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...