μSR INVESTIGATIONS AT PNPI
S.G. Barsov, A.L. Getalov, E.N. Komarov, V.P. Koptev, S.A. Kotov,A.E. Moroslip,
I.I. Pavlova, G.V. Shcherbakov, S.I. Vorobyev
1. Introduction
Magnetic properties of RMn2O5 manganites(R = Eu, Gd), of the nano-structured Fe3O4/D2O ferrofluid and of the EK-181 steel were investigated by the muon spin rotation (μSR) method. The experiments were carried out with the μSR set-up [1] placed at the polarized muon channel of the PNPI synchrocyclotron [2]. Muons of P=90MeV/c momentum with ΔP/P=0.02 (FWHM) were stopped inside of a sample under investigation, and positrons resulting from the muon decay were detected within a certain solid angle. The μSR set-up allows us to vary the sample temperature over 10–300K range and to apply an external magnetic field up to 1.5kOe.
Since muon decay is asymmetric with respect to the muon spin (magnetic moment) direction, the positron count rate varies in time not only due to finite muon life-time τμ, but also due to the muon spin behavior inside of the sample. In general, a decay positron time spectrum can be expressed as
(1)
where tis the time interval measured for every detected positron starting from the moment of the muon stop.
Apart from an accidental background B and the normalization factor N0, the total experimental asymmetry a0 is proportional to the initial muon polarization. The value of a0 is independent of the temperature and the magnetic field applied to a sample, while it depends on other experimental conditions (such as the beam momentum, the geometry and efficiency of the set-up, the size and density of the sample), which are fixed during one set of measurements. The specific value of a0 can be measured for a sample in the paramagnetic state.
The relaxation function G(t)in Eq. (1) originatesfrom the polarization behaviour of the muon ensemble inside of the sample resulting from the interaction of each muon magnetic moment with the local magnetic fieldhloc. Neglecting effects of the muon-electron bound state (muonium), such interaction leadsto the Larmour precession of the muonic magnetic moment with a frequency ωμdetermined by thehlocmagnitude. So,evaluationof the function G(t)and its parameters delivers information on the distribution of internal magnetic fields. Note that the μSR-method can be used in the absence of any external magnetic fields.
Taking into account that local fields may be unstable in time due to, e.g., spatial magnetic fluctuations near a phase transition, the G(t) function can be represented as a product of two functions:
G(t) = Gd(t)∙Gs(t). (2)
The dynamic relaxation function Gd(t) describes the influence of the hloc fields withtypical correlation times comparable or smaller than the muon precession period. This usually leads to an exponential decrease of polarization, so that the function Gd(t)takes the form:
Gd(t) = exp(–λt). (3)
On the other hand, local fields changing in time much slower than ωμ/2π can be considered as static ones. The static relaxation function is defined by the distribution of such local fields over the sample volume. Some specific relaxation functions corresponding to different types of the magnetic phase wereobtained in [3]. The explicit forms of Gs(t) used for data analyses are presented and discussed below in the corresponding sectionsof this paper.
2. Manganites EuMn2O5 and GdMn2O5
The materials RMn2O5 (R is a rare-earth ion) are considered to be promising materials for production of devices which are able to manipulate with both the electric and magnetic signals due to strong correlation
of the magnetic and electric phenomena observed. In particular, a large magnetoelectric effect was discovered in these substances at low temperatures, where coexistence of antiferromagnetic (AFM) and ferroelectric (FE) ordering takes place [4].
Here, we report results of a comparative study of EuMn2O5 and GdMn2O5 manganites by the μSR method. Since magnetic moments of rare-earth ions in these compounds are significantly different (namely, the ground state of Eu3+ is nonmagnetic, while the moment of Gd3+ is about 3.5 μB) such a study allows to clarify effects related to the R3+(Mn4+,Mn3+) exchange interaction. In addition, for each of the manganites a ceramic sample anda sample consisting of chaotically oriented macroscopic (2–3mm) single crystals were investigated. It is also worth mentioning that inthe case of GdMn2O5 the use of neutron scattering technique is practically impossible due to high absorption of neutrons by Gd nuclei.
Figures 1a, b and 2a, b show temperature dependencies of the dynamic relaxation rate λ obtained in the absence of external magnetic fields for EuMn2O5 and GdMn2O5, respectively. For all samples, the relaxation rate has a pronounced maximum at nearly the same temperature of about 40–45K, which corresponds to the paramagnetic–antiferromagnetic (PM–AFM) phase transition caused by the AFM ordering of the Mn3+ and Mn4+ magnetic moments.Although a large difference in the Eu3+ and Gd3+ moments does not affect the transition temperature, it manifests itself in the relaxation rate value, which is 10 times larger in GdMn2O5 than in EuMn2O5 even in the PM state (TTN1). An unusually large value of λ (λ≈1µs–1, Fig.2a, b), was found to be independent of temperature up to 300K.It may be caused by the presence of short-range magnetic correlations well above TN1, which has been observed in magnetic susceptibility measurements [5].
Fig. 1.Temperature dependencies of the dynamic relaxation rate in EuMn2O5: for a ceramic sample (a) and for a sample consisting of single crystals (b). The phase transitions indicated by arrows are discussed in the text
Fig. 2. Temperature dependences of the dynamic relaxation rate in GdMn2O5: for a ceramic sample (a) and for a sample consisting of single crystals (b). Solid circles represent the data taken during heating of the samples. The data taken during cooling are denoted
by open circles. Triangles show the results of measurements in the 280 Oe external magnetic field. The phase transitions indicated by arrows are discussed in the text
The anomalies in the temperature dependencies of λ below TN1correspond to the known ferroelectric phase transitions (TFE1 and TFE2 in Fig. 1a, b)[3] and the magnetic ordering of Gd3+ moments (TN2 in Fig.2a,b) [6]. In contrast to EuMn2O5, the anomaly at the temperatureTL (Fig.2b)is related to a lock-in transition (rearrangement)of the AFM order but not to FE phase transitions, which areknown [5] to take place in the 22–30K range. It is interesting to note that the anomaly at TLwas not seen in the ceramic sample of GdMn2O5.
The best description of the time spectra below the temperature TN1was achieved using the collinear (anti)ferromagnetic state model [3]:
dN/dt~{a1·[1/3+2/3·exp(–Δ1·t)·cos(Ω1·t)]+
+ a2·[1/3+2/3·exp(–Δ2·t)·cos(Ω2·t)]}·Gd(t), (4)
where theterms in square brackets represent a typical form of the static relaxation function inthe case of random orientation of internal magnetic fields. The muon spin precession frequency Ωi=2πFi is determined by the mean value of the fields, while the static relaxation rate Δiis defined by their spread. Two different precession frequencies observed below TN1 originate from two different sites of muon localization in the lattice cell. The partial asymmetries a1 and a2 depend on relative populations of the localization sites,but their sum (a1 + a2) is expected to be equal to the total asymmetry a0determined above the temperatureTN1.
Fig.3. Temperature dependence of the relative “residual” asymmetry as/a0 for a sample EuMn2O5 consisting of single crystals (closed circles) and for a ceramic sample (open circles). The arrows mark the transition temperature TFE1≈30K for a single crystal sample and the magnetic ordering temperature TN1≈ 40 K
Fig.4. Temperature dependence of the relative residual asymmetry as/a0 for a sample GdMn2O5: the levels of the normalized asymmetry as/a0= 1/3 (T < TN1) and as/a0= 1 (T > TN1) are marked by the dash-dotted lines: a – for a ceramic sample; b – for
a sample assembled from small single crystals (solid circles refer to heating, open circles refer to cooling); measurements in the external magnetic field H = 280 Oe are shown by triangles
However, it has been found that at T <TN1 some part of the initial muon polarization is lost so fast that (a1+a2)a0. To avoid an uncertainty related to the phase of the muon precession, the total asymmetry of the non-precession terms in (4) is presented in Figs.3 and 4a, b as a function of temperature. It is clearly seen that the normalized “residual” asymmetry as/a0 is significantly smallerthan its expected value 1/3 at TTN1 in all samples excluding GdMn2O5ceramics. The lack of as/a0 may be explained by formation of a muonium. Indeed, the magnetic ordering leads to some change of the charge distribution, and, as aresult, the probability of muonium production may be increased. An important role ofthe charge transfer processes was pointed outin astudy of the second optical harmonic in TbMn2O5[7]. In particular, it was found that the external magnetic field increases the charge transfer probability. In our study, the external magnetic field of 280Oe decreases the as/a0 value at TTN1 in EuMn2O5 samples, as well as in GdMn2O5 ceramics, but does not affect the “residual” asymmetry in the sample consisting of single crystals (Fig.4b).
Another evidence of modification of magnetic properties due to strong Gd-Mn interaction comes out from the temperature dependencies of Ω1 and Ω2, see Eq. (4). In contrast to the dependencies presented in Fig.5a, b for GdMn2O5, both precession frequencies in EuMn2O5 were observed to appear at the same temperature just below TN1, and tofollow quite well the Curie-Weiss temperature function which is typical for Heisenberg 3D magnets [3]. Despite the value of Ω1 (as well as the value of Ω2) is nearly the same at T30K for each of the samples under investigation, in the case of GdMn2O5 only the frequency Ω2follows the Curie-Weiss dependence. In the (TN1–TL) temperature range, the amplitude of Ω2 is very small (a2≈0), but the partial asymmetry a1is equal to the sum (a1+ a2)measured at T30K.So, the muon localization site responsible for the frequency Ω2is not occupied in this temperature range in GdMn2O5, while at
T30K its population becomes about 70–80%.
Fig.5. Temperature dependencies of the muon precession frequencies in internal magnetic fields in GdMn2O5:
a – in a ceramic sample; b – in a sample consisting of single crystals. Solid circles stand for the F1frequency, open circles– for the F2frequency. Arrows indicate the phase transition temperatures. Dotted curves show the fits ofF2dependencies by the Curie-Weiss function(1 – T/TL)β; TL= 35 K; β = 0.39 ± 0.02
3. Fe3O4-based nanostructured ferrofluid
A modification of magnetism in the objects withdimensions smaller than a domain size is of greatinterest from both scientific and practical points of view. Information on the progress in such studies of magnetic nanoparticlescan be found in review [8].
Magnetic systems consisting of nanoparticles of magnetite Fe3O4 or MeFe2O4, where Me denotes Mg, Cr, Mn, Fe, Co, or Zn, dispersed in organic or inorganic liquids, allow to vary the concentration of magnetic particles. The stability of magnetic fluids is ensured by the surfactant coating of the magnetic-particle surfaces which prevents their van der Waals and magnetic dipole-dipole conglutination. The magnetic moment of each nanoparticle at temperatures below the Curie temperature for Fe3O4is supposed to be equal to the total magneticmoment of iron ions. Such a systembehaves as a (super) paramagnetic material if nanoparticleconcentration in the medium is low (<5–7%).The magnetic structure of Fe3O4 single crystalsis well known [9]. This compound is a ferromagnet at the temperatures below the Curie temperatureTC=858K. The Verwey (metal–dielectric) structural transition occurs at the temperature TV123 K.
The studied ferrofluid (Fe3O4/2DBS/D2O) was a suspension of nanodispersed magnetite (Fe3O4) in heavy water (D2O) stabilized by the dodecylbenzenesulfonic acid (2DBS). The volumetric concentration of magnetic particles was 4.7%. One milliliter of the ferrofluid contained 0.244g of magnetite, and the ratio was 0.3g of the surfactant per 1g of Fe3O4.
The temperature dependencies of the relaxation rate and the precession frequency of the muon spin in the ferrofluid Fe3O4/2DBS/D2O were investigated in the temperature range from 26 to 300K [9]. The muon spin precession in a sample under investigation was compared with thatin a Cu sample. For the last one the experimental asymmetry of the decay position was a=0.302±0.002 at the external magnetic field H=280Oe.
For the Fe3O4/2DBS/D2O sample, the observed muon polarization fraction was about 30% smaller than that for the D2O sample,because the precession frequency of the muon stopped inside of magnetic nanoparticles is very large, and it is integrated due to a limited time resolution of the μSR set-up. Thus, only the precession of the muons stopped outside the particles could be resolved.
The fraction of muons stopped inside of nanoparticles is in agreement with the thickness of Fe3O4 along the muon beam, which is about 0.25g/cm2 to be compared with 1.2g/cm2 thickness of the sample.
Fig. 6. Shift of the muon-spin precession frequency: a – versus temperature for H = 280 Oe and b – versus external magnetic field
atT=200 K. The closed and open circles are the data for Fe3O4/2DBS/D2O and D2O, respectively. The samples were cooled in
the magnetic field
In the sample Fe3O4/2DBS/D2O, the muon relaxation rate was much higher than that in the D2O sample. This effect is completely due to interaction of the magnetic moments of muons and nanoparticles.When the magnetic field is absent, the magnetic moments of nanoparticles are directedarbitrarily. The external magnetic field gives rise to a small polarization of the magnetic moments of nanoparticles. As a result, the magnetic field in a sample is different from the external one. The frequency shift Δω=ω–ω(Cu) in D2O water and in the Fe3O4/2DBS/D2O sample with respect to the precession frequency in the Cu sample is shown in Fig.6 a, b. As one can see,in both samples the frequency shift does not depend on temperature. In the ferrofluid, it is about 6 timeslarger than that in D2O water and has an opposite sign. This effect is due to the fact that D2O water is diamagnetic,while the Fe3O4/2DBS/D2O sample is (super) paramagnetic.
The frequency shift Δω is proportional to the mean magnetic field ΔB generated by the nanoparticle magnetic moments. In one’s turn, the last one is proportional to the magnetization M of the sample:
Δω ~ γ·ΔВ ~ М,
where γ=13.5544kHz/Oe is the gyromagnetic ratio ofthe muon.
It was found experimentally that at small nanoparticle concentrations (<6−7%) the magnetization of paramagnets is described by the Langevin function [10]:
M=n·m·(cth ξ – 1/ξ),
where n is the number of nanoparticles per volume unit;m is the magnetic moment of the nanoparticle (J/T);ξ=μ0mH/kT, μ0=4π×10–7 is a constant, H is the magnetic field (A/m), k=1.38×10–23J/K is the Boltzmann constant, T is the absolute temperature.
Finally, one findsthat at T=200K the mean value of the magnetic moment of a nanoparticle is
,
hereμBis the Bohr magneton.
As the magnetic moment of the molecule Fe3O4 is 4.1 μB [11], the nanoparticle consists of
1.2×104 Fe3O4moleculesand, correspondingly, its size is about 12nm.
Thisvalue is in good agreement with the value 11.2nm derived by fitting the magnetization curves with the Langevin function [12] for the studied sample.
4. Construction steel EK-181
Nuclear and thermonuclear reactors of new generations require radiation-heat-resistant materials with fastdeactivation of an induced radioactivity. However, they should withstand high mechanical loads under intensive irradiation,which usually leads to an undesirable increase of the temperature of the brittle-ductile transition.
At present, it is assumed that materialswiththe desired properties can be obtained by appropriate thermaltreatment of chromium ferritic-martensitic steelswith formationof nanoscale structures (clusters, nanoscale secondary phases, etc.)[13]. The structures like these have been found,for example, in samples of the steel EK-181.
This sectionreports very preliminary results obtained by the µSR-method for 2 samples of the EK-181 steel produced in different technological ways. The firstsample was just annealed at 1070°C, while the second one was in addition quenched at 1070°C and then tempered at 720°C for 3 hours.The samples were investigated in the temperature range 80−300K. The best description of the time spectra of the muon magnetic moment precession in internal fields was obtained in the framework of the hypothesis suggesting that two phase states (the collinear ferromagnetic (CFM) and the spin glass(SG))coexist:
dN/dt~{aCFM·[1/3+2/3·exp(–ΔCFM·t)·cos(ΩCFM·t)]+
+aSG·[1/3+2/3·(1–exp(–ΔSG·t))]}·exp(–λ·t). (5)
In the area of the brittle-ductile transition, an anomality in the temperature dependence of the dynamic relaxation rate λ (at 180−200K, Fig.7) and the redistribution of the partial contributions aCFMand aSGwere observed(Fig.8).
We plan to continue systematic studies of these samples and, furthermore, to investigate the effect of the thermal aging, hardening and thermal cycling in the area of the phase γ-αtransition witha subsequent release of stresses near the brittle-ductile transition.
Conclusion
Thus, the µSR investigation of multiferroics again demonstrates the efficiency of this method for studying magnetic materials.The µSR investigation of RMn2O5 (R=Eu, Gd) samples (consisting of single crystals and ceramic grains) has revealed a number of interesting features of this compound. The charge density changes locally in both samples at the temperatures TTN; this change is manifested in additional depolarization of muons. The external magnetic field also leads to the loss of polarization in the samples at TTN and likely gives rise to additional redistribution of the charge density in the samples. The phase transitions observed at the temperatures TTN are not manifested in the distribution of the internal local magnetic fields. They are seen only in the temperature dependence of the dynamic relaxation rate λd(T). Theelectron density is redistributed at the phase transition point at the temperature TN. The mechanism of multiferroicity is possibly associated with this phenomenon.
The relaxation and shift of the precession frequency of the spin of a positive muon in the D2O medium, where Fe3O4 magnetic nanoparticles are randomly distributed, have been studied in a wide temperature range. The mean magnetic field generated by the magnetic moments of nanoparticles randomly distributed in the medium was determined experimentally. It was shown that the mean-field dependence on the external magnetic field does not contradict the Langevin law. The mean size and magnetic moment of the nanoparticles were estimated.
References
1.S.G. Barsov, S.I. Vorobyev, V.P. Koptev et al., Instr. and Exp. Techn. 50, 750 (2007).
2.S.G. Barsov, S.I. Vorobyev, V.P. Koptev et al., Preprint PNPI-2738, Gatchina (2007).
3.S.I. Vorobyev, E.I. Golovenchits, V.P. Koptev et al., JETP Lett. 91, 512 (2010).
4.S.I. Vorobyev, A.L. Getalov, E.I. Golovenchits et al., Preprint PNPI-2845, Gatchina (2010).
5.E. Golovenchits, and V. Sanina, Journ. Phys. Cond. Matter 16, 4325 (2004).
6.Yu.F.Popov, A.M.Kadomtseva, G.P.Vorobyev, S.S.Krotov, K.I.Kamilov, and M.M.Lukina,
Sov.Phys. Solid State 45, 205111 (2003).
7.Th. Lottermoser, D. Meier, R. Pisarev and M. Fiebig, Phys. Rev. B80, 100101(R) (2009).
8.B.M. Berkovski, V.F. Medvedev, and M.S. Krakov, Magnetic Fluids(Oxford Univ. Press, Oxford, 1993;
Khimiya, Moscow, 1989).
9.M. Balasoiu, S.G. Barsov, D. Bica et al., JETP Lett. 88, 243 (2008).
10.D. Bica, L. Vekas, M.V. Andreev et al., J.Magn.Matter311, 1721 (2007).
11.Physical Values: The Manual, Eds. by I.S. Grigoriev and E.Z. Meilikhov (Energoatomizdat, Moscow,
1991) (in Russian).
12.D. Bica, L. Vekas, M.V. Avdeev et al., J. Magn.Mater311, 1721 (2007).
13. A.G. Yoltukhovsky, M.V. Leontyeva-Smirnova, B.M. Cherna et al., in Structure Features of the Chrome
Steels with the Fast Radioactivity Drop, VANT2(63),142 (2004).
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