Magnetic order in acmite; NaFeSi - Mount Holyoke College

PHYSICS CHIMISIRY [ MIHIRAIS

Phys Chem Minerals (1989) 16:672-677

© Springer-Verlag1989

Magnetic Order in Acmite; NaFeSiz06 O. Ballet 1., J.M.D. Coey 2, G. Fillion 3, A. Ghose*, A. Hewat 5, and J.R. Regnard 6 t Institut ffir Kristallographie und Mineralogie, Goethe-Universit~it, D-6000 Frankfurt, Federal Republic of Germany 2 Physics Department, Trinity College, Dublin 2, Ireland a Laboratoire Louis Nrel, CNRS, BP 166, F-38042 Grenoble, France 4 Department of Earth Sciences, University of Washington, Seattle, WA 98195, USA 5 Institute Laue-Langevin, BP 85, F-38041 Grenoble, France 6 DRF/LIH, CEN-G, BP 85, F-38041 Grenoble, France

Abstract. The magnetic properties of two samples of acmite, one natural and the other synthetic, were determined using magnetization and susceptibility measurements, Mfssbauer spectroscopy and neutron diffraction. Exchange interactions are quite strongly antiferromagnetic, the paramagnetic Curie temperature being - 4 6 K for a purely ferric synthetic sample, but its Nrel temperature is only 8 K. The principal magnetic mode has the periodicity of the crystallographic structure and is made of ferromagnetic chains, coupled antiferromagnetically. Moments are oriented in a direction close to the chain axis, c. The antiferromagnetic exchange between adjacent Fe 3+ ions in the same chain is overcome by their coupling to a common Fe 3 + neighbour in the next chain. This indicates that the whole (SiO~) group can act as a superexchange ligand in silicates.

1. Introduction

Acmite (aegirine) is a sodium ferric clinopyroxene with ideal formula (Na){Fe3+}[Si2]O6 . The structure (Clark et al. 969) has iron in single zig-zag chains of edge-sharing octahedral MI sites, and sodium in the eight-fold coordinated M2 sites. The direct F e - - F e distance within the chains is 3.19 A whereas the separation of chains is 6.55 A in the ab plane, although the shortest F e - - F e distance between chains is 6.18 ~_. The structure is illustrated in Figure 1 a, while the positions of M1 sites in the unit cell and their symmetry relationships are sketched in Figure I b and i c. At first sight the structure appears to be an approximation to a l-d antiferromagnetic Heisenberg model, which ideally would show no magnetic phase transition. Despite the rather unfavourable F e - - O - - F e bond angles (100.6 °) it might be expected that the intrachain interaction would dominate the interchain coupling which involves an entire intervening SiO4 group. The assumption that indirect exchange via two oxygens ( F e - - O - - S i - - O - - F e ) is an order of magnitude weaker than that occurring via one oxygen ( F e - - O - - F e ) leads to the neglect of all exchange bonds except those like J12, between atoms 1 and 2 in Figure 1 b. There are contributions to J12 from direct exchange between the edge-sharing sites and from two equivalent F e - O - - F e superexchange paths linking these sites. Both contributions are expected to be antiferromagnetic (Goodenough

/963). In sheet-silicates, the exchange parameter between Fe 3+ in edge-sharing octahedra was found to be N - 1 K (Coey 1988). The ordered magnetic structure of acmite might therefore be expected to be composed of antiferromagnetically ordered M/chains, a three-dimensional structure being stabilized by weak interchain coupling. We have examined the magnetic properties of both natural and synthetic acmite. Our conclusion, contrary to the above expectation, is that the M1 chains are essentially ferromagnetic, as a result of competing negative intrachain and interchain interactions with the latter being the stronger.

2. Samples The synthetic sample was prepared at the US Bureau of Mines• It has been described by Ko et al. (1980), who found a 2-anomaly in the specific heat at 7 K, with integrated entropy up to 15 K of 11.3 J/mole K (76% of R in 6, the spin disorder entropy for an ion with S = 5/2). We carried out a refinement of the structure based on a Rietveld fit of powder neutron diffraction data taken at 14 K on the D1A spectrometer at the Institut Lau~ Langevin, Grenoble (Fig. 2). The wavelength was 1.96 A and 20 .... was 160 °. Parameters, including the fractional site occupancies for the three sites (assuming that no cations other than Fe 3 +, Na + and Si 4 + a r e present), are listed in Table 1. The R factor was 15.6 percent, because of the presence of some hematite as a second phase, which coloured the sample red. (The hematite peaks are not fitted by the solid line in Fig. 2.) The amount of hematite was estimated as 6 weight percent from a least squares fit to the Mrssbauer spectra taken at room temperature• No Fe 2 + was detected. Mrssbauer spectra were taken in 256 channels using a constant acceleration spectrometer with a source of 57Co in Rh. Baseline counts are typically 1 0 6 , and fit parameters together with the values of Z 2, the goodness of fit parameter, are listed in Table 2. The natural sample was from St. Hilaire, Quebec• Chemical analysis, together with the Fe 2 +:Fe a + ratio deduced from the room-temperature Mrssbauer spectrum, leads to the formula ",

(Nao.soCao.o~Mno.ol/{Fe • [Sil.99Alo.01]O

* 1948-1988

3+

"

o.7,T1o.o3Alo.t2Fe

6

The natural sample was pale green.

2+

o.o7} (1)

673

3. Results

t

0

9

Susceptibility o f the samples was measured using a 5T S Q U I D magnetometer. D a t a are shown in Figure 3. F r o m X- t : T p l o t s , one finds a Curie-Weiss law X = C / ( T - 0) with C = 4 . 4 , 0 = - 4 6 K and C = 3 . 8 , 0 = - 2 2 K for synthetic and natural samples, respectively. The m o l a r Curie constant for F e 3+ is C = 4 . 3 8 . (The susceptibility o f the synthetic sample was corrected for the presence o f the hematite.) Magnetization curves were measured at several temperatures in fields o f up to 19 T at the SNCI. They are practically straight lines, typical o f an antiferromagnet (Fig. 4).

Na site fM2)

AS/site

Table 1. Cell parameters, atomic positions and site occupancies a

for acmite at 14 K

sin#

Space group C2/e, Z = 4 a=9.68 (1); b= 8.83 (1);

O

O|174

eeO

O|174

OeeO

0

/X'x C/ ZK; V 00|

a)

O|

W/x

c= 5.30 (1);

t = 107.3 (2)

Atom

Wychoff x symbol

y

z

Fe (M1) Na (M2) Si 01 02

4e 4e

0 0

8f 8f 8f 8f

0.2890 0.1141 0.3592 0.3540

0.8991 (4) 0.2971 (9) 0.0918 (8) 0.0791 (4) 0.2559 (4) 0.0072 (4)

1/4 1/4 0.2377 0.1387 0.3010 0.0113

03

(5) (4) (4) (5)

Occupancy 0.496 (4) 0.489 (9) (9) 0.98 (1) (7) (7) (7)

VT/?

9

,,p

Table 2. Mrssbauer parameters for synthetic acmite

II

C

~

b

e2

T (K)

6 (mm/s)

e (mm/s)

Bhf (T)

Z2

296

0.41 (1) 0.52 (3)

0.29 (2) 0.20 (8)

51.9 (5)

394 560

1.5

Isomer shift relative to iron metal; e Quadrupole splitting or quadrupole shift; Bhf Hyperfine magnetic field; Z2 Goodness of fit parameter for 256 points 1;

2

c)

2

9

0

9

9

~

I

G i

I",

I

20

i

Fig. 1 a-e. Crystal structure of acmite (a) general view (b) positions of Fe 3+ ions (M1 sites) and (e) symmetry relations between MI sites; z is translation (1/2 1/2 O). Zigzag M1 chains (1, 2) and (3, 4) run parallel to g. The magnetic structure is indicated by the + and - signs in the lower part of a

1;

i

9

4

4

t

I

1

I

|

|

1

I

.

i

40

i

i

l

I

60

l

i

l

i

l

i

i

t

l

"

|

80

i | i i ~ i -t t t t i l i i i -

S,

100 20"

120

440

Fig. 2. Neutron diffraction pattern of synthetic acmite at 14 K, )~= 1.96 A. Note the presence of lines due to hematite that are not fitted by the theoretical profile (solid line)

674 I

10

xlO-3

I

I

|

3

I

!~

.

~, ~ , a ) x" ' '

h; /9

~2

0

"'"

I

I o

I

2o I

~2 s

0"

I

0

I00

I

I

200 300 T(K)

Fig. 3a, b. Temperature dependence of the inverse susceptibility of (a) natural and (b) synthetic acmite samples. The insert in (a) shows the susceptibility around the magnetic ordering point MSssbauer spectra, obtained at low temperatures show that samples order magnetically in the liquid helium temperature range. The lines of the magnetic hyperfine spectra for the natural sample are very broad with a full width at half maximum of 2.5 mm/s for the outer lines at 4.2 K and 0.9 mm/s at 1.6 K. No satisfactory fits to these data were achieved, presumably because of a distribution in exchange interactions introduced by a random distribution of Fe 2 § ions, A reasonable fit however was obtained to the 1.5 K spectrum of the synthetic sample, taking account of the presence of the hematite impurity (Fig. 5) and allowing the outer, middle and inner doublets of the magnetic hyperfine pattern to take slighly different linewidths. The weak central absorption near 0.5 mm/s is not fitted. Fit parameters for synthetic acmite are listed in Table 2. From the temperature-dependence of the hyperfine field, N6el points of 8 K and 6 K were estimated for the synthetic and natural samples, respectively. Magnetic neutron diffraction patterns for the synthetic sample were obtained on D1A at T = 1.5 K and T = 14 K with 2 = 1 . 9 6 ~ and 20=~x=160 ~ at T = 2 and 1 4 K with 2=3.06 A and 20re,x=65 ~ and on D2B at T = 4 K with 2 = 2.4 ~ and 20m,x= 160~ In Figure 6, a series of sharp magnetic peaks can be seen which are indexed on the crystallographic cell. The strong doublet at 20~ 20 ~ is indexed as 100 and 010. In addition there are weaker, broad (b) reflections at 20= 25 ~ and 47 ~, which cannot be indexed on the crystallographic cell.

1

I

0

I

10

15

20

Sort)

Fig. 4a, b. Magnetization curves of (a) natural and (b) synthetic acmite. Numbers refer to the temperature, in K

I

i

r

I

i

l

i

0'

~ 9

15t4

~

9

."

r

.O 0

§

*

i.§

§

"t

0 i

§

4. Discussion Both acmite samples exhibit predominantly antiferromagnetic exchange coupling in their susceptibility and magnetization, although both the 0-value and the greater magnetization of the natural sample at a given temperature and field indicate that the antiferromagnetic exchange is weakened by the presence of some Fe 2+, presumably because the Fe 2 + - F e 3+ exchange is ferromagnetic (c.f. glauconite, Ballet and Coey 1982). Trapping of the extra 3d electron

I

5

2O

20K i.

; I

I

-12 -8

I

I

-4

0

~.~

I

8 12 Velocity (totals)

Fig. 5. Mgssbauer spectra of synthetic acmite at 1.5 K, 4.2 K and 20 K. The spectrum of the hematite impurity is evident in the 20 K data

675 ,

,

i

l

l

l

l

t

,

l

l

i

"

l

l

l

D

Table 3. Different magnetic structures compatible with the crystallographic structure and having the same periodicity

;

o

g

.4 . 1.

.t

l

l

|

|

.

l

.

l.

.

l

|

l

Magnetic symmetry group (conjugations with time-reversal t-)

| f l l l l

I

" iilI 0

20

40

60

20" Fig. 6. Neutron diffraction patterns taken below (2 K) and above (14 K) the N6el point. 2 = 3.06 A the magnetic pattern is indexed on the crystallographic cell apart from the broad lines marked b. Note the diffuse magnetic scattering at 14 K at the positions of the 100 and 010 peaks

of the ferrous ion is expected to take place on M1 sites with Ca, rather than Na, M2 neighbours, and there will therefore be a distribution of exchange at the different iron sites, leading to a distribution of magnetic hyperfine splitring for both the Fe 2+ and Fe 3+ ions at nonzero temperature. Since more data are available on the synthetic sample, where complications due to a r a n d o m distribution of Fe 2 + are absent, we focus discussion on this material. In this compound, tTn/O] is 0.17, i.e. much less than 1. Possible reasons are a) quasi-one dimensional character of the magnetic ordering and b) frustration o f antiferromagnetic interactions in the magnetic ground state. It is clear from Figure 4 that the magnetic ground state is antiferromagnetic, in as much as there is no spontaneous magnetization. Apart from the ' b ' lines, the neutron diffraction of magnetic origin (Fig. 6) is quite similar to that of hedenbergite (Wiedenmann and Regnard 1986; Ghose et al. 1988a). The corresponding magnetic structure, giving the magnetic lines which are indexed on the crystallographic cell, is deduced by considering the extinction rules for the various magnetic symmetries which are compatible with the crystallographic symmetry. The magnetic sites being situated on the two-fold axis (2b), the magnetic moments can be either perpendicular to the b-direction, if 2b is combined with time-reversal t(2b" ~), or along it, when it is not. The reflection 010 exists, therefore the moments cannot lie along b. For the hkO reflections, contributions to the magnetic structure factors FM of the 1-2 chains and the 3-4 chains are the same when the translation t(1/2, 1/2, 0) is combined with t-(t. i); they are opposite, and hence cancel, when the translation is applied without {. The existence o f both 100 and 0t0 reflections means that the symmetry operation is T-~, i.e. p3 = -/11 and p 4 = - P 2 . FM(100) is then proportional to

Magnetic configurations Orien(successive directions of tation the moments in 1, 2, 3, 4)

2b

"C

1 {

/ 1

1 1

+ +

+ -

+ +

+ -

11 b I1 b

1 1 [ / 1 /

i 1 i 1 [ [

1 [ 1 7 [ 7

+ + + + + +

+ + --

+ +

+ -+

Lb IIb Zb 1[ b 2b ~ •

+ +

Magnetic mode for acmite

Table 4. Magnetic moments obtained by neutron diffraction. The magnetic movements tie within planes which are parallel to the c-a plane. They make an angle ~b with the c-direction ~r (K)

~, @~)

~ (~

1.s 2.0 4.0

3.s9 (5) 3.16 (5) 3.40 (4)

14 (4) 14 (4) 18,4 (7)

(~1+~2); its non-zero value means that p 1 = # 2 (i.e. 1 is not combined with t-). Hence, the magnetic configuration is collinear, with moments in sites 1, 2, 3 and 4 being respectively #, #, - p and - # along a direction in the c - - a plane. To every group of magnetic symmetry operations listed in Table 3 there belongs only collinear configurations. F r o m the magnetic mode of acmite, the chains are ferromagnetic, coupled antiferromagnetically to the four neighbouring chains. The moment p has been refined together with the lattice parameters by profile refinement. Table 4 shows that the moment direction lies at about 14 ~ from & The broad ' b ' reflections in Figure 6 could be due to the presence of a weak mode with non-zero propagation vector, corresponding to a modulation of the main configuration which would lower the frustration energy, but the solution requires further investigation. It is interesting to note that the direction of the moments appears to minimize the dipolar energy. The intrachain dipolar interaction favours the e-direction for the ferromagnetic moments, but the interchain dipolar interactions favour a direction which is perpendicular to the ab-plane. The observed direction seems to be a compromise. The magnetic structure eliminates possibility a) above (if the intrachain interactions were so much stronger than the interchain interactions, the former would have to be ferromagnetic to produce such a magnetic structure, and 0 would be positive). Explanation b) may be retained. Interand intrachain interactions are both antiferromagnetic, and in competition. However, the structure implies that chain to chain coupling via intervening SiO4 groups is dominant, and overcomes exchange a4thin the chain. We must therefore consider exchange interactions occurring via two oxygens, that is four non-equivalent classes of F e - - O - - S i - O - - F e paths. We shall call the corresponding parameters,

676

1

2

:%"

b

/..;/ "%',

/...UI

Fig. 7. Exchange couplings. Four unit-cells are represented, projected along the c-axis. The intrachain exchange parameter J12 (=) corresponds to direct and Fe--O--Fe indirect exchange. The interchain parameters J'13 ( - ) and Ji'3 ( - - ) correspond to Fe-O--Si--O--Fe indirect exchange within planes parallel to the abplane, and J~a (...), to Fe--O--Si--O--Fe indirect exchange between ions which belong to different z-levels. The Ml-positions which are indicated by the bigger dots are at the level 3/4, while the others lie in the z= 1/4 plane. Note the frustrating triangles 134 and 234

introduced in Figure 7, Ji4, J]'4, Ja3 and J1'3. J]4 couples the moments 1 and 4, or the moments 2 and 3. The paths of this class are connected from cell to cell along a + c , i.e. they couple a moment 1 to two moments 4, one of which is c/2 above its z-level, the other c/2 below. The paths corresponding to Ji'4 make just the same connection, so that we need only to consider J 1 4 = J l 4 q - J 1 4 . .[13 couples the moments 1 (or 2) to two moments 3 (or 4), and J]'3 to two other moments 3 (or 4) all at the same z-level. When the magnetic cell is the crystallographic cell, all moments 3, for instance, are equivalent, and we are left with three effective parameters, J~ 2, Ja 3 = J] 3 + J]'3 and J~4. The corresponding numbers of neighbours are then Z12 = 2, Z~ 3 = 2 and Z~4 =2. The frustration is clearly understood by considering for instance, how moments 1, 2 and 3, interact together. They form triangles of antiferromagnetic interactions which cannot be satisfied simultaneously. Therefore the weakest of the three has to yield. It appears that J12 must be the weakest since the chains are ferromagnetic. The covalent character for the bonding in the SiO4, group may account for its ability to act as a superexchange ligand. Transfer of electrons from the SiO 4 into the unoccupied spin down orbitals of an adjacent Fe a + ion will lead to an excess of spin up electrons elsewhere on the group, hence antiferromagnetic coupling with another adjacent Fe 3 +. That superexchange between two iron ions separated by a common SiO4 group can be significant was established previously by analysis of the spin flip transition in ferrous amphiboles (Moukarika et al. 1983; Ghose et al. 1987) and orthopyroxene (Wiedenmann etal. 1986; Ghose etal. 1988b). The iron garnets andradite (TN=11.5 K; Murad 1984) and almandine (TN = 7.5 K; Prandl 1971) also demonstrate that superexchange in silicates will propagate via the SiO4 group. Molecular-field theory (MFT) provides the expressions:

30/S(S+ 1) =Z~zJa2 + Z~3J13 + ZI4JI4 3T~NF/S(SW1)=alzZ~zJ12+at3Z13Jla-{-a14Z14J14

(2) (3)

where Ju are expressed in K. Expression (2) is always valid since at high-temperatures the short-range correlations of fluctuations, which are neglected by MFT, are actually negligible. Moreover with the Fe 3+ ions there is no problem with low-lying excited orbital levels which could limit the validity of the linearization leading to (2), since they are 6S-ions. Thus, Jlz +J13 + J l , = --7.9 K. The expression (3) gives the M F T value of the N6el temperature, which depends on the three coefficients a~2, a13 and a14 that represents the stable magnetic structure. These coefficients are each +_1 and correspond to the last three of the four signs that describe the magnetic configuration in Table 3. The stable magnet structure gives the highest T~ v. Therefore TNMF(+ -- - - ) > T~F( - -}- --), i.e. [Jlzl < [J13[, and T ~ F ( + - - - - ) > T ~ F ( - - - - + ) , i.e. IJ~21(O/3)~15K. The difference between this molecular field theory limit and the observed value of TN = 8 K may be ascribed to short-range correlations and fluctuations, which are neglected by MFT. In three-dimensional systems of isotropic (Heisenberg) spins, TN/T~yF--~0.7 is a typical value for S = 5/2 spins with 6 neighbours (de Jongh and Miedema 1974). However, in our case T N / T MF is equal at most to (8 K/15 K)=0.52. We conclude that the frustration has two effects: i) it makes T~ F smaller than 101, and ii) it lowers Ty from the molecular field value by creating more short-range fluctuations than in a non-frustrated three-dimensional system. The observation of weak, magnetic diffuse scattering around 100 and 010 reciprocal lattice vectors in the neutron pattern at 14 K (Figure 6), shows that short-range order still exists up to about twice the N6el temperature.

5. Conclusions Acmite has been shown to order antiferromagnetically, principally in a structure with ferromagnetic ferric chains. Exchange interactions are antiferromagnetic and frustrated, the dominant interactions being interchain coupling via an SiO4 group. Acmite is therefore in no sense a quasi onedimensional Heisenberg antiferromagnet. The ability for significant superexchange interactions to be transmitted across an SiO4 group is attributed to the covalent bonding of the group. These long-range interactions may well influence the magnetic structures of other iron silicates (Coey and Ghose 1988). For acmite, at least, this is the dominant magnetic exchange path.

Acknowledgements. This work was carried out in part when one of the authors (JMDC) was Collaborateur Temporaire Etranger at the Centre d'Etudes Nucl~aires de Grenoble. Support was also provided by the NSF under grant EAR 8618395 (SG and JMDC). We are indebted to RA Robie for the synthetic acmite, originally synthesized by Ko et al. for their calorimetric experiments.

References Ballet O, Coey JMD (1982) Magnetic properties of sheet silicates; 2:1 layer minerals. Phys Chem Minerals 8:218-229 Clark JR, Aplleman DE, Papike JJ (1969) Crystal chemical characteristics of clinopyroxenes based on eight new structure refinements. Mineral Soc Am Pap 2:31-50 Coey JMD (1988) Magnetic properties of iron in soil iron oxides and clay minerals. In : Stucki JW, Goodman BA, Schwertmann

677 U (eds) Iron in soils and clay minerals. Reidel, Dordrecht, pp 397-466 Coey JMD, Ghose S (1988) Magnetic phase transitions in silicate minerals. In: Ghose S, Coey JMD, Salje E (eds) Structural and magnetic phase transitions in minerals. Springer, Berlin Heidelberg New York, pp 162-184 Ghose S, Hewart AW, Dang NV (1987) Magnetic order in grunerire, FeTSisO22(OH)2 - a quasi-one-dimensional antiferromagnet with a spin canting transition. Plays Chem Minerals 14:36-44 Ghose S, Hewat AW, Weidner JR (1988a) Magnetic phase transition in hedenbergite, CaFeSizO6 - a quasi-one-dimensional antiferromagnet. Phys Chem Minerals (in press) Ghose S, Hewat AW, Dang NV (1988 b) Magnetic phase transition and spin canting in ferrosilite FezSi20 6 - a quasi-one-dimensional antiferromagnet. Phys Chem Minerals (in press) Goodenough JB (1963) Magnetism and the Chemical Bond. Interscience, New York de Jongh LJ, Miedema AR (1974) Experiments on simple magnetic model systems. Adv Phys 23 : 1-144

Ko II C, Ferrante M J, Stuve JM (1980) Thermophysical properties of acmite. Proc. 7th Symposium on Thermophysical Properties, Am Soc Mech Eng, p 392-395 Moukarika A, Coey JMD, Dang NV (1983) Magnetic order in crocidolite asbestos. Phys Chem Minerals 9:269-275 Murad E (1984) Magnetic order in andradite. Am Mineral 69 : 722-724 Prandl W (1971) Die Orientierung des elektrischen Feldgradienten und das innere Magnetfeld beim Almandin. Z Kristallogr 134: 334~349 Wiedenmann A, Regnard JR (1986) Neutron diffraction study of the magnetic ordering in proxenes Fe~MI_~SiO3. Solid State Commun 57:499-504 Wiedenmann A, Regnard JR, Fillion G, Hafner SS (1986) Magnetic properties and magnetic ordering of the orthopyroxenes FexMgl_xSiO3. J Phys C 19 : 3683-3696

Received June 9, 1988