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Critical Behavior of La0.75Sr0.25Mno3

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Critical Behavior of La0.75Sr0.25Mno3 PHYSICAL REVIEW B, VOLUME 65, 214424 Critical behavior of La0.75Sr0.25MnO3 D. Kim, B. L. Zink, and F. Hellman Department of Physics, University of California, San Diego, La Jolla, California 92093 J. M. D. Coey Physics Department, Trinity College, Dublin 2, Ireland ͑Received 17 November 2000; published 7 June 2002͒ Magnetization, susceptibility, and specific heat measurements were made on a single crystal of La0.75Sr0.25MnO3. The ferromagnetic-to-paramagnetic phase transition was found at 346 K and four critical exponents were measured as: ␣ϭ0.05Ϯ0.07, ␤ϭ0.40Ϯ0.02, ␥ϭ1.27Ϯ0.06, and ␦ϭ4.12Ϯ0.33. The values of critical exponents are all between mean-field values and three-dimensional-͑3D͒-Ising-model values. The scaling behavior is well obeyed for all measurements, and the associated exponent relations are well satisfied, validating the critical analysis. Although the cubic crystal structure of this material makes the 3D Heisenberg the expected model, uniaxial magnetic anisotropy arising from the shape of the sample causes the 3D Ising model to be important within the experimental temperature range. DOI: 10.1103/PhysRevB.65.214424 PACS number͑s͒: 75.40.Cx, 75.30.Vn, 64.60.Fr Ϫ␣ I. INTRODUCTION Cϩ͑T͒ϳA͉t͉ /␣, tϾ0, ͑ Ϫ␣Ј Interest in the perovskite manganites A1ϪxBxMnO3 A, CϪ͑T͒ϳAЈ͉t͉ /␣Ј, tϽ0, trivalent rare earth; B, divalent metal͒ has revived since the 1 ͑ ͒ ͒ϳ ͉ ͉␤ Ͻ discovery of colossal magnetoresistance CMR near the M S͑T B t , t 0, Curie temperature T for x near 0.3. Some manganites are C Ϫ␥ also believed to possess strongly spin-split bands, leading to ␹͑T͒ϳC͉t͉ , tϾ0, what is called half-metallicity ͑complete spin polarization of 1/␦ the charge carriers at the Fermi level͒. The magnetotransport M͑H͒ϳDH , tϭ0. behavior and the possibility of applications utilizing CMR or Here A, AЈ, B, C, and D are constants. Scaling requires that half-metallicity motivated intensive studies on the underly- ␣ϭ␣Ј. In addition, there are two exponent relations that 2,3 ing physics. Above TC , CMR perovskite manganites are limit the number of independent variables to two, paramagnetic insulators ͑insulating in the sense that the temperature dependence of the resistivity d␳/dTϽ0͒.As ␣ϩ2␤ϩ␥ϭ2, the temperature is decreased below TC , they become ferro- magnetic metals. Among the perovskite manganites, ␥ϭ␤͑␦Ϫ1͒. ͑ ͒ ϳ La1ϪxSrxMnO3 LSMO has the highest TC 370 K. Re- Separate studies of magnetization and specific heat critical placement of La by Pr, Nd, and Sm or of Sr by Ca, Ba, and phenomena have been reported, both on single crystals and 3,8–10 Pb results in distortions of MnO6 octahedra in the pseudocu- on polycrystalline samples. These have indicated incon- bic structure ͑hence increased electron-phonon coupling͒, sistent results, with magnetization critical exponents varying lower TC , and higher resistivity by several orders of fairly widely. For characterization of critical phenomena, 4 magnitude. The lower-TC materials are reported to exhibit high-quality samples with a large grain size and preferably a phase separation of metallic and insulating regions below single crystal are needed to avoid smearing of TC . For epi- 5 6 TC , leading to a possible first-order phase transition at TC . taxial thin-film samples, the small signal makes it hard to get La1ϪxSrxMnO3 however is the most metallic in the mangan- data of the quality needed for critical analysis, given the ite family and therefore has the most itinerant electrons. signal-to-noise ratio. Also as T gets near TC , the correlation There is a report of phase separation on the surface of LSMO length can be of the order of the thickness of the sample, thus by scanning-tunnel-microscope experiment, but other bulk switching from three-dimensional ͑3D͒ to 2D behavior. A 7 experiments indicate no phase separation. single crystal of La0.7Sr0.3MnO3 was measured by Ghosh For a second-order phase transition near the critical tem- et al., who found ␤ϭ0.37Ϯ0.04, ␥ϭ1.22Ϯ0.03, and ␦ perature, where a correlation length can be defined, the spe- ϭ4.25Ϯ0.2, fit with a reduced temperature t range of 0.002 ϵ ϭ 3 cific heat, spontaneous magnetization ͓M S M(H 0)͔, and to 0.03. Mohan et al. measured a polycrystalline sample of ␤ ͉ ץ ץ␹ϵ initial magnetic susceptibility ( M/ H Hϭ0) show La0.8Sr0.2MnO3 and found significantly different values: power-law dependence on the reduced temperature, tϵ(T ϭ0.50Ϯ0.02, ␥ϭ1.08Ϯ0.03, and ␦ϭ3.13Ϯ0.2 ͑all much Ϫ ͒ ͉ ͉Ͻ 9 TC)/TC . Also at TC , M has a power-law dependence closer to mean-field values with t 0.008. It is not clear if on H, the differences reflect the polycrystalline nature, the different 0163-1829/2002/65͑21͒/214424͑7͒/$20.0065 214424-1 ©2002 The American Physical Society D. KIM, B. L. ZINK, F. HELLMAN, AND J. M. D. COEY PHYSICAL REVIEW B 65 214424 composition, or the different t range. Neutron-scattering studies on a single crystal of La0.7Sr0.3MnO3 yielded a value of ␤ϭ0.295 but the t range used was somewhat far from the transition.10 Lin et al. measured magnetization exponents of ␤ϭ ␦ϭ La0.7Sr0.3MnO3 and found 0.31 and 5.1, fit in a non- specified t range, and a specific heat critical exponent ␣, which is anomalously large ͑ϩ0.16͒ and inconsistent with their magnetization data.8 For these reasons, we report here a study of the specific heat, magnetic susceptibility, and spon- taneous magnetization on a single sample of single crystal La0.75Sr0.25MnO3 very near TC . II. EXPERIMENT A. Specific-heat measurement Single crystal La0.75Sr0.25MnO3 was made by a floating- zone process. Viret et al. previously made small-angle, po- larized neutron-scattering measurements11 on a sample from the same batch. The sample used in the specific heat mea- surement is a thin flake of approximate dimensions 0.2 ϫ0.5ϫ0.5 mm3, weighing 212 ␮g. To make this measure- ment, we used a microcalorimeter originally developed by FIG. 1. Side view of microcalorimetry device and sample show- ͑ ͒ our group to measure the specific heat of thin films of thick- ing steps used to measure C P(T). a Measure C P1; includes Au ness 200–400 nm weighing 2–20 ␮g.12 For this experiment, conduction layer, Pt heater and thermometer, and SiN membrane. ͑ ͒ ␮ Ϫ b Measure C P2 after attaching 72 gofIn.C P2 C P1 we modified the design of the microcalorimeter to allow us ϭ ␮ ͑ ͒ heat capacity of 72- g In. c Measure C P3 after attaching an- to measure a bulk sample attached by indium. The modified ␮ ␮ Ϫ ␮ other 96 g of In and 212 gofLa0.75Sr0.25MnO3. C P3 C P2 calorimetry device consists of a 1.5- m-thick amorphous ϭ ␮ ϩ ␮ ϫ 2 heat capacity of 96 gofIn 212 gofLa0.75Sr0.25MnO3. Sub- silicon-nitride membrane of 5 5mm lateral size. The cen- ͓ϭ * Ϫ ͔ ϫ 2 ␮ traction of In contribution 96/72 (C P2 C P 1) gives C P of tral 2.5 2.5-mm sample area is covered by a 1.5- m-thick La Sr MnO evaporated gold film, which has high thermal conductivity. 0.75 0.25 3 Indium was used to thermally and physically attach the ␮ ␮ sample to the gold layer. Due to the high thermal conductiv- capacity of 96 g of In and 212 gofLa0.75Sr0.25MnO3. ity of the gold layer and the poor thermal conductivity of the Since we have already measured the specific heat of In in ␮ amorphous SiN membrane, the sample area is linked to the C P2, the heat capacity of 96 g of In can be subtracted, Si frame only by a very weak thermal link and is effectively yielding the heat capacity of La0.75Sr0.25MnO3. isothermal on the experimental time scale. On the front side of the membrane, platinum thermometers and heaters were B. Magnetization measurements evaporated and patterned by photolithography. The relax- ation method was used to measure the heat capacity. Refer- Another thin flake ͑0.2ϫ0.7ϫ0.8 mm3; 750 ␮g͒ of single ence 12 describes the experiment in more detail. crystal La0.75Sr0.25MnO3, grown and cut from the same batch Figure 1 shows a schematic of the series of experiments as the sample used in the specific heat experiment, was used performed to measure the specific heat C P of the single crys- for magnetization measurements. Room-temperature torque ͑ ͒ ͑ ͒ tal La0.75Sr0.25MnO3. Figures 1 a –1 c are side views of the magnetometry was first used to characterize the magnetic micro-calorimetry device in three different stages of the ex- anisotropy. Shape anisotropy was found to dominate the in- ͑ ͒ periment. Fig. 1 a shows the C P1 measurement; this in- trinsic cubic anisotropy. The sample has an easy plane of ͑ ϭ cludes the heat capacity of the Au layer, the Pt heater and magnetization perpendicular hard axis with KH 5.1 thermometer, and the silicon-nitride membrane. Seventy-two ϫ105 dyne/cm2͒, and within the plane, the easy axis is along micrograms of In is then bonded to the gold layer, using a the longest body diagonal of the slightly rhombic shape ϭ ϫ 4 2 hot plate to melt In, after which C P2 was measured as shown (KE 8.1 10 dyne/cm ). in Fig. 1͑b͒. The heat capacity of the 72 ␮g of In was deter- A Quantum Design dc superconducting quantum interfer- mined by subtracting C P1 from C P2.
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