Journal of Magnetism and Magnetic Materials 322 (2010) 3595–3600

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Journal of Magnetism and Magnetic Materials

0304-88

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/jmmm

Magnetic frustration effect in polycrystalline Ga2�xFexO3

N. Wang a, F.S. Wen a, L. Li a, Y.F. Lu a, S.C. Liu a, Y.F. Lu b, Z.Y. Liu a,n, B. Xu a, J.L. He a, D.L. Yu a, Y.J. Tian a

a State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, Chinab Northwest Institute for Nonferrous Metal Research, Xi’an 710016, China

a r t i c l e i n f o

Article history:

Received 10 April 2010

Received in revised form

10 July 2010Available online 23 July 2010

Keywords:

Frustration

Magnetic susceptibility

Multiferroic

Gallium compound

53/$ - see front matter & 2010 Elsevier B.V. A

016/j.jmmm.2010.07.018

esponding author. Tel.: +86 335 8074631; fa

ail address: liuzy0319@yahoo.com (Z.Y. Liu).

a b s t r a c t

In Ga2�xFexO3 with the Pc21n orthorhombic structure, owing to the site disorder of Fe ions on the four

nonequivalent sites of Fe1, Fe2, Ga1, and Ga2, there exists a significant amount of non-effective Fe ions

with no contribution to the ferrimagnetic ordering. These non-effective Fe ions have been found to

induce strong frequency dependent suppression of the peak height in the ac susceptibility,

demonstrating the frustration effect in the ferrimagnetic ordering background.

& 2010 Elsevier B.V. All rights reserved.

1. Introduction

Since the first synthesis of Ga2�xFexO3 (GFxO) (0.7rxr1.4) byRemeika [1] in 1959, GFxO has been attracting great interest dueto many interesting properties such as the piezoelectric, magneto-optic, and large magnetoelectric ones [1,2]. It has an orthorhom-bic crystal structure with the space group of Pc21n [3]. Fournonequivalent cation sites exist in GFxO, which are categorizedinto Fe1, Fe2, Ga1, and Ga2 [4,5]. The Fe1, Fe2, and Ga2 sites aresurrounded by distorted oxygen octahedra with the noncentro-symmetric structure, which is considered to be origin of thespontaneous polarization along the b axis [5].The Ga1 site islocated inside a nearly regular tetrahedral formed by four nearest-neighboring oxygens. The distribution of Fe ions are disordered onthe four cation sites. In addition to the Fe1 and Fe2 sites, the Ga1and Ga2 sites are also partially occupied by Fe ions. In comparisonto the Ga2 site, the Ga1 site is less favorable to the Fe ion becauseof the much higher energy [6]. For each cation on the sites of Fe1,Fe2, and Ga2, it has many paths to form the bonds of type M–O–Mwith neighboring cations via oxygen. Among the bonds, only one hasthe bond angle close to 1801, and the others have the bond angledeviating far away from 1801. For the bonds related to the Ga1 site,all of them are much less than 1801 [7]. Generally, the larger bondangle results in the stronger antiferromagnetic superexchangecoupling between the magnetic ions. The first largest bond angleof 1661 is related to the bond of Fe1–O–Fe2 or Fe2–O–Fe1, while thesecond largest bond angle of 1641 is found for the bond of Ga2–O–Fe1 [7]. Thus, the Fe3+ moments on the Fe2 and Ga2 sites alignantiparallel to those on the Fe1 sites. Though there has been great

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controversy [2,8] about the magnetic configuration in GFxO, theferrimagnetic ordering has been accepted and supported byMossbauer and neutron measurements [7,8]. The net spontaneousmagnetization comes from the site disorder of Fe ions. It has beenrecently suggested to originate from the Fe ions on the Ga2 sites [7].

Due to the bonds with the small bond angle, however, thesuperexchange coupling between neighboring Fe ions can bequite complicated. Some small-angle bonds correspond to anti-ferromagnetic coupling, while other small-angle bonds cancorrespond to ferromagnetic coupling [6]. Because of the randomoccupation of Fe ions on the sites of Fe1, Fe2, and Ga2, thereshould be some probability for each Fe ion to form the Fe–O–Ga orGa–O–Fe bond with the bond angle close to 1801. In this case, thestrongest antiferromagnetic superexchange coupling does notexist to constrain the Fe moment orientation. Hence, for these Feions without the strongest AFM superexchange coupling acting onthem, their directions are hard to be determined. Till date, noreport exists to show their magnetic behavior.

In this work, we have prepared a series of polycrystalline GFxOcompounds with 0.8rxr1.3 using the conventional solid statereaction. By varying the Fe content x, we are able to adjust thenumber of Fe ions with absence of the strongest antiferromag-netic superexchange coupling to restrict their moment directions.The magnetic behavior of these Fe ions have been investigated viathe measurements of dc magnetization and ac susceptibility,frustration effect has been observed due to their existence in theferrimagnetic ordering background.

2. Sample preparation and experimental measurements

The conventional solid state reaction was used to synthesizethe polycrystalline Ga2�xFexO3 samples with 0.8rxr1.3. Mixed

N. Wang et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3595–36003596

powders of Ga2O3 (99.99%) and Fe2O3 (99.99%) with molar ratiowere used as the starting materials. The synthesis was carried outin air at 1350 1C for 10 h, and after sintering the temperature wasslowly lowered to room temperature. The crystalline structures ofthe synthesized GFxO compounds were characterized by thepowder X-ray diffraction (XRD) measurements using a Rigakudiffractometer with Cu Ka radiation. The y�2y scanning wasperformed with a step size of 0.021 from 101 to 801. Rietveldrefinements were performed on the powder XRD patterns usingthe Fullprof program to determine the detailed information of thecrystalline structure. All the magnetization measurements weredone using a vibrating sample magnetometer (VSM) attachedonto a physical property measurement system (Quantum Design,PPMS-9). The field cooling (FC) magnetization (M) was measuredduring cooling down in a field of 150 Oe, while the zero fieldcooling (ZFC) magnetization was measured in 150 Oe duringwarming up after the cooling down in zero field. The hysteresisloops at 5 K were obtained after cooling down in zero field. In themeasurements of ac susceptibility, the sample was first cooleddown to 4 K, and then its ac susceptibility was collected in a dcfield of 150 Oe and an ac field with the amplitude of 5 Oe and aseries of frequencies from 100 Hz to 10 kHz.

Fig. 1. (Color online) (a) The measured (J) and calculated (solid line) powder XRD

patterns of GF0.8O. Below the XRD patterns is the difference between the measured

and calculated profiles. The vertical bars mark all possible Bragg reflections.

(b) The fractions kM of Fe ions on the four nonequivalent sites of M¼Fe1, Fe2, Ga1,

Ga2, which have been determined from the Rietveld analysis of the powder XRD

patterns. The solid lines are linear simulations to the experimental data.

3. Results and discussion

All the six samples of GFxO with 0.8rxr1.3 have beencharacterized by the powder XRD measurements and Rietveldrefinements. Fig. 1(a) gives a typical experimental XRD patternwith the refined one for the sample GF0.8O. All the observedpeaks can be indexed by reflections of the Pc21n orthorhombicstructure of GFxO, and no impurity phase was found. Thedetermined lattice parameters of a, b, and c are found to displaya monotonic increase with the Fe content x. Fig. 1(b) shows the Fepopulations on the four sites of Fe1, Fe2, Ga1, and Ga2, which aredetermined from the Rietveld analysis of the powder XRDpatterns. These values are comparable to those determined fromthe previous X-ray and neutron diffraction measurements [7].The predominant occupation of Fe ions occurs on the sites of Fe1,Fe2, and Ga2, and the occupation of Fe on Ga1 site is much lessfavorable because of the higher energy [6]. Just as proposed byLevine et al. [9], the fractions of Fe ions on the four nonequivalentsites have a linear dependence on the Fe content x, which can beexpressed as

kFe1 ¼ 0:41þ0:37x ð1Þ

kFe2 ¼ 0:10þ0:61x ð2Þ

kGa1 ¼�0:02þ0:17x ð3Þ

kGa2 ¼�0:49þ0:90x ð4Þ

Summation of Eqs. (1)–(4) gives kFe1þkFe2þkGa1þkGa2 ¼

2:05x� 2x. It satisfies the requirement that, for any givencomposition GFxO, the fractions of Fe ions on the four none-quivalent sites must be equal to 2x in total. Till date, GFxO can beonly grown for 0.7rxr2 [1,10–12]. From Eqs. (1)–(4), it can bedetermined that both kGa1 and kGa2 can be neglected as zero forxr0.6, while both kFe1 and kFe2 can be considered to be equal toone for xZ1.6, being consistent with the previous X-ray result [7].

The well-known ferrimagnetism of GFxO results mainly fromthe difference in the fractions of Fe ions on the Fe1, Fe2, and Ga2sites, and the Curie temperature of Tc has a strong dependence onthe Fe content x [1,7,9]. Fig. 2(a) and (b) displays the FC and ZFCmagnetization (M) versus temperature (T) curves for the sixpolycrystalline GFxO samples (0.8rxr1.3). In all the M–T curves,a sharp transition is observed at the Curie temperature of Tc, being

dependent on the Fe content x. As shown in Fig. 2(c), thedetermined Curie temperature is consistent with that obtainedfrom the GFxO single crystals [7,13], displaying an almost linearincrease with the increase of Fe content x. These observationshave confirmed our good control over x.

Below the Curie temperature of Tc, a bifurcation occurs in theFC and ZFC curves at a specific temperature of Tirr, being indicativeof the irreversibility below Tirr. In the ZFC curve of GF0.8O, a cusp isobserved below Tirr. With increase in the Fe content of x, it can beseen that the cusp shifts towards the higher temperature andbecomes broader, exhibiting strong dependence on the Fe contentx. The observed bifurcation and cusp in the FC and ZFC curves arecommon features in the frustrated magnetic systems such as spinglasses, cluster glasses [14,15], though these results are notsufficient to confirm the frustration effects in the polycrystallineGFxO samples.

The dependence of the high field magnetization M at 80 kOe onthe Fe content x has been obtained from the hysteresis loopsmeasured at 5 K. The high field magnetization is shown in Fig. 3,

Fig. 2. (Color online) (a, b) The ZFC and FC M–T curves for the six polycrystalline

samples of Ga2�xFexO3 and (c) the determined Curie temperature of Tc as a

function of the Fe content x.

Fig. 3. The high field magnetization M as a function of the Fe content x. The solid

line is the calculated M.

N. Wang et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3595–3600 3597

which is well consistent in magnitude with the corresponding oneobtained in the GFxO single crystal [7,9], displaying a monotonicrise with the increase of Fe content x. Levine et al. [9] proposed anexplanation about the dependence of the net spontaneousmagnetization on x in GFxO in terms of a statistical model,

which was first used by Gilleo [16] to deal with the magneticproperties in alloy systems. In the explanation, those Fe ions withnone or at most one superexchange linkages to neighboringFe ions were defined as the non-effective Fe ions, which wereconsidered to have no contribution to the net spontaneousmagnetization. The probability E of the non-effective Fe ionswere determined to be E¼0.44�0.314x on the bases of followingassumptions: (i) the fractions of Fe ions on the four nonequivalentsites of Fe1, Fe2, Ga1, and Ga2 were considered to have a lineardependence on x; (ii) kGa1 was always neglected to be zero,and kGa2 was considered as zero for xr0.7; (iii) the Fe1 and Fe2sites were assumed to be equally occupied, i.e., kFe1¼kFe2, andkFe1¼kFe2¼1 for xZ1.4. The net spontaneous magnetization wasthen calculated using the expression s¼ 5ð1�EÞkGa2=2x. However,some of the assumptions about the fractions of Fe ions on the foursites are not consistent with the X-ray and neutron results. TheFe1 and Fe2 sites are not equally occupied, i.e., kFe1akFe2,especially at low Fe content of x [7]. According to Eqs. (1)–(4),the Fe1 and Fe2 sites could be completely occupied by Fe ions ifxZ1.6 instead of 1.4, while the Ga1 and Ga2 sites could becompletely occupied by Ga ions if xr0.6 instead of 0.7. Recently,Ohkoshi et al. [11] have proposed an explanation of the x-dependence of the Curie temperature of GFxO in terms of themolecular field theory. For the higher Fe content of xZ1.6, thesites of Fe1 and Fe2 are completely occupied by the Fe ions. Agood agreement has been obtained to the experimental results.However, for xo1.6, the Fe ions begin to enter into the site of Ga2,and the calculated Curie temperature is obviously higher than theexperimental one. This might indicate that some of the Fe ionsmake no contribution to the ferrimagnetic ordering in GFxO withxo1.6.

In the present work, we use the considerations of Levine et al.[9] in the explanations of the Fe-content dependences of M and TC,but the fractions of Fe ions on the four nonequivalent sites aretaken to be the experimental ones. The maximum probability E ofthe non-effective Fe ion is considered to occur for xr0.6, and itsvalue has been simply estimated by using the average of kFe1 andkFe2 at x¼0.6 as k and inserting it into Eq. (8) of Ref. [9](E¼n(1�k)n�1

�(n�1)(1�k)n with n¼3). By accepting theassumption of Levine et al. that E decreases linearly to zero when

Fig. 4. (Color online) The measured ac susceptibilties for GF0.8O. The dc field is

150 Oe. The ac field has an amplitude of 5 Oe, and its frequency is changed from

100 Hz to 10 kHz. (a) The in-phase term of w0 , (b) the out-of-phase term of w00 . The

inset in (b) shows frequency-dependences of the normalized peak heights in the w0(K)and w00 (’) curves.

N. Wang et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3595–36003598

x reaches 1.6, the probability E should be represented by

E¼ 0:80�0:50x ð5Þ

Using Eq. (5), the high field magnetization s in Bohrmagnetron per Fe ion can be calculated by

s¼ 5

2xð1�EÞDk ð6Þ

In Eq. (6), if either (kFe2+kGa2)�(kFe1+kGa1) or (kFe2+kGa2)�kFe1

were taken as Dk, no good fit would be achieved to theexperimental data. As shown in Fig. 3, it has been found thatthe good fit of Eq. (6) to the experimental data can only beobtained if kGa2 is taken as Dk, implying that the net spontaneousmagnetization in GFxO originate mainly from the fraction of Feions on the Ga2 sites.

By considering the difference between kFe1 and kFe2, Eq. (14)in Ref. [9] for calculation of the curie temperature Tc should bere-expressed by

n¼ ð1�EÞð3kFe1kFe2þkFe1kGa2þkFe2kGa2Þ

xð7Þ

where n represents the number of superexchange linkages per Feion per formula unit. The Curie temperature Tc of iron oxidesdepends on n. For a large number of compounds with Fe3 + beingthe only magnetic ion, the value of Tc/n falls in the range from 106to 132 K, and the exact value depends on the superexchange angleand the distance between Fe3 + ions [9]. In the present calculationof Tc for GFxO, Tc/n has been taken to be 132 K, and Fig. 2(c) showsthat the calculated Tc has a reasonable agreement with theexperimentally determined one.

In GFxO, the ferrimagnetism does not come from all the Fe ions.Some amount of non-effective Fe ions exist, making no contribu-tion to the ferrimagnetism. These non-effective Fe ions exist in adisordering way among those Fe ions with the ferrimagneticordering via the antiferromagnetic superexchange coupling. Theyshould display different magnetic behavior, which unfortunatelyis still unclear so far.

In order to understand the magnetic behavior of the non-effective Fe ions in the ferrimagnetic ordering background, themeasurements of ac susceptibilities at a series of frequencies havebeen carried out on three GFxO samples with x¼0.8, 1.0, and 1.2.For GF0.8O as shown in Fig. 4, both the in-phase (w0) and out-of-phase (w00) terms of the ac susceptibility display a peak close to thetemperature of Tirr¼120 K, at which the FC and ZFC curvesbifurcate. The peak does not change in position with the increaseof frequency, but its height exhibits a strong frequencydependence as shown in Fig. 4(b). The peaks of w0 and w00 droplinearly in height with ln(f), and the drop for w00 is much faster. Atlow temperature after the peak, the w0 curve becomes rather flat,while the w00 curve shows complicated features. At high frequencyof 10 kHz, even w00 becomes negative. This feature is similar towhat was observed in the w00 curve of BiFeO3 single crystal [17],and its origin is not clear now. For GF1.0O, the measured w0 and w00curves in Fig. 5 exhibit a peak at temperature around Tirr¼200 K.Similar to GF0.8O, the peak heights in the w0 and w00 curves arestrongly suppressed at high frequency as shown in Fig. 5(b).However, the increase in Fe content x leads to more features in thew0 and w00 curves. In the w0 curve as shown in Fig. 5(a), a secondbroad peak appears in addition to the peak 1, though it is not veryobvious. In the w00 curve, the second broad peak becomes obviousas shown in Fig. 5(b), and its height is also strongly suppressed athigh frequency. When the temperature drops below 50 K, thethird weak peak is formed at high frequency. With the decrease offrequency, the weak peak becomes broader and its positionslightly shifts towards low temperature, showing the spin-glassbehavior. Similar to GF0.8O and GF1.0O, in the w0 and w00 curves ofGF1.2O as shown in Fig. 6, the first sharp peak appears at

temperature close to Tirr¼290 K, and the peak height is stronglysuppressed at high frequency. For x¼1.2, the second broad peakbecomes much more obvious in both w0 and w00 curves, exhibitingstrong suppression of height at high frequency as shown inFig. 6(a). In comparison to the first sharp peak, the second broadpeak becomes comparable in height in the w0 curve, while in thew00 curve, it is much enhanced in height.

The observed frequency dependences in the w0 and w00 curvesare similar to what have been observed not only in theconventional spin-glass systems such as Rb2Cu0.782Co0.218F4 [18]but also in the magnetically frustrated systems of LaMnO3 +d [19],Pr0.63Sr0.37MnO3, and Nd0.7Sr0.3MnO3 [20]. In the systems ofLaMnO3 +d [19], Pr0.63Sr0.37MnO3 and Nd0.7Sr0.3MnO3 [20], theferromagnetic and antiferromagnetic phases are considered tocoexist in the microscopic level. The local competition betweenthe two phases gives rise to the frustration effects similar to thosein conventional spin-glass systems, which are represented by theobserved frequency-dependent suppression of the peak height inthe w0 and w00 curves [19,20].

In GFxO, among the bonds related to the site of either Fe1or Fe2, only one bond has a bond angle of 1661 close to 1801(the largest one), and the others have the bond angle muchsmaller than 1801, which is either around 1201 or between 901

Fig. 5. (Color online) The measured ac susceptibilties for GF1.0O. The dc field is

150 Oe. The ac field has an amplitude of 5 Oe, and its frequency is changed from

100 Hz to 10 kHz. (a) The in-phase term of w0; (b) The out-of-phase term of w00 . The

inset in (b) shows frequency-dependences of the normalized peak heights in the w0and w00 curves (’—the sharp peak of w0; m—the sharp peak of w00; .—the broad

peak of w00).

Fig. 6. (Color online) The measured ac susceptibilties for GF1.2O. The dc field is

150 Oe. The ac field has an amplitude of 5 Oe, and its frequency is changed from

100 Hz to 10 kHz. (a) The in-phase term of w0 and (b) the out-of-phase term of w00 .The inset in (a) shows frequency-dependences of the normalized peak heights in

the w0 and w00 curves (’,K—The sharp and broad peaks of w0 , respectively;

m,.—the sharp and broad peaks of w00 , respectively).

N. Wang et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3595–3600 3599

and 1201. The largest bond angle of 1661 results in the strongestantiferromagnetic superexchange coupling between the neigh-boring Fe ions on Fe1 and Fe2 sites, giving rise to the observedferrimagnetic ordering [7]. Similarly, among the bonds related tothe Ga2 site, only one bond has a bond angle of 1641 close to 1801(the second largest one). The corresponding strong antiferromag-netic superexchange coupling leads to the antiparallel alignmentof the Fe3 + moment on the Ga2 site to that on the Fe1 site. The netspontaneous magnetization in GFxO is found to be mainly fromthe Fe ions on the Ga2 sites [9]. All the bonds related to the Ga1site have a bond angle of around 1201, much less than 1801, andthe Fe ions on the Ga1 sites are suggested to have less effect onthe ferrimagnetic ordering [7]. Owing to the site disorder of Feions, however, a significant amount of non-effective Fe ionsshould exist in the ferrimagnetic ordering background, and theyare considered to make no contribution to the ferrimagnetism. Incontrast to the Fe ions with the ferrimagnetic ordering, the non-effective Fe ions should exhibit different magnetic behavior. Atlow Fe content of x¼0.8, the non-effective Fe ions are mainlylocated at the sites of Fe1 and Fe2. Since the ferrimagnetism inGFxO is suggested to result from the occupations of Fe ions on theFe1 and Fe2 sites, the observed frequency suppression of the peak

height close to the Curie temperature could be attributed to thenon-effective Fe ions on the Fe1 and Fe2 sites. It is a demonstra-tion of the frustration behavior of the non-effective Fe ions. Withthe increase in the Fe content of x, more Ga2 sites are substitutedby the Fe ions. Thus, in addition to the non-effective Fe ions on theFe1 and Fe2 sites, a significant amount of non-effective Fe ionsshould also appear on the Ga2 sites. The non-effective Fe ions onthe Ga2 sites should also exhibit the frustration effect but atdifferent temperature, because the Ga2 site has a differentsurrounding environment than the Fe1 and Fe2 sites. For instance,at x¼1.0 as shown in Fig. 5, in addition to the first peak close tothe Curie temperature with the frequency suppression of theheight, the second broad peak occurs at temperature lower thanthe Curie temperature. The second broad peak also exhibits astrong frequency suppression of the height possibly induced bythe frustration of the non-effective Fe ions on the Ga2 sites. Whenthe Fe content of x is high enough, for example, at x¼1.2, the Fe1and Fe2 sites are mostly occupied by the Fe ions, i.e., both kFe1 andkFe2 are close to one. Though the number of Fe ions on the Ga2sites also increases with x, it is much smaller than one. Thus, thenon-effective Fe ions on the Ga2 sites could increase significantly,leading to the observed stronger frequency suppression of thesecond peak height than that of the first peak in w0 and w00 asshown in Fig. 6.

N. Wang et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3595–36003600

4. Conclusions

In summary, for the polycrystalline GFxO (0.8rxr1.3)synthesized using the conventional solid state reaction, thex-dependences of the Curie temperature Tc and the high fieldmagnetization M at 80 kOe have been found to be well consistentwith those observed in the GFxO single crystals, confirming ourgood control over x. Using the determined Fe fractions as a functionof x on the sites of Fe1, Fe2, and Ga2, M and Tc have been calculatedin terms of a simple statistical model [16]. The calculated M and Tc

as a function of x are found to be in a good agreement with theexperimental results. Owing to the site disorder of Fe ions on thefour nonequivalent sites, there exists a significant amount of non-effective Fe ions, which do not contribute to the ferrimagnetism.They are randomly distributed among the Fe ions with theferrimagnetic ordering, exhibiting a different magnetic behavior.Their presence in the ferrimagnetic ordering background gives riseto the observed frequency suppression of the peak height in the acsusceptibility, demonstrating the frustration effect.

Acknowledgements

We thank the Natural Science Foundations of China (GrantsNos. 50672082, 50871096, and 50821001), HeBei Province, China(Grant No. E2009001636), and PCSIRT (Grant No. IRT0650) forsupport of this work.

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