STRUCTURAL PHASE TRANSITION AND MAGNETISM OF Ni-As-TYPE TRANSITION METAL PNICTIDES

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STRUCTURAL PHASE TRANSITION AND

MAGNETISM OF Ni-As-TYPE TRANSITION METAL

PNICTIDES

K. Motizuki, M. Morifuji

To cite this version:

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JOURNAL DE PHYSIQUE

Colloque C8, Supplkment au no 12, Tome 49, dkcembre 1988

STRUCTURAL PHASE TRANSITION AND MAGNETISM OF Ni-As-TYPE TRANSITION METAL PNICTIDES

K. Motizuki and M. Morifuji

Department of Material Physics, Faculty of Engineering Science, Osaka University, Toyonaka 560, Japan

Abstract. - Structural transformation of CoAs and NiAs from NiAs-type to MnP-type are studied microscopically. Electron-lattice matrix elements and generalized susceptibilities are calculated on the basis of electronic bands obtained by APW method. Band calculation of FeAs having MnP-type structure is made for non-magnetic state. Results are discussed in connection with magnetic ordering.

Magnetic properties of NiAs-type transition metal compounds, such as MnAs, MnSb, and CoAs, were in- vestigated from the view-point of itinerant electrons by taking account of spin fluctuations [I]. Some of these compounds reveal a structural phase transition from the NiAs-type to MnP-type as temperature decreases. A crucial question is why this kind of structural transformation occurs in MnAs, CrAs, and CoAs, but not in MnSb, CrSb, and NiAs:

We have studied microscopically an instability of the NiAs-type structure on the basis of the electronic band structure, by taking into account the effect of the wave-

number and mode dependences of the electron-lattice interaction as well as the nesting of the Fermi surface. Results for Mn- and Cr-compounds were reported in reference [2]. In the present paper lattice instabilities of CoAs and NiAs are mainly studied.

A change of the electronic free energy due to a lattice distortion characterized by a particular phonon normal coordinate Qqx (q : the wave vector, X : the mode) is expressed as

The generalized electronic susceptibility

x

(qX) is pro- portional to a quantity defined by

-2 ~ r , * n ' k + q ' : [

E : ~

-

~ o , , ~ + .

9

nn' k

where n and n.' are band suffices. I,";, n'k' is the

electron-lattice matrix element which represents the strength of the coupling between two states ( n k ) and

(n'k') caused by the displacement of the vth atom in the a direction. In the framework of the APW method

I is obtained as

where Q n k is the Bloch function and AV represents

a change of the muffin-tin potential due to the dis-

placement of the vth atom along the a direction. The explicit expression of I is given in reference [2].

The NiAs-type crystal has a unit cell containing two metal atoms, 1 and 2, and two anion atoms, 3 and

4. The MnP-type distortion is described as a frozen longitudinal phonon of Mh mode. This mode consists of displacements of metal ions in the s and %direction and those of anions in the z-direction:

z-axis is taken to be parallel to the c-axis, and saxis is in the oplane and parallel t o the rM.

For CoAs and NiAs we have calculated I,";, n,k+q

for the phonon wave vector q = r M as functions of the wave vector k. Since we confine our consideration to the My mode, the matrix elements I should be cal-

culated for the two states of the bands whose product representation has a compatibility relation with the My representation. Furthermore, if one of the electronic states, nk and n'k

+

q, is above the Fermi level and another is below the Fermi level, the coupling between these two states can contribute to lower the electronic energy. We call this condition as A. The numer- ical calculation of 1 has been made in three cases: (1)

v = metal, a = x, (2) v = metal, cu = z, (3) v = anion,

a = Z. Results obtained for CoAs and NiAs are shown

in figure 1. Solid and dotted lines represent values of

I calculated for wave vectors k which satisfy and not satisfy the condition A, respectively. The results of figure 1 indicate that the displacements of metal atoms are the most likely to be realized in the =direction as observed. A quantity defined by

represents a reduction of the free energy due to displacement of the uth atom in the a-direction. We have calculated AFk as functions of k in three cases, (I),

( 2 ) , (3). From the results shown in figure 2, we have

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JOURNAL DE PHYSIQUE

CoAs

Ni As

B f l

(2) metal z

_.

.

1

i

K K K K

Fig. 1.

-

Electron-lattice matrix elements, I, calculated for CoAs and NiAs as functions of the wave vector k.

K K (2) metal r. K K

p~~

(3) Asz K K K

Fig. 2. - AFk l1I2 /AE calculated for CoAs and NiAs as functions of the wave vector k.

found that a reduction of the free energy in CoAs is larger than that in'NiAs. This is consistent with obser- vations that the transformation from the NiAs-type to the MnP-type is realized in CoAs but not in NiAs. The quantity AFk is strongly affected by the nesting effect

of the Ferrni surfaces by the wave vector q. Actually, a recent band calculation by a self-consistent APW method [3] shows that a good nesting of the Fermi surfaces by the wave vector q

=

r M can be expected for CoAs but not for NiAs. In conclusion we em~hasize

an important role of itinerant 3d electrons in the structural transformation of transition metal pnictides.

Magnetic properties of these compounds are also attributed to 3d electrons. An interesting point is whether the observed magnetic ordering can be ex- plained or not in the framework of itinerant d eleo trons. Among Ni-, Co-, Fe-arsenides, only FeAs (MnP- type structure in all temperatures) becomes a double helical magnet below

TN

= 77 K (41. Therefore, we

have performed a seIf-consistent APW band calcul* tion for non-magnetic state of MnP-type FeAs. Pro- cedure of the calculation is the same with that noted in reference [3]. The obtained Fermi surface consists of two hole pockets and two hole surfaces (a) and (b). From the'shape of (a) shown in figure 3, we may ex- pect a good nesting by a wave vector along the r X

direction. The observed helical structure is described by the wave vector N (3/4) rX. We suggest a possibil-

ity of a spin density wave for the helicd magnetism of FeAs.

(a)

hole surface

Fig. 3.

-

Fermi surfaces of FeAs having MnP-type crystal structure.

[I] Motizuki, K., J. Magn. Magn. Mater. 70 (1987)

1.

[2] Katoh, K. and Motizuki, K., J. Phys. Soc. Jpn

56 (1987) 655.

[3] Morifuji, M. and Motizuki, K., J. Magn. Magn. Mater. 70 (1987) 70.