The influence of 3d transition metal substitution on the magnetic properties of MnGaGe

J. Phys. Chum. Solids, 1975, Vol. 36, pp. 451-455. Pergamon Press.

Printed in Great Britain

THE INFLUENCE OF 3d TRANSITION METAL SUBSTITUTION ON THE MAGNETIC PROPERTIES OF MnGaGe* J. B. GOODENOUGH Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, MA 02173,U.S.A. and G. B. STREET,KENNETHLEE and J. C. SUITS IBM Research Laboratory, San Jose, California, U.S.A. (Receioed 12April 1974) Abstract--A study has been made of the effect of 3d transition element substitution on the magnetic moment and Curie temperature of MnGaGe. Substitution of 3d elements with atomic number less than Mn (i.e. Ti, V, or Cr) cause relatively small changes in magnetic properties, whereas substitution of Fe, Co, Ni and Cu cause a large reduction in moment and Curie temperature, e.g. substitution of 5 at.% Fe for Mn causes the moment to decrease by 30 per cent. The moment and ferromagnetism of MnGaGe are described in terms of a band model involving both strongly correlated and intinerant 3d electrons. The effect of 3d element substitution may be qualitatively understood in terms of this mode]. INTRODUCTION

compound MnGaGe[l, 21 is tetragonal and isostructural with Mn,Sb, with gallium occupying the manganese octahedral sites as shown in Fig. 1. MnGaGe is ferromagnetic with a Curie temperature of 185°C and exhibits a strong uniaxial anisotropy along the crystallographic c-axis. Studies on bulk polycrystalline samples, and particularly on evaporated [3] and sputtered [4] tilms, have shown that this tetragonal phase exists over a range of stoichiometry. The magnetic and magneto-optical properties of this tetragonal phase are strongly dependent on the stoichiometry[5]. We report here the effect on the magnetic properties of bulk MnGaGe produced by the substitution of 5 at.% of the manganese by each of the elements Ti, V, Cr, Fe, Co, Ni and Cu. We will interpret the resulting changes in magnetic moment in terms of a schematic band structure. The ternary

The Curie temperature measurements were obtained using a DuPont thermogravimetric balance, modified to provide a magnetic field gradient at the sample. Magnetization measurements were made using a vibrating sample magnetometer with a superconducting solenoid. Figure 2 is a plot of Curie temperature as a function of substituent. Figure 3 shows the saturation magnetization at 4~2°Kas a function of substituent.

EXPERIMENTAL

samples were preparedrl] by melting the metals together at lOOO”C,then quenching from the melt and annealing at 500°C. X-ray analysis revealed no significant amounts of second phase other than some unreacted germanium. The lattice constants did not vary from those of unsubstituted MnGaGe by more than l/2 per cent. The results of differential thermal analysis were similar to those reported previously [l] for the unsubstituted material. The

.Mn

OGa g=3.988

*The Lincoln Laboratory portion of this work was sponsored by the Department of the Air Force. 451

@Ge c,,=5.885

Fig. 1. Structure of MnGaGe with vertical arrows indicating the direction of the magnetic moment [6]by analogy with MnAlGe.

J. B. GO~DENOUGH~~~~.

452 200

160

G 0, 140 kU

120

100

80

1

”

““I

”

V

Ti

Cr

Mn

Fe

Co

Ni

Cu

X

Fii. 2. Curie temperaturesof MIL,+.,X~.~, GaGe samples. 50

I ’ ’

I

I

I

I

I

I

I

I

I

I

I

I

Cr

Mn

Fe

Co

Ni

Cu

46

34

301

’

’

Ti

V

X

Fig. 3. Saturation magnetization (4.2”K)of Mn,,.,Xo., GaGe samples. MODEL FOR MAGNETlC PROPERTIESMaGaGe

In order to understand the effect of these cation substitutions on the magnetic properties of MnGaGe, it is necessary first to have a model that expl~s the magnetic properties of MnGaGe. From measurements of anisotropy and by analogy with MnAlGe[6], we assume the magnetic structure of MnGaGe is as shown in Fig. 1. The

saturation magnetization for MnGaGe has been measured [l] as 166 pB at 4.2”K. The ferromagnetic order and the magnitude of the magnetization in MnGaGe can be understood from qualitative arguments about the band structure. However, we argue below that the occupancy of the manganese 3d bands is just sutllcient for ferromagnetic vs antiferromagnetic order. Therefore, any local decrease of the manganese 3d-band occupancy in the neighborhood of impurity atoms or of native defects can be expected to introduce antiferromagnetic Mn-Mn or Mn-impurity interactions that influence profoundly the magnitude of the macroscopic magnetization. Qualitative consideration of the band structure begins with the outer s and p electrons. The Ga-Ge array of Fig. 1 consists of two interpenetrating sublattices of similar symmetry. Translational symmetry splits the Ga-Ge s and p orbitals into 8 bonding and 8 antibonding states per molecule. As in a conventional semiconductor, the top of the bonding bands and the bottom of the antibonding bands would be separated by a finite energy gap, and phase stability is greatest if the Fermi energy falls in this gap. This latter would require formal transfer of one electron per molecule from the manganese array to the Ga-Ge array to give the formal valence state Mn’(GaGe)-. The interstitial manganese layers interact covalently with the Ga-Ge subarray. In addition, Mn-Mn interactions within basal planes broaden the manganese 4s and 4p bands; and the manganese 4s band would overlap the 3d bands and the Fermi energy to make the total number of electrons contributed by Mn atoms to the broad s-p bands at least comparable to that found in elemental, metallic manganese. Examination of the transition metals shows that the number of broad-band conduction electrons per atom increases with decreasing atomic number from a, ~0.6 in Ni to n. 2 1.0 in Mn. Therefore, we must anticipate for MnGaGe a manganeseatom contribution n, to the broad-band s and p electrons per molecule of nc = (1 + f)PB

(1)

where f is a small fraction. Since n, > 1, the stability requirement, represented by the formal-valence notation Mn’(GaGe)-, is fuElled. In the analysis to follow, the fraction f is the one variable parameter, and it is restricted to the narrow limits

O
(2)

because, relative to the 3d bands, the much greater widths and smaller density of states at the Fermi energy of the overlapping conduction bands does not permit rk in the metallic alloy MnGaGe to increase significantly over the value of n, found in elemental, metallic manganese.

The influenceof 3d transitionmetalsubstitutionon &e mapetic propertiesof MnGaGe From the structure of MnGaGe, see Fig. 1, three sets of 3d orbitals can be disti~isb~: (1) a &2 orbital that @bonds with like orbitals on the four near-neighbor Mn atoms in a basal plane, (2) the quasidegenerate dyz,dzz,dJy orbitals that r-bond with like orbitals on the four neighboring Mn atoms, but g-bond to the four Ga and four Ge nearest neighbors, and (3) a d,z orbital directed along the c-axis toward no near-neighbor atom. From our knowledge of the first-row transition elements, we must anticipate strongly correlated d,z etectrons. However, a Mn-Mn separation of only 2+gA within a basal plane requires that the d,rg electrons be itinerant, and covalent mixing with Ga and Ge s and p orbitals insures that the dS,d,,dx, electrons are also int~nerant [7,8]. By definition, strong correlations among dzzeiectrons means a splitting of the energy level for singly occupied d,l orbit& (the d:z level) from the level for doubly occupied d,z orbitals (the d$ level). The correlation energy U that splits these levels is the Coulombic energy between two electrons occupying the same orbital. If covalent mixing does not extend crystalline 36 orbitals significantly, the energy U may exceed the bandwith (or level width). Spontaneous atomic magnetic moments are associated with half-filled, strongly correlated orbitals. Thus a d$ configuration, which has no orbital magnetic moment, would contribute 1 pB per Mn atom to the m~eti~ation. From equations (1) and (2), the number of 3d electrons per manganese atom is Itd

=(7-&)=(6-f)

(3)

and 5.5 < nd < 6. Since fld = 5 corresponds to half-filled 3d orbitals, it follows that we must anticipate half-filled d,’ orbitals, the Fermi energy falling between the d:z and d$ levels, and hence a spontaneous Mn-atom magnetic moment. The presence of a spontaneous Mn atom moment from the dt2 etectrons is suficient to insure magnetic polarization of any narrow, partially filled 3d bands. Itinerantelectron fe~omagnetism can be readily distiu~~shed from strong-correlation ferrornagnetism if the bands are more than half-filled and less than three-quarters filled. We define a band-occupation number nr such that nr = 1 for half-tilled bands, nl = 2 for full bands. (The number 2 reflects the spin degeneracy.) Then for itinerant-electron ferromagnetism, the magnetization per band orbital is E7,gl

ma~eti~tian with atomic num~r may be interpreted in terms of equations (4) and (5) [7,8]. It follows from equation (5) that spontaneous, itinerant-electron ferromagnetism among electrons of the four itinerant 3d orbitals would contribute a magnetization per molecule ~p,‘(~~,-4)pe=(np-5)ps and the total magnetization per d,z efectron, is

(4)

&I = (m - l)#l for 1< nr s: 1.5

(51

whereas equation (4) applies over the entire range 1 zz nl 52 for strongly correlated electrons. The famous Slater-Pa&g curve for the variation of spontaneous

(6)

moiecule, including

Comparison with a measured moment of 14i6pe lmoiecule then implies an f =0*34

(8)

which is well within the narrow limits set by equation (2). The remaining question is whether the band occupancy is compatible with ferromagnetic vs antiferromagnetic order. Although superexchange interactions between half-filled d,r orbitals should be antiferromagnetic, the small overlrtp of dz2orbitals on ne~~~g Mn atoms makes these jnter~tions relatively weak. As among strongly correlated electrons, where the signs of the interatomic interactions are determined by the superexchange rules, spontaneous magnetism of half-filled bands (n, = 1) is characterized by antiferromagnetic order; of bands three-quarters filled or more (l-5 I noc 2) by ferromagnetic order [7]. A change from antiferromagnetic to ferromagnetic order occurs with increasing band occupation within the interval 1< m < 1.5, and a critical value of nt is anticipated near the middle of this interval. If the transition occurs where the ferromagnetic and an~e~oma~etic moments are equal, then the critical band occupation is nr = (3 - &)/2,where S is the reduction in the moment wAF= (Z- nr - 8)~s in the antiferromagnetic state due to electron transfer to and from neighboring atoms. The fraction 6 falls in the interval O-3< S < 0.8 for itinerant-electron magnetism [9], the larger values of 6 corresponding to broader bandwidths where spontaneous magnetism is induced by the presence of a localized atomic moment. For f = 0.34, the average band-occupancy number for the four itinerant 3d bands is $1= I-17

~i=(2-nl)~Bfor1.51~!2

453

(9)

which. requires S > O-66for stabilization of spontaneous fe~oma~netism. This condition is possible for a Mn-Mn separation of only 2.8 A and covalent mixing with Ga and Ge s and p orbitals. This observation has an immediate implicarion: Since the band occupancy is just sufficient

454

J. B. GOODENOLJOHet al.

for the establishment of ferromagnetic vs antiferromagnetic order, any local reduction in 3d-band occupation due to impurities or local defects should introduce local antiferromagnetic coupling. Thus, for example, any excess Mn-atom concentration would place Mn atoms on the Ga-Ge subarray, and these Mn atoms would be coupled antiferromagnetically with respect to the magnetization. The existence of such Mn atoms would reduce the macroscopically observed I*, and hence increase the inferred f of equation (8). Therefore, f = 0.34 should be considered an upper limit and fir = 1.17 a lower limit in MnGaGe. Thus far we have rationalized the magnitude of the magnetization of ferromagnetic MnGaGe and we have found that the number nd of manganese 3d electrons per molecule is only just sufficient for ferromagnetic coupling within manganese basal-plane layers. An overall ferromagnetism requires, in addition, an indirect ferromagnetic coupling between manganese layers via the f conduction electrons per molecule. Since f < 0.5, a ferromagnetic indirect exchange is compatible with our knowledge of this mechanism. This ferromagnetic indirect exchange also contributes to the intraplanar coupling, thus reducing the critical value of ii1 for ferromagnetism. From Fig. 3, dilute substitution of another transition metal for manganese in MnGaGe always decreases the magnetization. Moreover, the decrease is less for lighter transition-metal atoms then for heavier atoms, even though the lighter elements have fewer 3d electrons and the heavier atoms have more. In order to interpret this observation in terms of our qualitative band model, it is necessary to inquire into the local 3d-electron distribution at the impurity-ion centers. Each solute atom interacts with its nearest neighbors to form bonding and antibonding molecular-cluster 3d orbitals that are split by a finite energy. Moreover, the molecular-cluster bonding states should be filled before any nonbonding dg state. This requirement forces a solute atom substituting for Mn in MnGaGe to donate 1 electron to the bonding Ga-Ge s-p bands, n: electrons to the solute-Mn s band cf < n: < I), and 4 electrons to bonding solute-Mn 3d orbitals before the solute d,z level is occupied. A Cr solute atom has six outer electrons, and there is no localized atomic moment at a Cr atom (configuration d$‘) if n: = 1. From Fig. 3, Cr-atom substitutions for Mn in MnGaGe give a reduction in the magnetization that is well described by simple nonmagnetic dilution: Au ii: -47x emu/g. Therefore, we conclude that n:== 1 and the Cr atom carries no atomic moment. This conclusion n: = 1 is compatible with the fact that the 3d manifold at the lighter atom is less stable, so that 3d-electron charge density is transferred from the lighter solute atom to the Mn-atom nearest neighbors, charge neutrality then requiring an equivalent amount of

s-electron charge density to be transferred in the opposite direction. The lighter elements Ti and V, which have even less stable 3d manifolds, are necessarily nonmagnetic with configuration d$‘. In addition, electrons from the broad bands of Ti and V must be donated to the bonding molecular-cluster states, since there are an insufficient number of outer electrons on Ti and V to fill them. Because the 3d manifolds at the lighter transition-metal atoms are less stable, the bonding molecular-cluster orbitals are primarily Mn-3d in character, charge neutrality being maintained by an equivalent transfer of s-electron charge density to the solute atom. Therefore some antibonding, magnetic 3d electrons at the nearestneighbor Mn atoms are converted to nonmagnetic molecular-cluster bonding electrons. This conversion contributes an additional reduction in the magnetization. From Fig. 3, it would appear that this is an important contribution that increases with decreasing atomic number. However, there is no evidence that the decrease in antibonding electrons at Mn atoms nearest-neighbor to a solute atom causes antiferromagnetic Mn-Mn interactions. This is to be contrasted with the case for heavier solute atoms, see below. It is attributed to the fact that there is 3d-electron transfer from a lighter solute atom to its nearest-neighbor Mn atoms. For the heavier solute atoms this transfer is in the opposite direction. Substitutional atoms heavier than Mn have more 3d electrons, so they may have a localized atomic moment that couples parallel to the moments on the near-neighbor Mn atoms. Nevertheless, it is apparent from Fig. 3 that they cause a precipitous drop in the net magnetization. This apparent paradox may be reconciled as follows: The 3d manifolds at the heavier solute atoms are more stable than that at a Mn atom. Therefore, within a ferromagnetic five-atom cluster, consisting of a solute atom and its four near-neighbor Mn atoms, the bonding molecular-cluster orbitals are primarily solute-3d in character; antibonding molecular-cluster orbitals are primarily Mn3d in character. This situation is equivalent to 3d-electron transfer from the nearest-neighbor Mn atoms to the solute atom, charge neutrality being maintained via an equivalent shift of s-electron charge density in the opposite direction. However, a reduction in ii! in the local volume about the solute atom would induce an antiferromagnetic interaction between the five-atom cluster and the Mn-atom matrix, since fir is so close to the critical value for antiferromagnetic vs ferromagnetic interactions. Therefore, an isolated heavy-atom impurity can be expected to form a ferromagnetic five-atom cluster that couples antiparallel to the ferromagnetic host via antiferromagnetic Mn-Mn interactions. Comparison of this prediction with Fig. 3 requires, in addition, recognition that, for five-atom clusters, x = 0.05 is no longer a dilute impurityatom concentration. Interactions between impurity atoms

The intkrenceof 3d transitionmetalsubstitutionon the magneticpropertiesof MnGaGe separated by two manganese atoms would produce antiferromagnetically coupled clusters. Therefore, for heavier atoms Aa = -47(5x + h)e.m.u./g

magnetization with impurity-atom substitutions, changes that signal dilution by nonmagnetic solute atoms for the lighter transition elements and local antiferromagnetic Mn-Mn interactions for the heavier impurity atoms.

(11)

where the contribution 47h from unpaired clusters decreases with increasing x. For x = 0.05, Fig. 3 gives -15
the ordered alloy MnGaGe can be rationalized from qualitative considerations of the band structure. As in other manganese alloys, either ferromagnetic or antiferromagnetic Mn-Mn interactions may be encountered. The ferromagnetism of MnGaGe arises because the 3d-band occupancy just exceeds a critical value. Evidence that this is so comes from changes in the magnitude of the

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Acknowledgement-The authors wish to thank R. E. DeBrunce for technical assistance.

REFERENCES 1.Street G. B., Sawatzky E. and Lee K., J. Appl. Phys. 44,410 (1973). 2. Shibata K., Shinohara T. and Watanabe H., J. Phys. Sot. Japan 32, 1431(1972). 3. Lee K. and Suits J. C., ALP. Conj. Proc. 10,1429(1973). 4. Sawatzky E. and Street G. B., J. Appl. Phys. 44,1787(1973). 5. Street G. B., J. Solid State Chem. 7,316(1973). 6. Satya Murthy N. S., Begum R. J., Somanathan C. S. and M&thy M. R. L., J. Appl. Phys. 40, 1870(1969). 7. Goodenouah J. B.. Prop. in Solid State Chemistrv (Edited bv Reiss H.)rVol. 5, Chapr4. Pergamon Press, New York (1972): 8. Goodenough J. B., J. Solid State C/rem. 7, 428 (1973). 9. Goodenough J. B., Magnetism and the Chemical Bond. Interscience Wiley, New York (1%3).