PHYSICAL REVIEW B 84, 184422 (2011) Ferromagnetic transition and specific heat of Pr 0.6 Sr 0.4 MnO 3 S. R¨ oßler, 1,* Harikrishnan S. Nair, 2 U. K. R ¨ oßler, 3 C. M. N. Kumar, 2 Suja Elizabeth, 4 and S. Wirth 1 1 Max Planck Institute for Chemical Physics of Solids, N¨ othnitzer Straße 40, D-01187 Dresden, Germany 2 J¨ ulich Centre for Neutron Sciences-2, Peter Gr¨ unberg Institute-4, Forschungszentrum J¨ ulich GmbH, D-52425 J¨ ulich, Germany 3 IFW Dresden, Postfach 270016, D-01171 Dresden, Germany 4 Department of Physics, C.V. Raman Avenue, Indian Institute of Science, Bangalore-560012, India (Received 30 June 2011; revised manuscript received 20 October 2011; published 16 November 2011) The critical properties of orthorhombic Pr 0.6 Sr 0.4 MnO 3 single crystals were investigated by a series of static magnetization measurements along the three different crystallographic axes as well as by specific heat measurements. A careful range-of-fitting-analysis of the magnetization and susceptibility data obtained from the modified Arrott plots shows that Pr 0.6 Sr 0.4 MnO 3 has a very narrow critical regime. Nevertheless, the system belongs to the three-dimensional (3D) Heisenberg universality class with short-range exchange. The critical exponents obey Widom scaling and are in excellent agreement with the single scaling equation of state M(H, ) =| | β f ± (H/| | (β+γ ) ; with f + for T>T c and f − for T<T c . A detailed analysis of the specific heat that account for all relevant contributions allows us to extract and analyze the contribution related to the magnetic phase transition. The specific heat indicates the presence of a linear electronic term at low temperatures and a prominent contribution from crystal field excitations of Pr. A comparison with data from literature for PrMnO 3 shows that a Pr-Mn magnetic exchange is responsible for a sizable shift in the lowest lying excitation. DOI: 10.1103/PhysRevB.84.184422 PACS number(s): 75.47.Lx, 75.40.Cx I. INTRODUCTION Colossal magnetoresistive (CMR) oxides of the manganite family with the generic formula R 1−x A x MnO 3 (R = rare earth ion, A = alkaline earth or equivalent ion) possess a complex phase diagram that often includes charge order (CO)/orbital order (OO), metal-insulator (MI) transitions, and various mag- netic phases tunable as a function of composition, magnetic field and/or temperature. 1–3 The physical properties of these materials strongly depend on subtle structural distortions. The composition Pr 0.6 Sr 0.4 MnO 3 , which forms the subject of this paper, has been reported to constitute a ferromagnet with a Curie temperature T C ∼ 297 K. 4 Pr 0.6 Sr 0.4 MnO 3 also under- goes a structural phase transition from a high-temperature orthorhombic P nma to a low-temperature monoclinic I 2/a space group which was reported to take place at T str ∼ 100 K. 5 Powder neutron diffraction studies report structural phase separation below T str . 5 Furthermore, the magnetization curves (M-H ) measured below the structural transition temperature are found to be anomalous: The virgin curve stays outside the subsequent M-H hysteresis loops 6 thereby suggesting that the structural phase separation has a profound influence on the magnetic properties. Optical conductivity data 7 on Pr 0.6 Sr 0.4 MnO 3 in applied magnetic field deviate from the expected universal scaling. In particular, a nearly linear |M| dependence of the magneto-optical conductivity in the critical regime indicates strong ferromagnetic spin fluctuations of Mn above T C . 7 The irreversible magnetization processes related to the structural phase separation and the anomalous behavior of the magneto-optical conductivity motivated us to investigate some basic physical properties of Pr 0.6 Sr 0.4 MnO 3 single crystals in order to unambiguously distinguish between conventional and unconventional properties of this essentially metallic and ferromagnetic mixed-valent manganite. The main focus is the nature of the paramagnetic (PM)-ferromagnetic (FM) transition. Hence we present a scaling analysis of static magnetization data supplemented by a detailed analysis of the specific heat C p within the temperature range 2–350 K, that covers both the PM-FM transition and the structural transitions. The critical nature of manganites near a PM-FM phase transition have been the subject of many studies. 8–25 Different experimental techniques have been used in these investigations to obtain the critical exponent β of the spontaneous magne- tization. The values of the exponent from these reports were found in a range from 0.3 to 0.5 which covers the mean-field value (β = 0.5) as well as the values corresponding to the three-dimensional (3D) isotropic Heisenberg (β = 0.365) and the 3D Ising (β = 0.325) universality classes. In addition to the above variety of continuous phase transitions, first-order nature of the PM-FM transition was found in in the case of LaMnO 3.14 13 and La 0.7 Ca 0.3 MnO 3 . 26 The first-order phase transition has been recently found in the phase diagrams generated by large-scale Monte Carlo simulations within the two-orbital model Hamiltonian. 27 This suggests that the PM-FM transitions in manganites display different properties varying from continuous transitions due to short-range ex- change to first-order transitions. Although our preliminary investigations 6 of the resistivity at the paramagnetic-ferromagnetic (PM-FM) transition in Pr 0.6 Sr 0.4 MnO 3 already suggested that the critical exponents most probably belong to the class of conventional isotropic ferromagnets, a clear-cut evidence from the magnetization data was missing. Therefore, we here report a detailed analysis of magnetization. The results reveal that the modified Arrott plots provide straight lines for a range of exponents β and γ (see definition below), including those belonging to both the three-dimensional (3D) Heisenberg as well as 3D Ising universality classes. These observations suggested a possible role of anisotropy affecting the asymptotic critical properties. Furthermore, a very recent investigation 28 of critical behavior in polycrystalline Pr 0.55 Sr 0.45 MnO 3 by Fan et al. using the field dependence of magnetic entropy change reports expo- nents close to the mean-field values. In their method, only two 184422-1 1098-0121/2011/84(18)/184422(10) ©2011 American Physical Society