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MAGNÉTISME ET APPLICATIONDOMAIN WALL DYNAMICS IN THE ORTHOFERRITES
F. Rossol
To cite this version:
F. Rossol. MAGNÉTISME ET APPLICATIONDOMAIN WALL DYNAMICS IN THE ORTHOFERRITES. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-436-C1-442.
�10.1051/jphyscol:19711152�. �jpa-00213972�
DOMAIN WALL DYNAMICS IN THE ORTHOFERRITES
by F. C. ROSSOL
Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey
Résumé. — Des valeurs de la mobilité des parois des domaines entre 4 000 cm. s- 1. Oe~ i à 335 °K et 50 000 cm. s- x. Oe~l
à 78 °K, d'entre les plus grandes qu'on a trouvées dans les isolants magnétiques, sont-elles mesurées sur YFe03. Des faibles substitutions partielles de Tb+3 et Sm+3 pour Y+3 dans la matrice YFe03, exercent des effets amortissants forts sur le mouvement des parois. Une substitution nominale de 7 % (atomique) Tb diminue la mobilité de YFeO 3 pur de plus de trois ordres de grandeur à 78 °K. Un bon ajustement à une dépendance exponentielle de la température pour un temps de relaxation, associé à l'ion de Tb, est déduit de la contribution de celui-ci à la force amortissante des parois, à partir d'un modèle à relaxation lente.
Abstract. — Domain wall mobility values from 4,000cm.s-1.Oe~i at 335 °K to50,000 cm.s"1.Oe-1 at 78 °K,among the highest found in magnetic insulators, have been measured in YFeC>3. Small partial substitutions of Tb+3 and Sm+3
for Y+ 3 in the host YFeCb have strong damping effects on wall motion. A nominal 7 at. % Tb substitution reduces the mobility of pure YFeO 3 by more than three orders of magnitude at 78 °K. A good fit to an exponential temperature dependence for a relaxation time associated with the Tb ion is deduced from its contribution to the wall damping force on the basis of a slow relaxation model.
I. Introduction. — Yttrium and the rare-earth or- thoferrites are canted antiferromagnets in which can- ting of the iron sublattice magnetizations was shown by Treves [1] to arise from a combination of symmetric and antisymmetric exchange interactions. The anti- symmetric exchange confines the net magnetization to the a-c plane of the orthorhombic structure.
Although many of the properties of the orthoferrites have been measured and are understood (see the review paper by White [2]), there has been little pro- gress toward understanding the relaxation mechanisms that govern the motion of domain walls in these materials.
Rare-earth ion moment relaxation in substituted yttrium iron garnet (YIG) has been investigated by Harper and Teale [3-5] using measurements of the temperature dependence of domain wall mobility and by a number of workers [6-10] who measured the temperature dependence of microwave resonance line- widths. These efforts were quite successful in distin- guishing the dominant relaxation processes in the gar- nets. Shane [11] and Hagedorn and al. [12, 13] have shown that resonance can be observed at convenient microwave frequencies only for certain rare-earth orthoferrites in the narrow temperature range of reorientation of the easy axes of magnetization. How- ever, in this range, linewidth contributions from the rare-earth ions are obscured by other line broadening effects. The study of rare-earth ion moment relaxation in the orthoferrites appears, therefore, to depend heavily upon domain wall mobility measurements and their interpretation.
The next section presents the behavior of domain wall mobility measured in pure Y F e 03 and in mate- rials containing partial substitutions of terbium and samarium for the yttrium. In the following section, the contributions of the substituted terbium and sama- rium ions to the damping of wall motion are isolated and interpreted within the framework of a slow relaxa- tion model.
II. Measurements of wall mobility. — Domain wall motion in the orthoferrites has been found by Rossol [14] to have a frequency response predicted by a
simple relaxation model involving viscous damping. In this model the pressures acting on the moving wall include a damping pressure proportional to wall velo- city and a restoring pressure proportional to wall displacement in addition to the driving pressure.
Domain wall mobility in the orthoferrites can therefore be measured very conveniently using the oscillating wall technique described in reference [14]. In this method the wall mobility is deduced from the measu- rement of the frequency response of a single wall driven sinusoidally about an equilibrium position determined by a constant magnetic field gradient. The wall motion in single crystal plates about 50 um thick is observed stroboscopically by means of the Faraday effect. This method has the advantage otactually mea- suring a single wall subject to known pressures and avoids the ambiguities concerning the number of walls present or the average distance moved by a wall which arise in other methods. All of the measured mobility data discussed in this paper have been obtained using this oscillating wall technique.
Wall mobility measurements in Y F e 03 have yielded values from almost 4,000 cm.s"1.Oe""1 at 335 °K to 50,000 c m . s_ 1. O e_ 1 at 78 °K. These are among the highest values of mobility observed in magnetic insulators. In order to establish the nature of the behavior of wall mobility in Y F e 03 with temperature and to insure that the measured mobility does indeed reflect the mobility characteristic of the bulk material and not the roughness condition of the sample surface, the temperature dependence of wall mobility was mea- sured (Fig. 1) in three different single crystal platelets of YFe03. Among the samples are differences in growth batch and in surface preparation. A more detailed description of these measurements in Y F e 03
has been published previously by the author [15].
The Y F e 03 crystals were grown by Remeika [16]
from a flux composed of PbO and B203 and were shown by mass spectrographic analysis to have a total impurity level, except for Pb, of less than 20 ppm.
Remeika and Kometani [17] have shown that for Y F e 03 grown in this manner one can expect almost 0.3 % by weight of Pb to go into the lattice replacing yttrium ions. The samples are platelets normal to the
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711152
DOMAIN WALL DYNAMICS IN THE ORTHOFERRITES C l - 437
c-axis of the orthorhombic crystal structure, which is the easy direction for the net magnetization. The sample designated A (Fig. 1) was first polished with diamond powder in steps of decreasing particle size to a thickness of about 150 pm with the last diamond particle size not larger than 1 pm. The remainder of the polishing to the final thickness of 50 pm was
--tC S A M P L E - A
-.+...-.+. S A M P L E - B
-%--73-SAMPLE-C
1,000
0 50 100 150 200 250 300 350
T E M P E R A T U R E ("K)
FIG. 1. - Temperature dependence of domain wall mobility measured in three samples of YFeO3. Differences in their pre- paration are described in the text (After reference [l]).
accomplished with mechanical polishing on a very fine scale in combination with chemical polishing perfor- med equally on both sides of the sample plate. This surface treatment left sample A with a wall motion coercive force of less than 0.1 Oe. The measured wall mobility was found to be independent of the magnetic field gradient used to establish the static equilibrium position of the wall as required for the validity of the description of wall motion by the viscous damping model assumed in reference [14]. Although sample B came from a different batch, it was grown by the same flux method as was sample A and underwent the same surface processing. Sample C came from the same melt as sample B but was polished all the way to a 50 pm thickness using the 1 pm diamond powder, a procedure which left the sample with a wall motion coercivity too high to permit wall mobility measure- ment with the oscillating wall technique. Sample C was then given a fifteen hour anneal at 1,500 OC in an oxygen atmosphere, a treatment found by Heinlein and Pierce [l81 to be capable of removing the elastic and plastic strain introduced into the orthoferrites by rough polishing. The anneal reduced the coercivity of sample C to about 0.1 Oe and permitted measurement of the mobility. Although there are differences at the lower temperatures, the measured wall mobility for all three YFe0, samples shows essentially identical behavior above about 180 OK.
The substitution of only a small percentage of Tb+, ions for Y+, in YFe0, is accompanied by a very substantial reduction in domain wall mobility, particularly at low temperatures. This shows up dra- matically (Fig. 2) if the temperature dependence of the wall mobility measured in a sample with the nominal composition Yo,,3Tbo~o,Fe03 is compared
with the behavior of the mobility measured in sample A of the pure YFeO,. While at room temperature the wall mobility of the doped sample is reduced by only a factor of two from the mobility of YFeO,, it si reduced by more than three orders of magnitude at 78 OK. Wall motion damping in pure TbFeO, is consi- derably stronger yet, as evidenced by mobility mea- surements in this material (Fig. 2). The Tb doped YFeO, and the pure TbFeO, were grown using the same PbO-B203 flux method and were prepared for
TEMPERATURE (OK)
FIG. 2. -Temperature dependence of domain wall mobility measured in a sample with the nominal composition
Y0.93Tb0.07Fe03
and in pure TbFeO3 as compared with the temperature depen- dence of mobility measured in pure YFe03.
measurement using the same combination fine scale mechanical and chemical polishing technique used on the YFeO, sample A.
Measurements of domain wall mobility have been made on samples containing nominally 0.03, 3.5 and 40 atomic percent Sm+, substituted for Y+, in the YFeO,. These samples were also grown from a PbO-B203 flux melt and consisted of c-axis platelets polished to a thickness of approximately 50 pm by means of the same technique used on the pure YFeO, saniple A. The substitution of Smf for Yf reduces the wall mobility (Fig. 3) substantially from that measured in pure YFeO,, particularly at lower tem- peratures, much as the substitution of Tb+, does.
However, Sm+, appears to be somewhat less effective than Tbf in its ability to retard domain wall motion.
For the sample with 40 atomic percent Sm+, substitu- ted for Y+3, the temperature range of reorientation of the easy axis of magnetization from the c-axis to the
a-axis begins at about 270 OK and ends at 230 O K . As shown by Sherwood and al. [19], the reorientation range is sensitively dependent upon Sm+, concentra- tion, occurring at higher temperatures with larger proportions of Sm. The temperature dependence of mobility measured on this sample just above the
FIG. 3. - Temperature dependence of wall mobility measured in samples of composition Y1-zSmzFe03 for several different values of X. The wall mobility measured in pure YFeO3 is shown for comparison. Measurements on the sample with x = 0.4 reflect the decrease in uniaxial anisotropy as the tem- perature is reduced toward the reorientation range which has
its upper limit at about 270 OK for this sample.
-
UI
5 10-
- .
>
c
=! 5 - m 0
I
_t 2
0 5
,
reorientation range reflects the rapid variation of uni- axial anisotropy as predicted by Gyorgy and Hage- dorn [20]. The mobility was not measured below the reorientation range in this sample because the measu- ring technique does not work with the magnetiza- tion in the plane of the sample plate.
-
J-)Y%X:
-' " ' 1 " " 1 ~ " ~ 1 ' ~ " ' " ' ~ 1 ' " " ' ~ ~ '
n\+.:
111. Interpretation of the measured mobility. -
The high wall mobility measured in YFe0, (Fig. 1) as compared with that measured in the rare-earth orthoferrites (see reference [14]) suggests that the magnetic rare-earth ions may provide the dominating wall relaxation mechanisms. Since Y+, is diamagnetic, any wall relaxation mechanism involving coupling between the iron sublattice magnetizations and a rare- earth ion moment is, of course, not operative in pure YFeO,. But those mechanisms that are operative in pure YFeO, are expected to be operative in the rare- earth doped YFeO, as well. Although the detailed nature of these mechanisms is not clear, their combi- ned effect is at least characterized by the temperature de~endence of the wall mobility measured in pure
50 100 150 200 250 300 350
TEMPERATURE (*K)
YF~O,.
It is shown in reference [l51 that the behavior of the mobility measured in the three samples A, B and C (Fig. 1) is characteristic of the bulk crystal and not dependent on surface roughness. On the basis of the agreement of measured mobility values for all three
YFeO, samples in the tempsrature range above 180 O K , it is further concluded that the behavior in this range indeed represents the relaxation mechanisms common to both the pure and the doped YFeO,. The differences in mobility among the three samples at the lowest temperatures may be due to nonstoichiometry arising from growth in Pb-flux but this is not certain. Remeika and Kometani [l71 found that Pb goes into the lattice with a charge compensation mechanism involving the replacement of with Pbi2 accompanied by a change in valence of ]Fe+, to Fei4. Iron in both ionization states introduces the possibility of relaxation through (( electron hopping D as proposed by Galt [21].
Such a mechanism may cause a reduction in mobility at the lower temperatures that would be dependent upon Fef concentration. For the purpose of interpre- ting the behavior of the mobility in the Tb and Sm substituted YFeO, samples, the wall mobility measn- red in sample A (Fig. l), hereafter designated p,, is considered to be the mobility arising from those relaxation mechanisms common to all three YFeO, samples and the substituted YFeO,.
In the Tb and Sm substituted samples it is assumed that relaxation through coupling between the iron sublattice magnetizations and the rare-earth ion mo- ments contributes a wall damping pressure which is additive to the damping pressure produced by the other relaxation mechanisms operative in the pure YFeO, as well. The additivity of the wall damping pressures implies that
where pM is the mobility measured in the substituted sample and p, is the mobility that would be measured if relaxation through the rare-earth ions were the only active mechanism. Harper and Teale [3-51 have shown this to be a justifiable assumption in their interpreta- tion of the temperature dependence of wall mobility measured in Yb and Er doped YIG. Exchange and dipolar coupling between the iron and rare-earth ions provide means whereby energy level spacings of the rare-earth ions can vary with the directions of the iron sublattice magnetizations. The rate of energy loss from the motion of the iron moments then depends upon the relaxation time characterizing the population distribution among the rare-earth energy levels. Essen- tially this model, now known as the c( slow relaxation model )>, was used by Galt [21] and Clogston [22]
to describe losses arising from valence exchange or electron hopping. - - -
An expression for the contribution p, arising from the rare-earth ions can be obtained from the work of Harper and Teale [3]. They consider a system containing ions with energy levels z i and population densities ni per cm3 which are dependent upon the direction 8 of the net magnetization M relative to a crystallographic axis. For a domain wall moving in the y-direction in such a system is given by
where zi is the relaxation time for the population density n i to reach its thermal equilibrium value ni,.
DOMAIN WALL DYNAMICS IN THE ORTHOFERRITES C 1
-
439The directions of M in the domains on the two sides of the wall are B, and 8,. The quantity dB/dy for the orthoferrites, in accordance with the static domain wall theory of Kittel [23], satisfies
where A is the exchange constant and K is the uniaxial anisotropy constant.
I. TERBIUM SUBSTITUTED Y FeO,. - The Tb+, ion has a 4P8 configuration with a 7F, free ion ground state. It is not a Kramers ion, but there is evidence that the lowest crystal field state of the Tb+3 ion in the orthoferrite has an accidental degeneracy. Meta- magnetic transitions observed by Holmes and al. [24]
from magnetization measurements and optical spectra reported by Hufner and al. [25] show that the lowest crystal field state for Tb'3 in the isomorphic com- pound TbA10, is an accidental doublet composed of M, =
+
6. Specific heat measurements by De Comba- rieu and al. [26] on TbFeO, as well as TbAlO, and TbCoO, are consistent with the same accidental dou- blet in a11 three compounds.If the ground state doublet of splitting S is isolated sufficiently from higher states so that only the doublet is appreciably populated, the application of Boltzmann statistics to the populations of the two levels reduces eq. (2) to
where N is the number of Tb+3 ions per cm3, k is Boltzmann's constant and dO/dy has been replaced by means of eq. (3). Although the splitting S of the accidental doublet in TbFeO, is not known, it is expected to be small enough so that sech2(6/2 k T ) X 1 for T
>
78 OK. This expectation is based on the fact that in the orthoferrites, exchange and dipolar jnter- actions with the iron sublattices cause only very small splittings of those rare-earth ions having ground state doublets. For example Schuchert and al. [27] found a splitting of 1.5 cm-l for the ground state doublet of Dy+, in DyFeO, and Faulhaber and al. 1281 and Wood and al. 129, 301 found the ground state doublet of Er+3 in ErFeO, to be split by about 3 cm-' below the reorientation temperature and less than 1 cm-' above. A reorientation is not observed in YFeO,. In TbFeO, it occurs at 8.4 OK, according to Bertaut and al. [31]. Under these assumptions, p;' for a 1800 wall in the Tb doped YFeO,, where the easy direction of net magnetization lies along the c-axis, can be expressed as~ = ~ ) ' - ~ [ ~ ~ ) ' s i n O d B .
PD 8 MkT (5)
Absolute values of z cannot be deduced from the experimental values of pD because the nature of the accidental doublet is not known in detail sufficient for the evaluation of dS/dO. However, the relative tempe- rature dependence of z can be deduced by normalizing
p;' to one temperature. With eq. (5) normalized at 78 OK, z(T) is expressed as
It is assumed that 6 is essentially temperature inde- pendent. The neglect of the temperature dependence of the wall width factor (A/K)% is not unreasonable since Rossol 1321 has shown the domain wall energy, o, = ~(AK)&, in YFeO, to be essentially independent of temperature from 78 OK to room temperature and measurements of domain wall energy in the
Y0.93Tb0.07Fe03
sample show the same behavior with approximately the same wall energy as YFeO,. The temperature dependence of M is obtained from the magnetizations of YFeO, and TbFeO,, measured by Gorodetsky and Treves [33], in the linear combination indicated by the nominal formula for the doped sample. The mobility pD attributed to the Tb+, ions is determined from eq. (1) using the mobility measured in YFeO, sample A (Fig. 1) for p,.
Plots of (TM/p)T/(TM/p)T,780K as a function of T-l for the Yo~,3Tbo~07Fe03 sample (Fig. 4) with
FIG. 4. - Temperature dependence of TM/fl~a and T M / m normalized to their values at 78 OK. The deviation from expo- nential behavior observed for T M I ~ M near room temperature occurs because wall damping forces arising from other relaxa- tion mechanisms become comparable with those arising from
the Tb ions at these temperatures.
p = FM, the measured mobility, and with p = p, differ only near the room temperature end where U,'; is no longer a negligible fraction of ,U&'. The plot for p = pD is just a plot of eq. (6) and is quite well fit by a straight line indicating that z(T) has a temperature dependence approximated by eAlkT, where
A/k = 469 OK or A = 326 cm-
.
Without detailed knowledge of the ground state mul-
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