High magnetic field phase diagram and failure of the magnetic Grüneisen scaling in LiFePO4

Abstract

We report the magnetic phase diagram of single-crystalline LiFePO 4 in magnetic fields up to 58 T and present a detailed study of magneto-elastic coupling by means of high-resolution capacitance dilatometry. Large anomalies at T N in the thermal expansion coefficient α imply pronounced magneto-elastic coupling. Quantitative analysis yields the magnetic Grüneisen parameter γ mag = 6.7(5) · 10 −7 mol/J. The positive hydrostatic pressure dependence dT N /dp = 1.46(11) K/GPa is dominated by uniaxial effects along the a-axis. Failure of Grüneisen scaling below ≈ 40 K, i.e., below the peak temperature in the magneto-electric coupling coefficient [1], implies several competing degrees of freedom and indicates relevance of recently observed hybrid excitations [2].A broad and strongly magnetic-field-dependent anomaly in α in this temperature regime highlight the relevance of structure changes. Upon application of magnetic fields B||b-axis, a pronounced jump in the magnetisation implies spin-reorientation at B SF = 32 T as well as a precursing phase at 29 T and T = 1.5 K. In a two-sublattice mean-field model, the saturation field B sat,b = 64(2) T enables the determination of the effective antiferromagnetic exchange interaction J af = 2.68(5) meV as well as the anisotropies D b = −0.53(4) meV and D c = 0.44(8) meV. PACS numbers:In addition to exceptionally high applicability of lithium orthophosphates [3][4][5] for electrochemical energy storage in Li-ion batteries, competing magnetic interactions, magnetic anisotropy and coupling of spin and electric degrees of freedom yield complex magnetic behaviour in LiM PO 4 (M = Mn, Fe, Co, Ni). The rich resulting physics is, e.g., demonstrated by ferrotoroidicity in LiCoPO 4 and LiNiPO 4 [6-8]. In general, depending on the actual transition metal, LiM PO 4 develops long-range antiferromagnetic order at low temperatures and exhibits a large magneto-electric effect in the magnetically ordered phase [1, 9, 10]. The known magnetic phase diagrams of this family are rather complex, featuring incommensurate spin configurations, frustration, and usual magnetic excitations [11-17]. Magnetic phase diagrams have been reported for all lithium orthophosphates [15-17] except for LiFePO 4 . At B = 0 T, LiFePO 4 develops long-range antiferromagnetic order of S = 2 spins of the magnetic Fe 2+ -ions below T N = 50 K [18]. The ordered moment amounts to 4.09 µ B [1, 19] and the spins are mainly directed along the crystallographic b-axis (space group P nma) [19]. Notably, the ground state features a collinear rotation of the spins towards the a-axis as well as spin canting along the c-axis with an overall rotation of the ordered moments of 1.3(1) • off the b-axis [1, 2]. The observed spin canting suggests the presence of Dzyaloshinsky-Moriya (DM) interactions which may account for the magneto-electric coupling in LiFePO 4 . In particular, as spin canting is not compatible with P nma symmetry, a lower crystal symmetry might appear below T N [ 1,20]. Even in the absence of spin canting, an alternative me...

Mössbauer Spectroscopy of Triphylite (LiFePO4) at Low Temperatures

“…We mention an increase of the magnetization below temperature ∼ 17 K (Figure 3). Such an increase of the magnetization in LiFePO 4 has also been reported in References [14,17,36]. Rhee et al [17] related this effect to the influence of the spin-orbit coupling when it becomes comparable with the thermal energy at about 20 K, which results in an 'unquenching' of the orbital magnetic moments of Fe 2+ ions, thus increasing their total magnetic moment.…”

“…In this context, it is worth mentioning that the magnetoelectric effect is expected to appear in LiFePO 4 , as also discussed in Reference [13]. The high magnetic field phase diagram was studied as well [14]. 57 Fe Mössbauer spectroscopy (MS) is capable of detecting very small hyperfine splitting due to the interactions of 57 Fe nuclei with their surroundings.…”

Magnetoelastic coupling and Grüneisen scaling in NdB4

“…As the magnitude and the shape of the Schottky anomalies in the thermal expansion coefficients are completely determined by the energy gaps i and their pressure dependencies ∂ ln /∂ p i (see Eq. (2)), we conclude that there are rather small pressure dependencies of all i for hydrostatic pressure and uniaxial pressure along [110] and [001] (cf., [28,29]).…”

Exceptional field dependence of antiferromagnetic magnons in LiFePO$_4$

“…We recall the large size of ∆ 1 as compared to B SF . Specifically, the standard AFMR model would result in the effective g-factor of g = 3.3(1) which is unreasonably large and does not match to g b = 2.31 obtained from analysis of high-temperature magnetic susceptibility data 35 . Hence, one has to conclude that parameters obtained at zero magnetic field, i.e., single-ion anisotropy D and exchange interaction J, do not describe the experimental results obtained at high magnetic field.…”

“…Magnetization studies employed a coaxial pick-up coil system; the magnetization data were calibrated using data, obtained in static fields at 5 T (see Ref. [35]).…”