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POLARIZED NEUTRON DIFFRACTION IN
FERRITES
N. Satya Murthy
To cite this version:
POLARIZED NEUTRON DIFFRACTION IN FERRITES
N. S. SATYA MURTHYNuclear Physics Division, Bhabha Atomic Research Centre, Bombay 400 085, India
Résumé. — La technique de la diffraction des neutrons polarisés a trouvé de larges applications
dans l'étude des facteurs de forme magnétique et de la distribution des densités de moments dans les cristaux magnétiquement ordonnés. Dans cet exposé on présente après un rappel sur la technique utilisée, les résultats des études effectuées à Trombay sur des monocristaux de FesO A, naturels et de ferrite MnFeîCU. On termine par une brève mention des travaux effectués sur les poudres.
Abstract. — The technique of polarized neutron diffraction has found wide application in the investigation of magnetic form factors and magnetic moment density distribution in magnetically ordered crystals. Results of studies at Trombay on natural Fe304 and synthetic MnFe2C>4 ferrite
single crystals are presented in this talk after outlining the technique. A brief mention of powder work is made in the end.
1. Introduction. — The technique of polarized neu-tron diffraction [1] has been unique in elucidating the magnetic structures and in the precise deter-mination of spatial magnetic moment density distri-butions in a number of magnetic materials. Experi-ments performed on both powder and single crystal specimens exist in the literature. The earliest magnetic moment density investigations had been made on the structurally simple ferromagnetic transition metals Fe, Co and Ni and these formed the background for many theoretical efforts to explain the observed distributions [2, 3]. The list of materials studied has since rapidly expanded and provided impetus to further theoretical and experimental work. But there has been relatively little neutron diffraction work on cubic spinel ferrites with an objective to understand the moment density distributions. A number of powder diffraction studies for magnetic structure determination in ferrites have been made, however, since the early work of Shull et al. and Corliss and Hastings. Many single and mixed ferrite powders were studied at Trombay using polarized as well as unpolarized neutrons in the early phase of work on ferrites for magnetic structure investigations. These studies revealed for the first time the existence of Yafet-Kittel (Y-K) type of spin arrangements in the cubic nickel-zinc ferrites and also established phase transitions from the Y-K to Neel type of ordering [22]. More recently polarized neutron measurements have been made on single crystals of F e304 and M n F e204 which are both collinear
ferrimagnets. In the following the polarized neutron technique will be briefly outlined and the results on various ferrites studied will be discussed.
2. Polarized neutron technique. — The technique of polarized neutron diffraction [1, 3] utilizes the
inter-ference between nuclear and magnetic Bragg scattering from a magnetically ordered crystal for the precise determination of magnetic structure amplitudes (M). The magnetic structure amplitudes are simply the component amplitudes in a Fourier expansion of the spatially periodic moment density, so that
p(r) = A £ M ( T ) e -2™ - ' . (1)
Most generally, M i s a complex vector due to the vector nature of moment density but assuming a collinear density throughout the crystal [4] p(r) and M(x) are both treated as scalars in eq. (1). T is the reciprocal lattice vector and V the unit cell volume. If accurate M values are measured for all reflections in the crystal (which in practice suffices to restrict to reflections up to sin QjX ~ 1 A- 1, 29 = scattering
angle, X = wavelength of neutrons) then a Fourier inversion in reciprocal space can be performed to directly obtain the unpaired electron density respon-sible for the magnetization in the crystal.
For an incident beam of polarized neutrons with polarization P, the Bragg intensities are given by
J(T) = C { I N(x) |2 + | M(x) I2 q2 +
+ Re [N*(x) M(x)] P.q } (2) where N and M are the nuclear and magnetic structure amplitudes per unit cell, C is a constant and q is given by
q = x x n x x (3)
x is the unit scattering vector ( = t/| T |) and n is a unit vector along the moment direction in the crystal. This expression is strictly valid for a single domain crystal with collinear magnetic ordering. In general for the scattering of neutrons from ferromagnetics
C1-80 N. S. SATYA MURTHY which have to be kept in an external field to make where
A
them single-domain, q is parallel or antiparallel to the polarization vector P. Also, it is arranged in conventional experiments to keep the magnetization (and the polarization) vertical while the scattering takes place in the horizontal plane so that
and p.q =
+
P . (5)Non-collinear spin arrangements do occur in ferrites but that situation is excluded from the present discus- sion. N and M are in general complex but for centro- symmetric crystals these are real numbers. The expression for Bragg intensity in that case simplifies to
I(z) = C(N2
+
M' _f 2 NMP).
(6) N and M carry with them the appropriate Debye waller temperature factors for the different atomic species. In a polarized neutron experiment one defines a polarization or flipping ratio as the ratio of Bragg intensities for the two spin states of neutrons, I. e.,Eq. (7) provides a simple means to determine M values if N is known a priori. The advantages of this type of measurements are well known namely that it suffices to make peak intensity measurements rather than integrated intensities and that this arran- gement results in cancellation of any systematic errors. In crystals with simple structure, with one type of species only, the temperature factor corrections also cancel out if the Debye Waller correction is assumed same for the nuclear and magnetic ampli- tudes. The large sensitivity of polarized neutron technique derives from the presence of polarization dependent interference term. This facilitates the measurement of M, which is usually small at larger scattering angles due to the smaller magnetic form factor (and at times due to particular structural details for complex crystal structures). When both N
and M are small, the method continues to be useful but much of the advantage is lost due to poorer intensities requiring prohibitively large counting times in many cases. When N ss M, unpolarized neutron data has a better accuracy and can be used in conjunction with the polarized neutron measure- ments.
Eq. (7) does not suffice in general due to the need
to incorporate several corrections. When corrections due to imperfect flipping of neutron polarization
(f
5
1) and the depolarization and extinction in the sample are incorporated, eq. (7) is modified toand
f{
andfi
are obtained by replacing PD by PD(l - 2f)
in the expressions forfl
andf2
respec- tively. D is the polarization transmission in the crystal andf
is the polarization flipping efficiency of the r. f. flipper. Y , and Y- are the extinction factors(<
1) given bywhere g is the extinction parameter [5], f the effective average neutron path length in the crystal for the reflection concerned and
are the reflectivities for the two spin states of neutrons. We assume only secondary extinction in the crystal and treat it to be of type I or I1 [S].
There are essentially two ways of analysing the experimental magnetic structure amplitudes. The first obviously is to obtain the moment density from a Fourier synthesis of magnetic structure amplitudes (i. e., projected density on a given plane if reflections lying in a single zone only are used or a full three dimensional map if all the reflections have been measured). Such density maps are entirely model independent and provide a stringent check of any theoretical model. In the second approach one parti- tions the total moment density to belong to individual atoms in the crystal and then deduce the magnetic form factors for the different atoms with their respec- tive local moment values. The partitioning of the moment in this fashion can not be done uniquely even in principle [6]. In this approach one can allow for separate spin and orbital contribution [7] to the local moments, the diffuse moment [8] and aspheri- city [9] etc. This approach is clearly on weaker footing
if no clear cut separation into localized moments is possible but has the advantage that the analysis can be proceeded with even if a full zonal or three dimen- sional data is not available or is reliable only in part.
3. Structure factor types in cubic spinel ferrites.
-
TABLE 1 The large cell size of the ferrite has the undesirable
Structure factor types in spined ferrites for u = 0.25
Reflec- tion N M example
-
- 4(-JZ
bA+
2 bB) 4(JZ
pA+
2 pB) (11 1)-
8 bA PA (220)("1
4(- J2 bA - 2 bn) 4(JZ pA-
2 pB) (311) 16(bB-
2 bo) 16 PB (222) ( b ) 8(- bA+
2 b,+
4 bo) 4(2 PA+
4 pn) (400) 8(bA+
2 bB+
4 bo) 4(- 2 p,+
4 pB) (440)( a ) A) Site only : h
+
k-
4 n+
2, k -t I = 4 n -I- 2,h
+
I = 4 n ; cyclic.(6) B) Site only : h -I- k = 4 n
+
2, k -t I = 4 n+
2,h -I- I = 4 n
+
2 ; cyclic. These reflections have a large oxygen contribution also.three sites (A, B and oxygen). The form factors for a particular site in this case can be obtained after correctly subtracting out the other contributions. In principle the different sites in the ferrite should be associated with different temperature factors which are in general anisotropic and also different for nuclear and magnetic scattering. But, in the analysis of our data it has been assumed a priori that a common isotropic temperature factor applies. In this regard the A-site-only reflections have a relatively unambiguous position due to little conta- mination from the other sites.
4. Fe304. - Fe304 is a completely inverted spinel with the cation distribution (Fe3+) [Fe3 + F e Z + ] 0 4 and a ferrimagnetic ordering below 848 K. The microscopic electronic and magnetic properties of this ferrite are still not well understood and it has continued to be of great interest for more than over two decades. Apart from neutron scattering several other experimental techniques have been employed for its study like electrical conductivity, magnetiza- tion [lo], Mossbauer effect [ll], NMR [12], spin polarized photoelectron emission [13], and magneto- electric effect [14] to name a few. Polarized neutron measurements on Fe304 were first reported by Nathans et al. [15] who pointed out important diffe-
rences between the moment distributions at two cation sites. Much of the neutron scattering work in the recent past has however concentrated on the
study of its highly controversial low temperature phase (see for example Shirane et al. [16], Sokoloff [17] and other references therein). A more extensive polarized neutron study at room temperature was made later at Trombay [18] on reflections in the [110], [001] and [I121 zones and again recently on a thinner crystal in [I101 zone 1191. These studies have provided interesting information on the moment distribution in the crystal.
effect of increasing the chances of multiple Bragg scattering which in practice is very difficult to correct for [20]. Recent
<
110>
zone measurements are considered to be more acceptable in this regard and mainly these are discussed in detail in a companion paper in this conference. Magnetic structure ampli- tudes for various reflections were obtained by solving eq. (8) with proper account of extinction and depola- rization in the crystal. The depolarization coefficient was measured experimentally. The extinction para- meter g was obtained from unpolarized neutron measurements as well as independently from polarized neutron measurements. Finally the deduced magnetic structure amplitudes were analysed in terms of moment density and form factors as outlined in section 2.Both the moment density and form factors show that there is significant covalency in this crystal. The covalency is particularly large for the A-site which has a tetrahedral coordination to the oxygens. The localized moment on the A-site is concluded to be about 10
%
lower than the expected Fe3+ free ion value at room temperature. The A-site form factor is found to closely scale to the Fe3+ free ion form factor sin 8/d > 0.3A-'
and even more exactly to the Fe3+ tetrahedral form factor in Yttrium Iron garnet (YIG) [21]. In view of the same Fe-0 distance involved in the two cases, this agreement of Fe,04 and YIG results is not surprising. The behaviour of A-site form factor for sin 0/;1 < 0.3, where the covalency effects can be seen even more directly, could not however be made due to some ambiguity about (220) reflection. The B-site form factors were obtained after subtracting out the A-site contribution from reflections with contribution also from the B-site. These did not follow a smooth curve and indicated that the moment distribution on B-sites had sizeable asymmetry with an excess of E, and a deficiency of T,,-orbital population over the spherical distribution. The localised moment on B-sites also appeared to be less than the free ion value (average for Fez+ and Fe3+ ions) but the reduction was not as pronounced as for the A-site. Following Hubbard and Marshall [6], and making use of the estimated asymmetry of the A-site moment distribution in the ionic model, it has been argued that the predominant transfer of the moment from the A-site takes place through Tz molecular orbitals. It is found that there is moment density also on and around the oxygen sites and in the ionic model this is estimated to be 0.08 pB 1151 (I).C1-82 N. S. SATYA MURTHY [ M ~ ~ . ~ , ~ F ~ ~ . ~ ~ ~ ] o ~ . The A-sites are occupied predo-
minantly by Mn2 + ions and the B-sites by Fe3+ ions. A polarized neutron study of this ferrite offers an opportunity to study the form factor of Mn2+ in a tetrahedral and Fe3+ in an octahedral crystalline field of oxygen ions. Most of the work reported so far on Mn2+ involves an octahedral crystal field onlyz4.
First polarized neutron study of this ferrite was made at Trombay [IS] in 1973 for reflections in [I101 zone only. Further measurements were made recently for reflections in [I101 as well as in [I001 and [I121 zones. The cation distribution described above was arrived at from an unpolarized neutron study leading to following nuclear scattering parameters :
The cation distribution as mentioned above is deduced using
bM, =
-
0.36 x 10-l2 cm andThe A-site nuclear scattering amplitude is much smaller in this case than that in Fe304 due to the smaller amplitude for Mn and further due to some reduction from Fe-amplitude having an opposite sign. As a result, the oxygen contribution to A-site reflections becomes quite sizeable in comparison to the A-site contribution itself. This makes even some A-site reflections extremely sensitive to the u-parameter as examplified by few reflections in table 11. The
Typical examples of some u-parameter sensitive reflections in MnFe204
N for
hkl u = 0.260 6 u = 0.261 0 M
presence of such sensitive reflections in MnFe204 together with a severe extinction problem, posed serious difficulties in satisfactory evaluation of magnetic structure amplitudes of the affected reflection. The experimental data was analyzed as in the case of Fe,04. The extinction parameter could not however be fixed independently from the polarized neutron
measurements as the pathlengths for different reflec- tions were almost identical due to nearly square cross-section of the crystal. The depolarization in the sample was experimentally found to be negligible. The magnetic form factors for the A-site reflections deduced with an A-site moment of 3.95 pB and with nuclear parameters given in eq. (11) are shown in figure 1. The value for (220) has been taken from [001]
FIG. 1. - A-site-only experimental and spherically averaged A and B-site form factors in MnFezO4.
and [I121 zone data. The value obtained in [I101 zone was different suggesting the presence of multiple Bragg effects. The Mn2+ free ion form factor is also shown in the figure. Despite the large deviation of (642) and (660) form factors from the average curve it is apparent that the experimental Mn-form factor is contracted in comparison to the free ion curve. The spherically averaged form factors for the A- and B-sites are also shown in the figure. These were deduced by including 41 reflections lying in [I101 zone and assuming extrapolated values for 11 more reflections which could not be measured due to very weak inten- sities. The A-site spherically averaged form factor does not quite follow the average behaviour indicated by the A-site form factors however and this may be due to the ambiguities mentioned above.
6 . Powder diffraction studies. - While single crys- relative structure factor magnitudes for polarized tal studies promise to give the most accurate informa- and unpolarized cases and their relative sensitivities tion on individual magnetic structure amplitudes to the degree of inversion is shown in figure 3. In
there are serious problems in analysis due to the presence of extinction and multiple Bragg scattering. Powder diffraction studies, in contrast, are practically free from these difficulties. Use of polarized neutrons
adds further to the merit of powder work by effec- I
tively quadrupling the number of measurements
from which to extract the magnetic structure ampli- %" i
'0
tudes. A number of polarized neutron studies at
& -7 1,w
Trombay on powder samples of pure and mixed O
,,I
ferrites, e. g., MnFe204, NiFe204, Mg,Mn,-,Fe204 I" na
etc. [23], which provided useful structural as well as rn 1Y
\*
$'magnetic information, have clearly demonstrated $3
,.'
this. Results on NiFe204 1251 will be briefly described
as an example to highlight the enhanced sensitivity DEGREE OF INVERSlON Y
of polarized neutron studies.
FIG. 3.
-
Comparison between relative structure factor magni- In NiFe204 which is a cO1linear ferrimagnet7 the tudes for polarized and unpolarized neutron cases and theirunpolarized neutron diffraction is rather insensitive relative sensitivity to the degree of inversion. to determine the exact inversion due to the close
nuclear scattering amplitudes for Ni and Fe. On the
other hand with polarized neutrons an enhanced N~F~,o, it is found that the inversion is 100
%.
variation of I+ and I- intensities can be achieved 1, addition the magnetic moments of ~i and F~ ions due to quite different magnetic moments of Ni and are also available from the analysis assuming the Fe (2.2 and 4 e 8 PB respectively). Figure 2 shows the free ion magnetic form factors, for these.
0-
; > m - i
%r orr
I L (I*
20 ,s
Frc. 2. - Diffraction patterns of powder NiFe204 for polarized and unpolarized neutrons at room temperature.
diffraction patterns of powder NiFe204 for polarized and unpolarized neutrons at room temperature. The rf of (I,) and rf on (I-) patterns show the polarized neutron intensities with spin parallel and anti-parallel. to the magnetization respectively, while the magnetic
field off pattern shows two of the unpolarized neutron
intensities for comparison. Comparison between
7. Summary. - We have discussed in some detail the results of polarized neutron studies on Fe,04 and MnFe204. While number of difficulties arise in an unambiguous interpretation of these measurements which are related to the complexity of crystallographic structure, polarized neutron diffraction is a powerful technique for the study of ferrites. In Fe,04, the tetrahedral Fe3+ form factor scales closely to Fe3+ tetrahedral form factor in a structurally close com- pound Y3Fe,OI2 (YIG) [21]. The A-site localized moment in Fe304 is concluded to be about 10
%
less than the expected value (at room temperature). Reduction in moments have also been reported in YIG. Covalent reduction of moment on B-sites is found to be relatively smaller but there is significant asymmetry in the moment distribution. In MnFe204, the Mn2+ tetrahedral (A-site) form factor is seen to be contracted in comparison to the free ion form factor. Analysis does not suggest of a reduction in the A-site moment value. Example of NiFe204 was included in the discussion to highlight the sensi- tivity of polarized neutron diffraction even in the study of powder samples.
References
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