Single-crystal magnetism of sodium magnesium chromium(III) oxalate, NaMgCr(C2O4)3·9H2O

CltChllCAL

Volume 88, number 5

PttYSICS LClTlIRS

SINGLE-CRYSTAL MAGNETISM OF SODIUM MAGNESIUM CHROMIUM(H1) OXALATE, NaMgCr(C204)3B9H20 S. LAHIRY and R. KAKKAR Wpclrrmenr of Chemrsny, Unnersity of Delhr, Delhr-I 10007, Indu Recewed 5 hlarch 1982

hfagnctic amsotropres of a tr~gonal crystal of NahlgCr(C204)3-9H20 measured between 300 and 77 I: arc appro~lmatcly IO the square of the absolute temperature; moreover KII > K, although gl > g,, from EPR measuremcnts The signof D, the zero-field sphttmg. wtuch was not dctcrmmcd from EPR, rs shown to be ncgatrve.

inverselyproportional

ments down to 4 K would be desirable. The signand magmtude of D have also been determmcd.

1. Introduction Sodium

magnesium

aluminium

oxalate,

in whichthe trivalentA13+ NaMgAI(C,O,),-9Hg0, is replaced by Cr +, V3+, TIC+, Mn3’, Fc3+ and Co3+ [I] , rs a good host materral, firstly because the ion

crystal

system (space group)

is umaxral

[2,3]

2. Experimental

and sec-

ondly because the molecular symmetry

in such a trischelate 1s also uniaxial so that the spectral bands could be assigned uniquely. EPR and spectral studres of a

: Al2O3, : MgO; K3Cr( oxalate)3*3Hz0 and Cr(acetylacetonate) [4] have been reported. Spectral and EPR work on single crystals of Cr3+ : NaMgAI(C20J3*9H20 by a number of workers [ 1J-81 revealed the presence of ;I trtgonal crystal field, a fairly large zero-field sphtnumber of Cr3+ compounds such as Cr3+

Cr3+

the

Frossard [2], who first prepared Ihe crystal, reported composition as octahydrate, Nahl@I(C2O~)3*8H20,

but It was assigned the nonahydrrte

compontion,

NaMgAI(C,04)3-9H20, by Plpcr and Carhn [I J and this was accepted by later workers. Crystals of NaMgAI(C204)3-9H20 and NaMgCr(C20&-9H20 prepared followmg Piper and Carlm [I ] grow either as large hexagonal plates wrth the c axis perpendicular to the ban1 plane or as large prisms with perfect cleavage in the basal plant. The

axeswerelocated by taking tong (D),and the possibleexistenceof a weakferromag- crystallographic netic type of exchange interaction [6]. The sign of D was not determined. Moreover, the exact space group and the number of formula units per unit cell have not

been established [2,3] since a detailed X-ray structure determination of the compound has not been performed. A second form of the crystal reported by a number of authors was considered to be monoclinic [6] or rhombohedral [9] but no structural report aXlsts.

We report the results of magnetic anisotropy measurements in a single crystal and the average susceptibility of NaMgCr(C,O,),-9H,O between 300 and 77 K where the latter reveals the existence of a ferromagnetic type of exchange interaction, although measure-

singlccrystal X-ray rotation patterns and the cell dunensions calculated agreed with Frosnrd’s [3_]. Rotation patterns of hexagonal and prismatic-shaped crystals are supcrrmposable. Hexagonally shapedcrystalswere said to belong to the space group PTCI or P3CI [3,4] wherc;ls

the other form was assigned the rhombohedral space group tic or R3c [S] Certain structural charactcnstrcs assigned to the

hexagonaldiscformof the compoundby different authors are: space group PzIC(D&),z c = 12.47 _4 by Frossard p3CI(C$),z

= 2;a = 9.78,

[I?], and P3CI(Djd)

or

=6;a = b = 16.90, c = 12.52 A by Watson

[3]. The value of the cell dimension,a

= 16.90 A, re-

. 0 009-2614/82/0000-0000/S

02.75 0

I982 North-Holland

499

Volume 88. number 5

ClIllhlICAL

PIIYSICS

ported by Watson is 3*/? tunes the value (I = 9.78 A of

Frossard. probably the morphologcaliychosena axis by Watson is at an angle of 30” to the true n axis [IO]. However, for all the space groups wed above, all the molecular three-fold axes in the unit cell are parallel to the crystallographic c axis [5,7,9].Therefore,the principdmolecular suscepttbthty tensors Ei,, and R,

LCITCRS

21 hlay 1981

in anisotropy between a ground and an unground crystal is ~1.2 X 10m6emu at 292 K. Therefore, the contribution of shape anisotropy to the total x,, - x1 is very small. Moreover, the ture as above, and the difference

diamqnetic crystal

anisotropy

of the corresponding

A13+

is4 JO X 10m6emu.

are equivalent to the pnnclpal crystalline susceptibdlty tensors x,, and x1 respectively, where IIand 1 denote directlons parallel and perpendlculnr to the c axis (or the three-fold axis). Methods for measurmg the crystalline amsotropy (Ax) and the average susceptibility ji and the relations for calculating Ax, X and per are given by Lahiry et al. [I l] . Care was taken to use a fine quartz fibre for mea-

But, in a plane perpendicular to the c axis, the anisotropy of a prismatic rod-shaped crystal, either ground to a cube or unground, increases from a negligble value of 0.9 X IO-6 emu at 300 K to 3.95 X 10-e emu at 80 K. The anisotropy of a hexagonal disc-shaped crystal does not, however, increase between 300 and 80 K. It seems therefore, that the crystal symmetry (space group) of a prismatic crystal at low temperature does not remain trigonal. Moreover, our observation raises the question

suring the amsotropy.

whether the prismatic variety is really rhombohedral

In a plane contaimng the c axis, either a hexagonalor a disc-shaped crystal sets 3s 3-92 K with IIS c 3x1s parallel to the magnetic field. The anisotropy per mole xl, - xL or K,, -A’, of a hexagonal disc-shaped crystal increases from 16.0 X 10m6emu at 300 K to 354 X IO6 emu at 80 K (table I). A prismatic rod-shaped crystal, either ground to a cube or unground, exhibits similar behaviour in anisotropy values with decreasing tempera-

[8] or monoclinic [6].

Table I Euperime?M

values of the susceptibihty ano amsotropy at tifcrcnt tcmpcraturcs a)

TOi)

IO6Ix11 - xl1 IO6XM(cord

@mu)

(emu)

--

300

16.0

6324

280

19.3

6119

260

23.5

7305

240

29.0

7918

220

36.0

8658

200

45.3

9533

180

56.0

10610

160 140

120 100 80

76.0 1040

11976 13774

148.0 220.0

16129 19489

354

24618

XII.71 are the suscepbbhtics along and pcrpendrcuLuto the c-auls; jihtkorr) is the molx susceptibhty including a dia-

magneticcorrectlon01203 X lo6 emu. so0

3. Results and discussion The average molar suscepttbllity of the compound (table 1) obeys the Curie-Weiss law between 300 and 77 K with positive 0 ~4 K and the molar Curie constant C,, = 1.87. The magnetic moment calculated from experunental susceptibility values, 3.97 FB at 77 K ISalso larger than 3.89 I_(Bat 300 K. The magnetic moment calculated taking into account B = 4 K 1s3.87 PB in agreement with the spin-only value for the 4A2 ground

term. Therefore, a weak ferromagnetic-type exchange interaction appears to exist m the compound although susceptibility measurements down to 4 K would be desirable. Mortensen [S] attributed the fme structure in the 4A2-2E transition (=2 cm-l) m the diluted alt at 4.5 K to a ferromagnetic-type exchange interaction. The anisotropy in this Cr3+ salt arises from the interaction of the orbitally non-magnetic ground term 4A2 with the excited 4A2 and 48 terms (arising from a spht 4T2 term in the trigonal crystal field) through spin-orblt

interaction

and since

the spin-orbit

couplingconstantof Cr3+(A= 91 cm-l) is alsosmall. the anisotropy is expected to be small in agreement with experimental values (table I). The variation of anisotropy Ax = x,, - xL with decreasing temperature is also interesting since Ax is approximately inversely proportional to the square of the absolute temperature, T2, i.e. AxT2 versusT2 is approximately a straight line,

Volume 88. number 5

CIIChfICAL PIIYSICS LlXTCRS

TZx Id3

80 I

90 I

100 I

70 I

21 hldy 1982

60

50

I

I

40 I

30 I

20 I

IO I

26 24 -

642I I00

I 80

0 60

I I20

I 140

I lb0

I 180

I 220

I 200

I 240

I 260

I 280

I 300

Temperature m K Fig.

1. AXTVCISUS

Tyld

AxT*

versus T*

curves oTsod~um

mngncswm

chromrum(lll)

owhtc.

whtle a curve of &Tversus T is a hyperbola (ftg. 1). Moreover, It ISevident from the theoretical expresslon for the molecular amsotropy AK given in ref. [ 121 (where the effect of the exchange interactron was not taken into account),

et are the anisotropic reduction factors for orbital an-

AK = K,, - Kl = Np* [-2(o IIe?II -TO

1.982 [7,8] are close to one another and secondly q,, q do not dtffer much in this case, which can be shown by using energy-level separatrons from spectra [1,5,61. The anisotropy AK should, therefore, be approximately inversely proporttonal to T* which is found also from

+ (5/4W@I:

-g:)

- (W*T*)(g;:

+g,2),

(1)

with R,, = Nfl’(-2ol,,~f) + 5$4kT

- $D/k’T”,

(2)

KL = Nb2(-20&

+
(3)

r=f(Kll

+ 5$4kT

+2K,)

(4)

(where alI, a, are the coefficients of the anisotropic

l&andfielddefied by Schlapp and Penney [ 131; el,,

gular momentum), that the major contribution to AK comes from the third term while the first two terms in the expression (1) contrrbute very little, firstly because the experimental valuesg,, = I .977 and g, = I .979 and

the AxT*

versus Tz curve (fig.

I).

Secondly,the signof D wasnot dctctminedfrom

EPR studies [7,9]. The magnitude and sign of D was in thrs case determined from 3 plot of AK versus1/T2 and using experimental values ofgIl and g1 (lot. tit) yielding D = -0.55 cm-t. Moreover, II follows from expression (I) that a positive value of D coupled with experunental valuesofg,, and gl makes A’l > K,, while 501

Volume 88, number 5

CHEhllCALPHYSlCS

measurements yield uniquely E;,, > K1. A negative value of D along with experimentalgll,gL values, however, yields R,, > K, [cf. expression (I)] _ In this case,gl >g,, from EPRmeasurementswhde

LITTERS

Zl hlay 1982

alusotropy

K,, >K,

fromanisotropymeasurements;this is possible

since D is large

and the anisotropy

arises essentially

from the third term of expression (1). WC require 3 = -0.64 CITI’~and g,, = 1.978,g,

T.S. L.

Piper

and

R.L.

Orlin.

Frossard and Schwcu,

J. ChCm.

Mined

Phys.

35 (1961)

1809.

Pelrog. Mitt. 36 (1956)

1. [3] Watson, quoted in 0 S hlortenscn,

J. Chem. Phys. 47

(1967) 4215. [4] A. Abragam and B. Bkaney, Electron prnmagnetrc reso=

I .981 m order to fit the experimental values of anisotropies and susceptlblhties between 300 and 77 K with the theoretlcal expressions (l)-(4). it is to be noted that the susceptibihticsr here refer to the values obtained after correction for a positive B = 4 K. We have shown that the magnetic anisotropy is ap proxnnately inversely proportional to the square of the absolute temperature in the temperature range 30077 K. The sign of D has been uniquely determined to be negative. The inverse susceptibility versus temperature curve reveals the possible existence of a weak ferromagnetic type of exchange interaction with B = 4 K, although measurements down to 4 K would be desirable.

502

[l] [2]

nance of transition ions (OuTord Umv Press.. London, 1970). [S] 0 S Mortensen, J. Chem. Phys. 47 (1967) 4215. [6] R A. Condmte and L S. Forster, J. Mol. Spec(ry. 24 (1967)

496. [7] R.A. Bemheim and E F. Reichcnbacher, J. Chem. Phys. 51 (1969) 996. [S] Y. Kawaski and L.S Forsler. J. Chcm. Phys. 50 (1969) 1010.

[9] Mclean.qualed in’ Y. I;awz&i and L.S. Forslw, J. Chcm Phys. 50 (1969) 1010. [lOI C.W. Bunn. Chemical crystallogaphy

(Oxford

UNV.

Press,

London, 1973). [1 l] S. Lahiry and R. Kakkar.Chcm. Phys. Letters 78 (1981) 379. [ 121S. hlitra. D. Phd. Thesis, Calculta Umverslty, quoted m. P R. Saha, Indun J. Phys. 42 (1968) 372. [ 131 R. Schhpp and WC. Penney, Phys. Rev. 42 (1932) 666.