The sign of lattice and spin entropy change in the giant magnetocaloric materials with negative lattice expansions

Highlights

• Magnetocaloric materials often show negative lattice expansion.

• The sign of lattice (ΔS_Latt) and spin entropy change (ΔS_Spin) remains debate.

• The sign of ΔS_Latt and ΔS_Spin is clarified.

• For MM’X alloys, heat flow results prove the same signs of ΔS_Latt and Δ_Spin.

• For La(Fe,Si)₁₃, NRIXS evidences the same signs of ΔS_Latt and ΔS_Spin.

Abstract

Solid-state refrigeration based on the magnetocaloric effect (MCE) has garnered worldwide attention because of its superior energy conservation and its environmentally friendly impact. Many materials exhibiting magnetostructural/magnetoelastic transitions have been identified by their giant MCE as promising refrigerants. The common feature of these materials is their simultaneous magnetic and lattice transitions; some also undergo negative expansions, i.e., lattice contractions, along with a ferromagnetic (FM) to paramagnetic (PM) transition. For these materials, whether the signs of lattice and spin entropy change are the same or opposite has become a controversial issue, noting that a larger unit cell volume usually indicates softer phonons and therefore a bigger phonon entropy. On the basis of our experiments and published data, we demonstrate that the lattice and spin entropy changes retain the same sign at least for La(Fe,Si)₁₃-based compounds and MM’X alloys with giant MCE, for which the lattice undergoes negative expansion along with a FM to PM transition on heating. The clarification of the sign of lattice entropy change in the total entropy change is of particular importance for a comprehensive understanding of new materials with giant magnetocaloric effect and their design.

Introduction

Solid-state cooling based on the magnetocaloric effect (MCE) is a promising alternative to traditional vapor compression refrigeration because of its environment-friendly impact and in theory high energy efficiency [1], [2], [3], [4]. Since the discovery of the giant MCE in Gd₅(Si₂Ge₂), a number of first-order giant magnetocaloric materials have been discovered [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], which in turn promoted the development of the magnetic refrigeration technique. A common feature of these materials is that magnetic phase transition is always accompanied by a discontinuous change in lattice parameter and/or crystal symmetry. The giant MCE originates from a concurrent structural and magnetic transition. Rough estimations show that the lattice contribution accounts for 50%–60% or more of the total entropy change for the materials undergoing a magnetostructural/magnetoelastic transition [5], [7], and the magnitude of lattice entropy change (ΔS_Latt) is closely related to the volume change (ΔV/V) during the phase transition [7]. However, positive [8], [9] or negative [3], [10], [11], [12], [13], [15], [16], [17] lattice expansions may occur along with a ferromagnetic (FM) to paramagnetic (PM) transition among the different materials with giant MCE.

Typically, Gd₅(Si_xGe_1-x)₄ undergoes a positive expansion from a FM orthorhombic α-Gd₅Si₂Ge₂ to a PM monoclinic β-Gd₅Si₂Ge₂ structure with ΔV/V~+(0.4–1.0) % [8], [9]. Generally, a larger lattice volume indicates softer phonons and therefore a larger phonon entropy. Hence, understandably, the sign of ΔS_Latt is the same as that for the spin entropy change (ΔS_Spin) during the magnetostructural transition in Gd₅(Si_xGe_1-x)₄. Note that the spin entropy of the PM state is also larger than that of the FM state. In contrast, some materials with giant MCE show negative expansions, i.e., lattice contractions, during the FM to PM transition. For example, La(Fe,Si)₁₃-based compounds undergo a magnetoelastic phase transition with a space group (Fm-3c) unchanged while the lattice contracts by ΔV/V~−(1.2–1.6)% on heating during the FM to PM transition [3], [10], [18]. MnAs-based compounds undergo a magnetostructural transition from a FM hexagonal NiAs-type to a PM orthorhombic MnP-type structure, and the lattice contracts by ΔV/V~−(1.1–2.1) % [12], [13]. Furthermore, an abnormal lattice contraction with ΔV/V~−(2.8–3.9) % occurs in MnCoGe/MnNiGe-based alloys during the magnetostructural transition from a FM/AFM orthogonal TiNiSi-type to a PM hexagonal Ni₂In-type structure [16], [17], [19], [20]. For these materials, whether the sign of lattice and spin entropy change is the same or opposite has always been controversial and has puzzled many researchers [21], [22], [23], noting that the lattice parameter of the FM/AFM phase is larger than that of the PM phase. In general, an application of a magnetic field, which drives the system from a PM to a FM state, should increase the lattice entropy while simultaneously decreasing the spin entropy. The signs of lattice and spin entropy change should be opposite. Similar to La(Fe,Si)₁₃, the magnetic and structural transitions in MnAs also cannot be separated. A study on MnAs based on density functional theory (DFT) concluded that the phonon contribution to the total entropy change has the opposite sign to the spin entropy change [24], although no direct experimental evidence has been reported to date. For La(Fe,Si)₁₃, Jia and coworkers in our group once believed the spin entropy change was negative, whereas the phonon entropy change was positive but smaller, hence leading to an overall negative entropy change upon applying a magnetic field [21]. However, recent experimental investigations indicated that this is not the case. Landers and co-workers investigated the lattice vibrational entropy change ΔS_Latt in LaFe_11.6Si_1.4 by nuclear resonant inelastic X-ray scattering (NRIXS) [22], [23]. The results demonstrated that the ΔS_Latt obtained by this method is a sizable quantity and contributes cooperatively to the total entropy change ΔS during the phase transition for La(Fe,Si)₁₃ compounds. Moreover, earlier studies on the stoichiometric MnCoGe and MnNiGe alloys with separated structural and magnetic phase transitions indicated that the signs of ΔS_Latt and ΔS_Spin are the same although the alloys undergo negative expansion during the structural transition [19], [20]. In this paper, we present the details.