LOW TEMPERATURE PHASE TRANSITIONS AND MAGNETIC STRUCTURES OF PrB6.

Article abstract of DOI:10.1016/0038-1098(80)90129-5

Specific heat, thermal expansion and electrical resistivity measurements on PrB//6 single crystals show that there are two temperature phase transitions at 6. 9 and 4. 2 K, respectively, the latter temperature varying somewhat among different crystals. Neutron diffraction measurements were made on both single and polycrystalline samples of PrB//6. The neutron data indicate a spontaneous incommensurate magnetic ordering at 6. 9 K with Q equals (0. 23, 0. 23, 0. 5) 2 pi /a//o. At 4. 2 K a commensurate magnetic phase is seen with Q equals (0. 25, 0. 25, 0. 5) 2 pi /a//o coexisting with the incommensurate phase. At 1. 74 K, only the commensurate phase remains. A model is proposed for the commensurate antiferromagnetic structure and a profile analysis based on that model yields a magnetic moment of 1. 77 Bohr magnetrons per praseodymium ion at 1. 74 K.

Full text of DOI:10.1016/0038-1098(80)90129-5

Solid State ColxLlunications, Vol.36, pp.861—868.
Pergamon Press Ltd. 1980. Printed in Great Britain.
LOW TEM PER A TU R E PHASE TRANSITIONS AND
M AGNETIC STRU CTU RE OF PrB 6
C. M. M cC arthy, C. W. Tom pson, R. J. G raves, H . W . W hite
P hysics D epartm ent, U n iversity of M isso uri,
C olum bia, M issouri 65211
S
Z. Fisk
Institute for P ure and A pplied Physical S ciences
U niversity of C alifornia, San D iego, L a Jolla, C alifornia 92093
H . R. O tt
Laboratorium fur Festk~rperphysik
Eidgen~ssischeTechniache Hochechule, ZUrich, Switzerland
(Received 8 August 1980 by H. Suhi)
Specific heat, thermal expansion and electrical resistivity m e a s u re -
m ents on PrB 6 single cry stals show that th ere a re two low te m p e ra -
ture phase tran sitio n s a t 6. 9 K and 4. 2 K, resp ectiv ely ,
tem perature varying som ew hat am ong d ifferen t cry stals.
the la tte r
N eutron
diffraction m easu rem en ts w ere m ade on both single and p o ly c ry sta l-
line sam ples of P rB 6 . The neutron data indicate a spontaneous in -
com m ensurate m agnetic ordering a t 6. 9 K w ith
0. 5) 21T/a0. At 4. 2 K a com m ensurate m agnetic phase is seen w ith
(0. 25, 0. 25, 0. 5) ZTT/a0 coexisting w ith the incom m ensurate phase
At 1.74 1<, only the com m ensurate phase rem ain s. A m odel is p ro -
posed for the com m ensurate an tiferro m ag n etic stru c tu re and a p ro -
0
= (0. 23, 0. 23,
0
file an aly sis based on that m odel yields a m agnetic m om ent of
1.77 B ohr m agnetons per praseodym ium ion at 1.74 K .
I. Introduction
data points is not sufficiently fine to distinguish
any stru c tu re in the data.
At the present tim e the m agnetic p ro p erties
of the rare e a rth hexaborides a re not com plete-
M easurem ents of the low tem peratu re
th erm al expansion of single cry stal PrB 6 w hich
a re repo rted below gave the firs t clear in d ic a -
ly determ ined o r understood.
T hese m aterials
have a cubic cry stal stru c tu re that can be de-
scribed as C eC I type w ith a rare e a rth ion a t
each cube co rn er and a boron octahedron at the
tion of two low tem p eratu re
4 K ~nd 7 K, resp ectiv ely .
cal resistiv ity and specific heat m easu rem en ts
confirm ed th is. The neutron scattering in cas-
phase tran sitio n s a t
Subsequent e le c tri-
body cen ter.
X -ray m easurem ents1 have show n
th e lattice p aram eter of PrB 6 to be 4. 133 A at
room tem p eratu re.
urem ents rep o rted h ere w ere undertaken to
exam ine these m agnetic phases of Pr136 and to
d eterm in e the specific ordering of the Pr3+
P reviously only one m agnetic tran sitio n has
been rep o rted for P rB 6. B ased on re sistiv ity
m om ents.
and susceptibility m easu rem en ts,
al.2 rep o rted antiferrom ag netic
7 K. H acker e t al.3 rep o rted C u rie-W eiss b e -
havior above 100 K w ith a m om ent of 3. 64 ~ B
M atthias et
ordering below
II. E x perim en tal P rocedure
A . Specific H eat
and
0 = -41 K . and a N ~ e1 tem p eratu re of
8 .3 K. Lee et al.1 rep o rted a very sh arp anom -
aly in the specific heat corresponding to a tran -
sitio n at 6. 9 K. A close exam ination of th is
data below 5 K rev eals possibly significant dev-
iations betw een the ex p erim en tal points and a
sm oothly fitted curv e, although the m esh of
T he sam ple m aterial used for specific heat
m easu rem en ts consisted of an assem b ly of 23
sm all cry stallites w ith a total m ass of 190 m il-
lig ram s. T hese cry stals w ere grow n using
mnolten alum inum flux m ethod.
a
M easurem ents w ere m ade in a He4 c ry o -
5 R esearch supported by the N ational Science Foundation under G rant N o. D M R 77-08469.
861

862
MAGNETIC STRUCTURE OF PrB6
Vol. 36, No. 10
stat using a differential heating technique with
a calibrated germanium thermometer in a man-
ncr similar to that discussed earlier.4 No cx-
change gas w as used. T he precision of the
the wavevectors associated with these intensities~
These measurements were made on a triple axis
instrument. 3XE, at MURR w hich w as operated
in the constant energy elastic made, AE = 0.
M onochrom ator and analyzer cry stals w ere
both Cu(200) and yielded a beam of 1.066
neutrons on the sam ple w ith a flux of 6 x iAo6
n e u tro n s/c m 2 /se c .
m easu rem en ts,
based on run to run rep eata-
bility for pure copp er, is estim ated to be 0. 5%.
Due to the sm all size of the sam ple the accu-
racy of the m easu rem en ts repo rted h e re is e sti-
m tted to be n ear ± 2%.
Ill. R esults
B. E lectrical R esistivity and T herm al
E xpansion
A . Specific H eat
The e le c tric a l resistiv ity w as m easu red by
conventional 4-probe m ethod at 220 H z. E lec-
F ig u re 1 shows the m easured specific heat
of P r3 6 as a function of tem peratu re in the
range 1.7 K to 15 K. The prom inent features
a re the la rg e peak at 6.89 ± 0 .0 5 K for w hich
a
tric a l contact to the single cry stal w as m ade via
spot-w elded 0.002
of the low er anom aly in the resistiv ity v aried
from cry stal to cry stal. We believe th is v aria-
Pt w ire.
The tem p eratu re
the peak value of
C w as 81.6 Jo ule/m o le-K and
a m uch sm aller, but n ev erth eless d istin ct, peak
at 4 .2 2 ± 0 .0 5 K. The larg er peak can be id e n ti-
fied w ith the N ~ e l tem peratu re and w as rep orted
tion is due to ex trem e stra in sensitiv ity of the
low er transition, and this sensitiv ity req u ires
that care be taken to attach the leads using as
sm all a disch arge as possible.
T he the rm al expansion m easu rem en ts w ere
done using a capacitance d ilato m eter d escrib ed
e a rlie r by L ee.
I
H ow ever, th is peak is found
to be m uch higher and sh arp er in the present
w ork (peak height 81.6 Jfm ole-K com pared to
30 J/m o le-K ).
The peak at 4.22 K appears to
elsew h ere.
5
be c o rre la te d with the anom alies seen in the
the rn ial expansion and the electrical resistiv ity .
An attem pt was m ade to estim ate the e n -
C. N eutron S cattering M easurem ents
tro py change for the tran sitio n a t 6. 9 K. A plot
of C /T vs T w as extrapolated to give zero m a g -
netic contribution at 20 K and the sm all peak a t
N eutron scattering m easu rem en ts w ere
m ade on a larg e polycrystalline sam ple and on
a sm all single cry stal having a m ass of IS m g.
The polycrystallinc m aterial was p rep ared by
4. 2 K w as elim inated.
G raphical integration of
R ln(3. 4 ± 0.2).
the data then gave the re su lt ~S
the reduction of P r203 by B4C at about 1770
under high vacuum . In all cases, both w ith
K
A dditional u n certain ties in th is resu lt rem ain
because of unknow n o r poorly d eterm ined c o r-
rectio n s for lattice vibrations, electro n ic effects
poL ycrystalline and single cry stal sam p les, the
boron used in the prep arations w as highly en-
riched in the isotope I 111 (98. 5%) in o rd er to
m inim ize the effect of absorption of the rm al
neutrons by the isotope 10i~ .
and Schottky anom alies.
The value found here
for ~S is, how ever, totally consistent with the
expected value for a r5 triplet ground state.
Pow der sam p les w ere encapsulatec in a thin
w all alum inum sam ple holder suitably m ounted
B. E lectrical R esistivity and T herm al
E xpansion
in a helium cry o stat.
(O ur ex p erim en tal c o n d i-
tions requ ired that m easu rem en ts above 4. 2 K
and m easu rem en ts below 4. 2 K be perform ed in
T he electrical resistiv ity at low tem p era-
ture of a PrB 6 single cry stal is show n in Fig
-
d ifferen t cry o stats.
)
D iffraction data w as oh-
ore 2. A part from the sharp anom aly a t a p p ro x -
im ately 6. 95 K, th ere is a clear, sharp d ro p in
the resistiv ity a t approxim ately 4. 15 K. D uring
the m easu rem en t for w hich the data is show n,
the cooling of the sam ple w as stopped at 4.02 K,
and the sam ple w as allow ed to w arm to 4. 35 K,
before continuing cooling below 4 K. T here is
clear h y ste re sis present, w hich can be seen in
tam ed on ZXD, a double axis instrum ent at
M URR (M issouri U niversity R esearch R eactor),
using neutrons of w avelength 1. 293 A w ith
flux on sam ple of 2 x 106 n cu tro n s/cm 2 /sec.
D uring the accum ulation of data the sam ple w as
rotated in o rd e r to m inim ize the effects of pro-
ferred orientation,
a
G uided by the resu lts of the pow der data,
diffraction scans w ere perform ed on a sm all
single cry stal in o rd er to determ ine uniquely
the w ave vectors associated w ith the m agnetic
the figure.
Above 4. 30 K, the w arm ing and
cooling data coincide w ithin experim ental a c c u -
racy .
T he th erm al expansion data shown in F ig-
ure 3 v ery clearly shows two anom alies, peak-
ing at 6. 95 K and 3. 95 K, resp ectiv ely .
in ten sities.
The effects of sam ple absorp tio n .
extinction and problem s we encountered in o n -
enting the crystal in a sub 4. 2 K environm ent,
m ade it d ifficu lt to obtain m eaningful relative
intensity data for the single cry stal; how ever, it
w as possible to m ake p recise m easu rem en ts of
C. N eutron D iffraction
N eutron scattering m easu rem en ts m ade in

Vol. 36, No. 10
MAGNETIC STRUCTURE OF PrB6
863
8 1.6 at
25—
20—
6.89K
~
-4
0
I::
U
4.22K
• 1 ~‘• ~
A
.. •
5
—
- . . . -
.. /
-I.
0
~
I
I
I
I
I
14
0
2
4
6
8
10
12
TEMPERATURE ( K)
F ig u re 1. R epresentativ e data points for the
specific heat C in units of J/rnoL e-K v ersu s
the tem p eratu re
T
in units of degrees
K
for Pr13
6
the (110) plane in the recip ro cal lattice of the
single cry stal of PrB 6 gave intensities arisin g
from the m agnetic ordering a t positions of the
phases.
The tem p eratu re dependence of the in-
ten sity of th is peak in the incom m ensurate phase
is show n in F ig u re 5. T his data w as obtained by
m onitoring the intensity as the cry stal w as
w arm ed from 4. 2 K and then the cry stal w as r e -
m ounted in a d ifferen t cry o stat and the p ro cess
repeated on cooling from 4. 2 K. B ecause d if -
feren t cry o stats w ere used a slight re n o rin a liz a -
lion of the data w as req u ired in o rd er that the
i~ tte n sitie s a t 4. 2 K should coincide.
type (h ± F), k ± 5
Scans through these m agnetic reflectio n s w ere
m ade in the trip le axis m ode, A E 0, and in
,
1 ± 0 .5 ) w here F) ~ 0. 25.
both (1101 and [0011 d irectio n s. These scans
w ere m ade a t sev eral low tem p eratu res and
F ig u re 4 shows the re su lts.
T he low er curv e,
a [1101 directio n scan a t 1.74 K, shows neutron
intensity clearly peaked a t the point (1 /4, 1/4,
It should be noted that scans m ade in the
1/2), indicating
a
com m ensurate antiferrorn ag-
[0011 d irectio n indicated that m agnetic inten sities
o c c u rre d only for (i ± 0 .5 ) for the third index.
T hus, in th is (third) d irectio n , the spin ordering
remained commensurate with the lattice at all
temperatures and corresponds to a reversing of
nctic ordering w ith the m agnetic cell larg er
than the chem ical celL by facto rs of four in each
of two directions and by a factor of two in the
third direction. The upper curve in Figure 4,
taken at 6. 15 K, shows the neutron intensity
peaked at the position (0. 23, 0. 23, 0. 5) indicating
the antiferromagnetic ordering is either incom-
mensurate or of a very long period. The middle
curve, at an intermediate temperature 4.21 K,
hows the simultaneous coexistence of both
adjacent spins, which was exactly the case with
the spin arrangement of NdB6. 6
Figure 6 shows the results of a powder dif-
fraction scan at 78 K and the difference between
that data and powder data obtained at 1.74 K.
Data points were obtained for fixed monitor

864
MACNETIC STRUCTURE OF PrB6
Vol. 36, No. 10
1 ~ ~
I
I
I
I
I
3.0
-
PrB6
-
c ~ 2.0
-
I.0 ~
4.:
-
I
I
I
I
I
I
I
I
0.0
I
2
3
4
5
6
7
8
i [K]
Figure 2. Low temperature electrical resistiv-
ity of single crystal PrD6. Absolute value
obtained from comparison of data with that
of ref. 8.
counts (approxim ately 2. 5 mm per point) in equal
angular increments, ~.2O= 0. l~. The nuclear
cell parameters were obtained from the 78 K
data and the results of a least squares fit7 to the
data a re show n in the figure by the solid line,
T his fit gave a lattice parameter of 4. 120 ±
S tatistical accuracy for the magnetic data is
therefore rather poor, particularly so for peaks
like (3/4, 1/4, 3/2) which lie in the wings of a
nearby nuclear peak. The solid line presented
with the magnetic data is the calculated line pro-
file refined on the basis of an antiferrom ag n etic
m odel as rep resen ted by F ig u re 7. In th is r e -
finem ent the nuclear p aram eters w ere held a t
the values obtained from the 78 K fit and only
m agnetic p aram eters w ere allow ed to vary. F ig -
0. 001 A and the boron positional p aram eter
u
0. 301 ± 0. 001. (B oron atom s a re located a t
(1/2 ± u, 1/2, 1/2), (1 /2, 1/2 ± u, 1/2) and (1 /2,
1/2. 1/2 ± u).) B facto rs obtained for th is fit w ere
RTO TA L and RNUC
5. 02.
The low er portion of F ig u re 6 is due only to
the m agnetic scattering from the com m ensurate
=
1.39 and R PR O FIL E
=
ure 7 shows only the P r ions in a (100) plane.
T he individual m om ents in a 2 x 2 square array
of ions a re oriented p arallel to each other and
in (110) d irectio n s. A djacent (2 x 2) a rra y s a re
phase since it is a d irect su btractio n of the 78
data from the 1.74 K data. A ll of the data points
in the background regions a re not plotted in the
figure; rather a single point representative of a
1O-point average is shown. The magnetic intensi-
K
oriented an tip arallel to the firs t as show n. The
next lay er of Pr ions is arran g ed w ith m om ents
an tip arallel to those in the la y e r show n. T h ere-
fore the resulting m agnetic cell (tetragonal)
contains 32 Pr ions. In the data of Figure 6 all
ties are quite sm all com pared to the nuclear in-
tensitics-note that the scale of the magnetic inten-
sities is expanded by a fact’or of 8 in the figure.
peaks a re indexed on the basis of the cubic
chem ical cell rath er than th is expanded m agnetic
cell. M any o th er m odels w ere co n sid ered , but

Vol. 36, No. 10
MAGNETIC STRUCTURE OF Pr86
865
I
I
I
I
I
I
I
I
I
I
6
105a
[K~’J
PrB6
thermal expansion
.
5 .
4 .
3
.
2
I
I
I
I
I
I
2
4
6
8
10
12
14
i [i]
F ig u re 3. Low tem p eratu re lin ear th erm al e x -
pansion coefficient of single cry stal P rB 6.
only the m odel show n in F ig u re 7 gave reaso n -
able in ten sities w ithout in co rrect vanishings.
A ccording to the strong th erm al expansion
anom aly and the tem p eratu re dependence of the
In the fitting procedure each of the 32 Pr
positions was treated as a unique position. No
equivalent position rotation or translation ma-
tric e s and no magnetic rotation matrices were
used for this calculation. The results of the fit-
electrical resistivity it is quite possible that the
lower transition is a quadrupole induced struc-
tu ral ordering.
T he m agnetic ordering a t 6. 9 K
splits the I”~triplet ground state into three
singlets. The non-vanishing quadrupolar matrix
ting process gave a m agnetic m om ent of 1.77
±
i
2
2
elem ent ‘. ~O
i betw een the ground state s in g -
° ‘ 0 5 ~ B per ion a t 1.74 K w ith facto rs of
R
RTO TA L R M J~G 34. 2. T his relatively la rg e
=
let and ano ther of these singlets and the p re v i-
ously found strong asp h erical C oulom b charge
scatterin g of the conduction electro n s8 m ay lead
to a q uadru p olar ordering.
ting of the two singlet states involved accounts
fo r the sm all anom aly in the specific heat.
q uadru p olar ordering of th is type should lead to
R facto r for the m agnetic scattering is due to
the low intensity of the m agnetic scatterin g com -
pared to the nuclear scattering and the la rg e cx-
perim ental uncertainty that th erefo re resid es in
the data7 (note the e rro r b ars in F ig u re 6).
The m agnetic m om ent of 1.77 ~B is consid-
erab ly less than the satu ratio n m om ent expected
~ The fu rth er s p lit-
A
a rhom bohedral d isto rtio n of the cubic lattice,
feature w hich could not be estab lished in our e x -
p erim en ts, but the sym m etry of the low tem p er-
a
for the free ion, gJ ~ B
=
~ 20 ~ B’ M uch of
th is difference can be ascrib ed to the quenching
of the o rb ital contribution to th e m om ent by the
cry stallin e electric field. T he ground state of
P r in PrB 6 is a w ell separated t ’ ~trip let, as
a tu re m agnetic phase gives som e support for
th is in terp retatio n .
F u rth e rm o re we should
like to m ention, that stru ctu ral ordering is often
only seen in single cry stallin e sam p les of a
m a te ria l’0 and the lack of observation of th is
show n in re f. 8, and for
a pure t ~ trip let the
m axim um o rd ered m om ent is 2. 0 t~ B ’

866
MAGNETIC STRUCTURE OF PrB6
Vol. 36, No. 10
-
~E=0 SCANS ALONG (ES, .5)
400
~ 200-
6.15
K
0
-
~
I
.30
-
.2~0
.25
6 ~
-
a.
~400-
z
200-
4.21K
U
j
, ~
o
-
I
‘S —
—
‘~.“l .% .
.25
I
.20
.30
I -
~400-
200-
0
1.74K
.— ..— — — — q ’— -.
~
I
I
.20
.25
.30
REDUCED WAVEVECTOR
~
F ig u re 4. C onstant
E
scans w ith A E
=
0 along
the [1101 direction. The upper curve
(6. 15 K) shows the incom m ensurate phase
w hile the low er curve (1.74 K) show s the
com m ensu rate phase.
The m iddle curve
(4. 21 K) show s the coexistence of th e two
phases.
2
0
,1_—.—f—”
I
4
I
6
0
1
2
3
5
7
TEMPERATURE
(K)
F ig u re 5. T em p eratu re dependence of the in -
tensity of the PrB 6 (0. 23, 0. 23,0, 5) in c o m -
m en su rate m agnetic reflectio n .
The m a n -
ner in w hich m easu rem en ts w ere m ade is
d escrib ed in the text.

Vol. 36, No. 10
MAGNETIC STRUCTURE OF PrB6
867
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868
MAGNETIC STRUCTURE OF Pr36
Vol. 36, No. 10
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
I ,
F ig u re 7. Low tem p eratu re com m ensurate m a g -
netic stru c tu re proposed for P rB 6. Only
the P r ions in a (100) plane a re show n. The
next lay er of Pr ions, w hich rep resen ts the
other half of the magnetic unit cell, is
arranged with moments antiparallel to those
in the lay er show n.
low er tran sitio n in e a rlie r w ork m ay be ascrib ed
to th is fact. T he quadrupolar ordering and the
locking of the com m ensurate m agnetic stru c tu re
A cknow ledgm ents-T he
neutron scattering studies
w ere m ade possible by the support of the U n i-
v e rsity of M isso uri R esearch R eacto r. T he
is probably a first o rd er transition.
S train ef-
support of the A lum ni D evelopm ent B oard and
of the R esearch Council of the University of
M issouri is also gratefully acknow ledged.
fects between th e upper and low er tran sitio n
temperature account for the rather broad anom -
aly in the thermal expansion coefficient.
R E F E R E N C E S
1.
L E E , K. N ., BACHM.AN, R ., G EB A LLE, T . H ., and M A lTA , J. P., Physical Review
B2, 4580 (1970).
2.
M ATTHIAS, B. T ,, G EB A LLE, T . H ., ANDRES, K ,, CORENZW IT, E ., H U LL, G. W .,
and MALTA. J. P., Science 159, 2 (1968).
3.
H A C K ER , H ., SHIMADA. Y ., and CHUNG, K. S ., Physica Status Solidi, Section A 4,
459 (1971).
4.
5.
6.
WHITE, H. W., Journal of Chemical Physics 61, 4907 (1974).
O TT, H . R, and LUTHI, B .. Z eitsch rift fu er P hysik B28, 141 (1977).
M cCA RTH Y , C. M. and T O M P S O N , C . W .
,
Journal of Physics and Chemistry of Solids
(to be published) (1980).
7.
8.
9.
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