Magnetic Structure of Europium

Abstract

Neutron diffraction experiments on metallic europium have been conducted over a temperature range from room temperature to 4°K using a sample in the form of europium filings. The data show that the metal undergoes a transition to an antiferromagnetic state at a Neel temperature TN of 91 °K and that this ordering process continues until saturation develops at about 20°K. A model which conforms to the data consists of a helical spin structure with the magnetic moments lying parallel to a cube face and with the rotation axis directed perpendicular to the moments or along the [100] direction. The pitch of the helix was observed to change very slightly with temperature; the period was 3.5a at T/TN=1 and increased to 3.6a at T/TN=0.05 where a is the lattice spacing. On the basis of the above model and the intensities of the magnetic reflections, the calculated ordered moment at each atom site is 5.9±0.4 /J,B per atom. This measured moment is somewhat less than the maximum theoretical value of 7 [XB expected from divalent europium characterized by a spin only ground state of 8 57/2. Values of magnetic moment times magnetic form factor, /*/, as calculated from Eu coherent magnetic reflections are in agreement with similar values of /if derived from the compound EuO. The intensities of the magnetic diffraction peaks deviate from a Brillouin behavior and instead follow a temperature dependence proportional to (TN-T) 112 over a considerable region below the Neel temperature. The Debye temperature, as derived from the nuclear peak intensities, exhibited a variation from 70 to 120°K over a corresponding sample temperature range of 100 to 293°K.

Ab initio theory of exchange interactions in itinerant magnets

“…Such a situation indicates an instability of the FM state with respect to a more complicated spin structure. This feature agrees qualitatively with an experimentally observed helical spin structure, the wave vector of which lies along the G À H direction of the bcc BZ [16,17].…”

“…The magnitude of Q determines the angle w between magnetic moments in the neighboring (100) atomic planes. In the present case, it is equal to w ¼ 48 in surprising agreement with measured values w exp ¼ 49 [16] and w exp ¼ 47:6 AE 1:2 [17]. The resulting maximum JðQÞ can be used to get a MFA estimation of the Nel temperature, in complete analogy to Eq.…”

Exchange interactions, spin waves, and transition temperatures in itinerant magnets

“…Such a situation indicates an instability of the FM state with respect to a more complicated spin structure. This feature agrees qualitatively with an experimentally observed spin-spiral structure, the wave vector of which lies along the Γ − H direction in the bcc BZ [88,89].…”

“…since the spin structure observed for bcc Eu at low temperatures belongs to this class [88,89]. The minimum of the Hamiltonian H eff (2) corresponds then to the maximum of the lattice Fourier transform J(q) (6).…”

Electronic structure and superconductivity of europium

“…The bcc ground state is correctly determined with an equilibrium lattice constant of 8.25 bohr which is about 4 % below experiment (typical of LDA calculations) and a calculated bulk modulus of 14.8 GPa that is about 1 % greater than experiment. 14,15 The bcc and fcc total energies are very close with bcc equilibrium about 0.3 mRy below the fcc. Since our DFT calculations use temperature T =0 K, the enthalpy is equal to the Gibbs free energy G=E +pV -TS such that…”