Non-equilibrium states, relaxation, and noise in CMR

manganites.

Research proposal for Ph.D. studies

Submitted by: Barukh Dolgin, I.D. 308677319

Superviser: Prof. Grzegorz Jung

Department of Physics

Faculty of Natural Sciences

Ben-Gurion University of the Negev

July 15, 2012

Adviser’s name and signature:

Head of Department’s name and signature:

Approval of Dean of the Kreitman School of Advanced Graduate studies:

Abstract

This research is devoted to low-doped, mixed valence manganese oxides with the general for-mula R1−xAxMnO3 (R=rare earth, A=divalent or tetravalent cation, such as Ca, Sr, Ba or Pb).Manganites are strong phase separated compound. Many interesting phenomena in the manganitesarise from the close balance of the different possible phases, which can result in phase coexistence[1]. Since the balance between competing phases is often subtle, and small changes in composi-tion can lead the system toward non-equilibrium state, resulting in large changes in the materialproperties. Those changes could be obtained by changing various experimental parameters, suchas temperature, magnetic field, applied voltage, pressure, etc.

We are proposing to investigate magnetic and transport properties of manganite systems, thruvarious noise and magnetic measurements. The main goals of the search will focus on following:

• Investigation of non-modulation noise in CMR manganites, its origin and properties.

• Investigation of the critical parameters in various metastable states.

• Investigation of non-Gaussian noise in manganites, its properties and relationship to thedynamics of the system.

• Investigation of fluctuations and metastable effects in manganite with the nano scale size.Confrontation of the properties having the same chemical composition as the bulk. The mainidea is the predicted significant reduction of phase separation upon reduction of the systemsize to nano-scale, and its roll on the dynamics of the system.

• Investigation the relationship between the magnetic and transport noise, their role in CMRmanganites.

• Investigation of the glassy phase, seen at low temperatures in low-doped CMR compounds,its influence of the measured transport and magnetic noise.

The proposed research will shed light on origins and mechanisms of the complex interactionsbetween competitive phases in CMR manganites.

Noise investigations beyond a simple estimate of the magnitude of the noise level will contribute,together with other experiments, to better understanding of electrical and magnetic properties ofCMR manganites. The expected significance of the proposed research consists in providing deeperinsight into the physics of metastable resistivity states and enlightening hitherto not explainedproblems. Our results will give an important input for theoretical modeling of phenomena of 1/fnoise and metastable resistivity, what will provide future experimental work with better theoreticalguidance. In terms of applications, the issue of non-Gaussian noise is of particular importance.Strong 1/f noise and RTN fluctuations are unacceptable in low frequency sensors. Even in highfrequency applications, well above the characteristic frequencies of the telegraphic noise, resistivityjumps induce high frequency components in the frequency spectrum of the device response.

i

Contents

1 Introduction 1

1.1 Phase separation, equilibrium and non equilibrium states . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Magnetic characteristics and relaxations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Noise in CMR manganites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Equilibrium and non-equilibrium noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.5 Gaussian and non-Gaussian noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.6 Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Goals of the research 6

3 Methodology 6

4 Preliminary results and discussions 7

4.1 Transport properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4.2 Magnetic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.2.1 Magnetization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.2.2 AC susceptibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.2.3 Magnetization relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5 Expected innovations 18

ii

1 Introduction

The proposed research concerns mixed valence manganese oxides R1−xAxMnO3 (R=rare earth,A=divalent or tetravalent cation, such as Ca, Sr, Ba or Pb). Some of their properties have beenknown for long, however, the discovery of so-called ”colossal magnetoresistance” (CMR) around theferromagnetic transition temperature TC triggered a revived interest in these manganites and thepotential applications of the CMR effect. The intense research showed a large variety of phenomenaand phases in these materials stemming from an interplay of the structural, charge, orbital andspin degrees of freedom that involve comparable energy scales [1].

1.1 Phase separation, equilibrium and non equilibrium states

A system that is in thermodynamic equilibrium experiences no changes when it is isolatedfrom its surroundings. In manganese oxide base compound, the simultaneous presence of usuallyferromagnetic (FM) and antiferromagnetic (AFM) or paramagnetic (PM) phases, results in a multi-phase coexistence. Since the balance between competing phases is often subtle, and small changesin composition can lead the system toward non-equilibrium state, resulting in large changes in thematerial properties. Those changes could be obtained by changing various experimental parameters,such as temperature, magnetic field, applied voltage, pressure, etc. The application of a magneticfield, for example, tilts the balance toward the FM state, inducing the growth of the metallicdomains and a large drop of the electrical resistivity. The competition between the coexistingphases opens the possibility for the appearance of locally metastable states, giving rise to interestingtime dependent effects, as cooling rate dependence, relaxation, giant and even colossal 1/f noise,two-level fluctuations, non-equilibrium fluctuations, noise and others [2, 3].

The perturbated system tends to return to equilibrium, and the interactions between variousdegrees of freedom accompanied by different relaxation behaviour in magnetization and resistivityproperties of the material involved. For each experimental method applied , one can observedifferent behaviour, such as decay, fluctuation or jump-like.

In recent years, a plethora of unusual nonequilibrium dynamics and time-dependent phenomenain phase-separated perovskite manganites have been reported. In particular, relaxation and memoryeffects in magnetization and resistivity, irreversibility of magnetization, frequency-dependent acsusceptibility, aging, and rejuvenation, similar to those observed in classical spin glasses, weredetected in colossal magnetoresistance manganites. On the other hand, the glassy behavior inphase-separated manganites is strongly connected with the dynamical coexistence of magneticallydistinct phases and therefore, manganites do not behave like canonical spin glasses. In manganites,the most important prerequisites for the spin-glass-like behavior, frustration, and disorder arecaused by competing interactions together with the phase separation associated randomness inspin positions. Since the dominant interactions leading to frustration appear between nano sizedphase-separated clusters, the glassy state in manganites is referred to as a cluster spin glass [4–7].

For the La1−xCaxMnO3 manganites for x below the percolation threshold xC = 0.225, as thesystem cooled below the TC, experimental data indicates additional phase transition, which is ac-companied by peculiar features, such as strong frequency dependence of ac susceptibility, remark-able rotation of the easy magnetization axis, excess specific heat, and orthorhombicity reductionbelow the critical point. The ensemble of such features is considered to be a fingerprint of a clusterspin-glass (SG) transition in disordered manganites. Remarkably, all glass-like features disappearwhen the doping level x in La1−xCaxMnO3 bulk samples approaches and exceeds the percolation

1

threshold xC [4–7]. For this reason, those systems are widely researched for over a decade, and yetnot fully understand.

1.2 Magnetic characteristics and relaxations

In order to characterize magnetic materials, one usually measures the magnetic field dependanceof the magnetization at a constant temperature, making a so called hysteresis measurement. It isoften interesting in the case of ferromagnets, to estimate the coercive field, as well as the saturationand the remanent magnetization. The shape of the measured curve will depend on the shape ofthe sample (as M ∝ 1/N). The magnitude of the coercive field and remanent magnetization willmainly depend on the quality of the material and its magnetic anisotropy. Defects can pin domainsso that they will not be able to follow the magnetic field reversal, increasing the coercivity [8].

To follow the evolution of saturation magnetization, one can perform 1) ac susceptibility mea-surements, the dynamical susceptibility χ has two components: one is in-phase (χ′) with the exci-tation, while the other is dissipative out-of-phase (χ′′) component. χ can be measured on coolingor heating the sample. 2) dc measurements, in this case the most common protocols as follows:

• Zero-field-cooled (ZFC) magnetization: the sample is cooled to zero field. A small magneticfield, necessary to probe the system is applied at the lowest temperature, and the magneti-zation recorded on heating

• Field-cooled (FC) magnetization: the sample is cooled in a small field down to the lowesttemperature, while the magnetization is recorded. One can also collect the magnetization onre-heating.

• Thermo-remanent (TRM) magnetization: the sample is cooled in a small field. The fieldis removed at the lowest temperature, and the magnetization is recorded in zero field onre-heating

• Isothermal remanent (IRM) magnetization: The sample is cooled in zero magnetic field andthe magnetization measured in zero field on re-heating. During the cooling, a halt is madeand small field is applied at a constant temperature. After some duration, the field is thenswitched back to zero and the cooling resumed.

The temperature dependance or even time dependance of the TRM and IRM magnetization isusually of a greater interest in the case of spin glasses and disordered systems. If a spin glass is cooledfrom a high temperature in the paramagnetic state down to a constant temperature in the frustratedphase, the spin configuration rearranges toward the equilibrium state for this temperature. As aconsequence, the response of the system depends on the time it has been relaxing at the constanttemperature. From magnetic field dependence of TRM and IRM, we obtain magnetic fingerprints ofthe irreversible magnetization, which indicate that glass properties are more pronounced in smallerNPs [4, 8, 9].

It turns out, especially for the CMR manganite systems, that each magnetization obtainedduring different cooling method stated above, is characterizing different state of the same system.Such magnetization behaviour provide us a unique information of interaction between spins andmagnetic degrees of freedom in the system, since it is governed by a different mechanism. As the sizeof the system decrease to nanometer scale, some of the basic magnetic properties become strongly

2

size dependent and differ significantly from the properties of the bulk material [10–15]. In suchnano systems, there is no need to perform transport measurements, since the transport is mainlydominated by the properties of the contact between the grains and not by the properties of the grainsthemselves. The intense study of relaxations can shed a light regarding those interactions and theirorigins. Ensembles of nano particles (NPs) with weak interparticle magnetic interactions showsuperparamagnetic (SPM) behavior. Systems with pronounced interparticle interactions exhibitcollective behavior capable of overcoming anisotropic properties of individual particles. Stronglyinteracting and dense NP systems showing SG behavior are referred to, by analogy with atomic spinglasses in bulk materials, as superspin glasses (SSG) [15, 16]. SSG NP systems exhibit peculiar slowdynamics, aging, rejuvenation phenomena, and memory effects [17–22]. NP ensembles at higherdensities and stronger interparticle interactions convert into so-called superferromagnetic (SFM)state in which, below some temperature, the magnetic moments of all NPs are correlated in aferromagnetic-like fashion [23, 24].

Our recent studies, showed that when the system is reached to a specific temperature using theZFC, TRM or IRM cooling, then regardless whether the the field is applied or removed (dependingon the cooling protocol), one can observe system relaxation. This is remarkably strange and unusualphenomena, since the system should be already magnetic organized.

1.3 Noise in CMR manganites

Manganites are strong phase separated compound, therefore any changes in experimental com-position can lead the system toward non-equilibrium state, system relaxation to equilibrium mayresult in different type of noise, although it may as well remain an equilibrium noise. Typically,noise is characterized by the amount of noise power per unit frequency bandwidth, known as thepower spectrum density (PSD).

Transport and magnetic noise in magnetic materials may originate from various sources suchas defect motion, magnetic domain or spin fluctuations, charge carriers crossing an energy barrier,electronic traps, current redistribution within inhomogeneous materials. All these potential micro-scopic sources behave like fluctuators; once they are activated and physically coupled to the chargecarriers constituting the current, they induce specific resistance or current fluctuations giving riseto electrical and magnetic noise we measure.

Main types of fluctuations maybe classified as:

1. Thermal noise, is the noise of thermal equilibrium fluctuations. For the case of thermallyfluctuating resistors can be described as SV (f) = 4kBTR [25, 26].

2. Shot noise, results from the granularity of charge carriers and its PSD is SI(f) = 2eI, wheree is an electron charge and I is the current flowing through the device [27].

3. Random Telegraphic nose (RTN), is a process in which the observed value, switchesbetween two, ”up” and ”down” or more fixed levels. For thermally activated transitions, anasymmetrical two-well system with an energy barrier E ±∆E separating the two states, theaverage time τi(T,H) spent in the ith state is expressed by: τi(T,H) = τi,0exp(Ei/kBT ), andthe PSD of the RTN has a Lorentzian form [29]:

SV (f) =S0V (0)

cosh[ ∆EkBT ][cosh

2( ∆EkBT + ω2τ2]

, (1)

3

where τ is the total transition rate.

Elementary two-level fluctuators (TLF), each generating a RTN waveform, are the buildingblocks constituting source of 1/f noise in many solid systems.

4. 1/f noise, 1/f noise spectra in condensed-matter systems are believed to come fromassembly of elementary fluctuators with well defined characteristic relaxation rates λ [28].The spectrum of each elementary fluctuator is Lorentzian, and the resulting normalized PSDof the fluctuating quantity X ,

S(f) =SX(f)

X2=

∫λ

λ2 + f2P (λ)dλ, (2)

will have 1/fα form, with α = 1 for the distribution function P (λ) ∝ 1/λ. If the elementaryfluctuators are thermally activated, the characteristic rate λ(∆) = λ0 exp(−∆/kBT ), and therequired distribution of λ is provided by flat distribution of activation energies, P (∆) = const.

Dutta and Horn (DH), have shown that 1/fα spectra with α ≈ 1 arise not only forP (∆) = const. but also for the distribution function P (∆) that does not vary much in therange of ∆ from |kBT ln(λ0/f1)| till |kBT ln(λ0/f2)| , where f1 and f2 are the lowest andthe highest frequency of the measurements, respectively [30]. The detailed discussion of DHmodel assumptions can be seen in reference [31].

When P (∆) is a slowly varying function of the activation energy ∆ then

S(f, T )f ∝ kBTP (∆̃ = kBT ln(λ0/f)) (3)

DH model leads to a specific relation between temperature derivative of the spectral density∂ ln(S(f, T )f)/∂ lnT and the derivative ∂ ln(S(f, T )f)/∂ ln f :

∂ ln(S(f, T )f)

∂ lnT= 1− ln(λ0/f)

∂ ln(S(f, T )f)

∂ ln f. (4)

Equation 4 contains crucial reciprocity between the frequency and temperature dependenceof the noise magnitude and is frequently used as a self-consistency test for the validity of DHapproach for a given physical system. Flat distribution of temperature independent activationenergies in DH model gives rise to a pure 1/f spectrum and a linear temperature dependence ofthe noise level at low frequencies. Departures of α from unity indicate non-zero derivatives ofenergy distribution dP (∆)/d∆, and excess of high (α < 1), or low energy (α > 1) fluctuatorsin the ensemble.

1.4 Equilibrium and non-equilibrium noise

Conductivity noise with 1/f spectrum is generally related to resistance fluctuations which aremeasured by applying dc current and recorded as voltage fluctuations. When the resistance fluc-tuations are just probed by current, and not influenced by its flow, then, in linear systems, PSD ofthe noise scales as the square of the bias current. Such noise is called equilibrium noise or modu-lation noise as well. In this case the normalized PSD is SV

V 2 = SR

R2 = SI

I2 = const.. Consequently, If

4

the fluctuations are bias dependent, then the PSD SV 6= I2, and the observed noise is then callednon-equilibrium or non-modulation noise.

Generally, CMR manganites exhibit equilibrium noise, however, during our initial investigation,under specific experimental condition, an appearance of non-equilibrium noise was observed [39].

1.5 Gaussian and non-Gaussian noise

The noise generated by an assembly of fluctuators, as the 1/f noise discussed above, is Gaussian,even if the contributing elementary fluctuations are not Gaussian. From the statistical point of view,all the information carried by Gaussian noise is contained in the second-order correlation function,and is equivalent to the information that can be inferred from the dynamic response measurements.On the other hand, the non-Gaussian noise may carry more physical information than the responsedata. Proper characterization of non-Gaussian noise requires measurements of higher momentsbeyond standard two-point correlations. Nevertheless, just the mere appearance of non-Gaussianfluctuations already enlightens the origin of the noise, namely that the noise is not produced by acombined action of many fluctuators.

In mezzoscopic samples, the small volume of the system allows to relate the non-Gaussiannoise a limited, very small, number of active fluctuators. In larger samples, the non-Gaussianityof the noise is a signature of a single, or just a handful, of elementary fluctuators influencingsystem properties on a length-scale comparable with the system size. In rare cases of stronglyinhomogeneous materials, the non-Gaussian noise is measured also in macroscopic volumes. Thereexist several reports on non-Gaussian resistance fluctuations in CMR manganites. Non-Gaussiannoise in CMR manganites frequently takes form of two-level random telegraph noise (RTN) whichis considered to be an experimental hint to phase separation [32–35].

Most recently, in La0.80Ca0.20MnO3 manganite single crystals, which is very close to compositionof the sample used by us in the preliminary experiments which revealed nonequilibrium noise, largenon-Gaussian 1/f noise has been observed in the ferromagnetic insulating state at low tempera-tures [36]. Non-Gaussian character of the fluctuations was demonstrated through measurementsof the probability density function and second spectra (fourth moment) measurements. It wasobserved that the noise becomes non-Gaussian when the material is cooled down below the ferro-magnetic transition temperature. With further cooling deeper into the phase separated state, thenoise becomes even more non-Gaussian. Moreover, the observed temperature dependent 1/f noisemagnitude shows a sharp freeze out with temperature on cooling into very low temperatures. Theauthors proposed that the non-Gaussian noise arises from charge fluctuations in a correlated glassyphase of the polaronic carriers which develop in these systems according to numerical simulationstudies. Let us underline that the regime of appearance of non-Gaussian 1/f noise is the sameone at which we have reported appearance of the nonequillibrium 1/f noise. However, the majordifference is that non-Gaussian character of the noise was revealed in almost equilibrium conditionsusing a very small excitation with ac bias current while the nonequilibrium noise appears at strongdc bias. At this moment it is unclear whether two phenomena appear simultaneously and to whichextend their physical mechanisms are related.

1.6 Relaxation

Most of the literature reports noise in manganites concerning the transport noise. Measurementsof magnetic noise are complex and require the use of very sensitive SQUID sensors, however, for a

5

magnetic system in equilibrium, the relationship between the magnetic fluctuations and the systemresponse can be described as:

Sx(ω) =2kBT

ωImχ̂(ω), (5)

where χ̂(ω) is the Fourier transform of the susceptibility χ(t). Therefore, for Gaussian processes,by probing AC susceptibility response and/or relaxation of the system, one can obtain same infor-mation as from the PSD measurements of the magnetic fluctuations.

2 Goals of the research

The goal of the research is to investigate metastable states, explore unusual relaxation behaviorand non-equilibrium noise for CMR compounds with different compositions. With each investiga-tion on the manganese oxides, a new phenomenas arisen and yet are not fully could be explained,especially their origins and dynamics. The main goals of my research the follow:

• Investigations of non-modulation noise in CMR manganites, its origin and properties. Theinitial results demonstrate that this noise fulfills the requirements of Dutta-Horn model whatallows one to obtain an insight into the energy landscape of moving charge carriers from thenoise data.

• Investigation of the critical voltage in various metastable states. The initial results showedthreshold value of bias, which corresponds well to the energy of Jahn-Teller distortion inmanganites.

• Investigation of non-Gaussian noise in manganites, its properties and relationship to thedynamics of the system.

• Investigation of fluctuations and metastable effects in manganite with the nano scale size.Confrontation of the properties having the same chemical composition as the bulk. The mainidea is the predicted significant reduction of phase separation upon reduction of the systemsize to nano-scale, and its roll on the dynamics of the system. Our initial results show aprominent influence of the system size on its dynamics.

• Investigations of the relationship between magnetic and transport noise. Their role in CMRmanganites.

• Investigation of the glassy phase, seen at low temperatures in low-doped CMR compounds,its influence of the measured transport and magnetic noise.

The proposed research will shed light on origins and mechanisms of the complex interactionsbetween competitive phases in CMR manganites.

3 Methodology

Electrical transport properties and conductivity noise is measured in a conventional 4-pointcontact arrangement by biasing the sample with dc current supplied by high output impedance

6

current source and measuring the resulting voltage or voltage fluctuations. The samples, used inthe experiments, are usually single crystals grown by a floating-zone method (FZM) [37]. As growncrystals are cut into individual samples for a resistive measurements. Each sample has a form of≈ 6 × 3.2 × 1.9 mm3 bars, with the longest dimension along the 〈110〉 crystallographic direction.Current and voltage leads are indium soldered to the pre-evaporated gold contacts, deposited onto the bars by thermal evaporation vacuum. For noise measurements the sample is thermallyanchored to the sample holder of a variable temperature liquid nitrogen cryostat. Four in-linecontacts are placed along the longest dimension of the bar. The separation between the voltagecontacts is usually 0.3 mm. The voltage signal is amplified by a home made room temperaturelow noise preamplifier, located at the top of the cryostat, and further processed by a computerassisted digital signal analyzer. To eliminate environmental interferences and noise contributed bythe measuring chain, the PSD measured at zero current is subtracted from the data obtained at agiven current flow for each measurement. This method was widely used during our early research[38, 39], therefore all the necessary measuring and analyzing programs were fully checked and areoperational, thus no additional add ons are needed for further research of different systems andallowing us to extend the investigation of new compositions in similarity to a described above,without any delay.

Magnetic properties are measured using the Physical Properties Measurement System (PPMS).Magnetization measurements will be executed using the vibrating sample magnetometer (VSM)and the DC/AC magnetic option of the system. Samples for magnetic measurements are usuallyprepared by compacting powders, at room temperature under pressure of the order of 5 kbar, intoa cylinder-shape form of 2.4 mm in diameter and 3.3 mm in height.

4 Preliminary results and discussions

4.1 Transport properties

Our initial investigation of transport properties were conducted on single crystal with composi-tion La0.82Ca0.18MnO3. We have observed different regimes, as seen in Figure 1, where the samplehas the same resistivity under very different dissipation mechanisms. Noise investigations are ex-pected to clarify the interplay between different phases in the phase separated state (for examplebetween the PM and FM phases in the La0.82Ca0.18MnO3). Following measurements includedvarious noise measurements at different temperatures and are explained in details below.

As the initial goal of research, presented here, demonstrate that equilibrium 1/f noise inLa0.82Ca0.18MnO3 single crystals preserves its character under changing temperature, despite sig-nificant changes in magnetic and transport properties of the investigated system (see Figure 1).Bias dependent nonequilibrium 1/f fluctuations appear only at low temperatures, well below theCurie temperature (see Figure 2). Properties of the nonequilibrium 1/f noise differ significantlyfrom those of quasi-equilibrium one. A combined analysis of noise and transport characteristicspermits us to associate marked changes in the noise behavior to changes in the low temperatureintrinsic tunneling mechanism [39].

At low temperatures, where electrical transport in our sample is dominated by tunneling mecha-nism [40], at currents exceeding some threshold current I ∼ 1 mA, the proportionality of the voltagenoise to I2 breaks down and the resistivity fluctuations start to be influenced by the current. Thisis a manifestation of a nonequilibrium 1/f noise similar to that frequently observed in nonlin-

7

90 120 150 180 210 240 270 3001

10

100

TJT

Res

ista

nce

()

Temperature (K)

TC = TM-I

FMI+FMM FMM PMI

hoppingIntrinsictunneling

perc

olat

ing

met

al

Figure 1: Temperature dependence resistivity of La0.82Ca0.18MnO3 single crystal, as measuredduring the research. TJT is a temperature where Jahn-Teller transition occur. TC is a Curietemperature, which in LCMO happens to be also a Metal-Insulation (M-I) transition. Magneticand transport properties of the sample is also shown.

102 103

0.1 1 1010-17

10-15

10-13

10-11

10-9

S V at

1 H

z (V

2 /Hz)

Current (mA)

(dln(S))/dln(I)=2

290 K

79 K

Current density (A/m2)

10-3 10-2 10-1 10010-17

10-15

10-13

10-11

10-9

79 K 126 K 150 K 175 K 185 K 225 K 290 K

S V at

1 H

z (V

2 /Hz)

Voltage (V)

Figure 2: Summarized noise intensity data at various temperatures: Current (on the left) andVoltage (on the right) dependencies of the noise intensity at f = 1 Hz.

ear, non-ohmic systems [41]. However, in a difference to other nonlinear systems, the crossoverto non-equilibrium noise in our sample is not associated with the onset of strong nonlinearity inthe current-voltage (I − V ) characteristics [42]. Moreover, the intensity of non-equilibrium noiseinitially decreases with increasing bias, to change in a non-monotonic way with further increase ofthe bias.

The puzzling properties of the low temperature noise in La0.82Ca0.18MnO3 single crystallinesample should be related to the underlying changes in its transport properties. An efficient wayto approach the problem is to detect possible changes in the energy environment of the fluctuatorsresponsible for the noise. A tool for such analysis is provided by relevant theoretical models ofnon-exponential relaxation kinetics resulting in 1/f noise [30, 31].

During the following investigation of the sample, we have observed noise in various metastablestates of La0.82Ca0.18MnO3 crystals and in other crystals with different composition and the state ofaging. One of the interesting conclusions of research described in paper [39] is that non equilibriumnoise appears above some threshold value of bias, which in voltage terms falls between 100 and200 mV. This value corresponds well to the energy of Jahn - Terller distortion in manganites. Inrecently concluded noise measurements in various metastable states, induced in La0.82Ca0.18MnO3

crystals by subjecting them to short current/electric field pulses at low temperatures, see Figure 3.

8

50 100 150 200 250 300

0.1

1

10

50 100 150 200 250 3001

10

100

1000

R /

RT C

Temperature (K)

Res

ista

nce

()

Temperature (K)

pristine state 2nd state 1st state

Figure 3: Temperature dependance of resistivity in the pristine and two metastable states ofLa0.82Ca0.18MnO3. The inset shows the collapse of R(T ) curves to a single dependence afternormalizing the resistivity to R(T C).

We found that the onset of non equilibrium noise apparently does not depend on the crystalstate, even if the resistivity differs by orders of magnitude, and is always close to some 100 mV, seeFigure 4, as in the pristine sample at low temperature. For the full representation of noise intensityat different temperatures of the various metastable states, refer to Figure 5. This suggests thatnon equilibrium onset is associated with some fundamental material properties, such as, e.g., JahnTeller distortion.

0.01 0.1 110-11

10-10

10-9

SV /

V2 a

t 1H

z [H

z-1]

Voltage (V)

pristine state 1st state 2nd state 3d state (heating)

V1 V2

Figure 4: Noise spectral density normalized to V 2 as a function of bias voltage for the pristine andtwo consecutive metastable resistivity states. Note that the threshold voltage for the onset of nonequilibrium 1/f noise in all states is the same, V1 ∼ 200 mV. The nature of V2 ∼ 1 mV is stillunclear to us.

The paper describing these results is currently in preparation. A possibility that non equilibriumnoise is related to Jahn Teller distortions is currently further investigated by investigating transportnoise in crystals with lower level of Ca-doping, and consequently, with higher resistivity, whatenables reaching the threshold voltage at lower currents and higher temperatures. Further researchwas obviously needed to enlighten the observed phenomena.

9

0.1 1 10

10-16

10-15

10-14

10-13

10-12

10-11

10-10 79K 126K 150K 175K 185K 225K 290K

SV a

t 1 H

z [ V

2 / H

z ]

Current(mA)

Pristine state

0.1 1 10

10-11

10-10

10-9

10-8

Pristine state 79K 126K 150K 175K 185K 225K 290K

SV /

V2 a

t 1 H

z [ H

z-1 ]

Current(mA)

0.1 1 10

10-16

10-15

10-14

10-13

10-12

10-11

10-10

10-9

1st State

79K 126K 150K 175K 185K 225K 290K

SV a

t 1 H

z [ V

2 / H

z ]

Current (mA)0.1 1 10

10-11

10-10

10-9

10-8

1st State

79K 126K 150K 175K 185K 225K 290K

SV /

V2 a

t 1 H

z [ H

z-1 ]

Current (mA)

0.1 1 1010-16

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

SV a

t 1 H

z [ V

2 / H

z ]

2nd State

79K 146K 161K 175K 182K 225K 290K

Curret (mA)0.1 1 10

10-11

10-10

10-9

10-8

79K 146K 161K 175K 182K 225K 290K

2nd State

SV /

V2 a

t 1 H

z [ H

z-1 ]

Curret (mA)

Figure 5: Summarized noise intensity data at various metastable states of La0.82Ca0.18MnO3 atdifferent temperatures at f = 1 Hz.

10

The rich variety of the phase diagram of the La1−xCaxMnO3 [44], allows us to investigatethe extended range of the LCMO system as well as to extend the research to other types of themanganites. Nowadays, we are investigating LCMO with the x = 0.12, since the La0.82Ca0.18MnO3

was destroyed during the transition to one of the metastable state and the behavior of the newsample seems to be similar (at pristine state) as the previous one (see Figure 6).

50 100 150 200 250 3001

10

100

1000

Res

ista

nce

( )

Temperature ( K )

La0.88

Ca0.12

MnO3

La0.82

Ca0.18

MnO3 Pristine State

Figure 6: Temperature dependance curve of the pristine state for La1−xAxMnO3 with x = 0.18and x = 0.12, as was measured during the research.

4.2 Magnetic properties

4.2.1 Magnetization

Temperature dependence of the field cooled (MFC) and zero field cooled (MZFC) magnetizationof LCMO12 and LCMO60 at various magnetic fields is shown in Figs. 7 and 8. One can seeunambiguous differences in the behavior of small and large particles. The magnetization of LCMO60in very small magnetic field of H = 10 Oe is shown in Fig. 7(a). The characteristics exhibits a widemaximum at TCO = 198 K that can be associated with charge ordering within cores of NPs. A sharppeak at low temperatures is attributed to appearance of weak FM moment at T = TC = 41 K. Achange in the slope of M(T ) at T ≈ 80 K is likely a signature of paramagnetic to antiferromagnetictransition in the core of LCMO60 NPs. It appears, that charge ordering peak in LCMO60 occursat temperature that is slightly lower than the CO temperature TCO ≈ 220 K of the bulk samplewith the same composition [45, 49? ]. Data of MFC(T ) and MZFC(T ) obtained for LCMO60 atintermediate filed H = 1000 Oe, see Fig. 7(b), show that the position of the CO peak remainsunchanged. One can see splitting between MFC(T ) and MZFC(T ) at T ∼ 100 K and sharp increaseof magnetization below TC = 41 K. Increase of the magnetic field to H =10 kOe, illustrated inFig.7(c) leads to 12 K shift of the CO peak towards low temperatures and significant suppression ofsplitting between MFC(T ) and MZFC(T ). At temperatures above TCO, MFC(T ) and MZFC(T ) curvesdo not differ significantly. In the temperature range between 110 K and TCO MFC(T ) and MZFC(T )measured at 1000 Oe and 10 kOe exhibit small, 2.5 − 3.0 K, thermal hysteresis between coolingand heating cycles. Similar small hysteresis is observed in the vicinity of CO peak, pointing out tothe structural phase transition of the first order.

Magnetization of smaller LCMO12 particles is quite different and resembles behavior of a su-perparamagnet (SPM) and superspin glass (SSG) system. Generally, MZFC(T ) of SPM and SSG

11

0.06

0.08

0.10

0.12

0.14

0 60 120 180 240 3000.6

0.9

1.2

(b)

ZFC

FC

M (e

mu/

g)

H =1000 Oe

ZFC

FC

(c)

Temperature (K)

H=10 kOe

0.0012

0.0015

0.0018

ZFC

H =10 Oe

TN

TC

TCO

LCMO60

(a)

Figure 7: (a) ZFC magnetization for LCMO60 sample in H = 10 Oe. The ZFC and FC magneti-zation for LCMO60 sample in H = 1000 Oe (b) and in H = 10 kOe (c)

peaks at temperatures which qualitatively agree with the blocking or freezing temperature for SPMor SSG, respectively [47]. MFC(T ) of SPM monotonously increases with decreasing temperature.Field cooled magnetization of SSG behaves in a similar way, until it saturates and becomes almosttemperature independent, or even exhibits a shallow minimum, upon cooling below the freezingtemperature. Figure 8(a) shows thatMZFC of LCMO12 in H = 1 kOe exhibits a maximum at T ≈ 70K which that can be tentatively associated with the blocking temperature TB. High magnetic fieldof H =10 kOe makes the temperature dependence of LCMO12 almost featureless, see Fig. 8(b).Characteristic low temperature splitting between MZFC and MFC is almost completely suppressed.As shown in the inset to Fig. 8(b), at 5 K MZFC(H) increases rapidly with increasing field forrelatively small magnetic fields, following a typical FM behavior. With further field increase themagnetization continues to increase almost linearly, pointing out to the presence of a major AFMphase. The field dependence of MZFC in LCMO12 at higher fields is steeper than that of LCMO60,indicating an enhancement of FM contribution and weakening of the AFM in smaller particles.

As shown in in Figs. 8(c,d), the difference between MFC(T ) and MZFC(T ) of LCMO60 peaksin the vicinity of TCO. In LCMO12, the corresponding peak is totally absent due to suppressionof CO phase. As pointed out in the literature, the pronounced CO peak hinders magnetizationsignatures of the transition to the AFM state at Nel temperature TN < TCO, what makes difficultstraightforward identification of TN even in the bulk La0.23Ca0.77MnO3 [48]. A detailed phasediagram of La1−xCaxMnO3, established using neutron diffraction and magnetization measurements,puts the bulk TN at 190 K [49]. On the other hand, the onset of difference between MFC and MZFC in

12

0.0

0.3

0.6

0.9

0 100 2000.0

0.3

0.6

0 100 2000.0

0.1

0.2

0 60 120 180 240 300

0.6

1.2

1.8

2.4

3.0

LCMO12

(a)

FC

M (e

mu/

g)

ZFC

H =1000 Oe

H =1000 Oe

MFC

- M

ZFC (e

mu/

g)

T (K)

LCMO12 LCMO60

x15(c) H=10 kOe

x5

LCMO12 LCMO60

MFC

- M

ZFC (e

mu/

g)

T (K)

(d)

(b)

ZFC

M (e

mu/

g)

Temperature (K)

FC H=10 kOe

0 30 60 900

3

6

9LCMO12

M (e

mu/

g)

H (kOe)

M0

T=5 K

LCMO60

Figure 8: a) The ZFC and FC magnetization for LCMO12 sample in H = 1000 Oe; (b) The ZFCand FC magnetization for LCMO12 sample in H = 10 kOe; Inset shows magnetic field dependenceof the magnetization measured at T = 5 K for LCMO12 and LCMO60 samples after ZFC. (c) and(d) The difference between MZFC and MFC magnetization for LCMO12 and LCMO60 samples asa function of temperature after measurements at H=1000 Oe (c) and 10 kOe (d).

La0.23Ca0.77MnO3 at T < TCO can be interpreted as a hall mark of paramagnetic to AFM transition,while additional increase in the difference between MFC and MZFC with decreasing temperatureas appearance of weak FM moment in monoclinic phase [48]. This lead to estimation of the bulkTN as being close to 130 K [48]. Using the same assumptions, one may conclude that the transitionto AFM state in LCMO60 NPs occurs below T ∼ 100 K, while weak FM moment appears atT ∼ 41 K. Unfortunately, the determination of transition temperatures of smaller particles frommagnetization curves seems problematic.

4.2.2 AC susceptibility

Temperature and frequency behavior of ac susceptibility for LCMO12 and LCMO60 is illus-trated in Fig. 9. Susceptibility of LCMO12 strongly varies with temperature and exhibits a singlefrequency dependent maximum. The real and imaginary components reach their maxima at dif-ferent temperatures; e.g., at 10 Hz χ′(T ) peaks at Tf = 129 K while χ′′(T ) at Tf = 117 K. In ourrecent experiments we have demonstrated that LCMO12 NPs exhibit pronounced exchange biaseffect related to the presence of two magnetically different phases below 100 K [50].Features associated with magnetic transitions into these phases in χ′(T ) and χ′′(T ) are completely

13

0 50 100 150 200 250 300

0.0010

0.0015

0.0020

0.0025

0.0000

0.0003

0.0006

0.0009

0.0012

0.000

0.005

0.010

0.015

0.020

0.025

0 50 100 150 200 250 3000.00000

0.00003

0.00006

0.00009

f

hac

=10 Oe' (em

u/g)

Temperature (K)

10 Hz 100 Hz 1000 Hz 10000 Hz

LCMO60

(c)

LCMO60

(b)

f

'' (em

u/g)

100 Hz 1000 Hz 10000 Hz

LCMO12

hac

=10 Oe

LCMO60

10 Hz 100 Hz 1000 Hz 10000 Hz

LCMO12

hac

=10 Oe

f

(a)

(d) hac

=10 Oe 100 Hz 1000 Hz 10000 Hz

Temperature (K)

LCMO60

Figure 9: (a,b) Temperature dependence of real χ′ and imaginary χ′′ components of ac susceptibilityof LCMO12 and LCMO60 measured during heating at different frequencies 10, 100, 1000, 10000Hz and probing magnetic field of 10 Oe; (c,d) real χ’(T) and imaginary χ′′(T ) component of acsusceptibility of LCMO60, measured at different frequencies 10, 100, 1000, 10000 Hz. Since χ′′(T )at 10 Hz appears on a high level of background noise, we show only the dependence recorded athigher frequencies.

masked by a wide maximum in Fig. 9(a,b). LCMO12 samples exhibit features characteristic of bothSPM and SSG systems [47, 51]. Figure 9(b) shows that χ′′(T ) below the peak temperature does notdepend on frequency. Similar frequency independent susceptibility has been observed previously ininteracting ferrimagnetic γ - Fe2O3 [? ] and antiferromagnetic NiO [52] NPs. One can easily noticethat the temperature of the susceptibility maximum depends on the frequency. Frequency shiftof the peak temperature is usually quantitatively characterized by a factor K = ∆Tf/[Tf∆ log(f)],where Tf is the temperature of the maximum of χ and ∆Tf is the temperature shift at a givenfrequency difference ∆f [51]. The estimated K factor for LCMO12 is ∼ 0.005 for χ′ and ∼ 0.04 forχ′′, and falls into a typical range for known spin glasses [51]. It should be underlined that K factorin superparamagnets is significantly larger [51, 52].

Temperature dependence of LCMO60 ac susceptibility is much more complex, see Fig. 9(c,d).The real part χ′(T ) displays wide frequency dependent peak around 186 K, the temperature cor-responding to the temperature of magnetization peak associated with CO transition. The out-of-phase susceptibility component χ′′(T ) peaks around 170 K. At low temperatures, both real andimaginary components display cascades of peaks; at 10 K, 40 K, and 71 K in χ′(T ), and at 10 K, 40K, and 65 K in χ′′(T ) . In recent studies of magnetic properties of bulk La0.23Ca0.77MnO3 it wasshow that the volume fraction of charge-disordered (CD) phase is close to 20% and that a weak FMmoment may result from slight spin canting of spins in the CD-monoclinic volume, or alternatively,

14

from FM contribution linked with the interface between CO and CD domains [45]. Moreover, tem-perature dependence of magnetization exhibits several changes of its slope below 75 K. The latterbehavior was associated with appearance of FM contribution and transition from dynamic to staticPS regime at TC ≈ 64 K. The origin of our low temperature peaks in χ′(T ) and χ′′(T ) in Fig. 9remains however unclear at present. One may note that ac-susceptibility is more sensitive the dcmagnetization to changes in the magnetic state of a system. Therefore, susceptibility of NPs mayalso display peaks associated with a complex PS, as it was observed in the bulk [45, 48].

4.2.3 Magnetization relaxation

When magnetically disordered system, such as e.g. spin glass, is cooled down from the PM stateto a certain temperature in a frustrated phase, the spin configuration rearranges itself towards theequilibrium state at this temperature and exhibits therefore a relaxation of magnetization at aconstant temperature. The magnetic dynamicse of the system can be monitored by measuring re-laxation of the thermoremanent (TRM) and isothermoremanent magnetization (IRM). The results,obtained at temperatures T = 10, 40, 100, 150 K are shown in Figure 10. At each protocol, wemaintained field for 10 min at the target temperature, prior to switching the magnetic field it offor on (depending on the cooling protocol) with the maximal rate available for our PPMS system(200 Oe/s), and magnetization was immediately recorded. Since the relaxation of magnetizationhappens also during the removal of magnetic field this introduces some error into our measure-ments. Observe that the removal process is longer the larger is the magnetic field. Obviously,higher values of TRM, as compared to IRM, are expected because TRM relaxation starts from ahigh magnetization value [53].

0 2000 4000 6000 8000 10000

0.0

0.3

0.6

0.9

T =150 K

T =100 K

T =40 K

M (e

mu/

g)

Time (s)

LCMO12

TRM after FC 10 kOe T =10 K

0 2000 4000 6000 8000 10000

0.012

0.016

0.020

M (e

mu/

g)

Time (s)

T =150 K

0 2000 4000 6000 8000 100000.00

0.05

0.10

0.15

0.20

0.25

T =150 K

T =100 K

T =40 K

T =10 K

M (e

mu/

g)

Time (s)

LCMO12

IRM

0 2000 4000 6000 8000 10000

0.008

0.010

0.012

0.014

M (e

mu/

g)

Time (s)

T=150 K

Figure 10: Time variation of the TRM (on the left) and IRM (on the right) magnetization ofLCMO12 samples after FC at H = 10 kOe recorded at various temperatures10, 40, 100, 150 K.Inset shows time variation of the TRM magnetization at T = 150 K.

The magnetization relaxation after switching off the aligning field is often described by astretched exponential, M(t) = M0−Mg exp[−(t/τ)β ], with a distribution of relaxation times in theensemble. If the energy barriers are uniformly distributed, between zero and some maximum value,the logarithmic behavior is good approximation for the decay of thermoremanent magnetization[52, 54]:

M(t) = M0 − S log(t), (6)

15

where M0 is a constant and S is the magnetic viscosity [54]. It should be noted that M0 is themagnetization at t = 1 and therefore it depends on the unit of time used, while the coefficient Sdoes not have such a dependence [52]. Alternatively, power law can be used to describe the timeevolution of the remanent magnetization [52, 55–57]:

M(t) = M0t−n, (7)

where exponent n should increase with increasing temperature. We want to underline that Eqs.6 and 7 have already been used used to describe time dependence of TRM in various SG systems[51, 52, 57, 58].

Logarithmic and power law provide best fit for TRM(t) at 10 K, 40 K, and 100 K, and forIRM(t) for 10 K and 40 K, while both approximations give only very rough fits for IRM(t) at 100K. Our fit is characterized by a coefficient of determination R2, which is markedly lower than thatreported for TRM data for 5.1 nm NiO NPs [52]. This may be a consequence of considerably morecomplex mechanism of magnetic relaxation in LCMO12 NPs with respect to that in NiO NPs. Insupport of this observation note that even bulk LCMO samples exhibit quite complex relaxation ofresistivity stemming from intricate balance between static and dynamic phase-separation regimes,as determined by an appearance of a small FM moment associated with the CD volume [45, 48].One may expect even more complex effects in NPs form of such manganite system. Indeed, theanalysis of temperature dependence of spontaneous magnetization in our recent experiments leadus to a conclusion that two distinct sources of ferromagnetism exist in our system [9, 50], a featurethat may result in an intrinsic relaxation of magnetization associated with dynamic coexistence ofdifferent ferromagnetic phases.

At T = 150 K, the temperature significantly higher than the temperatures of maxima in magneticsusceptibility and higher than the blocking temperature, we observe an unusual upward relaxationof both TRM and IRM in the full time scale, as shown in the insets in Figure 10. This behavior in-dicates that the FM contribution associated with ferromagnetic clusters at the surface of LCMO12NPs increases after switching off the magnetic field. It should be noted that some glassy sys-tems exhibit unusual behavior of magnetic relaxation [57, 59] in which magnetic relaxation changesthe sign in different time spans. For example, time dependence of ZFC magnetization of phase-separated Nd2/3Ca1/3MnO3 manganite shows initially a positive slope within the first 20 min. ofthe time record, then reaches the maximum, and unexpectedly decreases with further increase ofthe observation time up to 180 min [59]. Although the very existence of up and down relaxationhas been discussed in the literature, the nature of a decrease of ZFC magnetization after some 20min. remains unclear. A competition between relaxation processes characterized by different char-acteristic rates was proposed to explain unusual upward relaxation of TRM in granular multilayers[Co80Fe20(1.4nm)/Al2O3(3nm)]10 at intermediate times [57]. These granular systems were foundto show generic spin-glass behaviour for nominal CoFe thicknesses below 1 nm, and superferromag-netic (SFM) behaviour in samples with the thickness exceeding 1.2nm. Two complementary slowrelaxation processes are separately driven by magnetic field and temperature. While the power-law-like decrease of thermoremanent magnetization refers to the decay into a multi domain statein the absence of a stabilizing field, the intermediate increase of the thermoremanent moment isattributed to the post alignment of the thermally disordered superspins in SFM domains [57].

As pointed already, bulk La0.23Ca0.77MnO3 manganite demonstrate markedly different relaxationregimes [45, 48]. The first one is typical for various electron-doped manganites and is associated withdefective formation of the charge-ordered phase. The second one results from the coexistence of theCO phase with domains of charge-disordered phase. The pronounced relaxation of magnetization

16

is observed at temperature as high as 170 K, while change in the sign of time variation of resistivityat T ≈ 125 K and T ≈ 70 K was associated with transition from static (at T < 70 K and in therange 125− 190 K) to dynamic phase separation regime between 70 and 125 K [45, 48].

As discussed previously, in the background of AFM ordered cores of electron-doped La1−xCaxMnO3

manganite NPs, small sized FM clusters are formed in the disordered spin matrix at surfaces ofNPs. Therefore, the FM-like DE correlations appearing across the interface between two NPs mightresult in the formation of some collective state and SFM-like behavior [9, 60]. The possibility oftwo different relaxation processes in the case of the SFM domain state was discussed by Chen etal. [57] First, the orientations of the superspins are correlated by the fluctuation of the randombonds to form domains. Second, inside the domains the superspins remain noncollinear mainly dueto random anisotropies. This might result in the occurrence of two kinds of relaxation processesupon changing field and/or temperature [57].It should be noted also that domain wall processes arefast in nonzero and slow in zero field. Moreover, there are superspin alignment processes, whichare slow in both nonzero and zero fields [57]. The temperature is a very decisive ingredient of theSFM order therefore, equilibrium configurations to be attained will change whenever T is varied[57]. Since at T ≥ 150 K there is only one ferromagnetic moment attributed to FM domains formedin the shell of La0.23Ca0.77MnO3 NPs [9, 50], we suggest that very slow up relaxation process isattributed to domain walls processes and superspin alignment processes. At temperatures belowTN ∼ 100 K in LCMO12, as evidenced by the appearance the exchange bias effect [50] and especiallyby the appearance of a second FM phase resulting in intrinsic phase separation in NPs cores, theTRM relaxation changes its sign. It appears that the magnetic transitions play a crucial role indetermining the dynamic properties of the magnetic phase coexistence.

Magnetic field dependence of the TRM magnetization and IRM magnetization is known to pro-vide clear fingerprints of irreversible magnetization in various nano systems [61–63]. As shown byBenitez et al., magnetic field dependence of TRM and IRM is markedly different for superparam-agnetic, superspin glasses, two (2D), and three dimensional (3D) diluted AFM systems [61, 62]. Anideal AFM bulk system is expected to show zero TRM and zero IRM, independently of the field andtemperature [61, 62, 64]. In SG systems, TRM increases rapidly with increasing field and exhibitsa characteristic peak at intermediate fields, while IRM increases monotonously with increasing fieldand joins the TRM curve at some saturation fields. A SPM system shows a qualitatively similarTRM/IRM behavior; however, in SPM system there is no characteristic TRM peak and IRM inweak fields is very small [61, 62, 64].

Magnetic field dependence of TRM/IRM magnetization of SCMO12 and SCMO60 at 10 K isshown in Fig. 11. At small fields, both TRM and IRM strongly increase with increasing field,as expected for a SSG system [61, 62, 64]. The magnetization increase slows down significantlyfor fields exceeding H ∼ 5 kOe. Although TRM and IRM do not coincide at high fields, as isexpected for SPM and SSG systems, their values at H ∼ 90 kOe are nevertheless comparable.Figure 11 contains more noticeable features; TRM and IRM of smaller LCMO12 NPs in H > 5kOe is significantly larger than that of larger LCMO60 particles. In particular, TRM of LCMO12in H = 90 kOe is 70 times larger than that of LCMO60. TRM of LCMO12 changes only slightly atfields above 40 kOe, it shows a broad slight maximum between 55− 70 kOe and slightly decreasesin fields above 80 kOe. Looking into TRM/IRM plot of LCMO NPs and taking into account thatIRM of SPM is very small in relatively weak fields, we conclude that we deal with SSG featuresand enhanced role of glassy component in smaller LCMO12 NPs.

17

0 20 40 60 800.0

0.2

0.4

0.6

0.8

1.0

1.2

LCMO12 IRM LCMO12 TRM

M (e

mu/

g)

La0.23

Ca0.77

MnO3

T=10 K

M (e

mu/

g)

H (kOe)

0.000

0.005

0.010

0.015

0.020

LCMO60 IRM LCMO60 TRM

Figure 11: Field dependence of TRM and IRM for SCNO12 and SCMO60 NPs at 10 K.

5 Expected innovations

Noise investigations beyond a simple estimate of the magnitude of the noise level will contribute,together with other experiments, to better understanding of electrical and magnetic properties ofCMR manganites. The expected significance of the proposed research consists in providing deeperinsight into the physics of metastable resistivity states and enlightening hitherto not explainedproblems. Our results will give an important input for theoretical modeling of phenomena of 1/fnoise and metastable resistivity, what will provide future experimental work with better theoreticalguidance. In terms of applications, the issue of non-Gaussian noise is of particular importance.Strong 1/f noise and RTN fluctuations are unacceptable in low frequency sensors. Even in highfrequency applications, well above the characteristic frequencies of the telegraphic noise, resistivityjumps induce high frequency components in the frequency spectrum of the device response.

18

References

[1] L. P. Gor’kov, V.Z. Kresin, JETP Lett. 67 (1998) 985.

[2] M. Uehara, S. Mori, C. H. Chen and S.-W. Cheong, ”Percolative Phase Separation UnderliesColossal Magnetoresistance in Mixed-Valent Manganites”, Nature 399, 560 (1999).

[3] E. Dagotto, S. Yunoki and A. Moreo, ”Phase Separation Tendencies in Manganites as a PossibleExplanation of the CMR Effect”, Materials Science and Engineering B 63, 65 (1999).

[4] V. Markovich, I. Fita, A. Wisniewski, D. Mogilyansky, R. Puzniak, L. Titelman, C. Martin,and G. Gorodetsky, Phys. Rev. B 81, 094440 (2010).

[5] V. Markovich, G. Jung, I. Fita, A. Wisniewski, Ya. Yuzhelevsky, D. Mogilyansky, R. Puzniak,L. Titelman, and G. Gorodetsky, J. Supercond. Nov. Magn., 24, 861-865 (2011).

[6] V. Markovich, G. Jung, Ya. Yuzhelevsky, G. Gorodetsky, Ya. M. Mukovskii, J. Appl. Phys.109, 07D702 (2011).

[7] Ya. Yuzhelevsky, V. Markovich, G. Jung, G. Gorodetsky, J. Appl. Phys. 109, 063908 (2011).

[8] M. J. Benitez, O. Petracic, H. Tuysuz, F. Schuth, and H. Zabel, Phys. Rev. B 83, 134424(2011).

[9] V. Markovich, I. Fita, A. Wisniewski, D. Mogilyansky, R. Puzniak, L. Titelman, C. Martin,and G. Gorodetsky, Phys. Rev. B 81, 094428 (2010).

[10] J. L. Dormann, D. Fiorani, and E. Tronc, Adv. Chem. Phys 98, 283 (1997).

[11] L. Neel, Ann. Geophys. C.N.R.S. 5, 99 (1949).

[12] W. F. Brown, Jr., Phys. Rev. 130, 1677 (1963).

[13] X. Batlle and A. Labarta, J. Phys. D 35, R15 (2002).

[14] P. E. Jnsson, Adv. Chem. Phys. 128, 191 (2004).

[15] O. Petracic, X. Chen, S. Bedanta, W. Kleemann, S. Sahoo, S. Cardoso, and P. P. Freitas, J.Magn. Magn. Mater. 300, 192 (2006).

[16] S. Bedanta and W. Kleemann, J. Phys. D 42, 013001 (2009).

[17] Y. Sun, M. B. Salamon, K. Garnier, and R. S. Averback, Phys. Rev. Lett. 91, 167206 (2003).

[18] G. M. Tsoi, L. E. Wenger, U. Senaratne, R. J. Tackett, E. C. Buc, R. Naik, P. P. Vaishnava,and V. Naik, Phys. Rev. B 72, 014445 (2005); G. M. Tsoi, U. Senaratne, R. J. Tackett, E.C. Buc, R. Naik, P. P. Vaishnava, V. M. Naik, and L. E. Wenger, J. Appl. Phys. 97, 10J507(2005).

[19] R. K. Zheng, H. Gu, B. Xu, and X. X. Zhang, Phys. Rev. B 72, 014416 (2005).

[20] T. Jnsson, P. Nordblad, and P. Svedlindh, Phys. Rev. B 57, 497 (1998); M. F. Hansen, T.Jnsson, P. Nordblad, and P. Svedlindh, J. Phys.: Condens. Matter 14, 4901 (2002).

19

[21] M. Sasaki, P. E. Jonsson, H. Takayama, and P. Nordblad, Phys. Rev. Lett. 93, 139701 (2004);M. Sasaki, P. E. Jonsson, H. Takayama, and H. Mamiya, Phys. Rev. B 71, 104405 (2005).

[22] M. Bandyopadhyay and S. Dattagupta, Phys. Rev. B 74, 214410 (2006).

[23] S. Mrup, M. B. Madsen, J. Franck, J. Villadsen, and C. J. W. Koch, J. Magn. Magn. Mater.40, 163 (1983).

[24] D. G. Rancourt and J. M. Daniels, Phys. Rev. B 29, 2410 (1984).

[25] J. B. Johnson, Nature 119, 50 (1927); Phys. Rev. 29, 367 (1927).

[26] H. Nyquist, Phys. Rev. 32, 110 (1928).

[27] W. Schottky, Ann. Phys. (Leipzig) 57, 541 (1918).

[28] B. Raquet, Electronic Noise in Magnetic Materials and Devices, Springer-Verlag Berlin (2001).

[29] Sh. Kogan, Electronic Noise and Fluctuations in Solids, Cambridge University Press, Cam-bridge (1996).

[30] P. Dutta and P. M. Horn, Rev. Mod. Phys. 53, 497 (1981).

[31] M. B. Weissman, Rev. Mod. Phys. 60, 537 (1998).

[32] B. Raquet, A. Anane, S. Wirth, P. Xiong, and S. von Molnar, Phys. Rev. Lett. 84, 4485 (2000);

[33] A. Anane, B. Raquet, S. von Molnar, L. Pinsard-Godart, and A. Revcolevschi, J.Appl. Phys.87, 5025 (2000);

[34] R. D. Merithew, M. B. Weissman, F. M. Hess, P. Spradling, E. R. Nowak, J.ODonnell, J. N.Eckstein, Y. Tokura, and Y. Tomioka, Phys. Rev. Lett. 84, 3442 (2000);

[35] V Markovich, G. Gorodetsky, G. Jung, D. A.Shulyatev and Ya. M. Mukovskii, Fluct. NoiseLett. 1, L105 (2001).

[36] Sudeshna Samanta and A. K. Raychaudhuri, Phys. Rev. 85, 045127 (2012).

[37] D. A Shulyatev, A. A. Arsenov, S. G. Karabashev, Ya. M. Mukovskii, J. Crys. Growth, 198/199,511 (1999).

[38] X. D. Wu, B. Dolgin, G. Jung, V. Markovich, Y. Yuzhelevski, M. Belogolovskii, and Ya. M.Mukovskii, Appl. Phys. Lett. 90, 242110 (2007).

[39] M. Belogolovskii, G. Jung, V. Markovich, B. Dolgin, X. D. Wu and Y. Yuzhelevski, J. Appl.Phys. 109, 073920 (2011)

[40] Y. Yuzhelevski, V. Markovich, V. Dikovsky, G. Gorodetsky, G. Jung, D. A. Shulyatev, andYa. M. Mukovskii, Phys. Rev. B 64, 224428 (2001).

[41] G. P. Zhigalski, Phys. Usp., 46, 449 (2003).

[42] A. Gokce, E. R. Nowak, S. H. Yang and S. S. P. Parkin, J. Appl. Phys. 99, 08A906 (2006).

20

[43] B. Raquet, A. Anane, S. Wirth, P. Xiong, and S. von Molnar, Phys. Rev. Lett. 84, 4485 (2000).

[44] J. B. Goodenough, in Handbook on the Physics and Chemistry of Rare Earth, edited by K.A. Gschneidner, Jr., J.-C. G. Bunzli, and V. Pecharsky (Elsevier Science, New York, 2003),Vol. 33.

[45] D. Niebieskikwiat, J. Tao, J. M. Zuo, and M. B. Salamon, Phys. Rev. B. 78, 014434 (2008).

[46] M. Pissas, G. Kallias, M. Hofmann, and D. M. Tobbens, Phys. Rev. B 65, 064413 (2002).

[47] S. Bedanta and W. Kleemann, J. Phys. D: Appl. Phys. 42, 013001 (2009).

[48] J. Tao, D. Niebieskikwiat, M. B. Salamon, and J. M. Zuo, Phys. Rev. Lett. 94, 147206 (2005).

[49] M. Pissas and G. Kallias, Phys. Rev. B 68, 134414 (2003).

[50] V. Markovich, G. Jung, A. Wisniewski, D. Mogilyansky, R. Puzniak, A. Kohn, X. D. Wu, K.Suzuki, and G. Gorodetsky, to be published elsewhere.

[51] J. A. Mydosh, Spin Glasses (Taylor and Francis, London, 1993).

[52] S. D. Tiwari and K. P. Rajeev, Phys. Rev. B Phys. Rev. B 72, 104433 (2005).

[53] M. J. Benitez, O. Petracic, H. Tysz, F. Schth, and H. Zabel, Phys. Rev. B 83, 134424 (2011).

[54] C. N. Guy, J. Phys. F: Met. Phys. 8, 1309 (1968).

[55] M. Ulrich, J. Garca-Otero, J. Rivas, and A Bunde, Phys. Rev. B 67, 024416 (2003).

[56] R. S. Patel, D. Kumar, A. K. Majumdar, Phys. Rev. B 66, 054408 (2002).

[57] X. Chen, W. Kleemann, O. Petracic, O. Sichelschmidt, S. Cardoso, and P. P. Freitas, Phys.Rev. B 68, 054433 (2003).

[58] F. Rivadulla, M. A. Lpez-Quintela, and J. Rivas, Phys. Rev. Lett. 93, 1672064 (2004).

[59] E. Fertman, S. Dolya, V. Desnenko, A. Beznosov, M. Kaj?akov, and A. Feher J. Magn. Magn.Mater. 324, 3213 (2012).

[60] V. Markovich, I. Fita, A. Wisniewski, D. Mogilyansky, R. Puzniak, L. Titelman, and G.Gorodetsky, J. Appl. Phys. 108, 063918 (2010).

[61] M. J. Benitez, O. Petracic, E. L. Salabas, F. Radu, H. Tysz, F. Schth, and H. Zabel, Phys.Rev. Lett. 101, 097206 (2008).

[62] M. J. Benitez, O. Petracic, H. Tysz, F. Schth, and H. Zabel, Phys. Rev. B 83, 134424 (2011).

[63] F. C. Montenegro, S. M. Rezende, and M. D. Coutinho-Filho, Rev. Bras. Fs. 21, 192 (1991).

[64] P. K. Manna, S. M. Yusuf, R. Shukla, and A. K. Tyagi, Phys. Rev. B 83,184412 (2011).

21