Spin reorientation transition: phase diagrams and entropy change
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Spin reorientation transition: phase diagrams and entropy change Vittorio Basso, Carlo P. Sasso, Michaela Kuepferling Istituto Nazionale di Ricerca Metrologica Strada delle Cacce 91, I-10135, Torino, Italy ABSTRACT In this paper we review the phase diagram and derive the entropy change for spin reorientation transitions by considering first order magnetization process theory with temperature dependent magneto-crystalline anisotropy constants. We derive the magnetic field-induced entropy change Δs for a transition between easy axis and easy plane, showing that for alternating magnetic field, Δs has a change of sign at the reorientation temperature, while for rotating magnetic field its sign is definite. We apply the model to CoZn W-type barium ferrite. INTRODUCTION In a spin reorientation process the spontaneous magnetization changes orientation when the temperature is changed because of the presence of competing anisotropies with different temperature dependences [1]. The subject has been investigated in the past [2,3], but a renewed interest on the topic has been challenged by the consideration of the presence of an entropy change at the spin reorientation transition and the associated magnetocaloric effect [1]. Even if the intensity of the entropy change is not high [1], magnetic materials with a spin reorientation may represent an interesting new class of materials for magnetic refrigeration because the entropy change can be achieved by rotating a magnetic field of constant amplitude instead of the usual process in which one has to apply and remove large magnetic fields. The first possibility corresponds to a solution of technical interest for magnetic cooling devices [4]. Magnetic materials with a spin reorientation around room temperature include: Er2Fe14B with TSR = 323 K and Tm2Fe14B with TSR = 310.7 K [5–8]; (ErGd)2Fe14B with TSR in the range 211-326 K [9], Er2(CoFe)17 with TSR = 292 K [10]; and NdCo5 that has a transition between easy plane and easy cone at 250 K and between easy cone and easy axis at 290 K [11, 12]. Below room temperature, Er2Fe14Si3 has TSR = 116 K [13] and W-type hexagonal ferrite of composition BaCo0.62Zn1.38Fe16O27 has TSR = 205 K [14]. To describe the spin reorientation process one has to consider the magnetic anisotropy at high orders. This phenomenology has been investigated in detail by Asti [2] in his first order magnetization process theory. Here we follow the same approach by taking uniaxial anisotropy energy up to the third order. By considering temperature dependent anisotropy constants, we derive the entropy change associated with the reorientation of the spins. As a case of interest for the magnetocaloric effect, we consider the first order transition between easy plane P and easy axis A. Within this phenomenological approach we discuss the entropy change in CoZn W-type ferrite of composition BaCo0.62Zn1.38Fe16O27 [14,17]. THEORY Let us consider the Gibbs free energy of a magnetic material by taking the uniaxial anisotropy energy and the applied magnetic field energy. We use
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