Pis’ma v ZhETF, vol. 109, iss. 12, pp. 826 - 827

June 25

Ordering of Fe and Zn ions and magnetic properties of FeZnMo₃O₈

S. V. Streltsov^+∗1), D.-J. Huang^×, I. V. Solovyev^∗◦, D. I. Khomskii^∇

⁺M. N. Mikheev Institute of Metal Physics, Russian Academy of Science, 620041 Ekaterinburg, Russia

^∗Ural Federal University, 620002 Ekaterinburg, Russia

^×National Synchrotron Radiation Research Center, 30076 Hsinchu, Taiwan

^◦National Institute for Materials Sciences, Tsukuba, 305-0044 Ibaraki, Japan

^∇II. Physikalisches Institut, Universität zu Köln, D-50937 Köln, Germany

Submitted 27 April 2019

Resubmitted 27 April 2019

Accepted 16

May 2019

DOI: 10.1134/S0370274X1912004X

One of the main problems in mixed

The bulk experimental data show that the substitu-

(Fe_1-xZn_x)₂Mo₃O₈ materials is the distribution of

tion of Fe by Zn in Fe₂Mo₃O₈ changes magnetic ordering

constituent ions among inequivalent sites, octahedral

from antiferromagnetic (AFM) to ferromagnetic (FM),

and tetrahedral ones [1, 2]. Also the magnitude and the

in particular for half-doping x = 1, in FeZnMo₃O₈[1, 3].

sign of exchange interactions in these materials is not

Our preliminary spectroscopic data [4] point toward

clear a priori. As one sees from the crystal structure,

preferential location of Zn in tetrahedral sites; this also

shown in Fig. 1, there are several inequivalent exchange

agrees with the old estimates [5]. If true, this would

make the magnetic subsystem in FeZnMo₃O₈ relatively

simple: only octahedral sites would be occupied by mag-

netic ions Fe²⁺, so that only one type of exchange, the

diagonal interlayer Fe-Fe exchange J^cOO remains, and if

this would be ferromagnetic, it could explain the ob-

served magnetic behavior. However, from the existing

experimental data one cannot yet make definite conclu-

sions in this respect, although they indeed point in this

direction.

We used pseudopotential VASP code to calcu-

late electronic, magnetic, and structural properties of

Fig. 1. (Color online) Different possible exchange coupling

FeZnMo₃O₈ [6]. Exchange parameters for Heisenberg

parameters in M2Mo3O8 type of structures

model were calculated using JaSS code [7].

We start our investigation by studying effect of ex-

passes even for nearest neighbour interaction: in-plane

change interaction on distribution of Fe and Zn ions

J^abOT and interlayer J^cOO, J^cTT, and J^cOT exchanges.

among octahedral and tetrahedral positions. In particu-

Moreover, the “vertical” exchanges between octahedral

lar we calculated exchange parameters in FeZnMo₃O₈

and tetrahedral Fe ions might be also different - J^cOT

for various occupations of four available positions in

and J^cTO, because of the orientation of MO₄ tetrahedra

the unit cell by two Fe ions keeping the crystal struc-

(which all point in the same direction, this is in fact

ture untouched. Finding total energy difference between

what makes these systems polar). Since Fe₂Mo₃O₈ is

FM and AFM configurations we obtain that J^abOT =

known to be a multiferroic, i.e., a material in which

= 0.96 meV, J^cOT = -0.61 meV, J^cTT = 0.03 meV, and

electronic, magnetic, and structural properties are

J^cOO = 0.01 meV, if Heisenberg model is written in the

∑

strongly coupled, one might expect that exchange

form H =_i=j J_ij S_iS_j . Thus, one may see from these

interaction may affect crystal structure of doped

results that exchange interaction would stabilize config-

(Fe_1-xZn_x)₂Mo₃O₈ as well.

uration with Fe ions occupying equally tetrahedral and

octahedral positions, but concentrated in the same plane

¹⁾e-mail: streltsov@imp.uran.ru

(to maximize gain in magnetic energy due to J^abOT).

826

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2019

Ordering of Fe and Zn ions and magnetic properties of FeZnMo₃O₈

827

Next we relaxed the crystal structure of FeZnMo₃O₈

[3, 9, 10]. The most important question here is the dis-

for different Fe and Mo distributions in two possible

tribution of Fe and Zn at different positions (octahedral,

magnetic orders (FM and AFM). Results are summa-

tetrahedral) existing in these systems. This is very im-

rized in Table 1. First, one may see that the state with

portant for all the properties of corresponding systems.

all Fe ions occupying octahedral positions has the lowest

We demonstrated that there is very strong preference of

total energy. Moreover, the energy of any 50 : 50 config-

Zn to occupy the tetrahedral sites, so that for 50 % sub-

uration (50 % Fe is octahedral and 50 % Zn is in tetra-

stitution, in the title compound FeZnMo₃O₈, all tetra-

hedral positions) is equal to about half of the energy

hedral sites are occupied by nonmagnetic Zn, and mag-

difference between configurations, where all Fe ions are

netic Fe ions are all in octahedral positions. This, to-

in octahedral positions. This means that this is not mag-

gether with the ferromagnetic octahedral-octahedral ex-

netic energy, but lattice distortions (i.e., elastic energy),

change, which we calculated theoretically, naturally ex-

which decides which positions are occupied by Fe ions.

plains ferromagnetic ordering observed in FeZnMo₃O₈

Quite naturally, the energy scales of magnetic and elas-

experimentally. These results will be also very useful

tic interactions differ by about three orders of magni-

for interpreting spectroscopic data on FeZnMo₃O₈ [4].

tude.

Apparently the tendency of relative distribution of dif-

ferent ions in this class of materials, determined, as we

Table 1. Energies (per formula unit) of different distributions of

demonstrated above, mainly by the size of respective

Fe and Zn ions among octahedral (O1 and O2) and tetrahedral

(T1 and T2) positions, as obtained after optimization of the ionic

ions, might also work in other systems of this interest-

positions in the GGA + U (Generalized gradient approximation

ing class.

taking into account Coulomb correlations) calculations

The work was supported by Russian Science Foun-

Magnetic order

Energy, eV

dation via project 17-12-01207.

Zn Zn

Full text of the paper is published in JETP Letters

Zn Zn

AFM

0.0002

journal. DOI: 10.1134/S0021364019120026

1.2702

AFM

1.2698

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0.6405

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Preferable occupations of octahedral positions by Fe

4. H.-Y. Huang, A. Singh, A. Nag, K. Zhou, A. Wal-

and not by Zn ions is due to its larger ionic radius

ters, M. Garcia-Fernandez, J. Okamoto, A. Chainani,

(R^octa

= 0.78Å, R^octa

= 0.74Å and R^tetra

= 0.63Å,

Fe²⁺

Zn²⁺

Fe²⁺

Y.-M. Sheu, T. Kurumaji, Y. Tokura, C.-T. Chen, and

R^tetra

= 0.60Å [8]), so that it is natural for larger

Zn²⁺

D.-J. Huang, Book of Abstracts, APS March Meeting

ions to go in a larger polyhedron. Indeed, if we put

2019, C02.00004 (2019).

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∑_m

(φ_i - φ₀)²/(m - 1) (here m is the number of

i=1

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To summarise, we studied theoretically the very in-

8. R. D. Shannon, Acta Crystallogr. Sect. A 32, 751 (1976).

teresting system of the novel class M₂Mo₃O₈ (M = Mn,

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Fe, Co, Ni, Zn) with polar crystal structure, which shows

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diverse magnetic properties and very interesting mag-

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mixed materials of this class (Fe_1-xZn_x)₂Mo₃O₈, for

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which most experimental studies are done at present

Lett. 119, 077206 (2017).

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2019