Griffiths phase and colossal magnetoresistance in Nd0.5Sr0.5MnO3 oxygen-deficient thin films

Journal of Magnetism and Magnetic Materials 334 (2013) 74–81

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Griffiths phase and colossal magnetoresistance in Nd0.5Sr0.5MnO3 oxygen-deficient thin films N.I. Solin a,n, A.V. Korolyov a, Yu.V. Medvedev b, Yu.M. Nikolaenko b, V.A. Khokhlov b, A.Yu. Prokhorov b, G.G. Levchenko b a b

Institute of Metal Physics, S. Kovalevskaya Street 18, Yekaterinburg 620990, Russia Donetsk Institute for Physics and Engineering, Donetsk, R. Luxemburg Street 72, Donetsk 83114, Ukraine

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 July 2012 Received in revised form 20 November 2012 Available online 21 January 2013

This work is devoted to study the influence of the Griffiths phase in colossal magnetoresistance manganites. Griffiths-phase-like behavior of the paramagnetic susceptibility w0 is observed in Nd0.5Sr0.5MnO3 oxygen-deficient thin films fabricated by magnetron sputtering deposition. In Nd0.5Sr0.5MnO3  d films with oxygen deficiency for TG E260–280 K4T4TC ¼ 138 K (TG and TC—Griffiths and Curie temperatures, respectively), paramagnetic matrix consists of a magnetic phase with shortrange order ( 1–1.5 nm) (which is responsible for the colossal magnetoresistance (CMR) above TC), and is embedded in this matrix region with long-range ferromagnetic order (b10 nm), responsible for the Griffiths phase-like behavior of the paramagnetic susceptibility. Electrical resistivity is caused by carrier tunneling between the localized states and obeys the Efros–Shklovskii law. Magnetic resistivity is caused by change of the localized state sizes under the magnetic field. The temperature and magnetic field dependencies of size of the phase inhomogeneity inclusions, found from measurements of magnetotransport properties, can be satisfactorily described by the model of thermodynamic phase separation into metallic droplets of small radius in a paramagnetic matrix. Intrinsic nanoscale inhomogeneities caused by thermodynamic phase separation, rather than the Griffiths phase, determine the electrical resistivity and colossal magnetoresistance of the films. In half-doped manganites, the nature of longrange ordered magnetic phases may be related, besides the chemical heterogeneity, to proximity to a ferromagnetic–antiferromagnetic boundary at the phase diagram as well. The results are in good agreement with the model of existence of an analog of Griffiths phase temperature in half-doped manganites. & 2013 Elsevier B.V. All rights reserved.

Keywords: Griffiths phase Nd0.5Sr0.5MnO3 Transport Magnetic property

1. Introduction Considerable interest to Griffiths phase (GP) is due to a suggestion [1] that it is an origin of the colossal magnetic resistance (CMR) effect. Among various heterogeneous phases, formation of ferromagnetic (FM) clusters under temperatures much higher than those of long-range ordering TC is a widespread phenomenon [2–6]. They are often associated with a Griffiths singularity, originally proposed for a randomly diluted Ising FM [7]. In a lattice consisting of magnetic atoms connected by exchange couplings, J, between the nearest neighbors, at Griffiths temperature TG, a magnetic transition takes place. Some atoms in the lattice may be absent, or the lattice is randomly occupied by nonmagnetic atoms. If so, the transition occurs at TC oTG. Magnetic clusters with properties of an undiluted medium can

n

Corresponding author. Tel.: þ7 343 378 35 51; fax: þ 7 343 374 52 44. E-mail addresses: [email protected], [email protected] (N.I. Solin).

0304-8853/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmmm.2013.01.009

emerge in such the disordered medium. When the cluster size increases (Griffiths phase), the free energy and magnetization at TG 4T4TC have no analytical expression in a magnetic field H¼0 [7]. Bray [8] has generalized the Griffiths model so that it allows a treatment of GP-like properties in various systems, including manganites. The Nagaev phase separation model [9] allows for the existence of self-localized states of conduction electrons of the FM droplet type (magnetic fluctuations of a small radius or ferrons [10]) above TC. It was actively discussed in the 1970s [11]. The introduction of a quenched disorder into the system leads to intrinsic nanoscale inhomogeneities, which also occur in ideal crystals and allow the coexistence of conductive and nonconductive phases not only in antiferromagnetic (AFM) matrix but also in paramagnetic (PM) temperature ranges up to  T* ¼TC (T* is the Griffiths temperature analog [7]) for conductive manganites [12]. Magnetic, optical, magnetic transport, as well as resonance studies [2–6,13] of manganites, cobaltites and other compounds show their magnetic inhomogeneity and provide

N.I. Solin et al. / Journal of Magnetism and Magnetic Materials 334 (2013) 74–81

evidence of the existence of a short-range ordered (SRO) phase with cluster diameter d 1–2 nm in the paramagnetic temperature range [14,15]. The Griffiths phase is characterized by a strong deviation of the paramagnetic susceptibility w0 from the Curie–Weiss (CW) law in weak magnetic fields at T ETG 4TC [7]. The strong dependence of w0 on H and the additional peak in the paramagnetic resonance spectrum are usually explained by the existence of a Griffiths phase [3]. However, such behavior is also typical for a chemically inhomogeneous medium containing magnetic clusters of large sizes with a higher TC. In the compounds which exhibit a phase of Griffiths [3–6], the TC depends on the composition in the case of the substitution of one ion by another. As a consequence, the existence of Griffiths phase is in question [16–18]. In many cases, when GP nature is considered, its connection with the CMR effect is neglected. Also, the main question remains beyond the discussion, namely, whether the Griffiths phase is of a thermodynamic origin or it is caused by chemical inhomogeneities of the sample. Intrinsic and extrinsic inhomogeneities must play sufficiently different roles. Intrinsic inhomogeneities have thermodynamic origins [1,9,10,12]. Therefore, they should be influenced by the magnetic field, temperature and other factors, according to predictions of the phase separation model. External heterogeneities should be different from the intrinsic ones. There are ways to describe the magnetic inhomogeneous media with phase separation [10,19,20]. Identification of the mechanisms of the magnetic, electrical and magneto-transport properties of manganites, their evolution with a change in doping, as well as comparison of the experimental data with conclusions of a cluster model, can provide an important progress in the understanding of the nature of a inhomogeneous state at T4TC [21,22]. Our work is devoted to this problem. Most of the studies of Griffiths phase in manganites are connected with the disorder caused by replacement of a trivalent rare-earth ion R3 þ by a divalent metal ion Me2 þ . It is believed that the Griffiths phase cannot arise in half-doped manganites [23]. Clear Griffiths-phase-like behavior of w0(T) was observed in half-doped Pr0.5Sr0.5MnO3, where a part of the Mn ions is replaced by Ga ions [6]. Similarly, one can expect that discontinuity of the carrier transfer chain Mn–O–Mn in the form of oxygen deficiency may also promote cluster formation. This paper is directed to clarification of the nature of magnetic inhomogeneities and their relation to the CMR effect in Nd0.5Sr0.5MnO3  d oxygen-deficient films. The studied films were Nd0.5Sr0.5MnO3  d with TC 5TG ¼TC ffi 250 K for Nd0.5Sr0.5MnO3. The bulk crystals of Nd0.5Sr0.5MnO3 show FM metallic state below TC ffi 250 K. At TCO ffi150 K the crystal becomes an AFM insulator with a charge/orbital order (CO/OO) [24]. At low temperatures the crystal contains three magnetic phases: (i) an orthorhombic FM one, (ii) an A-type AFM phase, and (iii) CE-type monoclinic AFM CO/OO phase [25]. Temperature dependence of the paramagnetic susceptibility w0(T) for the studied film Nd0.5Sr0.5MnO3 d shows Griffiths-phaselike behavior under weak magnetic fields. Magnetic properties studied under magnetic fields below 5 T show an appearance of small (d  1–1.5 nm) and large (db10 nm) clusters at temperatures below 260–280 K. Electrical resistivity is caused by charge–carrier tunneling between the localized states and obeys the Efros– Shklovskii law [26,27]. Magnetic resistance (MR) is caused by change of the localized state size under a magnetic field [20]. Temperature and magnetic field dependencies of the change of localized state parameters are derived from magnetic transport measurements. The dependencies have been compared with conclusions of a thermodynamic phase separation model. It was shown that the nature of magnetic resistance is mainly determined by short-range ordered magnetic phases, while the large clusters are not of great importance. The nature of the large clusters is not clear.

75

2. Materials and methods The films with a thickness of about 120 nm were prepared by dc magnetron sputtering of a ceramic target in the gas mixture of argon and oxygen (16%) on single-crystalline LaAlO3 (001) substrates heated up to 6501 C. The target was prepared by common ceramic technology from Nd, Sr, and Mn oxides. The as-grown film has high enough electrical resistivity (r 41010 O at To100 K) and has no appreciable MR value under magnetic field H¼1 T. The as-grown films were further annealed in air at 900 1C up to 11 h. The preparation technology of the films has been described in detail elsewhere [28]. The film annealed at T ¼9001 C for 5 h (sample 1) shows the r(T) maximum near 180 K and MR(T) maximum near 150 K. Annealing of the film for 11 h shifts the MR peak to TE240 K. The influence of temperature and the annealing time in oxygen (or air) atmosphere on TC is well known [29] and is explained by oxygen content change during the magnetron sputtering of the film and its recovery during the annealing. Here, results of research on sample 1 are discussed. Chemical composition of the films was studied using an electron microscope JSM-6490LV JEOL (Japan) with a microanalyzer. The results show that the chemical composition of the films prepared at the same conditions remains the same within the experimental error (  4%) and corresponds to the formula Nd0.5Sr0.5MnO3. The y–2y X-ray diffraction (XRD) patterns were obtained using a Rigaku diffractometer with Cu Ka radiation. Only fundamental Bragg peaks of high intensity for the film and the substrate were observed, indicating that the deposition results in a highly c-oriented crystal structure. A high-resolution electronmicroscopy (HREM) study was carried out using a Philips CM300UT-FEG microscope with a field emission gun operated at 300 kV. According to this study, prepared films have orthorhombic crystal structure with parameters close to pseudocubic ones: c/O2Ea EbE0.3912 nm. Resistance measurements were carried out by the usual fourprobe technique. The contacts were produced from indium by an ultrasonic soldering iron. The magnetic and electric studies were carried out on PPMS facilities and an MPMS-5XL SQUID magnetometer at the Magnetic Research Center of the Institute of Metal Physics (Yekaterinburg, Russia). The studies were carried out under magnetic fields directed along the film surface.

3. Results and discussion Magnetization of the Nd0.5Sr0.5MnO3  d film was measured under magnetic field H¼0.01 T (left axis in Fig. 1). Curie temperature, TC ¼138 K, was defined as an inflection point in temperature of magnetization M(T). Absence of an anomaly at TCO E150 K is explained by a strong connection between orbital and charge ordering in Nd0.5Sr0.5MnO3 and the lattice distortions. The CO/OO state in Nd0.5Sr0.5MnO3 was observed in a very narrow interval near x¼0.5 [24], and strongly depends on the oxygen content [30]. The stress caused by the substrate and accommodation of the film to large lattice distortions at the first-order phase transition has an influence on the formation of the CO/OO phase in Nd0.5Sr0.5MnO3 films [31–33]. The temperature dependence of PM susceptibility w0 1(T) at H¼1 T of the studied Nd0.5Sr0.5MnO3  d film (right axis in Fig. 1) at T4300 K can be described by the Curie–Weiss relation w0 1(T)  m2eff/3k(T y), where y is the paramagnetic Curie temperature y E210710 K and meff ¼5.4 70.1 mB is an effective moment. At temperatures below 300 K the dependence w0 1(T) significantly deviates from the CW law. It can be described using a temperature-dependent effective moment meff(T) [d(w0 1(T))/dT]  1/2 (see inset of Fig. 1). At high temperatures (Tffi 350–400 K) the meff

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N.I. Solin et al. / Journal of Magnetism and Magnetic Materials 334 (2013) 74–81

250

350

T, K

5

0.3 H=1 T

0.0

0 0

100

200

M, a.u.

4 150

H=0.01 T

1

8

1/χ 0, 103* g/cm3

neff,μΒ/Mn

0.6

10

10

μeff theor

1/χ0, 103 g/cm3

μeff,μB

12

0

-1 0.00

-0.05

0.05

H, T

5

H=5 T

300

H=3 T H=2 T H=1 T H=0,5 T

T, K Fig. 1. Temperature dependence of magnetization at H¼ 0.01 T (left axis) and inverse PM susceptibility w0 1 at H¼ 1 T (right axis) of a Nd0.5Sr0.5MnO3  d film. The inset shows temperature dependence of an effective moment meff at H ¼1 T.

0 100

200

300

400

T, K Fig. 2. Temperature dependence of an inverse PM susceptibility w0 1 of a Nd0.5Sr0.5MnO3  d film at H¼ 0.1–5 T. The top inset shows a hysteresis loop at T¼225 K.

30 ΔMFM, Gs

3 200 K 220 K

2

240 K 260 K

1 0

20

M, Gs

0

1

2

H, T

10

3

0 320 K 300 K 280 K 260 K

0

1

240 K 220 K 200 K

2

H, T

ΔMFM,Gs

value is close to the expected theoretical one mtheor eff ¼5.1670.04 mB. Down to 250 K it steeply grows with lowering temperature, and at To250 K it sharply increases up to 10–12 mB. mtheor has been eff calculated using the following assumptions. At high temperatures, the ground state of Nd3þ is determined by values gJ ¼8/11, J¼9/2 and meff(Nd3 þ )¼ gJ[J(Jþ1)]1/2 ¼3.62 mB. For Mn3þ and Mn4 þ ions the orbital moments are frozen, gJ ¼2, S¼2 or 3/2, meff(Mn4 þ )¼3.87 mB, and meff(Mn3 þ ) is 4.90 mB. In the case of x¼½, the value of mtheor eff (Nd3 þ )¼[0.5meff(Nd3 þ )2 þ(0.5 2d)meff (Mn4þ )2 þ(0.5þ2d)meff(Mn3 þ )]1/2 E5.10(1þ0.4d) mB ffi5.1670.04 mB for d E 0.1–0.2. A deviation from the CW law indicates that a competition appears between paramagnetism and the forming ferromagnetic droplets. The results indicate that the magnetic inhomogeneities arise at high temperatures (Tffi350 K), and they sharply rise at temperatures below T*E260 KETC for Nd0.5Sr0.5MnO3. Such a behavior of w0 1(T) and enhanced meff values are typical for manganites [2]. Bulk Nd0.5Sr0.5MnO3 and Nd0.5Ca0.5MnO3 crystals show meff values close to mtheor at T4300–450 K and an increase in meff with eff decreasing temperature [34,35]. In La0.7Ca0.3MnO3 the magnetic inhomogeneity arises below the temperature of the structural transition TOR ¼705 K from a rhombohedral to orthorhombic lattice, and increases with lowering temperature [18]. It was supposed in Ref. [18] that the lower symmetry promotes Jan–Teller distortions and a local double exchange. An analysis using the double exchange model shows the presence of a magnetic short-range ordered phase at T¼0 and its retention at T4TC [36]. The CW law for La0.9Ca0.1MnO3 is valid at T4450 KETOO0 only, i.e., at temperatures higher than the transition from an orthorhombic Pnmb phase to a pseudocubic one [37]. Varma [20] explained meff increase in manganites by formation of the spin polarons near an electron localized on Mn4 þ ion at TbTC and polarization of the nearest Mn ions. Fig. 2 shows temperature dependencies of w0 1(T) at H¼0.1C5 T. It is seen that above 260–280 K the 1/w0 value is independent of magnetic field and is almost constant at H¼ 0.1C3 (5) T. Below 250– 270 K the PM susceptibility depends on magnetic field and shows a behavior typical for the Griffiths phase [5]: (i) strong deviation of the paramagnetic susceptibility w0 from the Curie–Weiss law in weak magnetic fields at To260 KETC for Nd0.5Sr0.5MnO3; and (ii) suppression of the susceptibility under higher magnetic fields. The w0 suppression under high magnetic fields can be explained if to assume that the FM component of the clusters is masked by linear increase of the PM contribution of the matrix [4]. Such a behavior may correspond to microstructure consisting of either a strongly diluted system of FM clusters when a total

H=0,1 T

0 200

3

300 T, K

4

400

5

Fig. 3. Magnetic-field dependence of the magnetization of a Nd0.5Sr0.5MnO3  d film in the temperature interval of 200–320 K. The top inset presents field dependence of the FM component DMFM at T¼200–260 K. The bottom inset presents temperature dependence of DMFM extrapolated to zero field.

contribution of FM clusters is small in comparison with that of a PM matrix or a system of large clusters with weak magnetic correlations and a small magnetic moment [4]. Our results point out to a more complex microstructure. Below T¼250–270 K the PM susceptibility decreases with increasing magnetic field and deviates from the CW law. Such a behavior was observed in cobaltites as well [5]. Fig. 3, presents the field dependences of magnetization for H¼0.01C5 T and T¼ TG 760 K (200–320 K). At T 4280 K the magnetization M(H, T) ¼ w0(T)  H is proportional to the magnetic

N.I. Solin et al. / Journal of Magnetism and Magnetic Materials 334 (2013) 74–81

MðH,TÞ ¼ DMFM ðH,TÞ þ w0 ðH,TÞ  H

ð1Þ

To explain the M(H) behavior, one should assume the existence of large and small particles. The first part of Eq. (1) describes the large particles, while the second one small particles. Large particles arise at TG E260 K and their contribution DMFM increases with decreasing temperature (lower inset Fig. 3). The value of DMFM(H) increases rapidly in small fields, H¼ 0.05C0.1 T, and saturates at magnetic fields about 0.5 T (upper inset of Fig. 3). Small particles also occur at TETG E260 K. In sufficiently large monodomain particles, anisotropic forces hold the magnetization vector aligned in a direction corresponding to the minimum energy. When the size of droplets approaches the interatomic distances, the particle energy KeffVcl (Keff is the effective energy of the magnetic anisotropy and Vcl is the cluster volume) decreases below the thermal level, the magnetization vector loses stability and starts performing thermal motions of the Brownian type (although the saturation magnetization and the Curie temperature may still retain the values characteristic of the continuous solid). The dependence of the magnetization Icl of such superparamagnetic (SPM) clusters on the temperature and magnetic field is described by the Langevin formula, if KeffVcl okBT [38]: Icl ¼ NM cl ½cthðxÞ21=xÞ,

ð2Þ

where x ¼MclH/kBT, Mcl ¼nclS is the magnetic moment of a cluster, S is the magnetic moment of a molecule, ncl is the number of molecules in a cluster, N is the number of SPM clusters in a unit volume of the sample, and kB is the Boltzmann constant. The variations of DMFM(H) observed in the fields up to 0.5 T can be roughly described in terms of expression (3) with Mcl ¼ (3 8) 104 mB (see the dashed lines at the inset in Fig. 2). This case corresponds (in a spherical model) to a cluster with a diameter of about 10 nm or Vcl¼10  18 cm3. Manganites usually have the anisotropy energy  105 erg/cm3. These clusters are probably not SPM, since kT oKeff Vcl. The magnetic hysteresis loop representative for FM is observed in the PM region at ¼225 KE1.6 TC (see inset Fig. 2). The hysteretic shape of the M(H) and the estimates show that these inhomogeneities (large clusters) are not SPM. Such a behavior of the DMFM(H) dependence (upper inset of Fig. 3) can be explained by an effect of a demagnetization field HN ¼Nf  M and the field of anisotropy of large clusters (here, Nf is the demagnetization factor and M is the cluster magnetization). Thus, the saturation as well as the hysteretic shape of the field and temperature dependencies of magnetization indicate that the long-range ordered FM regions arise in a Nd0.5Sr0.5MnO3  d film at To260 K. Volume of the large clusters is estimated from DMFM value at 200 K which is approximately equal to 3–5% of the film volume. Fig. 4 shows magnetic field dependencies of w0(H)/w0(H¼1 T) at T¼200–320 K. At T4280 K w0 does not depend, while, below 280 K w0 depends on the magnetic field and at T ¼200 KE1.45 TC, H¼5 T the w0 decrease is about 15% in comparison with its value in weak magnetic fields. Noteworthy is a nonlinear dependence of magnetization at high magnetic fields, which increases with lowering temperature. Such a behavior is typical for a paraprocess when the temperature is approaching TC. The dashed line labeled

1.00

320-300 K 280 K Brn200 K

χ0(H)/ χ0(H=1 T)

field with temperature dependent w0(T). Below T¼250–260 K the form of M(H) is essentially changed (Fig. 3): the magnetization becomes a nonlinear function of H, it rises sharply at Ho0.1– 0.2 T, and then monotonically nonlinearly increases. It is seen (dashed lines in Fig. 3) that at T¼260 K M(H) deviates from a straight line at H ffi3–4 T. As the temperature falls, M(H) deviates from a straight line at lower magnetic field (HZ1.5 T at T¼200 K). The behavior of M(H) is typical for a paramagnet while introducing FM particles of different size into it:

77

0.95

260 K Mcl,μB

Dcl, nm

125

1.5

240 K

Dcl

220 K

0.90

75 1.0

Mcl 25 200

250

300

200 K

T, K

0.85

0

3

5 H, T

Fig. 4. Field dependencies of relative values of the PM susceptibility w0(H)/ w0(H¼ 1 T) of a Nd0.5Sr0.5MnO3  d film in the temperature range of 200–320 K. Points show experimental data, whereas the lines show accounted results. The inset presents temperature dependencies of magnetic moment of the clusters Mcl and their sizes Dcl. Lines are drown for eye.

Brn 200 K in Fig. 4 shows a w0(H)/w0(H¼0) variation caused by ordering of spin magnetic moments of PM matrix at the field H, which were disordered by a thermal motion (paraprocess) at 200 K. The magnetization is calculated in the framework of an average field model on the basis of the Brillouin equation for TC ¼138 K and S ¼2. It is seen that the paraprocess gives a significant contribution, but is essentially less than observed w0(H)/w0(H¼0) values. To explain w0(H)/w0(H¼0) behavior at high magnetic fields, it is necessary to suppose that besides large clusters (d Z10 nm) in the sample there are small clusters too. Variations in w0(H)/ w0(H¼ 1 T) in high fields at fixed temperatures (depicted by symbols) can be described by corresponding expressions for w0(H)/w0(H¼0) in Eq. (2), and estimation of Mcl is possible. In Fig. 4 can be seen the calculation results (shown by solid lines). In the inset of Fig. 4 the temperature dependencies Mcl(T) and estimated from Mcl cluster sizes Dcl are shown. The estimation was performed in the frame in a spherical model at S ¼2 and lattice parameter aMn–Mn ¼0.4 nm. It can be seen that the clusters are formed near T* ffi260–280 K, further, their size only slightly changes with temperature decrease. Thus, small and large clusters coexist in the Nd0.5Sr0.5MnO3  d film at T below 250 K. The long-range ordered FM islands (clusters) more than 10 nm in size are embedded in a paramagnetic matrix containing magnetic short-range ordered phases. The same result was observed in La0.7Ca0.3MnO3 films near TC by tunneling spectroscopy [39]. Our estimates show that the distance between large clusters is about 102–103 nm. Obviously, this distance is too large that the clusters could determine the electrical properties of the studied film. Fig. 5 shows magneto-transport data for a Nd0.5Sr0.5MnO3  d film. Temperature dependence of resistivity is typical for manganite behavior without any anomalies near TCO ¼150 K. Under the magnetic field r(T) and MR(T) peaks shift to higher temperatures (see the top right inset in Fig. 5). Note that a ‘‘nonmetal–metal’’ transition occurs at temperatures above TC by 30–40 K. In the PM region, the electrical resistivity exhibits semiconducting behavior

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N.I. Solin et al. / Journal of Magnetism and Magnetic Materials 334 (2013) 74–81 0

self-localized states of conducting electrons of FM droplet type (clusters, FM fluctuations of small radius) gives the following expression for variation of the cluster size Rcl(H) in the PM dielectric matrix [10,19]: DRcl =R0cl  ½Rcl ðT,HÞRcl ðT,H ¼ 0Þ=Rcl ðT,H ¼ 0Þ ¼ MH=5kB Tnlnð2S þ1Þ,

-1

10

-2

DRcl =R0cl ¼ w0 H2 =5kB Tnlnð2S þ 1Þ ¼ bPM H2 =½5TðTyÞ,

300

400

Fig. 5. Temperature dependencies of electrical resistivity of a Nd0.5Sr0.5MnO3  d film in the magnetic field H¼ 0, 3, 6 and 9 T. The left top inset shows the temperature dependence of an activation energy of electrical resistivity DEr. The right top inset shows temperature dependencies of magnetic resistance MRH  r(H¼ 0)/r(H) at H ¼1, 3, 6 and 9 T. The bottom inset shows verification of the ES dependence log r  T  1/2 at H¼0 and 9 T.

and is described by a formula r(T) exp(DEr/kT), where DEr is an activation energy depending on T (see the top left inset in Fig. 5). MR arises at high temperatures and weakly depends on T down to 250 K. Activation energy DEr sharply decreases at To250 K. Similarities between magnetic and electrical properties are clearly seen, that indicate association of magnetic inhomogeneities with the electrical properties in the PM temperature region. In the paramagnetic region for phase-separated environment, the dominant mechanism of conductivity due to hopping (tunneling) of carriers between localized states (clusters) [20], and is described by the Efros–Shklovskii (ES) law [26,27]:

rðTÞ ¼ r0 exp½ðT0 =TÞ1=2 ,

ð3Þ

where T0 EC0e2/eRls is the jump activation temperature, Rls is the size of the localized state, C0 is a constant factor, e is the electron charge, e is the dielectric constant, and r0 depends weakly on the temperature. The estimates [20] show that in manganites with some nonmagnetic randomness [40], an electron–electron interaction can lead to formation of an Efros–Shklovsky gap in the state density near the mobility edge. Reduction of disorder in a magnetic field causes Rls increase and decrease in electrical resistivity [20]. Besides the granular metals [41] and compensated semiconductors [26], the ES law is observed for cobaltites [15,42] and weakly doped lanthanum manganites [22,37,43,44]. It is seen from the bottom inset in Fig. 5 that at H ¼0 r(T) obeys the ES law in the interval 320–190 K with T0 ¼ 24  103 K. At H¼9 T the ES dependence is not valid due to Rls(H) change under the magnetic field. There is a great uncertainty of Co in (3) [26,27]. It is therefore impossible to determine the size of the localized states in a magnetic field. To carry out the estimation, we take C0 ¼1 and e ¼1 [40]. Then from T0 ¼ 24000 K we can obtain a value of Rls ¼2 nm at H¼0, that is close to the values obtained from magnetic measurements, Rls ERcl. But relative variation of localized states size DRls =R0ls can be calculated from the electrical resistivity change in the magnetic field MRH  r(H¼0)/r(H) [21]: 1=2

 ½Rls ðT,HÞRls ðT,H ¼ 0Þ=Rls ðT,H ¼ 0Þ ¼ 1=½1ðT=T 0 Þ

2

 lnMRH  1:

DRls  ½5TðTyÞ=R0ls ¼ bPM H2

ð7Þ

DRls*T*(T  y)/R0ls H2

for T¼320–250 K (see The values of Fig. 6) at y ¼235 K (that is close to the value of y ¼210710 K obtained from the magnetic experiments) approximately lie on a straight line. It confirms the validity of the Eq. (7). 320 K 280 K 260 K 250 K 230 K

10

0

20

10

40

T=245 K T=260 K T=300 K T=305 K T=310K

5

H2,

80

T2

0

0

Θ=235 K

H, T 9 8 7 6 5 4 3 2 1

60

30

0

0

ΔRls / Rls, %

200

T, K

ΔRls/Rls, %

100

2

0

ð6Þ

where bPM is a value determined by the acceptors concentration, molar weight, magnetic moment S and other known parameters of the material [21]. The bottom inset in Fig. 6 shows temperature dependencies of DRls =R0ls at fixed values of H¼ 1–9 T obtained using Eq. (4). Size of the localized states increases smoothly with increase of the magnetic field and lowering temperature. Increasing the size of the localized states at 50% reduces the resistivity of more than ten times (see Fig. 5 and 6). Let’s further check correspondence of the obtained results on DRls =R0ls to a phase separation model. The top inset in Fig. 6 shows the magnetic field dependencies of relative change of the localized states size DRls =R0ls for five fixed temperatures obtained from the measurements of r and MRH. It is seen that the dependence DRls =R0ls H2 obeys well in the interval 320–245 K and starts to deviate from this dependence when approaching to T¼ y ¼210710 K. The dependence DRls =R0ls  w0H2 in the PM temperature region was predicted in [10,20]. If the variations of DRls =R0ls are due to an intrinsic process of phase separation then expression (7) should be independent of T:

2

10

DRls =R0ls

ð5Þ

where n Ex is the concentration of the carriers (acceptors), R0ls  Rcl(T, H¼0) T  1/5 [10,20] weakly depends on temperature. The magnetization at T4 y can be determined from the CW law: M¼ w0H¼CH/(T  y), where C is the Curie constant. Then we have:

[Rls(H)-Rls(H=0)* T*(T-Θ)]/Rls(H=0), 10 K

ρ, Ω cm

10

200

40

250

T, K

300

80

H2, T2

ð4Þ The theory of phase separation [10] allows to determine regularities of the change of localized state sizes in the PM region. Minimization of a free energy correction at formation of

Fig. 6. Field dependencies of DRls*T*(T–y)/R0ls  H2 of a Nd0.5Sr0.5MnO3  d film at fixed temperatures in the interval 245–310 K. The top inset shows field dependencies of DRls =R0ls  H2 at T¼ 230–320 K. The bottom inset shows temperature dependencies of DRls =R0ls at H¼ 1–9 T.

N.I. Solin et al. / Journal of Magnetism and Magnetic Materials 334 (2013) 74–81

If variations of DRls =R0ls are due to the intrinsic processes of the phase separation then expression (8) for any H must display the same linear temperature dependence: R0ls  H2 =DRls T ¼ 5ðTyÞ=bPM  w1 0

ð8Þ

It is seen (Fig. 7) that the experimental results are very similar to the dependencies w0 1(T) shown in Fig. 1. The values of R0ls *H2/ DRlsT in the temperature interval 250–320 K obey a temperature dependence close to a straight line (symbols in Fig. 7) for all values of H¼1–9 T. The values of y ffi 235 K are close to ones obtained from the magnetic measurements. Deviation from linearity occurs below TE250 K (solid and dashed lines for H¼9 and 1 T, correspondingly). The next examination of expression (6) validity consists in the determination of the sample susceptibility w0 from the magnetic field dependencies DRls/Rls  H2 at fixed temperature. All the parameters necessary to obtain bPM are known [21], except a concentration of the carriers. From a phase diagram of Nd1 xSrxMnO3 and taking for the estimation TMI E160 K, we can roughly suppose that nE0.1–0.2. The inset in Fig. 7 shows the temperature dependencies of 1/w0 obtained from the measurement of the magnetization at H¼1 T, and the dependencies of 1/wMR calculated for n¼ 0.1 from the MR measure0 ment which are shown in the inset in Fig. 6. Magnitudes of y are close,E210 and E235 K but the deviation from linearity occurs near T¼300 and 250 K, correspondingly. In the ES model it is supposed that the sizes of the localized states are the same [27]. A linear dependence log r  (T0/T)1/2 was observed in granular composites [41] which are, in a sense, the analog of phase-separated systems. In the case of small volume of the granular composites, as well as in magnetically inhomogeneous manganites the conductivity is caused by tunneling (or jumps) of the carriers between metal particles (Fe, Co) divided by an insulator (Al2O3, SiO2) with the thickness s. Energy needed for the formation of an electron–hole pair is approximately equal to an energy of Coulomb blockade EC  e2/eRgr where Rgr is the metal particle size. In the case of disordered medium, we are dealing with particles of different sizes and the tunneling distance can be comparable with the particle size. If so, there are preferable

H2*Rls0*TΔRls,T2/ K

8

4

χMR-1 χ0

200

-1

275

4

χ0-1, 103*g/cm3

8

350

0

T, K H=1T H=3T H=6T H=9T 9T 1T

0

200

240

280

320

T, K Fig. 7. Temperature dependencies of R0ls *H2/DRlsT at fixed H (indicated in the figure). The insets show temperature dependencies of inverse magnetic susceptibility obtained from measurements of magnetization  1/w0 and magnetotransport properties  1/wMR.

79

channels and the carriers are tunneling not between the nearest particles but between the particles divided by temperature dependent distances s with the same energy of Coulomb blockade, i.e. of the same size [41]. Therefore, the localized states contribute to magnetization but not all of them contribute to the MR. It explains the difference between the dependencies of w0(T,H) obtained from magnetic and electrical measurements. We believe that the susceptibility wMRðTÞ defined from magneto0 transport studies characterizes the properties of ‘‘pure’’ paramagnetic matrix and does not take into account the effect of large magnetic inhomogeneities. Studies of magnetotransport properties show that the intrinsic small-scale inhomogeneities, caused by thermodynamic phase separation determine the nature of the colossal magnetoresistance in the PM temperature region for the Nd0.5Sr0.5MnO3  d film. Large droplets, responsible for the Griffiths phase, possibly influence the electrical properties as well. It reveals itself in the peaks of electrical resistivity and the MR in ideal crystals near TC [45,46]. In the Nd0.5Sr0.5MnO3  d film a phase transition ‘‘nonmetal–metal’’ occurs at temperature higher than TC by 35–40 K. Qualitatively, it can be explained in the following way. With lowering temperature, small clusters merge and form large (more than 10 nm in diameter) conductive clusters [39]. They connect the large droplets, creating a conductive circuit at T4TC. What is the reason of formation of short-range and long-range ordering phases near T¼250–280 K in the Nd0.5Sr0.5MnO3  d film? A quenched disorder is the necessary condition for formation of these phases [45,46]. The manganites are intrinsically disordered due to random distribution of cations of different sizes and valency when R3 þ is substituted by Me2 þ . Excess electron localizes at eight Mn ions, forming the cluster unit cell (polaron) with the size Dcl ¼O3a ¼0.7 nm, where a ¼RMn–Mn ¼0.4 nm. Interaction of the carriers with magnetic moments lowers the energy at parallel orientation of their moments that forms a ‘‘ferromagnetic’’ region around the carrier, i.e., a paramagnetic polaron and elevated values of meff [20]. Because of the advantage in exchange energy and elastic lattice stresses the polarons can merge into larger clusters. As a consequence, short-range ordering or smallscale phase separation occurs at the temperature close to maximal TC at the phase diagram. The appearance of short-range ordered phase is accompanied by anomalies in the linear expansion coefficient close to TG [2,47]. In fact, Griffiths [7] postulated the formation of large clusters. Depending on homogeneity of the acceptors distribution, large clusters, i.e., long-range ordered phase, may also form as a result of uncontrolled technological processes [48]. It is a trivial explanation of existence of the Griffiths phase [16,17]. Owing to a statistical distribution of the acceptors, independently on the method of the crystal fabrication, a certain probability exists that the large clusters may arise. This probability is especially large near a percolation threshold although a region of their existence on a phase diagram is narrow [23]. The experiments [39] show that for xE1/3 near TC large and small clusters coexist. Are they polaron complexes [18] or GP [1]? So far the question is open. The authors [3,23] suggested that GP can be caused by correlating disorder of short-ordered (SRO) magnetic phases. Neutron studies show that in weakly-doped lanthanum manganites at low temperatures magnetic nanoclusters are correlated and embedded into a modulated canted AFM structure [49]. The studies of magnetic field influence of the static properties, spinwave spectrum [49] of weakly-doped lanthanum manganites La1  xAxMnO3 (A¼Ca, Sr) with x ¼0,07C0,1 validate the picture of a modulated canted CAF state, where FM and AFM components are strongly connected. In particular, magnetization of the clusters is certainly oriented relative to the crystallographic axes. At present, any evidence for the cluster correlation in the PM

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region is absent. Most likely, the results testify to a role of a chemical-composition inhomogeneities of the crystals in the experimental studies of GP. It is known [48] that La1  xAxMnO3 (A ¼Ca, Sr) crystals grown by the floatingzone technique have an inhomogeneous distribution of La, Ca, and Sr along the growth direction. In well certified crystals La1  xSrxMnO3 (x ¼0,1) [50] like those studied in [3], an additional lines of the PM resonance are not observed [51], and PM susceptibility in a weak field does not show a Griffith-like behavior for x¼0.1 [50] and x¼0.07 [21,22]. For x¼0.2 and at T4270 K additional lines of the PM resonance are observed [51] in contrast to Ref. [3]. Our studies do not allow a conclusion about the nature of the phase with long-range order in films Nd0.5Sr0.5MnO3  d. Lack of the oxygen in the chain of electron transfer Mn–O–Mn is a specific method of the introduction of a quenched disorder and lowering of the temperature of the magnetic ordering. We do not expect that the lack of oxygen may be of on origin of GP appearance except for their strongly non-uniform distribution. There are two kinds of PS: electronic PS leading to nano-scale clusters, and structural PS [12,45,46] connected with competitive macroscopic phases. Half-doped manganites are at the boundary of a phase diagram ‘‘FM metal–AFM metal’’. Magnetic interaction between AFM and FM phases appears rather complex. One can suppose that the transition may be accompanied by formation of large clusters [6]. In some papers, a new phenomenon was observed, namely, that the cluster size is not increased but decreases under magnetic field [4,52]. Experiments for neutron small-angle scattering show [4] that a moderate magnetic field seems to hinder the growth of large magnetic clusters within the PM phase, although the anomalous susceptibility exponent suggests the persistence of the cluster-like system. We believe that these results can be explained by existence of the clusters of different sizes.

4. Conclusions Electrical and magnetic properties of oxygen-deficient Nd0.5Sr0.5MnO3 d film are discussed through the model of phase separation. Below 250–280 K the paramagnetic matrix consists of a phase with short-range magnetic order (1–1.5 nm), which is interspersed phase (about 3–5% of the film volume) with longrange ferromagnetic order (b10 nm). Temperature dependence of the resistivity is described by the Efros–Shklovskii law and explained by tunneling of carriers between localized states, and magnetoresistance—by the increase of their size in a magnetic field. From the measurements of electrical resistivity in magnetic fields we found the temperature and field dependences of the size of the localized states and compared them with the model of phase separation. Intrinsic nanoscale heterogeneity caused by thermodynamic phase separation determines, basically, electrical resistivity and colossal magnetic resistance in PM temperature region and can be satisfactorily described in the model of the small-scale phase separation. Short-range ordered phase arises near TC in Nd0.5Sr0.5MnO3 by thermodynamic reasons due to the development of polarons that gives the gain in exchange energy and the elastic stresses. Large clusters define GP-like behavior of PM susceptibility. It is assumed that the large clusters in half-doped manganites may arise due to not only chemical heterogeneity but also by their proximity to the boundary of the FM–AFM transition in the phase diagram.

Acknowledgments This work was supported by the Scientific Collaboration Program of the Ural and Far Eastern Branches of the Russian Academy of Sciences (Project no. 12-C-2-1026).

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