The dynamics of internal magnetic correlations in Tb 0.95 Bi 0.05 MnO 3 multiferroic in the temperature range of 10–290 K has been studied. Separation into two phases with different relaxations of the polarization of muons in the basic matrix of the crystal and the phase separation regions has been detected for the first time both in a magnetically disordered state at T < T N = 40 K and in a paramagnetic state in a transverse magnetic field of 290 G in a temperature range of 80–150 K. A muon ferromagnetic complex (Mn 3+ -Mu-Mn 4+ ), where the hyperfine interaction in a muonium depolarizes a muon in a time less than 10 −8 s, is formed at T < 40 K in phase separation regions containing pairs of Mn 3+ and Mn 4+ ions, as well as electrons that recharge them. In the matrix of the original crystal containing only Mn 3+ ions, a muonium is formed with a broken hyperfine bond. In this case, muons are depolarized at a high rate because of their interactions with the local magnetic fields of a cycloid. At temperatures of 80–150 K, one phase in the phase separation regions constitutes approximately 50% and is characterized by long relaxation times about 10 µs (described by the Gaussian relaxation function). The other phase is formed by Mn 3+ -Mn 3+ correlations in the short-range magnetic order regions in the matrix of the original crystal, which are weakly sensitive to a magnetic field of 290 G.

An anomalously strong relaxation of the muon polarization in a magnetically ordered state in the TbMnO3 multiferroic has been revealed by the method below the μSR Néel temperature (42 K). Such a relaxation is due to the muon channel of relaxation of the polarization and the interaction of the magnetic moment of the muon with inhomogeneities of the internal magnetic field of an ordered state in the form of a cycloid. Above the Néel temperature, beginning with temperatures depending on the applied magnetic field, a two-phase state has been revealed where one phase has an anomalously strong relaxation of the muon polarization for a paramagnetic state. These features of the paramagnetic state are due to short-range magnetic order domains that appear in strongly frustrated TbMnO3. A true paramagnetic state has been observed only at T ≥ 150 K.

A comparative μSR study of ceramic samples of the EuMn 2 O 5 and Eu 0.8 Ce 0.2 Mn 2 O 5 multiferroics is performed in the temperature range from 15 to 300 K. It is found that the Ce doping of the EuMn 2 O 5 sample slightly reduces the temperature of the magnetic phase transition from T N = 45 K for the EuMn 2 O 5 sample to T N = 42.5 K for the Eu 0.8 Ce 0.2 Mn 2 O 5 sample. Below the temperature T N for both samples, there are two types of localization of a thermalized muon with different temperature dependences of the precession frequency of the magnetic moment of the muon in an internal magnetic field. The higher frequency in both samples refers to the initial antiferromagnetic matrix. The behavior of this frequency in Eu 0.8 Ce 0.2 Mn 2 O 5 follows the Curie–Weiss law with the exponent β = 0.29 ± 0.02, which differs from the value β = 0.39 standard for 3D Heisenberg magnetics and is observed in EuMn 2 O 5 , because of the strong frustration of the doped sample. The temperature-independent low frequency is due to the presence of Mn 3+ –Mn 4+ ferromagnetic pairs located along the b axis of the antiferromagnetic matrix and in the regions of phase separation, which contain such ion pairs and e g electrons recharging them. In both samples, polarization losses are the same (about 20%) and are associated with the formation of Mn 4+ –Mn 4+ + Mu complexes near Mn 3+ –Mn 4+ ferromagnetic pairs. In the temperature interval from 25 to 45 K, the separation of the Eu 0.8 Ce 0.2 Mn 2 O 5 structure into two fractions where the relaxation rates of polarization of muons differ by an order of magnitude is revealed. This effect is due to a change in the state of regions of phase separation (1D superlattices) at the indicated temperatures. Such effect in EuMn 2 O 5 is significantly weaker.

Muon polarization losses in plastic scintillators of two types and in fused quartz have been studied by the μSR method. The muon and muonium spin precession spectra have been measured on the μSR setup placed at the output of the muon channel of the Gatchina synchrocyclotron. It has been shown that a significant fraction of stopped muons participate in the formation of the muonium. As a result, these muons lose their polarization completely. The magnitude of muon depolarization depends considerably on the type of plastic. It has been found that the muon spin precession frequency in fused quartz in an external magnetic field (F Q, μ = 0.116 ± 0.002 MHz) is shifted with respect to that in plastic scintillators (F 1, μ = 0.101 ± 0.005 MHz and F 2, μ = 0.101 ± 0.002 MHz).

The GdMn 2 O 5 multiferroic (a ceramic sample and a sample consisting of a large array of randomly oriented single crystals with linear dimensions 2–3 mm) has been studied by the μSR method within the temperature range 10–300 K. Three anomalies in the temperature behavior of the parameters of the muon polarization relaxation function, namely, close to the phase transition driven by the onset of long-range magnetic order in the manganese ion subsystem ( T N 1 = 40–41 K), near the lock-in transition initiated by an abrupt change of the wave vector of magnetic order ( T L = 35 K), and close to the Gd 3+ ion ordering temperature ( T N 2 = 15 K), have been found. An analysis of the time spectra of muon spin precession in the internal magnetic field of the samples has revealed two positions of preferable muon localization sites in samples, which differ in precession frequencies and the character of their behavior with temperature. The lower-frequency precession driven by Mn 4+ ions, ferromagnetic Mn4 + -Mn 4+ + muonium complexes, and Gd 3+ ions is observed throughout the temperature region T < T N 1 and is practically independent of temperature. At temperatures T < T L = 35 K, a higher-frequency precession associated with Mn 3+ ions appears also. It is characterized by a temperature dependence ∼( T / T N 1 ) β with the index β = 0.39, which is typical of Heisenberg-type 3D magnets. For T < T N 1 , a deficiency of the rest total asymmetry is observed. This phenomenon can probably be assigned to formation of muonium, which suggests that charge transfer processes play an important role in formation of long-range magnetic order.

The present paper is devoted to studying the multiferroics HoMnO 3 , YMnO 3 , EuMn 2 O 5 , and GdMn 2 O 5 by means of the µSR-method. Determination of the dynamic relaxation parameter 7n and the distribution of the local magnetic fields results in a clear phase diagram.

The magnetic properties of the EuMn2O5 multiferroic (samples consisting of single crystals and ceramic samples) have been investigated by the muon-spin-relaxation (μSR) method in the temperature range of 10–300 K. Below the magnetic ordering temperature T N = 40 K, the loss of the polarization of muons and the effect of the external magnetic field have been observed. Both phenomena can be explained by an additional channel of the depolarization of muons owing to the appearance of muons in a medium with a low electron density due to the charge separation process (the redistribution of the electron density in the phase transition process). The "memory" phenomenon has been revealed in a sample in the external magnetic field; the memory relaxation time depends on the size of the structure units of the samples (single crystals or ceramic grains).

1. Investigation of the magnetic properties of homogeneous copper-manganese alloys. In this work, the magnetic properties of homogeneous copper-manganese alloys Cu1-xMnx were studiedby the muon spin relaxation technique on the synchrocyclotron at the PNPI RAS [1]. Samples were homogenized by quenching in water after their heat treatment in a muffle furnase at a temperature of 1100 K for 100 h. In our experiments, we measured the time distributions of positrons Ne(t) that were formed as a result of the decay μ→e+ e μ ν ν + (the muon lifetime is τμ≈2.19711·10 s) and emitted in the direction of the initial muon polarization (polarized muon beams were used) in a time window Δt~4.5·τμ after each muon was stopped in the sample, as well as the integrated yields of these positrons [2]. The time distributions were approximated by the function Ne(t) = N0 · [1 + a0 · G(t)] · exp (-t /τμ), (1) where the normalization constant N0 and the maximum asymmetry a0 characterize the experimental conditions specific for each sample and do not depend on the muon depolarization. The muon spin relaxation function G(t) determined from the time distribution Ne(t) reflects the effect of local magnetic fields on the muon spin at the site of its stopping. In particular, we have G(t)=1 in the absence of depolarization and G(t)=0 for nonpolarized muons. Figure 1 present the normalized integrated yields of positrons for samples with different concentrations of magnetic atoms Ne(norm)=((ne/n0)−1)/a0. This integrated yield does not depend on the sample geometry, parameters of the muon spin relaxation setup, and muon beam polarization and provides general model-independent information on muon depolarization under local magnetic fields. The parameters n0 and a0 were determined at a temperature considerably higher than the temperature of the transition to the magnetically ordered phase. Specifically, the normalized integrated yield Ne(norm) measured for the Cu0.2Mn0.8 sample at temperatures T>330 K in zero magnetic field tends to unity. This circumstance suggests the absence of muon depolarization in the far paramagnetic range, in which the frequency of oscillations of electronic moments is too high (~10 Hz) for their magnetic field to change substantially the muon polarization. The paramagnetic state is also indicated by the complete depolarization of muons in a relatively weak transverse external magnetic field of ~580 Oe. In the temperature range 320−290 K, the normalized integrated yield Ne(norm) changes drastically and then reaches a value of ~1/3. This suggests that the sample transforms into a magnetically ordered state with an isotropic (on a local, cluster, or domain level) orientation of static internal local magnetic field. This behavior is in good agreement with the phase diagram previously proposed in [А. Banerjеe, A.K. Majumdar. PRB, 46 (14), pp. 8958–8973, (1992)], according to which the antiferromagnetic transition at TN~300 K occurs in a homogeneous alloy with the concentration x=0.8. The normalized integrated yield Ne(norm) equal to 1/3 is retained to T≈200 K. With a further decrease in the temperature, the normalized integrated yield Ne(norm) decreases sharply almost to zero. This indicates that in the given temperature range; there arises a strong dynamic depolarization of muons. The temperature dependence of the normalized integrated yield Ne(norm) in the range 200–20 K is characteristic of frustrated magnets, which undergo transition to a low-temperature spin-glass state through an intermediate magnetically ordered phase with a long-range order. In this case, the dynamic polarization is associated with the transformation of the magnetic structure in the transition range [3]. 0 50 100 150 200 250 300 350 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 C u 1-x Mn x

The magnetically ordered and paramagnetic states of erbium at temperatures T < T, and T > TN, where TN = 84.4 K is the NCel temperature, have been studied by the muon method. A large crystalline specimen of erbium was used with preferred orientation of the hexagonal c axes of the individual single crystals. The correlation functions GII (T ) and G, ( T ) which describe the fluctuations of the longitudinal and transverse (relative to the c axis) components of the internal magnetic field acting on a muon at T > TN were measured. The G, ( T ) dependence was also measured at T < T,. It is shown that for T > TN the correlator G, is constant over the whole temperature range investigated, TN < T 5 300K, while GII increases to a limited extent as T+TN. The limited range of the GII (T ) dependence as T+TN is regarded as an indication that a weak first-order phase transition takes place in erbium at T, = 84.4 K.

A ferrofluid based on Fe 3 O 4 nanoparticles dispersed in heavy water D 2 O is studied using the μSR method. The experiment has been carried out at temperatures 26–300 K. It is found that the diamagnetic (muon) fraction is formed in the ferrofluid in about the same amount as in D 2 O, but the muon-spin relaxation rate in the ferrofluid is much higher than in D 2 O. A significant shift of the muon-spin precession frequency in the ferrofluid is observed. It is shown that the shift of the muon precession frequency as a function of the external magnetic field is described by the Langevin function typical of paramagnetic magnetization. The mean magnetic field in the medium due to magnetic-nanoparticle polarization in an external field is experimentally determined. The nanoparticle sizes are estimated.

The magnetic characteristics of homogeneous copper—manganese alloys Cu1 − x Mn x are studied by the muon spin relaxation technique for the first time. It is revealed that the specific magnetic phase, which is most likely characterized by a fast spin dynamics and the absence of long-range order, is formed in alloys with concentrations 0.2 < x < 0.7 in the temperature range 10–330 K. The complete magnetic phase diagram is constructed.

The Pd1−x Fe x )0.95Mn0.05 alloy with random competing interaction was studied by measuring the muon spin relaxation in an external transverse magnetic field and in a zero magnetic field. Using the measured temperature dependence of the dynamic relaxation rate λ and the characteristics of the distribution of local static fields, the phase states of the sample under study are refined. In particular, it is shown that the ferromagnetic and spin-glass states coexist simultaneously in the sample below 25 K. Combined studies of the sample using the μSR and neutron depolarization methods made it possible to determine the size of magnetic inhomogeneities to be 2–6 μm in the temperature range 5–40 K.

The μSR setup for investigating the distribution of magnetic fields in solids using the muon spin rotation (μSR) method is described. The setup is characterized by a high degree of homogeneity of the magnetic field at the site of the sample under investigation, compensation of scattered magnetic fields to a level of −10−2 G, and a time resolution of 2.5 ns (the full width at half-maximum). The setup is suitable for μSR measurements on samples in the temperature range of 5–300 K with a precision of ±0.1 K.

The magnetic properties of multiferroics HoMnO3 and YMnO3 have been investigated using the muon (μSR) method. Analysis of the dependence of the dynamical relaxation rate λ and characteristics of the distribution of local static fields makes it possible to more precisely determine the phase states of the samples under investigation.

The lifetime of a negative muon in the 1S state in the isotopes 84Kr and 136Xe was measured. The values obtained, τ(84Kr)=139.2±2.9 ns and τ(136Xe)=111.0±4.6 ns, correspond to total nuclear capture rates Λc(84Kr)=6.75±0.15 μs−1 and Λ c(136Xe)=8.6±0.4 μs−1. Theoretical calculations of the rate of nuclear capture of a negative muon are performed for the Kr isotopes. The experimental results are compared with the theoretical calculations.

It was shown that in the frustrated ferromagnet belonging to the group of structurally ordered Fe_x Mn 1-x Pt 3 alloys the temperature of the transition from the ferromagnetic state to the asperomagnetic state followed a Gabay–Toulouse line.

The magnetic state properties have been studied in YBa2Cu3O6+x with (0.06<x<0.32). The increase of muon depolarization rate was found below 100K in all samples. In contrast to the previousμSR-studies two precession signals with the frequencies close to 4MHz was observed at T=20÷80K. Possible reasons of the phenomena at T<100K are discussed.