true magnetic structure of the ferrimagnetic garnet y3fe5o12 and magnetic moments of iron ions

Journal of Magnetism and Magnetic Materials 191 (1999) 137—145

True magnetic structure of the ferrimagnetic garnet Y3Fe

5O

12and magnetic moments of iron ions

D. Rodic!,*, M. Mitric!, R. Tellgren", H. Rundlof", A. Kremenovic!

!Laboratory of Solid State Physics, Institute of Nuclear Sciences Vinca, P.O. Box 522, 11001 Belgrade, Yugoslavia"Department of Inorganic Chemistry, The Angstrom Laboratory, Uppsala University, Box 538, S- 75121, Uppsala, Sweden

Received 28 April 1998; received in revised form 28 June 1998

Abstract

To examine and emphasize the difference between approximative and true magnetic structure, we choose ferrimagneticgarnet Y

3Fe

5O

12whose magnetic properties are well known. In order to study the magnetic structure, neutron

diffraction experiments were done on powder sample of Y3Fe

5O

12at 10 and 295 K at zero field and at 295 K in the

applied field B"0.2 T. Using these data the crystal and magnetic structures were first refined in the space group Ia3d.Beside the use of a cubic space group, for a magnetically ordered crystal, this solution suffers from unrealistic magneticmoment per formula unit, which are all significantly above 5 l

Band temperature factors at 10 K which lead to unreliable

Debye temperature. To satisfy compatibility of the symmetry of the magnetic moments (oriented along the body diagonalin cubic system) and crystal symmetry, the crystal and magnetic structures were also refined in the trigonal space groupR31 . In this group the magnetic moments orientation, along the principal axis, is compatible with the symmetry of localpositions. The magnetic R factors are significantly lower than in cubic system. The magnetic moment per formula unit:3.1 l

B, from the diffraction measurements in the field, is close to the result obtained by classical measurements of

magnetization. ( 1999 Elsevier Science B.V. All rights reserved.

Keywords: Magnetic structure; Magnetic moment; True; R factors

1. Introduction

It is very well known that ferrimagnetics, whichcrystallize in cubic system in paramagnetic phase,cannot possess the cubic symmetry in the magneti-cally ordered phase [1]. This fact is based on theCurie principle which requires that the crystalsymmetry must be a subgroup of the group of

*Corresponding author. Tel.: #38-11-4440871; fax: #38-11-4440195.

symmetry of every physical quantity (e.g. orderedmagnetic) [3]. On the other hand, Landau’s theoryof phase transitions also requires lowering of thesymmetry at the Curie point [2]. The mechanismwhich lowers the crystal symmetry below the Curiepoint is the spontaneous magnetostriction, that in-creases with lower temperature.

Even if the above-mentioned facts are very wellknown many magnetic structures are approxim-ately solved in nonadmissible gray groups [3],which do not allow the existence of spontan-eous magnetic moment (see e.g Refs. [4,5]). These

0304-8853/99/$ — see front matter ( 1999 Elsevier Science B.V. All rights reserved.PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 3 1 7 - 5

solutions, except principle error in symmetry mayproduce wrong values of the physical quantities. Anexample is given in this paper.

Y3Fe

5O

12(YIG) is prototype for rare earth iron

garnets-REIG. Its crystal structure was describedin the space group Ia3d [6]. The magnetic mo-ments in 24d and 16a positions are antiferromag-netically coupled and oriented along the bodydiagonal [7,8]. In heavy REIG, at room temper-ature, the magnetic structure of the iron sublatticeis the same as in the YIG, the magnetic moment ofRE3` is antiparallel to the total magnetic momentof the iron sublattice [9].

At low temperature the strong spontaneous mag-netostriction takes place and the magnetic struc-ture of heavy REIG (with ¸O0) changes intoumbrella and double umbrella structures (the mag-netic space group R31 c@) [10—12]. HoIG below 30K changes from the space group R31 c into R31[12]. The magnetostriction is the strongest inTbIG [13,14] and the magnetic structure ofTbIG, at low temperature, is refined in the spacegroup R31 [15]. In this space group the orientetionof the magnetic moments of YIG, along the bodydiagonal in Ia3d group, is invariant under the sitegroup symmetry. To check this possibility, wehave performed neutron diffraction experiments.The neutron diffraction experiment in the magneticfield is made to compare magnetic momentsobtained from neutron diffraction with the mag-netic moments obtained from magnetization meas-urements.

2. Experiment

The polycrystalline sample Y3Fe

5O

12was ob-

tained according to the described procedure in Ref.[16]. The X-ray diffraction experiment, done ata Philips goniometer with CuKa

1,2radiation in the

2h region 15.00—115.00°, steplength 0.02° and expo-sure time 5 s per step, showed no presence of otherphases than the expected garnet phase.

The neutron diffraction experiment was done atthe research reactor R2 in Studsvik, Sweden. Thedata were collected at 10 and 295 K and at 295 K inan applied magnetic field, perpendicular to thescattering plane, of B"0.2 T. The temperature of

10 K, with a stability better than $1 K, was reach-ed with a Displex CS-1003 system refrigerator.

The monochromatic neutron beam was obtainedby a double monochromator system, using reflec-tions from the (2 2 0) planes of two copper crystalsgiving a final wavelength of 1.468(1) As . (In order toobtain accurate results the neutron wavelengthwas calibrated by using refined value of thelattice constant from the X-ray diffraction data.)After collimation of a

1"12@ and a

2"10@, the

neutron flux at the sample was about106 cm~2 s~1. The specimen in the form of pelletsof total volume about 5 cm3 were kept in avanadium tube with a diameter of 11 mm. Tendetectors scanned over the 2h range 5.00—128.04°with the steplength 0.08°. The intensities were stat-istically analysed and added.

3. Results

3.1. Refinement in the space group Ia3d

The crystal and magnetic structures were refinedusing the Rietveld’s profile method and the pro-gram Fullprof [17]. The magnetic and nuclear re-flections, which overlap, were indexed in the spacegroup Ia3d. The sample is a collinear magnetic,with the magnetic propagation vector k"(0, 0, 0).In the space group Ia3d, yttrium ions occupydodecahedral 24c positions with local symmetry2 2 2, iron ions occupy tetrahedral 24d positions,local symmetry 41 , and octahedral 16a positionswith local symmetry 31 and only oxygen ions occupythe general 96h positions with three degrees offreedom. In the refinement procedure, the startingmodel was the crystal and magnetic structure ofTb

2.5Y

0.5IG [18]. The supposed magnetic form

factors corresponds to Fe3`. The pseudo-Voigtpeak shape was assumed. In the last cycle of therefinement, 20 parameters were varied: one scalefactor, one zero point, one assymetry parameter,one mixing parameter, three parameters for thebackground description, three parameters forthe description of the halfwidths and one lat-tice constant parameter. The remaining, atomic,parameters were three free coordinates of the oxy-gen ion, four B factors for ions in four different

138 D. Rodic et al. / Journal of Magnetism and Magnetic Materials 191 (1999) 137—145

Table 1The refined parameters of nuclear and magnetic structure of YIG at 10 and 295 K (B"0 and 0.2 T) in the space group Ia3d. R

B, R

.!',

R1, R

81and R

%91denote Bragg, magnetic, profile, weighted profile and expected conventional Rietveld’s R factors

10 K 295 K 295 K (B"0.2T)

a (As ) 12.3563 (5) 12.3723 (6) 12.3738 (6)O

x!0.0270 (2) !0.0270 (2) !0.0271 (2)

Oy

0.0568 (2) 0.0566 (2) 0.0569 (2)O

z0.1504 (2) 0.1505 (2) 0.1506 (2)

BY

(As 2) 0.46 (5) 0.47 (5) 0.46 (5)BF%(24$)

(As 2) 0.43 (4) 0.52 (4) 0.48 (5)BF%(16!)

(As 2) 0.23 (4) 0.30 (4) 0.34 (4)BO

(As 2) 0.46 (4) 0.52 (4) 0.49 (4)k(Fe)

24$(l

B) !5.37 (9) !4.74 (9) !5.52 (9)

k(Fe)16!

(lB) 4.11 (7) 3.80 (7) 4.63 (7)

RB

(%) 4.309 3.127 5.327R

.!'(%) 7.591 5.982 6.038

R1(%) 10.4 10.2 10.9

R81

(%) 12.2 12.7 12.8R

%91(%) 5.23 4.87 4.63

crystallographic positions and two magnetic mo-ments for the two iron ions in 24d and 16apositions.

The mutual orientation of the magnetic momentsshows that the sample is collinear ferrimagnetic.The parameters of the nuclear and magnetic struc-tures are listed in Table 1.

3.2. Refinement of the crystal and magneticstructures in the space group R31

In order to refine the crystal and the magneticstructure in the exact space group the unit cell hasbeen changed into rhombohedral with hexagonalaxes. The recalculation of the unit-cell parametershas been done starting from the refined values inthe space group Ia3d. The atomic positions havebeen recalculated from the atomic positions of YIGin the cubic space group. These values have beenthe starting parameters for the refinement in thespace group R31 . In this space group Y3` ionsoccupy dodecahedral 18f and 18f positions withlocal symmetry 1, Fe3` ions occupy octahedral 3a,3b, 9d, 9e and tetrahedral 18f and 18f positions withlocal symmetries 31 , 31 , 11 , 11 , 1 and 1, respectively. Theoxygen ions are in eight crystallographically differ-ent general 18f positions. The magnetic form factor

for Fe3` has been supposed. The profiles have beendescribed by the pseudoVoigt functions.

In the last cycle of the refinement, 51 parameterswere varied: one scale factor, one zero point correc-tion, one assymetry parameter, one mixing para-meter, three parameters for the description of thebackground, three parameters for the description ofhalfwidths and two lattice parameters. The remain-ing atomic parameters were: the free coordinates ofions in general position for two (crystallographi-cally different) Y3`, two Fe3`, eight O2~, one tem-perature B factor for all ions, one magnetic momentfor Fe3` in octahedral 3a, 3b, 9d and 9e positionsand one magnetic moment for both Fe3` in tet-rahedral positions.

The magnetic moments are antiparallel alongthe principal axis. The parameters of the nuclearand magnetic structures are given in Tables2—4. The neutron diffraction pattern is shown inFig. 1.

3.3. Constrained refinements in space groups Ia3dand R31

In order to get results for total magnetic momentand Debye temperature which are in agreementwith independent physical observations we have

D. Rodic et al. / Journal of Magnetism and Magnetic Materials 191 (1999) 137—145 139

Table 2The parameters of nuclear and magnetic structure of YIG at 10 K in the space group R31

Atoms and positions Fractional coordinates kz(l

B)

x y z

Y118&

0.127 (2) !0.002 (3) 0.251 (4)Y2

18&0.292 (3) 0.333 (4) 0.584 (6)

Fe3!

0 0 0 4.01 (5)Fe

3"0 0 1/2 4.01 (5)

Fe9$

0 1/2 1/2 4.01 (5)Fe

9%1/2 0 0 4.01 (5)

Fe118&

0.208 (2) 0.168 (3) 0.414 (4) !3.95 (5)Fe2

18&0.294 (2) !0.168 (3) 0.584 (4) !3.95 (5)

O118&

0.089 (4) 0.094 (4) 0.124 (4)O2

18&0.260 (4) 0.116 (4) 0.328 (4)

O318&

!0.420 (4) !0.370 (4) 0.549 (5)O4

18&0.490 (4) 0.098 (4) 0.428 (4)

O518&

!0.003 (3) !0.093 (4) 0.384 (4)O6

18&0.147 (3) !0.114 (4) 0.186 (3)

O718&

!0.051 (4) 0.367 (3) !0.044 (5)O8

18&0.394 (4) !0.093 (3) 0.077 (4)

B (As 2) 0.24 (2)a (As ) 17.484 (2)c (As ) 10.690 (2)R

B(%) 3.10

R.!'

(%) 4.98R

1(%) 8.26

R81

(%) 9.82R

%91(%) 5.09

performed constrained refinements. In the con-strained refinements, we coupled magnetic mo-ments in octahedral and tetrahedral positions toobtain total magnetic moment of 5.0 l

Bat 10 K and

3.5 lB

at 295 K [9]. In the same refinements, theoverall B factor for all ions was constrained be-tween 0.12 and 0.14 As 2 at 10 K and between 0.28and 0.32 As 2 at 295 K. These B factors led to re-ported Debye temperatures between 550 and 600 K[19,20].

The constrained refinements in the space groupIa3d do not converge due to large shifts of B valueswhich are 0.20 and 0.11 As 2 at 10 and 295 K, respec-tively. These refinements are characterized by rep-etition of rather high R factors which are:R

1"15.6%, R

81"16.5%, R

%91"5.23%, R

B"

11.47% and R.!'

"11.20% at 10 K; R1"12.2%,

R81

"14.1%, R%91

"4.87%, RB"6.764% and

R.!'

"9.589% at 295 K; R1"12.8%, R

81"14.4%,

R%91

"4.64%, RB"8.304% and R

.!'"11.50% at

295 K in applied field.The constrained refinement in the space group

R31 at 10 K does not converge. The overall B factorhas gone out of limit, similarly as in the constrainedrefinements in the space group Ia3d. In this refine-ment the R factors, which repeat from cycle to cycle,are: R

1"9.35%, R

81"10.6%, R

%91"5.10%,

RB"4.095% and R

.!'"6.150%. The constrained

refinements in the space group R31 at 295 K con-verge. The results are similar to those given inTables 3 and 4. In zero field, B factor is 0.31(2) A2,magnetic moments at octahedral positions are3.60(3) l

Band at tetrahedral positions are

!3.56(3) lB. The other results are the same, within

the standard deviation as in Table 3. The reliabilityfactors are: R

1"8.56%, R

81"10.5%, R

%91"

4.75%, RB"2.876% and R

.!'"4.964%. In

applied field, B factor is 0.30(2) A2, magnetic


Table 3The parameters of nuclear and magnetic structure of YIG at 295 K, in zero field, in the space group R31


B)

x y z

Y118&

0.125 (3) !0.003 (3) 0.252(4)Y2

18&0.291 (3) 0.334 (3) 0.584 (4)

Fe3!

0 0 0 3.73 (5)Fe

3"0 0 1/2 3.73 (5)

Fe3"

0 1/2 1/2 3.73 (5)Fe

9%1/2 0 0 3.73 (5)

Fe118&

0.208 (4) 0.167 (2) 0.410 (2) !3.40 (5)Fe2

18&0.290 (2) !0.170 (2) 0.583 (3) !3.40 (5)

O118&

0.092 (3) 0.098 (3) 0.120 (4)O2

18&0.261 (3) 0.117 (3) 0.327 (4)

O318&

!0.423 (3) !0.374 (3) 0.548(4)O4

18&0.487 (4) 0.097 (3) 0.421 (4)

O518&

0.000 (3) !0.090 (3) 0.382 (4)O6

18&0.146 (3) !0.112 (3) 0.179 (4)

O718&

!0.046 (2) 0.370 (3) !0.042 (4)O8

18&0.394 (3) !0.091 (2) 0.072 (3)

B (As 2) 0.32 (2)a (As ) 17.508 (2)c (As ) 10.701 (2)R

B(%) 2.79

R.!'

(%) 3.67R

1(%) 8.16

R81

(%) 10.2R

%91(%) 4.75

moments at octahedral positions are 4.40(3) lB

andat tetrahedral positions are !4.10(3) l

B. The frac-

tional coordinates are the same, within the experi-mental error, as in Table 4. The following R factorsare reached: R

1"8.52%, R

81"9.86%, R

%91"

4.51%, RB"3.404% and R

.!'"2.262%.

4. Discussion

All the R factors which are obtained from theRietveld fits in the space group R31 are better thanthe corresponding factors in Ia3d (Tables 1—4), butsince the number of refinable parameters is 51 inthe space group R31 in comparison with 20 in thespace group Ia3d significance test is made to showwhich hypothesis is better. The ratios of weightedprofile R factors in the cubic and rhombohedralspace groups are 1.24, 1.24 and 1.31 for the refine-

ments at 10, 295 and 295 K in the applied field,respectively. On the other hand, the table of signifi-cance points for the R factor ratio [21] for dimen-sion 31 with 1487 degrees of freedom at significancelevel 0.01 indicates a ratio of about 1.02. Since theratios of weighted profile factors greatly exceedsthis value, we can assert that decreases of R factorsin rhombohedral space group are significant.

In the space group Ia3d, at 10 K, the magneticmoment of Fe3` in tetrahedral 24d position coarse-ly agrees (within the experimental error) with theexpected result 5 l

B/Fe3`. By summing up ionic

radii r(Fe3`)"0.49 As and r(O2~)"1.38 As [5] thebond length of 1.87 As is obtained (for the same site)in complete agreement with our value of 1.865(2) As(room-temperature data).

The magnetic moment of the Fe ions in theoctahedral 16a position, at 10 K, is 4.11 l

B(Table 1)

which approximately corresponds to the expected


Table 4The parameters of nuclear and magnetic structure of YIG at 295 K, in the applied field B"0.2 T, in the space group R31


B)

x y z

Y118&

0.123 (2) !0.002 (3) 0.248 (4)Y2

18&0.292 (2) 0.336 (3) 0.581 (4)

Fe3!

0 0 0 4.47 (4)Fe

3"0 0 1/2 4.47 (4)

Fe9$

1/2 0 1/2 4.47 (4)Fe

9%1/2 0 0 4.47 (4)

Fe118&

0.206 (2) 0.166 (3) 0.416 (3) !4.02 (5)Fe2

18&0.293 (2) !0.164 (3) 0.577 (3) !4.02 (5)

O118&

0.079 (3) 0.085 (4) 0.123 (5)O2

18&0.259 (4) 0.113 (3) 0.328 (7)

O318&

!0.424 (4) !0.372 (4) 0.542 (5)O4

18&0.489 (4) 0.101 (4) 0.424 (5)

O518&

!0.005 (4) !0.088 (4) 0.379 (6)O6

18&0.143 (3) !0.118 (4) 0.171 (6)

O718&

!0.057 (3) 0.372 (3) !0.049 (4)O8

18&0.387 (4) !0.103 (4) 0.075 (5)

B07%3!--

(As 2) 0.31 (2)a (As ) 17.504 (2)c (As ) 10.711 (2)R

B(%) 3.199

R.!'

(%) 2.600R

1(%) 8.42

R81

(%) 9.78R

%91(%) 4.51

spin-only value for Fe2` (4 lB) rather than to the

expected value for Fe3` (5 lB). On the other hand,

for the octahedral site r(Fe3`)"0.645 As ,r(Fe2`)"0.770 As , r(O2~)"1.38 As [5]. By sum-ming up ionic radii for the octahedral site, theobtained bond lengths for Fe3`—O2~ andFe2`—O2~ are 2.025 and 2.15 As , respectively, incomparison with experimentally found bond lengthof 2.021(2) As at 295 K. The ionic model of the bondFe3`—O2~ corresponds completely to the octahed-ral site. Note that introduction of another magneticform factor(e.g for Fe2`) does not change the re-sults for the magnetic moments, within the experi-mental error (Fig. 2).

The total magnetic moments, per formula unit, inall cases in space group Ia3d are above 6 l

B(Table

5) in comparison with 5 lB

which is the expectedvalue from magnetiztion measurements at heliumtemperature. Hence, we can say that the cubic

space group is not a good enough approximationfor the symmetry of YIG.

The Bragg and magnetic R factors (Table 1,columns 2 and 3) are smaller at 295 K than at 10 K.That can be a consequence of spontaneous mag-netostriction which is more pronounced at lowtemperatures. Namely, the supposed cubic sym-metry is a better approximation for higher temper-atures. In agreement with the facts just mentionedis the calculation of the Debye temperatures, fromthe mass-averaged B factors, which are 480(30) and210(10) K, at 295 and 10 K, respectively. The re-ported results for Debye temperature of YIG are550 and 600 K [19,20].

Note that all ions have the same coordination inthe space group R31 as in the space group Ia3d.Y3` ions, in both space groups, are surrounded byeight anions which form a dodecahedron. The ironion in 24d position (in Ia3d) and the iron ions in


Fig. 1. The observed (points) and calculated intensities (continuous line), of the neutron diffraction pattern of YIG at 10 K, in the spacegroup R31 . The line at the bottom represents the difference between the observed and the calculated intensities.

two general 18f positions (in R31 ) are tetrahedrallycoordinated by oxygen anions. The iron ionin 16a position (in Ia3d) and the iron ions inspecial positions 3a, 3b, 9d, 9e (in R31 ) are octahed-rally surrounded by oxygens. The oxygen ions(in both space groups) are coordinated by twoyttrium and two iron ions. All coordination poly-hedra are more irregular in the space group R31than in the space group Ia3d, which is a conse-quence of the refinement of the coordinates. Thecation—anion distances are (in average) the same,within the experimental error, in both spacegroups.

Keeping in mind the coordination of the ironions, which affects the magnetic moments, we haverefined the magnetic moments in the same coord-ination, in the space group R31 , with the same

parameter. In this space group the total magneticmoments per formula unit, in all the cases aresmaller than in the cubic symmetry. The change ofproposed space group leads magnetic momentsfrom nonallowed region, above 5 l

Bin cubic sym-

metry, into allowed region, below 5 lB, in trigonal

symmetry. The magnetic moments from diffractionmeasurements are smaller than those obtainedfrom the magnetic measurements [15]. From thecomparison of the magnetic moments obtained inB"0 T and B"0.2 T (Tables 3—5) it follows thatthe applied magnetic field increases magnetic mo-ments toward the values obtained in a saturatedfield. There are two reasons for the change of resultsfor the magnetic moments: change of the spacegroups and applied field. Note that moments inboth octahedral and tetrahedral sites at 295 K are


Fig. 2. The projection of Fe ions in the unit cell on the (0 1 1) plane. The z-coordinates are given in the picture. The full and the emptycircles represent two different spin orientations.

Table 5Magnetic moments per formula unit in neutron diffracton ex-periment and magnetization measurements in the fields 1 and2 T [21,9]

k (lB) (Ia3d) k (l

B) (R31 )k (l

B)

This work 1 T [22] 2 T [9]

10 K, B"0 T 7.9 (4) 3.8 (2) 4.25 5.0295 K, B"0 T 6.2 (4) 2.7 (2) 3.05 3.5295 K, B"0.2 T 7.3 (4) 3.1 (2)

significantly different in the case of B"0 T (cubicsymmetry) and in the case B"0.2 T (trigonal sym-metry).

The correct constrained refinements are possibleonly in the trigonal space group at room temper-

ature. Only in this case the supposed B factor,calculated from independent measurements[19,20], is the same as in the nonconstrained refine-ments (Tables 3 and 4).

5. Conclusions

The crystal and magnetic structures of YIG arerefined for the first time, to our knowledge, in thespace group R31 and the magnetic white group R

I31 .

In this group, the symmetry of the magnetic mo-ment governs the symmetry of the crystal (in agree-ment with the Curie principle). The bond lengthscorrespond to the ionic model Y3

3#Fe3

5#O2~

12.

The obtained results for the magnetic momentsand moment per formula unit are dependent onthe supposed space group and applied field. Only


results obtained in trigonal symmetry, especially inthe applied field, are comparable with the resultsfrom classical magnetic measurements.

In conclusion, the ferrimagnetic phase is in lower,trigonal, symmetry when compared with the para-magnetic phase. It also has been recently found thatthe magnetic ordering also influences magnetiztionof oxygen ions in YIG [23]. The Debye’s temper-atures which increase from 10 to 295 K measure-ments, toward an expectable value [18—20] showthat the crystal gradually changes from trigonal tocubic symmetry. The proposed space group R31should be applicable for all collinear ferrimagneticgarnets with easy magnetization axis [1 1 1] in cu-bic space group.

References

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true magnetic structure of the ferrimagnetic garnet y3fe5o12 and magnetic moments of iron ions

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