Ferrimagnetic structure of Mn2Co2C

J.Phys.Chem. Solids

Pergamon Press 1969.Vol. 30,pp. 939-945. Printed in Great Britain.

FERRIMAGNETIC

STRUCTURE

OF Mn,Co,C

N.S. SATYA MURTHY,R.J.BEGUM,C. S. SOMANATHAN, B. S. SRINNASAN and M. R. L. N. MURTHY Bhabha Atomic Research Centre, Trombay, Bombay-74, India (Received 20 August 1968) Abstmet.-The carbide Mn&o,C has been found to be fenimagnetic with a Neel temperature of 535°C by means of neutron diifraction. It has a cubic unit cell with an Mn atom at the cube comer and the carbon atom at the body centre. The face centre sites are taken up by the other Mn and the two Co atoms in a statistical manner. The Mn moments are aligned anti-parallel to each other while the two Co moments are parallel to the comer Mn moment. The most reasonable values for the moments are: 4.0 pg for the comer Mn atom, 3.36 pLgfor the face centre Mn and 1.25 CLI) for each Co atom. The smaller moments of the face centre atoms arise from the influence of the carbon atom. Polarised neutrons were used to choose a structure having cubic symmetry over one of tetragonal symmetry. INTROIXJCTION

having the composition (M, iW)J where one or both of the atoms M and M’ belong to the 3d transition group and X is either nitrogen or carbon have been studied extensively [ l-71 on account of their interesting magnetic. properties. Fe,N [41 is ferromagnetic with a large magnetic moment of about 9 ~&.mit cell, while most manganese compounds exhibit ferrimagnetic properties as in the case of Mn,N [6,7], which has a net magnetic moment of 1a2 &unit cell. The crystal structure is usually cubic in which the metal atoms form a f.c.c. lattice and the carbon or the nitrogen atom goes to the body centre. The corner metal atom has the normal magnetic moment but the face centre atoms always have different magnetic moments. This difference has been attributed to the bonding interaction between the face centre metal atoms and the non-metal atom, both nigrogen and carbon being regarded as electron donors. But careful X-ray scattering factor measurements by Elliott [8] and by Kuriyama ef af.[9] indicate that the valence state of nitrogen in Mn,N and (Fe, Ni),N is such that it is more likely to behave as an ‘acceptor’ of electrons rather than as a ‘donor’. The present study was undertaken with a view to a further understanding of the role of the non-magnetic atom SEVERAL

COMPOUNDS

in the atomic and magnetic ordering processes in these compounds. Mn,Co,C is a particularly interesting compound in that the binary f.c.c. alloy MnCo [IO] is highly disordered and non-magnetic at room temperature and shows a tendency for antiferromagnetic ordering only at very low temperatures when carefully annealed. But X-ray and magnetisation studies by Holtzman [5,1 l] show that Mn,Co,C is an ordered magnetic compound. According to him it is ferrimagnetic with a net magnetic moment of 3.14 &unit cell at liquid nitrogen temperature and a transition temperature higher than 600°C. Polarised neutrons can be used to advantage in the study of ferrimagnetic structures to fix the directions of the individual moments with respect to the net magnetisation. The large intensity variations for the two states of neutron polarisation for the same reflections not only provide a clue to the correct relative spin arrangement but enable a more accurate determination of the individual moment values. As in the earlier neutron diffraction study of Mn,N by Takei et a1.[6] polarised neutrons have been used in the present case to resolve the structure in favour of a cubic model rather than one of tetragonal symmetry suggested by Holtzman. 939

940

N. S. SATYA EXPERIMENTAL DETAILS

Fifty atomic per cent each of spectroscopically pure Mn flakes and Co chips were melted in an arc furnace under a pressure of 1 CL.The alloy buttons so formed (about 100 g) were repeatedly melted to ensure the formation of a homogeneous alloy. They were crushed into powder and intimately mixed with carbon of electrolytic purity (taken slightly in excess of the required 20 at,% to ensure complete carbonisation) and melted in an induction furnace at a temperature of 1400°C to allow carbon to dissolve in the molten alloy. The resulting mass was cooled slowly in the furnace. The hard brittle product was powdered to 100 mesh particles. The material was found to be strongly magnetic. The unreacted carbon was removed by magnetic separation. An X-ray examination using Cu Ko radiation revealed the presence of a single phase with a cubic unit cell of a, = 3.786 A, agreeing very well with Holtzman’s value of 3.79 A. Thin walled flat aluminium cassettes were used for taking the diffraction patterns of the

MURTHY

et al.

sample at room temperature and at liquid nitrogen temperature with unpolarised neutrons. The sample was enclosed in vanadium tubes with vanadium end plugs for the high temperature data With a magnetic field applied parallel to the scattering vector the variation of the (100) and (110) reflection intensities was studied. A field of 4.5 kOe was found to saturate the sample. Figure 1 shows the diffraction patterns at room temperature and at 600°C. The pattern at nitrogen temperature gave relative intensities which were substantially the same as those at the room temperature showing that the magnetic moments at room temperature are not very much different from their saturation values. The nearly complete disappearance of (110) reflection at 600°C indicates that it is almost purely magnetic in origin. The temperature dependence of this peak as well as that of (100) was followed which lead to a transition temperature of 535°C. For measurements on the polarised neutron spectrometer the sample was pressed into

Fig. 1. Unpolarised Neutron diffraction patterns of Mn,Co& at room temperature and at 600°C. A= 1.25 A. C refers to a peak due to free carbon present in the sample.

FERRIMAGNETIC

STRUCTURE

OF Mn,Co&

941

pellets 16 mm in dia. and 3 mm thick using a pressure of 1 kbar. The magnetic field on the sample was 6 kOe applied at right angles to the scattering vector. Patterns were taken for both the neutron spin states, parallel and antiparallel to the direction of magnetisation of the sample. The ratio, R, of the intensites with the two neutron spin states is given by R =Xj[N2+W-2PDNM(2FXj[Nz + M2 + 2 PDNM]

l)]

where the summation is over the number of reflections occuring at a particular Bragg angle. Here j is the multiplicity of {hkl} reflections, P is the polarisation of the incident neutron beam, D is the polarisation transmission through the sample and F is the flipping efficiency of the r.f. field used to reverse the neutron spin. N and M refer respectively to the nuclear and magnetic structures factors. It should be noted that R values will show significant departure from unity only for high values of PD and hence D should be fairly large. In order to bring out the striking differences in the diffraction patterns for the two neutron spin states, the behaviour of (100) and (110) reflections with respect to the neutron polarisation is shown in Fig. 2. Also shown for comparison are the patterns with unpolarised neutrons at room temperature (F 2 CCN2 + # M2), at a temperature beyond TN(F 2 = N2) and with an applied field along the scattering vector (F 2 a N2). It can be seen that the intensities are strongly dependent on the neutron polarisation and depending on the signs of their structure factors, different reflections behave differently with respect to the neutron polarisation, so that there are, in effect, two additional sets of diffraction data for the same material. In the present case, while the (100) reflection has a higher intensity with r.f. on than with r.f. off, the opposite is the case with the (110) reflection. This is due to the fact that N and M have opposite signs for (100) whereas they are of the the same sign for the (110) reflection. It should

15

bm$m 28

25

Fig. 2. The diffraction patterns of the first two peaks of Mn,ColC under various conditions: (a), (b) and (c) show patterns taken with unpolarised neutrons; (a) at room temperature, (b) at room temperature with a saturating magnetic field applied parallel to the scattering vector and (c) at 600°C above TN. Polarised neutron patterns are (d) with the incident neutron spin antiparallel to the direction of net magnetisation of the sample and (e) with the neutron spin parallel to the magnetisation.

also be noted that the coherence between N and M enables accurate estimate of the nuclear component of the (110) reflection which was barely measurable in the high temperature unpolarised neutron diffraction pattern. RIWJLTS

The data were analysed in terms of various possible models. Holtzman suggested that Mn atoms occupy (000) and (&O) sites while Co atoms take up (404) and (OS) positions, giving a structure of tetragonal symmetry. Although no experimental evidence of any crystallographic distortion was found to support a tetragonal unit cell, the observed intensities were compared with the ones calculated on the basis of Holtzman’s model (Model I). Table 1 lists the observed and calculated

942

N. S. SATYA

MURTHY

etal.

Table 1. Comparison of the observed and calculated intensities of Mn,Co,C 6oo*c hkl

Calc.

Obs.

100 110 111 200 210 211 220 221 300 I 311 320 321 Agreement factor (on F*)

Model I

Model II

100~00 25.63 20.34 2.73 64.84 -

100~00 4.71 26.53 3.55 64.74 -

100~00 33.93 14.92 3.17 46.10 13.62 2.21

lOO*OO 23.58 28.21 6.15 61-88 4.93 4.20

Model IIB

2.22

2-89

57.05

36.69

399.57

30.02

42.20

42.74

ll*OS 16.74 -

1944 16.73 -

22.03 23.39 3.90

10.38 17-22 32.64

19.72 24.91 2.36

19.21 25.16 2.41

13.8%

9.6%

Bm &,

4.00 Ercs

FMn, = -3-36 &$

i-%0 =

Model IIA

lOO*oO 25.34 27.88 7.80 61 a01 5.85 3.90

intensities. It is seen that several of the intensities show agreement with Model I, the disagreement in the case of high temperature data being only for two reflections, namely (110) and (22 1,300). Model II corresponds to a structure with cubic symmetry in which the comer site is occupied by an Mn atom and the face centres are taken up s~tistic~ly by the other Mn and the two Co atoms. To analyse the room temperature data, the following set of moment values were chosen: #%n, =

Model IA

1.25 *s

where Mn, stands for the comer manganese atom and Mnr, for the face centre atom. These values were based on a straight forward reduction of the magnetic moments of the face centre atoms due to bonding interaction with the carbon atom at the body centre. The moments were assumed to be directed along any of the three cubic axes while for the tetragonal case the c-axis was assumed to be the direction of the moments. Any ferromagnetic alignment of spins can be ruled out as it requires all the moments to have unrealistically

lOOGO 24.20 25.50 4.78 63.01 5.38 3.57

= 194 X 10-*BcmZ = 0.62 x lo-‘@ cm2

small values. The fact that the (1 IO) intensity is almost entirely magnetic in origin and that (111) and (200) have low magnetic contributions bears this out. The calculated intensities are shown in the columns IA and IIA. The agreement of the room temperature data with Model II is definitely better, but it should be noted that only weak and outer reflections like (211), (311) and (321) are crucial for choosing between the two models. There is also the possibility that the compound is not fully stoichiometric and the amount of carbon deficiency can be adjusted to give a better agreement of the experimental data with Model I. Polarised neutron intensity ratios were examined for several reflections in order to choose between the two structures. Table 2 gives a comparison of the observed R values with the ones calculated on the two models Table 2. Polarised neutron ratios, R,for Mn,Co,C. P = 0.95, D = 0.76, F = 0.95 hkl

Obs.

Model IA

Calculated Model IIA

Model IIB

100 110 111 210

5.65 0.52 3.25 3.02

1.37 0.29 5.18 1.18

5-51 0.42 5.16 2.52

5.47 0.42 4.09 2.66

FERRIMAGNETIC

STRUCTURE

for the (loo), (llO), (111) and (210) reflections. The experimental values of P, D and F are also shown in the table. A single crystal of Co-Fe was used as an analyser to measure D. There is now a striking difference between the values based on the two models for the more prominent reflections and the experimental data clearly favours the cubic model. Also from the signs of the structure factors it can be concluded that the magnetic moment of the face centre Mn atom is directed opposite to the net magnetisation while those of Co atoms are along the net magnetisation. No other spin configuration will be compatible with the observed data The magnetic structure of the carbide as deduced above is shown in Fig. 3. a, =3.786B

OF Mn,Co$Z

943

netic moment values phich would give almost the same numbers for the above two expressions cannot be distinguished by neutron diffraction techniques from the set A mentioned earlier. Curiously enough, this happens to be the case with the following set of moment values which were suggested by Takei et a1.[71 (TMS) for Mn,C on the basis of extrapolation of their data on carbon substituted Mn,N compounds:

l-h,,

=

PC0

=

-1.23

PB

0.26 ,$,.

The intensities calculated on this set of moment values are also shown in. Table 1 as Model IIB. DISCUSSION

0 Ml

zoo0

Fig. 3. The unit cell of Mn,Co,C with the arrows indicating magnetic moment directions.

It should be noted that the magnetic structure factors for the cubic case are of two kinds: (PM,, + 3~4 or (POW,-pu), where pun, refers to the magnetic scattering amplitude of the Mn, atom and pM = 4(2pc0 - Pi,,,) is the composite magnetic scattering amplitude of the f.c. sites. In the case of M&N, however, the situation is simpler in view of all the face centre atoms being of one kind. So any other set of mag-

The fact that the binary MnCo alloy shows very little tendency for magnetic ordering while the carbide with the same proportion of metal atoms is highly ordered indicates that carbon plays an important role in stabilising the structure. This is a consequence of the difference in the carbide forming habits of Mn and Co. Cobalt being known to have a greater affinity for carbon is accommodated at the two face centre sites which are closer to carbon, while the remaining site is occupied by Mn. The other Mn atom is relegated to the comer site which is too far from the bodycentre site to have any appreciable interaction with carbon. MnCo has a cell constant of 3.615 A. A saturation magnetisation study by Crangle [ 121 of Mn-Co alloys in the composition range 18 at.% Mn indicates than on increasing the Mn content there is a reduction in the magnetisation per atom suggesting an antiparallel alignment of Mn and Co spins. This can be seen qualitatively to be due to an overlap of Mn and Co 3 d orbitals. The MnCo distance in the alloy is 2.55 A which is smaller than the sum of their radii, namely, I.35 A for Mn and 1.22 A for Co (according to recent self consistent Hartree-Fock calculations). In the case of the carbide there is an

N. S. SATYA

944

expansion of the unit cell to accommodate the carbon atom at the body centre and the significant interatomic distances are: or

Mn, - Mnrr C-Mn,, Mnr-C

or

Co = 2.677 A Co

= 1*893A = 3.279 A.

There is now no overlap between the Mn and Co atoms and hence a ferromagnetic interaction is expected between them, while between the Mn atoms an antiferromagnetic interaction persists as the Mn,- Mn,, distance is still smaller than twice the Mn radius. Any superexchange interaction among the face centre atoms via the carbon orbitals is weak because of the unfavourable, 90” angle. Thus the magnetic structure is brought about by direct exchange interactions among the metal atoms. Although the two cubic models IIA and IIB cannot be distinguished by means of neutron diffraction, set A is preferable as these moment values can be explained in a sample way, without any ad hoc assumptions. The carbon 2p electrons can be assumed to spend some of their time in the neighbourhood of the f.c.c. atoms, thereby decreasing their effective magnetic moment values. In fact, it may be thought of that the two p electrons of carbon spend a third of their time near each face centre atom and this would result in an increase of 0.67 in the effective electron concentration of each atom. Thus the Mn moment is reduced by 064 from its normal value of 4.0 pus while each Co moment is reduced by 0.48 pB from the normal Co moment of 1.73 pB. The smaller reduction in the Co moment may be due to its larger bonding interaction with carbon. Set B necessitates the assumption of a definite number of electrons being donated by the carbon atom to the face centre atoms. THS [7] studied the carbon substituted M&N system, Mn,N,_,C, as well as partially filled compounds like Mn,N,.,, and extrapolated their results to the case of the hypothetical

MURTHY

et&.

carbide M&C. They assumed that in (M, iW)&Y compounds, the magnetic moment of the corner Mn atom remains essentially constant, while the face centre atoms lose 3 pg when X 1s nitrogen and 2 pB when it is a carbon atom. This was supported by their experimental results on Mn,N, Mn,N,.,,, Mn,AlC [2], Mn,N,.,,C,.,, etc. But this argument failed to explain their observed magnetic moment values in the case of Mn4N0.,. According to THS, this change in the face centre moments arises because of a reversal in the relative positions of the two sub-

ad hoc and need not be expected to be followed by carbides as well. Moreover, it may be pointed out that in Fe,N [4] the face centre moments have also been explained without recourse to any such assumptions. The present interpretation of the moments is analogous to the situation in Fe,N. The study of compounds such as the present one undoubtedly leads to a better understanding of magnetism in covalent compounds and of the role of non magnetic atoms in magnetic structures. It would be worthwhile to investigate carbides and nitrides for other concentrations of Mn and Co.

AcknowledgementsWe are grateful to Dr. P. K. Iyengar for his keen interest in the work. We thank Mr. M. G. Natera and Mr. S. I. Youssef for assistance with the calculations.

REFERENCES 1. WIENER G. W. and BERGER J. A., J. Metals 7, 360 (1955). 2. BUTTERS R. G. and MYERS H. P., Phil. Mug. 46, 895 (1955). 3. BROCKHOUSE B. N. and MYERS H. P., Can. J. Phvs. 35.3 13 ( 1957). 4. FRAZER B. C., Phys. Rev. 112,75 1 (1958). 5. HOLTZMAN A. H. and CONARD II G. P.. J. uppl. Phys. 30,103s (1959).

FERRIMAGNETIC

STRUCTURE

6. TAKE1 W. J., SHIRANE G. and FRAZER B. C., Phys. Rev. 119,122 (1960). 7. TAKE1 W. J., HEIKES R. R. and SHIRANE G., Phys. Rev. 125,1893 (1962). 8. ELLIOTT N., Phys. Rev. 129,112O (1963). 9. KURIYAMA M., HOSOYA S. and SUZUKI T., Phys. Rev. 130,898 (1963).

OF Mn&o,C

945

10. SIDHU S. S., SATYA MURTHY N. S.,CAMPOS F. P. and ZAUBERIS D. D., Pittsburgh Difiaction Conf. (1961). Unpublished. 11. HOLTZMAN A. H., Ph.D. Thesis, Lehigh University(1958). 12. CRANGLE J., Phil. Mug. 7,589 (1957).