Appl. Phys. A 73, 327–330 (2001) / Digital Object Identifier (DOI) 10.1007/s003390100735 Applied Physics AMaterialsScience & Processing

Ferrimagnetic resonance of manganese ferrites with iron excessA.G. Flores∗, V. Raposo, L. Torres, J. Iñiguez

Departamento de Fısica Aplicada, Universidad de Salamanca, 37071 Salamanca, Spain

Received: 25 May 2000/Accepted: 9 October 2000/Published online: 26 April 2001 – Springer-Verlag 2001

Abstract. Ferrimagnetic resonance linewidths of polycrys-talline and single crystal manganese ferrites, MnxFe3−xO4with x < 1.0, were measured at 8.9 GHz in the range77–320 K. Conductivity measurements were carried out from100 Hz to 40 MHz. The behavior of the ferrimagnetic reson-ance linewidth and of the resonance field was different fromthat obtained for manganese ferrites with x = 1. These dif-ferences are attributed to the presence of a resonance modein addition to the uniform resonance mode. The variation ofthe skin depth as a function of the temperature and the highconductivity of the samples is responsible for the appearanceof this extra mode. This assumption is corroborated by theanalysis of the asymmetry of the absorption curve.

PACS: 76.50+g

It is well known that magnetic resonance analysis consti-tutes a powerful technique in the research of magnetic andtransport properties of different materials [1–5]. Chemicalcomposition and crystalline structure in oxide compoundslike perovskites, manganites, ferrites and garnets is usuallytested by means of electron spin resonance (ESR) and fer-romagnetic resonance (FMR) linewidth studies [2, 3]. Theseworks clearly show the noteworthy linewidth versus tempera-ture dependence. This dependence is explained in terms of thedemagnetizing fields associated with the superficial porosity,as well as chemical and crystalline inhomogeneities and eddycurrent contributions [6].

Recently, many studies of magnetic resonance in dopedmixed manganites, RxB1−xMnO3 (0 < x < 1, R = rare earthand B = Ca, Sr, Ba, Pb, have been published [7, 8]. These andother perovskites are of interest because of their very largemagneto-resistance. It is important when studying these sys-tems to make sure that the samples are well characterized andof good quality [9]. X-ray powder diffraction frequently doesnot indicate the presence of spurious phases or give any ev-idence suggesting that the samples are inhomogeneous. On

∗Corresponding author.(Fax: +34-23/294-584, E-mail: anagf@gugu.usal.es)

the other hand, it has been shown that magnetic resonance isan extremely sensitive and useful technique for studying thequality of the samples in these systems [2, 3].

In order to show how the ferrimagnetic resonance al-lows us to analyze the magnetic properties in oxide materi-als, preliminary research in manganese ferrites, MnxFe3−xO4(x = 0.8 and x = 0.9), is presented. This work is a contin-uation of the ongoing research by our group in manganeseferrites [4, 5].

1 Experiments

Single crystal Mn0.8Fe2.2O4 was grown by the float-zonetechnique and annealed for 72 h in CO2 at temperatures in therange 1150–1190 ◦C. Polycrystalline samples, Mn0.8Fe2.2O4and Mn0.9Fe2.1O4, were fabricated by the ceramic methodin a thermogravimetric apparatus manufactured by Setaram(TG-DTA 92). Both samples were sintered at 1300 ◦C in CO2for 4 h. All samples were characterized by X-ray diffrac-tion and displayed a single spinel phase. Single crystalcomposition was confirmed by inductively coupled plasmaspectrometry.

In order to carry out FMR measurements, the sampleswere spherically shaped by an abrasive technique that is ca-pable of attaining sample diameters less than 1.6 mm [10].FMR measurements were made by monitoring the reflectedwave in a TE111 mode cylindrical cavity working at X-bandfrequency (8.9 GHz) [4]. A dielectric support (Teflon) witha center hole was placed at the bottom of the cavity to in-troduce the sample in such a way that it was free to orientalong the external field. The system was fully computerizedand the operational temperature range was 77–320 K. Thefull FMR line-shape was stored at each temperature in orderto analyze the real and imaginary parts of the susceptibilityand to obtain the FMR linewidth and the resonance field bymeans of a nonlinear fitting technique [11]. This techniqueis based on a modified Bloch–Bloembergen formalism of thetorque equation [12] involving the addition of phenomeno-logical damping terms that account for the relaxation of themagnetization. The corresponding relationship between the

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imaginary part of the susceptibility and the FMR linewidthand resonance field is given by [11]:

χ ′′

χ ′′max

= (∆H/2)2H[4H2

0 + (∆H/2)2]

H0

[(H2

0 − H2 + (∆H/2)2)2 +4H2(∆H/2)2

] (1)

where H is the static field, ∆H is the FMR linewidth and H0the resonance field. (Gaussian units are used throughout thiswork).

2 Results and discussion

In Fig. 1, the variation of the FMR linewidth with temperaturefor all samples in the study is exhibited. The values presentedfor the FMR linewidths in these samples of MnxFe3−xO4with x < 1 (both single crystal and polycrystalline) are muchhigher than those shown for samples with x = 1. FMR

Fig. 1. FMR linewidths of single and polycrystalline manganese ferrites,Mn0.8Fe2.2O4 and Mn0.9Fe2.1O4

linewidths for MnFe2O4 are lower than 250 Oe, as can beseen in [4].

Resonance fields for these samples also differ from thoseof manganese ferrites with x = 1 [4]. As can be seen in Fig. 2,for the sample Mn0.9Fe2.1O4 (Fig. 2c) the resonance field in-creases with temperature, reaching a maximum at tempera-tures close to 125 K. Resonance fields for single and poly-crystalline samples with x = 0.8 decrease with temperature(Fig. 2a,b).

As is well known, in different ferrites (e.g. manganese fer-rites) resistivity changes close to stoichiometric composition;it is very low in the region of iron excess [13, 14]. This be-havior can be observed in Fig. 3. Therefore, the Q value of thecavity is reduced considerably, and it is necessary to introducesamples with diameters larger than 1.3 mm if an absorptioncurve is to be observed.

For samples of these sizes, the skin depth at room tem-perature (δ ≈ 0.2 mm) [13] is smaller than the radius of thesample. Consequently, the microwave field will no longer

Fig. 2. Resonance field vs. temperature for single crystal and polycrystallineferrite Mn0.8Fe2.2O4 and for polycrystalline ferrite Mn0.9Fe2.1O4

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Fig. 3. Real and imaginary parts of impedance vs. frequency forMn1.0Fe2.0O4 and Mn0.9Fe2.1O4 at room temperature

be uniform inside the whole sample. We predict a model inwhich a new precession mode will be generated in additionto the uniform mode. This new mode is called the ‘superficialmode’, since it is created by the penetration of the microwavefield into only a small superficial layer of the same order ofmagnitude as the skin depth.

As temperature decreases, conductivity also decreases;therefore, skin depth increases and becomes comparable tothe radius of the sample [13]. So, the microwave field be-comes uniform in a larger volume until it becomes uniformin the whole sample at a given temperature (called the criticaltemperature). Below this temperature only the uniform modewill precess. Similar results are found for high-resistivitysamples [15, 16].

Changes in the resonance field (Fig. 2) are attributed tothis variation of the skin depth inside the sample. At tempera-tures below the critical temperature, the resonance occurs inthe whole volume of the sample; therefore the resonance field,given by the Kittel resonance condition [17], increases withtemperature (same behavior as other manganese ferrites withx = 1 [4]).

As temperature increases, the skin depth goes down andbecomes comparable to the radius of the sample at the criti-cal temperature. The superficial mode appears, and the Kittelcondition (valid only for the uniform mode) will no longer beapplicable for temperatures higher than the critical tempera-ture. Therefore, when the new mode appears, a change in theresonance field is expected. This occurs for Mn0.9Fe2.1O4 attemperatures close to 125 K, as can be seen in Fig. 2c. Forthis sample, the critical temperature is 125 K, and the skindepth at this temperature is expected to be half the diameter ofthe sample, δ ≈ (1.3 mm)/2 = 0.75 mm. In this way, a linear

variation of the skin depth from 0.75 mm at 125 K to 0.2 mmat room temperature is predicted using FMR measurements.Studies of the conductivity performed by Lotgering confirmour results [13]. For Mn0.8Fe2.2O4 (Fig. 2a,b), the resonancefield decreases with temperature from 77 to 320 K. The skindepth is less than the sample radius in this range of tem-peratures; thus, the superficial mode dominates the resonance.A maximum is expected to occur at lower temperatures, whenthe skin depth becomes larger than the radius of the sampleand the uniform mode precesses alone.

When the resonance is made up of different modes, the re-sulting absorption curve is given by the sum of all the modespresented. Consequently, a non-symmetric absorption curveis obtained. In this case, the uniform mode and the superfi-cial one appear together near the critical temperature, whenthe skin depth is comparable to the radius of the sample. ForMn0.9Fe2.1O4, this occurs close to 125 K. The asymmetry ofthe absorption curve has been defined as a/(a +b), as seenin the inset of Fig. 4 [18]. A maximum in the asymmetry isobtained close to 125 K as predicted, confirming our theoryabout the contribution of the superficial mode.

Because of the high conductivity of the samples, FMRlinewidths are much higher than for Mn1.0Fe2.0O4 [4].Linewidths obtained for single and polycrystallineMn0.8Fe2.2O4 ferrites are similar. This fact indicates thatpolycrystalline contributions (porosity and anisotropy con-tributions [6]) are not important in polycrystalline sam-ples. In such a case, only single-crystal mechanisms arepresent [6]. Eddy current contributions dominate the micro-scopic processes because of the high conductivity of thesamples.

From the results presented above, it can be deduced thatthe high conductivity of the samples is crucial to understand-ing the microscopic processes in FMR of manganese ferriteswith iron excess. The analysis of both resonance field and

Fig. 4. Asymmetry of the absorption resonance curve for the polycrystallinesample Mn0.9Fe2.1O4

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linewidth asymmetry makes it possible to propose a theoryin which a superficial mode is generated next to the uni-form mode at temperatures higher than a critical temperature.Estimation of this critical temperature allows us to considera linear variation of the skin depth with temperature fromFMR experiments similar to that predicted by conductivitymeasurements [13].

Acknowledgements. This work has been partially supported by projectMAT98-0416-C03-03.

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