-
22 MM cc--aaxxiiss ment for Pr. This transition is evidenced by a clear spe-
cificheatanomalyandbyArrottplotsofM(H)forH //
c-axis. The second magnetic transition is due to antifer-
00
00 11 22 33 44 55 romagnetic order ⊥ c-axis and shows as a weak shoulder
mm 00HH ((TT)) in specific heat close to 32 K, and in low fields ⊥ c-axis
PrNiSi at 5 K by M(T), where a peak occurs close to 32 K. Further-
10 6 2 3
more, spin-flop-like transitions are only clearly observed
below 32 K.
8 M // c-axis
The ferromagnetic order // c-axis is further corrobo-
u.) M^ ^^^ c-axis ratedbythestrongandstronglytemperature-dependent
/f.B 6 H coercivity that occurs for M // c-axis, which shows it-
mM ( c-axis 10 M^ ^^^ c-axis Pr6Ni2Si3 at 5 K12 self in nearly square magnetization loops at low tem-
4 M^^^^ M// mM (/f.u.)B468H(svine(Mcy^t)^^o^r mHec-aasxisurement) 6810mM (/f.u.)B proewratduormesa.inSwucahllslowohpischocacruersitnrofnegrrlyompaingnneedts, wonithobnsatar--
2 2 4 cles of atomic size. The coercivity in Pr Ni Si becomes
0 M('n^ ^^o^r mc-aalx' ims easurement) 2 strongerwithdecreasingtemperatures,w6hic2hm3aybeex-
-20 1 2 3 4 5 0
0 m0H^c-axis (T) pected for any coercive magnet. We find no clear evi-
0 1 2 3 4 5
dence that the behavior of the coercive field is related
m H (T)
0 to the development of antiferromagnetic order ⊥ c-axis.
Thecauseofthenarrowdomainwalls,whicharenotusu-
FIG.13: Pr Ni Si field-dependentmagnetization,measured allyobservedinpuresinglecrystalsisnotpresentlyclear,
6 2 3
at5Kbothparallel(ML)andperpendicular(MT)totheap- but may be related to the instrinsic crystallographic dis-
plied field, resulting in a vector-summed magnetization |M|. order we have found13.
Theantiferromagneticorder⊥c-axisinturniscorrob-
orated by a magnetization process, similar to a spin-flop
transition,whichstartscloseto2Tat2KforH⊥c-axis.
at ∼ 60◦ from c-axis (Fig. 12) decomposed25 in a com- That this magnetization process is only due to magneti-
ponent // c-axis and a component ⊥ c-axis. For com- zation for H⊥ c-axis is evidenced by measurements of
parison,field-dependentlongitudinalmagnetizationmea- the magnetization vector for H applied at an angle of
sured with H applied // c-axis and with H applied ⊥ 60◦ withthec-axis. AlthoughthefactthatM //c-axis
S
c-axis are shown in the upper panel of Fig. 13. In both is substantially smaller than the full free-ion Pr moment
theloweranduppperpanel, weshowanalmostconstant enables additional magnetic order, there is no evidence
magnetization // c-axis, whereas the magnetization ⊥ that here these two magnetic orderings // c-axis and ⊥
shows a spin-flop like transition. The inset of the lower c-axis are linked.
panel of Fig. 13 shows the magnetization ⊥ c-axis ob- Themagneticpropertiesofsingle-crystallinePr Ni Si
6 2 3
tained by vector magnetometry with H projected ⊥ c- is consistent with the magnetic properties of the
axis, compared to the longitudinal magnetization from other members of the structure series, Pr Ni Si and
5 2 3
the upper panel of Fig. 13. Thus the spin-flop like pro- Pr Ni Si , which order also ferromagnetially at 50 and
15 7 10
cess⊥c-axisoccursindependentfromthemagnetization at 60 K, respectively. Both these compounds also show,
// c-axis, and is only due to the H ⊥ c-axis. besidestheCurie-temperatureanomaly,shouldersinspe-
cific heat, at 27 K and at 33 K, respectively, below
which temperatures for both these compounds in the,
IV. DISCUSSION AND CONCLUSIONS polycrystalline, magnetization metamagnetic-like behav-
ior appears.
The experimental results shown above indicate quite Preliminary studies on single crystals26 of these com-
clearly that the magnetic order in the intermetallic com- pounds indicate that they also order ferromagnetically
pound Pr Ni Si has both ferromagnetic and antiferro- // c-axis and antiferromagnetically ⊥ c-axis. Further-
6 2 3
magnetic components, which may be callled ’exotic’ fol- more, a preliminary neutron powder diffraction27 mea-
9
surement of Pr Ni Si , indicated that Pr moments order also clarifies these.
5 2 3
ferromagnetically // c-axis, and the moment on the site
comparable to Pr1 in Fig. 1 has a small moment // c-
axis compared to the other Pr sites. Also, a separate
incommensurate diffraction peak was found at low tem-
V. ACKNOWLEDGMENTS
perature, which we assume is due to antiferromagnetic
order mainly on this crystallographic site.
Concluding, the above presented results on Pr Ni Si We are indebted to S. L. Bud’ko, Y. Mozharivskyj,
6 2 3
indicate that its ordered state manifests both ferromag- and J. Frederick for valuable discussions and for help
neticandantiferromagneticcomponents. Theresultsare with the experiments. Work at the Ames Laboratory
not only consistent with results obtained on other mem- was supported by the Department of Energy, Basic En-
bers of the structure series of which it forms part, but ergySciencesunderContractNo. DE-AC02-07CH11358.
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