Itinerant ferromagnetism in actinide $5f$-electron systems: Phenomenological analysis with spin fluctuation theory

Itinerant ferromagnetism in actinide $5 f$ -electron systems: Phenomenological analysis with spin fluctuation theory

Naoyuki Tateiwa, Jiří Pospíšil, Yoshinori Haga, Hironori Sakai, Tatsuma D. Matsuda, and Etsuji Yamamoto

Phys. Rev. B 96, 035125 – Published 14 July 2017

Abstract

We have carried out an analysis of magnetic data in 69 uranium, 7 neptunium, and 4 plutonium ferromagnets with the spin fluctuation theory developed by Takahashi [Y. Takahashi, J. Phys. Soc. Jpn. 55, 3553 (1986)]. The basic and spin fluctuation parameters of the actinide ferromagnets are determined and the applicability of the spin fluctuation theory to actinide $5 f$ system has been discussed. Itinerant ferromagnets of the $3 d$ transition metals and their intermetallics follow a generalized Rhodes-Wohlfarth relation between $p_{eff} / p_{s}$ and $T_{C} / T_{0}$ , viz., $p_{eff} / p_{s} \propto {(T_{C} / T_{0})}^{- 3 / 2}$ . Here, $p_{s}$ , $p_{eff}$ , $T_{C}$ , and $T_{0}$ are the spontaneous and effective magnetic moments, the Curie temperature, and the width of spin fluctuation spectrum in energy space, respectively. The same relation is satisfied for $T_{C} / T_{0} < 1.0$ in the actinide ferromagnets. However, the relation is not satisfied in a few ferromagnets with $T_{C} / T_{0} \sim 1.0$ that corresponds to local moment system in the spin fluctuation theory. The deviation from the theoretical relation may be due to several other effects not included in the spin fluctuation theory such as the crystalline electric field effect on the $5 f$ electrons from ligand atoms. The value of the spontaneous magnetic moment $p_{s}$ increases linearly as a function of $T_{C} / T_{0}$ in the uranium and neptunium ferromagnets below ${(T_{C} / T_{0})}_{kink} = 0.32 \pm 0.02$ , where a kink structure appears in relation between the two quantities. $p_{s}$ increases more weakly above ${(T_{C} / T_{0})}_{kink}$ . A possible interpretation with the $T_{C} / T_{0}$ dependence of $p_{s}$ is given.

Received 11 April 2017

DOI:https://doi.org/10.1103/PhysRevB.96.035125

Physics Subject Headings (PhySH)

Ferromagnetism Methods in magnetism

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Naoyuki Tateiwa^1,*, Jiří Pospíšil^1,2, Yoshinori Haga¹, Hironori Sakai¹, Tatsuma D. Matsuda³, and Etsuji Yamamoto¹

¹Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Naka, Ibaraki 319-1195, Japan
²Charles University in Prague, Faculty of Mathematics and Physics, Department of Condensed Matter Physics, Ke Karlovu 5, 121 16 Prague 2, Czechia
³Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan

^*tateiwa.naoyuki@jaea.go.jp

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Vol. 96, Iss. 3 — 15 July 2017

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Figure 1
Temperature dependencies of (a) the magnetization $M$ under magnetic field and (b) the inverse of the magnetic susceptibility $1 / χ$ for several uranium ferromagnets ${UCu}_{2} {Ge}_{2}$ , URhAl, ${URh}_{6} {Ge}_{4}$ , URhSi, and URhGe in magnetic fields of 0.5, 0.2, 0.1, 0.1, and 0.1 T, respectively, applied along the magnetic easy axes. The Curie temperatures $T_{C}$ are denoted by arrows. Solid lines are results of fits to the temperature dependence of the inverse of the magnetic susceptibility $1 / χ$ with the Curie-Weiss or modified Curie-Weiss law.
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Figure 2
$M^{2}$ versus $H / M$ plot (Arrott plots) at $T^{*} = 2.0 K$ for ${UCu}_{2} {Ge}_{2}$ , URhAl, ${URh}_{6} {Ge}_{4}$ , URhSi, and URhGe in applied magnetic field along the magnetic easy axes.
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Figure 3
Generalized Rhodes-Wohlfarth plot. Data points for uranium, neptunium, and plutonium compounds are plotted as closed circles, squares, and triangles, respectively. The data of UCoGe are cited from Ref. [76]. Data for intermetallic ferromagnetic compounds of the transition $3 d$ metals cited from Refs. [74, 75, 76] are represented as closed antitriangles. The solid line is the theoretical relation between $T_{C} / T_{0}$ and $p_{eff} / p_{s}$ , Eq. (11) in Takahashi's spin fluctuation theory [76].
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Figure 4
Relations between the spontaneous magnetic moment $p_{s}$ and $T_{C} / T_{0}$ for uranium, neptunium, and plutonium compounds plotted as closed circles, squares, and triangles, respectively. Data points for intermetallic ferromagnetic compounds of the transition $3 d$ metals represented as antitriangles are cited from Refs. [74, 75, 76]. The dotted line is a fit to the data of the uranium and neptunium ferromagnets for $T_{C} / T_{0} < {(T_{C} / T_{0})}_{kink} = 0.32 \pm 0.02$ with the function $p (T_{C} / T_{0}) = a {(T_{C} / T_{0})}^{- n}$ where $a$ and $n$ are fitting parameters.
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Figure 5
(a) Relative change $Δ / f (T_{C} / T_{0})$ as a function of $T_{C} / T_{0}$ for the actinide ferromagnets. $Δ = {(p_{eff} / p_{s})}_{\exp} - f (T_{C} / T_{0})$ , where $f (T_{C} / T_{0}) = 1.4 {(T_{C} / T_{0})}^{- 2 / 3}$ [Eq. (11)] from the Takahashi's spin fluctuation theory. (b) Relative change $Δ^{'} / f^{'} (T_{C} / T_{0})$ as a function of $T_{C} / T_{0}$ where $Δ^{'} = {(p_{eff} / p_{s})}_{\exp} - f^{'} (T_{C} / T_{0})$ and $f^{'} (T_{C} / T_{0}) = a {(T_{C} / T_{0})}^{- 2 / 3}$ . The value of $a$ is determined from the fit with the function $f^{'} (T_{C} / T_{0})$ to the data points of ${(p_{eff} / p_{s})}_{\exp}$ for $T_{C} / T_{0} < 1.0$ .
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Figure 6
Relation between $p_{eff} / p_{s}$ and $T_{C} / T_{0}$ in (a) a UTX (T: Co, Rh, Ir, and Pt, X: Al, Ga, and Sn) series with hexagonal ZrNiAl-type crystal structure, (b) ferromagnetic superconductors URhGe and UCoGe and related doping systems with orthorhombic TiNiSi-type structure, and (c) itinerant ferromagents in the $3 d$ system $Y {({Co}_{1 - x} {Al}_{x})}_{2}$ [85, 86], ${Ni}_{3} {Al}_{1 - x} {Ga}_{x}$ [92], ( ${Fe}_{1 - x} {Co}_{x})_{3} {Mo}_{3} N$ [96], ${Fe}_{x} {Co}_{1 - x} Si$ [88], and ${Ni}_{x} {Rh}_{1 - x}$ [76].
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