Localization of 5f-electrons and pressure effects on magnetism in U intermetallics in the light of spin-fluctuation theory

UCoGa and URhGa, two isostructural compounds show opposite signs of the initial response of Curie temperature to applied hydrostatic premenssure. To determine the physical origin of this contradiction the magnetization data measured with respect to temperature, magnetic field and hydrostatic pressure were analyzed in the framework of the Takahashi’s spin-fluctuation theory. The parameters T0 and TA characterizing the distribution widths of the spin-fluctuation spectrum in the energy and wave vector space, respectively, and TC/T0, the degree of the 5f-electron localization have been determined. Examination of available experimental data for the other UTX (T = a transition metal, X = Al, Ga) ferromagnets having the ZrNiAl-type structure revealed some correlations between the degree of the 5f-electron localization represented by the spinfluctuation parameters and the response of Curie-temperature on the applied pressure. These observations may be applied more generally to describe the localization and magnetic behaviors of the majority of the uranium ferromagnetic compounds. Introduction Nowadays, quantum criticality is a heavily studied phenomenon in pure crystalline materials. In most cases, hydrostatic pressure is used to suppress magnetic ordering and to reach the desired quantum-critical behavior at finite temperatures. In the present study, we focus on a group of compounds from the UTX family (T-transition metal, Xp-metal) crystallizing in the hexagonal ZrNiAl structure. Many of these compounds are ferromagnetic with a relatively large span of Curie temperatures and magnitudes of ordered moments [1] and may therefore be used to study discontinuous phase transitions with variable parameters of magnetic order, yet with a fixed crystal structure. In several of these compounds the presence of a discontinuous phase diagram has been recently confirmed (e.g. UCoAl [2,3], URhAl [4], UCoGa [5]). On the other hand, two members of this group, UPtAl [6] and URhGa [7], respectively, show an initial (in the range of several GPa) increase of TC with increasing pressure. It is therefore desirable to be able to predict the pressure behavior of TC in these compounds. In this paper, Takahashi’s spin-fluctuation theory (TSFT) [8] is used to determine if an increasing TC with increasing pressure can be expected. In this theory, the total amplitude of the local spin fluctuations (SF) is constant as a function of temperature. This enables one to determine the value of F1, the mode-mode coupling term as the coefficient of the M 4 term in the Landau expansion of the free energy Fm(M) = Fm(0) + 1 2(gμB) 2χ M + F1 4(gμB) N0 3M , and the values of T0 and TA, which represent the distribution widths of the SF spectrum in energy and wave vector space, respectively ( TC T0 ) 5 6 ⁄ = Ms 2 5gC4 3 ⁄ ( 15cF1 2TC ) 1 2 ⁄ , (2) ( TC TA ) 5 3 ⁄ = Ms 2 5gC4 3 ⁄ ( 2TC 15cF1 ) 1 3 ⁄ , (3) where g is the gyro-magnetic ratio, μB is the Bohr’s magneton and N0 is the Avogadro number, Ms is the spontaneous magnetic moment, C4/3 is constant (= 1.006089 ···) and c = 1⁄2. The value of F1 is determined from the Curie temperature and the slope of the Arrott plot (M 2 vs M/H) at low temperatures [8]. The ratio TC/T0 corresponds to the degree of localization of the electrons responsible for the magnetization and ranges from TC/T0 = 1 for the entirely localized case to TC/T0 → 0 for completely delocalized [8]. The compounds targeted by the study are UCoGa, with TC = 48 K [9,10] and TC decreasing with applied pressure [5], and URhGa with TC = 41 K [10] and TC increasing with pressures up to 6 GPa [7]. The analysis of magnetization data observed at ambient pressure reveals a clear difference of the corresponding F1, T0, TA and TC/T0 values obtained for the two UTX compounds. A considerably higher degree of 5f-electron localization (higher TC/T0) in conjunction with the narrower SF spectrum both in energy and wave-vector space (smaller T0 and TA) have been documented for URhGa in comparison with UCoGa. The results of the analysis of pressure induced changes of F1, T0, TA and TC/T0 corroborate the proposed scenario of dTC/dP > 0 for URhGa in contrast to dTC/dP < 0 for UCoGa. Experimental Single crystals of UCoGa and URhGa were prepared by the Czochralski method using a tri-arc furnace. For UCoGa, details of the single-crystal preparation and annealing are presented elsewhere [11]. URhGa was grown with a pulling speed of 12 mm/hr. The ingot was wrapped in tantalum foil and annealed at 900 °C in an evacuated quartz tube. Magnetization measurements at ambient and hydrostatic pressures were performed in a MPMS XL 7T magnetometer (Quantum Design). Since the UTX compounds crystallizing in the hexagonal ZrNiAl structure exhibit huge uniaxial magnetocrystalline anisotropy with the entire magnetic moment concentrated to the c-axis [1] only the magnetization data for this field direction were measured and used for the presented analysis. For pressure experiments, a small CuBe hydrostatic cell [12] was used, with Daphne 7373 oil as a pressure medium. The superconducting transition of Pb was used to determine the pressure in the cell at low temperatures. Results and Discussion The temperature dependencies of the magnetization of UCoGa and URhGa measured in a low applied field (0.1 T) at various pressures are shown in Figs. 1 and 2, respectively. The values of Curie temperature (TC) were estimated as the temperature of the inflection point of these thermomagnetic curves. For UCoGa, TC decreases while for URhGa TC increases with increasing pressure in agreement with earlier high pressure studies [5,7]. The phase transition in both compounds at ambient pressure is continuous (a second order transition). 0 10 20 30 40 50 60 0.0 0.1 0.2 0.3 0.4 0.5 0.6