Mechanochemical Synthesis and Magnetic Characterization of Nanosized Cubic Spinel FeCr2S4 Particles [original]

Mechanochemical Synthesis and Magnetic Characterization of

Nanosized Cubic Spinel FeCr2S4Particles

Anna-Lena Hansen, Reinhard K. Kremer,*Eva M. Heppke, Martin Lerch, and Wolfgang Bensch*

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ABSTRACT: Nanosized samples of the cubic thiospinel FeCr2S4were synthesized by

ball milling of FeS and Cr2S3precursors followed by a distinct temperature treatment

between 500 and 800 °C. Depending on the applied temperature, volume weighted mean

(Lvol) particle sizes of 56 nm (500 °C), 86 nm (600 °C), and 123 nm (800 °C) were

obtained. All samples show a transition into the ferrimagnetic state at a Curie

temperature TCof ∼167 K only slightly depending on the annealing temperature. Above

TC, ferromagnetic spin clusters survive and Curie−Weiss behavior is observed only at T

≫TC, with Tdepending on the heat treatments and the external magnetic ﬁeld applied.

Zero-ﬁeld-cooled and ﬁeld-cooled magnetic susceptibilities diverge signiﬁcantly below TC

in contrast to what is observed for conventionally solid-state-prepared polycrystalline

samples. In the low-temperature region, all samples show a transition into the orbital

ordered state at about 9 K, which is more pronounced for the samples heated to higher

temperatures. This observation is a clear indication that the cation disorder is very low

because a pronounced disorder would suppress this magnetic transition. The unusual magnetic properties of the samples at low

temperatures and diﬀerent external magnetic ﬁelds can be clearly related to diﬀerent factors like structural microstrain and

magnetocrystalline anisotropy.

■INTRODUCTION

Binary and ternary chromium chalcogenides exhibit a large

variety of chemical and physical properties explaining the

intense research of these materials. Examples for the diversity

of properties are a large linear negative thermal expansion,

the

tuneable thermoelectric properties,

2−5

a large magnetocaloric

eﬀect,

the photocatalytic properties in dye degradation,

the

tuning of magnetic properties by Li intercalation,

ferrimag-

netic properties in nanosheets,

the application as stable

electrode material in sodium-ion batteries,

or the generation

of nanoscale networks.

One of the most intensely

investigated ternary chromium chalcogenides is the iron

chromium thiospinel FeCr2S4, which crystallizes in the normal

cubic spinel structure with the general formula AB2X4(space

group: Fd3m, no. 227). The S2−anions are arranged in a close-

packed face-centered cubic (fcc) lattice, creating tetrahedral

(A) and octahedral (B) voids, which are partially occupied by

the Fe and Cr cations. The Fe2+ cations occupy 1/8 of the

tetrahedral voids and the Cr3+ cation 1/2 of the octahedral

positions. The d-orbitals of the Fe2+ cations are split into an

energetically lower edoublet and an upper t2triplet. The 3d6

electrons are distributed over the orbitals according to Hund’s

rule, yielding a high-spin conﬁguration with S= 2, and these

cations are Jahn−Teller active. The 3d3electrons of the Cr3+

cations occupy the t2g level with S= 3/2. The magnetic and

especially the magnetoelectric properties of FeCr2S4attracted

particular attention.

12−14

Three main exchange couplings aﬀect

the magnetic behavior of FeCr2S4: nearest-neighbor ferromag-

netic B−B (Cr−Cr) interactions, the more distant neighbor

antiferromagnetic B−B interactions, and the 120°A−B

superexchange interaction that is antiferromagnetic. By

neutron powder diﬀraction, FeCr2S4has been shown to

order ferrimagnetically below ∼180 K with Fe and Cr

moments aligned collinear antiparallel.

Already early on

unusual physical properties like a complex behavior of the Hall

resistivity,

anisotropic resistivity and magnetoresistance

eﬀects due to spin disorder were reported.

Mossbauer

spectroscopic investigations on polycrystalline FeCr2S4dem-

onstrated an unusual behavior of the electric ﬁeld gradient at

the Fe2+ site at about 10 K.

18,19

Further, low-temperature

Mossbauer spectroscopy studies indicated a static cooperative

Jahn−Teller (JT) distortion (c/a< 1) on the tetrahedral site,

stabilizing the 5Egground state of the Fe2+ cations.

20−22

Heat

capacity measurements at low temperatures exhibited a λ-like

anomaly around this temperature but the particular shape of

this anomaly depends on the stoichiometry of the sample.

23,24

Received: March 16, 2021

Accepted: April 20, 2021

Published: May 10, 2021

Article

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Colossal magnetoresistance (CMR) behavior was observed

with a magnitude comparable to that found in manganites.

However, adverse to the manganites, the CMR is not caused

by double exchange or a JT distortion.

26,27

It was proposed

that by increasing the temperature, long-range magnetic order

gradually breaks down by approaching TCaccompanied by the

formation of nanosized spin clusters, which survive well above

TC. In an external magnetic ﬁeld above TC, the rapidly

ﬂuctuating spin clusters coalesce and generate bulk-like

ferromagnetism, which leads to the lowering of electrical

resistivity. Evidence for superexchange interactions between

Fe2+ and Cr3+ cations in FeCr2S4was obtained using resonant

inelastic X-ray scattering (RIXS) investigations.

Below the Curie temperature TC, which varies between

177

and 167 K,

30−32

several unusual features were observed

in the temperature-dependent magnetization curves: A cusp-

like anomaly occurs at Tm∼60 K as well as a splitting of the

zfc−fc susceptibility data below this temperature.

30,33−35

The

divergence of the zfc−fc susceptibilities resembles a glassy

behavior, which is exceptional for a stoichiometric and ordered

system. Spin-glass-like states were also postulated to exist

below 60 K due to ﬂuctuating competing exchange interactions

in conjunction with high magnetocrystalline anisotropy for the

Fe2+ moments at the tetrahedral site being strongly

antiferromagnetically coupled with Cr3+ cations.

This

unusual magnetic behavior was attributed to changes in the

domain structure

and the appearance of noncubic magneto-

crystalline anisotropy.

The latter was proposed to be the

result of the structure transformation, generating pinning

centers for magnetic domain walls. But neutron scattering

investigations demonstrated that the magnetic structure is of

simple Neel type well down to 4 K with μ(Cr) = 2.9 μBand

μ(Fe) = 4.2 μB, giving a total magnetic moment μ= 1.6 μB(TC

= 180 K).

In other neutron diﬀraction studies, the values

1.92 μB/fu (fu = formula unit)

and 1.59 μB/fu were

determined.

A broadening of Bragg reﬂections in X-ray

powder diﬀraction patterns below TCwas attributed to

inhomogeneous lattice distortions.

Low-temperature high-

resolution transmission electron microscopy on oriented single

crystals of FeCr2S4showed a cubic to triclinic structural phase

transition within crystallographic domains and an overall

symmetry reduction from Fd3mto F43m.

The proposed

structural transformation at Tm≈60 K could be revealed with

ultrasonic measurements on single crystals.

An anomaly in

the magnetization versus ﬁeld curve was observed for μ0H=

5.5 T, which was attributed to the development of a new

magnetic phase, most probably from the incommensurate

noncollinear spin structure

to the commensurate collinear

spin structure.

Spin reorientation at 60 K was also reported

from ultrasound studies on dense polycrystalline samples.

magnetic susceptibility measurements performed on oriented

single crystals showed a pronounced frequency dependence

between 90 and 20 K for both the real and imaginary parts of

the ac susceptibility. The observations made for the ﬁeld and

temperature dependence were explained by domain wall

pinning. Below 60 K, changes in the domain structure and

appearance of pinning centers caused by structural changes

were suggested to lead to spin-glass-like magnetic anomalies

below 60 K.

A second anomaly in the magnetic susceptibility data was

observed at around 9 K and attributed to orbital order-

ing.

18,19,38,45−47

It was argued that this anomaly occurs due to a

unit cell volume contraction and that a cooperative JT eﬀect

and spin−orbit coupling of the Fe2+ ion compete, leading to

spin reorientation at about 60 K, which gives rise to the onset

of short-range orbital ordering at this temperature.

It is

noteworthy that the anomaly at T∼9 K can be suppressed in

polycrystalline specimens by applying large magnetic ﬁelds.

For single crystals, experimental evidence was presented that

an orbital glass phase is formed at TOO ∼9K.

32,33,35,42,43,47

The Curie temperature and the anomaly at 9 K are only weakly

shifted at high external ﬁelds up to 9 T. At lower magnetic

ﬁelds, the magnetic moments of Fe2+ and Cr3+ are lower than

the spin-only values, and only for μ0Hext = 5.5 T, the expected

spin-only values are reached. The dielectric permeability shows

a linear correlation with the magnetization of the sample,

which is consistent with the existence of ferroelectric

polarization and a multiferroic ground state below 10 K.

12,13

The critical exponents, β,γ, and δ, for the paramagnetic to

ferrimagnetic phase transition were determined using diﬀerent

approaches. βand γare found close to the mean ﬁeld theory

values, whereas δis higher than expected, which has been

attributed to incomplete ferrimagnetic transition and the

presence of short-range ordering above TC.

A perpetual problem with FeCr2S4samples, crystals and

polycrystalline material, is that often the physical properties

depend essentially on the detailed synthesis conditions, causing

hardly controllable minute compositional mismatch and/or

positional disorder of the cations. Consequently, samples

synthesized by conventional high-temperature techniques

often showed diﬀerences in the magnetization and zfc−fc

curves compared to, e.g., a material obtained by the ﬁeld-

activated sintering technique (FAST). However, for the FAST

sample, the magnetic anomaly at TOO ∼9 K was found absent

and the anomaly normally occurring at Tm∼60 K is shifted to

a lower temperature. In addition, the transition from

paramagnetic to the ferrimagnetic state is less sharp for the

FAST sample. All observations have been attributed to residual

structural disorder in the samples prepared with FAST.

summarize, the magnetic characteristics of single-crystalline

and polycrystalline FeCr2S4samples are as follows: (i) a

transition from paramagnetic to the ferrimagnetic state occurs

at TC∼170 K; (ii) below the Curie temperature, structural

changes or lattice distortions as well as spin reorientation set

in, leading to magnetic anomalies at about 60 K; and (iii)

orbital ordering is observed at TOO ≈9K.

In the past, all investigations were performed on well-

crystallized polycrystalline samples of FeCr2S4or on single

crystals, which were prepared by chemical vapor deposition.

The only exception is the study of FAST samples reported in

ref 50, which showed a diﬀerent magnetic behavior compared

to single crystals or microcrystalline samples. A systematic

study of the changes of the magnetic behavior as a function of

sizes of coherently scattering domains was not performed until

now on FeCr2S4. For the preparation of nanoparticles, several

synthetic approaches were well established. Very often solvent-

mediated methods are applied, which have the disadvantage

that the surfaces of the crystallites are covered by capping

molecules. To avoid such impurities, mechanochemistry is a

promising approach. While this synthetic approach is applied

in many areas of inorganic and organic chemistry, it has rarely

been utilized for the preparation of ternary sulﬁdes. Hence, we

decided using the mechanochemical technique for the ﬁrst

time for the generation of nanosized FeCr2S4materials. The

main aim of the present study is to get better insights into the

variation of the magnetic properties in the nanoregime and

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thereforeweintentionallysynthesized nanosized FeCr2S4

polycrystalline samples with particle size distributions ranging

between 10 and 50 nm by reacting ball-milled mixtures of FeS

and Cr2S3at temperatures between 500 and 800 °C. With

increasing annealing temperature, we ﬁnd a continuous

increase of the particle size, a moderate increase of saturation

magnetic moment, and a variation of magnetocrystalline

anisotropy. We attribute these observations to the variation

of the defect structure with the annealing temperature

modifying the approach to magnetic saturation.

■RESULTS AND DISCUSSION

Particle Size. The XRPD patterns of the three samples and

the results of the Rietveld reﬁnements assuming the space

group Fd3m(no. 227) (Fe: 8a; Cr: 16d; S: 32e, 0.383) are

displayed in Figure 1. All samples are phase pure and the cubic

lattice parameters were reﬁned to 9.9832(1) Å (500 °C),

9.9922(1) Å (600 °C), and 9.9923(1) Å (800 °C). The cubic

lattice parameter aof the 500 °C sample is signiﬁcantly smaller

than values reported in the literature. There data scattering in a

very narrow band around 10 Å

13,50−55

can be found, while in

ref 33, the authors obtained a= 9.983 Å for one sample,

mentioning that the lattice parameter depends on the

stoichiometry, but unfortunately the exact composition was

not reported. Even for a sample with crystallite sizes between

40 and 45 nm, awas determined to 10.008(1) Å.

We note

that the cubic lattice parameter ais signiﬁcantly reduced at low

temperatures, from 9.9894(3) Å at 180 K to 9.9808(3) Å at 5

In a further study, a decrease from 9.9813(3) Å (175 K)

to 9.9756(3) Å (10 K) was reported.

Increasing the annealing temperature of our samples has two

eﬀects revealed by the XRPD patterns:

1.Thebroadbulgebelow∼30°in 2θdecreases

signiﬁcantly in intensity and almost vanishes for the

800 °C sample, which is assigned to a reduction of

incoherently scattering defects.

2. As demonstrated for the 311 Bragg reﬂections (the right

side of Figure 1), increasing the annealing temperature

leads to a linewidth reduction, indicating an increase in

the sizes of coherently scattering domains.

This eﬀect is also clearly seen in the parameters of ﬁtted log-

normal distribution of the coherently scattering domains

(Figure 2). The mean particle size value μand the variance σ

vary continuously with the annealing temperature. Whereas μ

increases by more than a factor of 2, σdecreases as shown in

Figure 3. The volume weighted mean (Lvol) increases from 56

nm (500 °C) to 86 nm (600 °C) ending at 123 nm for the

sample heated at 800 °C.

The strain values ε0obtained from the Rietveld reﬁnements

decrease with the annealing temperature from 7.4 ×10−4(500

Figure 1. Results of the Rietveld reﬁnements of the powder patterns of the three samples. Bragg indices of some prominent reﬂections are given.

Black: collected data; red: reﬁned data; and blue: diﬀerence curves. The vertical bars indicate the positions of Bragg reﬂections used to calculate the

patterns. The insets show an enlarged view of the 311 reﬂection.

Figure 2. Size distribution of the coherently scattering domains

analyzed from the XRPD patterns according to eq 3 as a function of

annealing temperature, as indicated. The shaded areas indicate log-

normal distributions with parameters given in the inset.

Figure 3. Mean value μand variance σof the log-normal distributions

(eq 3) of the coherently scattering domains as a function of annealing

temperature.

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°C) to 1.8 ×10−4(600 °C) to ﬁnally reach 9 ×10−5for the

samples annealed at 800 °C. The smaller value for the lattice

parameter of the sample prepared at 500 °C may be caused by

thelargernumberofnanocrystallitescomparedtothe

materials heated at higher temperatures. In the literature,

mainly a lattice expansion was reported for oxides even for

particles larger than 100 nm,

while a lattice contraction was

observed for metallic nanoparticles.

However, there are also

observations that the lattice contracts with decreasing particle

size, e.g., for α-Fe2O3.

This phenomenon was explained by an

increased covalency of the Fe−O bond on the nanoscale.

Because the Cr−S and Fe−S bonds are much more covalent

than in oxides, we assume that the unit cell contraction is

based on a similar phenomenon.

Magnetic Properties. Figure 4 displays the inverse

magnetic susceptibilities collected at 1, 2, and 4 T. At

suﬃciently high temperatures and signiﬁcantly above the Curie

temperature, the inverse susceptibilities converge to Curie−

Weiss behavior with the same slope for all three samples

similar to that observed by Gibart et al.

On approaching the

ferrimagnetic Curie temperature, the susceptibilities become

ﬁeld-dependent with the largest ﬁeld splitting seen for the 800

°C sample. We attribute this splitting to ferrimagnetic spin

clusters, which can be saturated with increasing ﬁeld, leading to

an increase of the inverse susceptibilities with larger measuring

ﬁelds.

For all samples, a transition to the ferrimagnetic state is

determined at TC∼167 K, in agreement with the literature

where values between 177

and 167 K were reported.

30−32

Bifurcation of the zfc−fc data occurs at 120, 110, and 100 K

(Figure 5) for the samples prepared at 500, 600, and 800 °C,

respectively. Below the bifurcation, the zfc curves continuously

decrease and settle into a plateau below ∼25 K. A clear step-

like drop of the magnetic susceptibility occurs at ∼9 K for the

800 and 600 °C samples, which is caused by the long-range

orbital ordering as discussed in the literature. This anomaly is

less well developed for the sample prepared at 500 °C. The

decrease of the zfc susceptibility with decreasing temperature

can be attributed to microscopic modiﬁcations in the long-

range ordered magnetic structure and/or diﬀerent magneto-

crystalline anisotropy due to varying amounts of structural

defects, aﬀecting the temperature dependence of the domain

dynamics. Notable is the diﬀerent behavior of the samples.

Whereas for the 800 °C sample, “melting”of the domain

structure on approaching from low temperatures starts at about

50 K, a sizeable increase of the zfc susceptibility of the 500 °C

sample begins only at about 75 K, indicating more eﬀective

domain pinning. Below the bifurcation and before settling into

saturation, the fc susceptibilities pass through shallow maxima,

most pronounced for the 800 °C sample.

Figure 6 displays magnetization curves collected at 4 K in

external ﬁelds up to 9 T. The saturated moment increases with

the preparation temperature from 1.76 μB, 1.80 μB, to 1.83 μB

at 9 T for the 500, 600, and 800 °C samples, respectively. For

the collinear ferrimagnetic structure, a saturated magnetic

moment of 1.6 μBwas reported from high-magnetic-ﬁeld

experiments.

DFT-based calculations predicted saturation

values of 2.0 μB

and 1.92 μB.

For polycrystalline

compounds, the data reported in the literature are, e.g., 1.55

μBgiven in ref 60 or ∼1.6 μBreported in refs 12,37. For the

Figure 4. Inverse molar magnetic susceptibilities of the three FeCr2S4

samples prepared at diﬀerent temperatures: (a) 500 °C, (b) 600 °C,

and (c) 800 °C. Blue, red, and black colored traces refer to data

collected at 1, 2, and 4 T, respectively. The dashed lines indicate

Curie−Weiss laws approaching the high-temperature behavior of the

data collected at 4 T.

Figure 5. zfc−fc magnetic susceptibilities measured at 0.1 T. The

arrows mark the transition into the orbital ordered state at ∼9K.

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samples investigated here, the values are noticeably larger but

do not fully reach the theoretically predicted values. The

increase of the magnetic moment with the annealing

temperature may be explained by reduced surface spin canting,

a smaller magnetic dead-layer and/or a reduced number of

defects on the Cr and Fe sublattices. One may speculate that

the larger values obtained here are caused by an imperfect

collinear magnetic structure, which may be due to microstrain

that is signiﬁcantly reduced with increasing annealing temper-

ature (see above). We note that the saturation value of the

sample annealed at 800 °C matches that measured on a single

crystal for the <111> direction (1.84 μB), which is the hard

magnetic axis.

Also apparent from the magnetization curves is the

diﬀerence in the behavior at small ﬁelds where domain wall

motions are the prevailing process of magnetization. For the

800 °C sample, magnetization grows rapidly, whereas for the

500 °C sample, after a pedestal at low ﬁelds, the magnetization

increases with about the same slope as for the other samples.

The magnetization behavior reﬂecting domain wall motion at

low ﬁelds correlates with the magnitude of the microstrain

derived from the XRPD measurements. The diﬀerent magnet-

ization versus ﬁeld behavior at low temperatures can be

attributed to varying crystalline anisotropy energies for the

diﬀerent samples.

The work W(M) done when magnetizing to a certain ﬁeld

μ0His given by the area between the M−Hcurve and the

magnetization axis. It can be obtained by integration according

WM HM M() ( )d

∫

=′

′

(1)

For cubic crystals, the anisotropy energy is usually described

by the three anisotropy coeﬃcients Ki(i= 0, 1, 2), which

weighs the products of even powers of the directional cosines

measured with respect to the distinguished magnetization axes

system. For a polycrystalline sample with a random orientation

of the crystallites with respect to the external ﬁeld, the

anisotropy work Wcan only be taken as a qualitative measure

of the anisotropy energy. Integration of the area of the 4 K

magnetization curves, as indicated by the shaded areas in

Figure 7, indicates that the anisotropy energy (see the inset of

Figure 7) decreases with increasing preparation temperature by

about 15%, paralleling the decrease of the microstrain for

higher preparation temperatures. In addition, higher prepara-

tion temperatures appear to reduce imperfections in the

samples and the crystal anisotropy.

The magnetization of the samples was recorded at diﬀerent

temperatures up to T= 175 K somewhat higher than TC

(Figure 8). As expected, the magnetic moment obtained at the

highest magnetic ﬁeld decreases with increasing temperature.

But even at 175 K, the magnetization is not linear as expected

for a paramagnetic material, and a magnetic moment of ≈0.75

μBis observed for all samples, which is again an indication for

the presence of spin clusters, which survived at T>TC.

At suﬃciently high ﬁelds (see Figure 8) in the regime where

magnetization processes by domain rotation (μ0H≳2T)

prevail, it has been found that the ﬁeld dependence of the

magnetization provides information about the type of defects

in the sample (“law of approach”).

61−65

Generally, the

approach to saturation is expanded in a polynomial of powers

of the inverse magnetic ﬁeld according to

HM a Ha H

() (1 /( ) /( ) )

sat 1 020

μμ

= − − − ···

+(2)

The coeﬃcient a1is interpreted to describe inclusions and/

or microstress and a2is due to crystal anisotropy. At

temperatures well below the Curie temperature, the term

a0μ0H, which represents the ﬁeld-induced increase in the

spontaneous magnetization of the domains or forced magnet-

ization, is usually very small and neglected. A plot of the

magnetization of the three FeCr2S4samples as a function of

inverse external ﬁeld (Figure 8), 1/μ0H, shows that the

magnetizations at 4 K for very high ﬁelds follow very well

straight lines with no signiﬁcant slope change. Considering the

ﬁeld range from 0.5 to 9 T and ﬁtting the experimental data to

eq 2 reveals that the deviations toward lower ﬁelds can be

favorably taken care of by additionally considering the term ∝

1/(μ0H)2, as displayed in Figure 9.

Figure 6. Magnetization at 4 K of the three samples prepared at 500,

600, and 800 °C, as indicated. The inset displays an enlarged view of

the low-ﬁeld regime.

Figure 7. Magnetic moment per fu as a function of external magnetic

ﬁeld at 4 K. The shaded areas highlight the integral ∫μ0HdM′. The

inset displays the integral ∫0

Msatμ0H(M′)dM′(black dots) correspond-

ing to the color shaded areas in the main frame and the microstrain

(red dots, see the text above) as a function of preparation

temperatures of the three samples prepared at the temperatures, as

indicated. The dashed and dotted lines in the inset are guides to the

eye.

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