When the crystal field anisotropy is dominant, the directions of the magnetic moments are determined by the minima in the expression for E,. In the heavy rare earth metals, there also exists a strong coupling between magnetic and elastic energies, which produces magnetostrictive dilations by rotation of the magnetic moment from the light to a hard magnetic direction. The experimental values of the linear strains in the three major axial directions are shown, for example, for dysprosium and holmium in fig.
Therefore, there is rather little point in the direct measurement of the crystal field splitting of rare earth ions in the pure elemental rare earth metals. Summary of the magnetic properties of rare earth metals: spin structure in zero applied field (see Fig. 2). Summary of the magnetic properties of rare earth metals: crystal field parameters at 300 K for alloys with diamagnetic hcp metals, Y, Lu and SC [77T I].
Summary of the magnetic properties of rare earth metals: electronic specific heat coefficient, Debye temperature and I-point temperatures in the specific heat vs.
Rare earth metals: General
In the helical structure, magnetic moments are in the hexagonal basal plane and each magnetic moment rotates by an angle, w, when one goes from a plane perpendicular c to the next plane at a distance c/2. The period of the oscillation is equal to 2JQ and the angle of rotation, CD, of the magnetic moments is equal to w=Qc/2. a) shows the variation of the wavenumber Qc/2x (scale on the left) or of the oscillation period 2JQc (scale on the right) as a function of T/T, for the heavy rare earths. Magnetic susceptibility for the hexagonal a and c directions of single crystals of Sc, Y and Lu, and for a polycrystal of La as a function of temperature [73 S 1, 73 S 21.
The linear high-temperature curves are extrapolation to zero temperature of the linear high-extrapolated to zero temperature (indicated by arrows) to tempcraturc curves [72 L 11.
Drulis, M. Drulis
Cerium
Temperature dependence of the peak intensity of the (QOQ3) magnetic satellite reflection observed in dhcp Pr when a uniaxial stress of 800 bar is applied along the [1210] a direction. TN in dhcp Pr calculated as a function of the one-sided pressure in the o direction, using the mcan-ficld model of [79 H 23. 0 indicates the angle between the magnetic field and the hexagonal c-axis of the single crystal.
-Partitions of the fields of the lower levels of Pr3+. on hex pages in dhcp Pr. Experimental results for the elastic constant cb6 in dhcp Pr as a function of the applied magnetic field in all three symmetry directions at 4.2 K. The lines are only connecting the experimental points [78P 11.
POH-
Gadolinium
Dependence of the magnetic moment of Gd single crystals on the magnetic field along the a axis at 269.8 K, the b axis at 270.1 K, and the c axis at 270.4 K, showing that the c axis is the easy magnetization axis just below Tc [ 63N 1- j. Temperature dependence of the angle between the direction of easy magnetization and the c axis in Gd. magnetic torque curves Gd in the plane containing the c axis; w is the angle between the direction of the applied magnetic field and the c; axis.
From the magnetic torque curves, the position of the easy magnetization axis as a function of temperature was determined, cf. Full line is a theoretical illuminated (From neighborhood of the Curie temperature. The general characteristics of Vleck equation) including exchange interaction between the results show that transition temperature T, magnetic moments with 0 = 310 K (64 A 1-J. Since the magnon anisotropy in Gd is neglected, the curves are directly proportional to the values of the interplanar exchange integrals Jzbvc.
Temperature dependence of the magnetic excitation spectrum of Gd at 4 =0.15.2n/c in the [OOOl] c direction, obtained from inelastic neutron scattering studies. Magnetic specific heat of Gd metal plotted as a sum of the electronic, magnetic (Cmag = BT”) and lattice. Anisotropy constants K, and K, of Gd plotted as a function of the magnetic moment of the sample.
IO3 erg/cm3 and m is the magnetization relative to the zero temperature value [67 G 11. Experimental values of the anisotropy constants K2, K, and K6 vs. The solid lines are the experimental data of [63 B l ] after correction for thermal expansion of the nonmagnetic lattice. The dashed lines are the theoretical determination of [71 B 1-J. a) Temperature dependence of the electrical resistance of Gd single crystals along the b and c axes.
POH -
Terbium
Magnetization along the b-axis of Tb as a function of the internal magnetic field for different temperatures, showing a licld-induced AFeF transition C83Gl-J. Magnon energy gap squared for various temperatures as a function of the internal magnetic field in the easy (solid symbols) and hard (open symbols) direction [75H 23. Temperature dependence of the experimental forced magnetostriction coefficients of Tb along the a, b , and c -axis for H parallel to the b-axis.
Temperature dependence of the FMR field in Tb at 100 GHz with the field along the hard plane axis. Temperature dependence of the critical magnetic field, If, in a direction Dy for a magnetic phase transition from a helical to a ferromagnetic or fan-like state, determined from magnetization curves [78 H I]. Change of Helmholtz free energy with magnetic field applied in Dy hard direction of magnetization.
Temperature variation of the electrical resistances of Dy single crystal in the temperature range covered, 4.2. Time dependence of the residual remanent magnetization (RRM),M, of Dy with the temperature as a parameter. Magnetic field dependence of the transmitted power at 37.6GHz in Dy with the field applied along a hard axis in the basal plane.
Temperature dependence of the resonant magnetic field in Dy with the field applied along the hard magnetic axis at (a) 40 GHz and (b) 100 GHz. Temperature dependence of the helical twist angle, w, of the helical spin state for a Ho sample with. Temperature dependence of the critical magnetic fields in Ho. a) Values of Hcl, Hcz and H, for a magnetic field applied along the b-axis.
Temperature dependence of the low-field magnetic susceptibility (open circles) of Ho taken from the initial slopes of the magnetization curves parallel to the b axis. Temperature dependence of the electrical resistivity, Q, of Ho for (a) polycrystals [6OC 21 and (b) a single crystal along the a and c axes [69 N I].
Erbium
The appearance of higher-order satellites shows that the structure of the c-axis magnetic moment deviates from a purely sinusoidal modulation [74 H 21. The intensity of integrated neutron scattering (100) of the nuclear reflection of a single crystal of Er and its first-order satellites (100) ' compared to the observation of first-order magnetic satellites of all nuclear reflections except (001) shows that the magnetic moment of the c axis is of Er orders at r84K in a sinusoidally modulated magnetic structure with a wave vector parallel to the c axis.
An N&l temperature Th' of 84.4 K was obtained by extrapolating the intensities of the first-order satellites. Amplitudes of the nlh-order harmonics of (a) the c-axis magnetic moment structure, py', and (b) the basal plane magnetic moment structure, p i , for Er at T > T, . Tc, the magnetic moment on the c-axis, p, and the moments in the basal plane, pI, of the conical magnetic structure are shown.
Solid and open symbols refer to rising and falling temperatures respectively [74 H 23. H. Drulis, M. Drulis Land&Bknstein New series 111/19dl New series 111/19dl .. plane amplitudes of the magnetization waves in H = 0 and 20 kOe as a function of the temperature for a single crystal of Er. The Yd and Sh harmonic amplitudes are increased by a factor of two [74A I].. axial amplitudes, p\i), from the magnetizing waves up to the Ilth harmonic as a function of temperature for a single crystal of Er at T>T, . For T < Tc, the c-axis magnetic moment, p, and its experimental ambiguity are shown for the conical magnetic structure [74A I]. First-order wavelengths of the magnetic moment-modulating waves in a single crystal of Er metal at H = 0 and 20 kOe.
Temperature dependence of the magnetic periodicity, Q, in Er, as obtained from single crystal neutron diffraction results. Critical magnetic fields along the c axis required to transform the quasi-antiphase domain configuration into the conical ferromagnetic state of Er vs. The magnification curves for the a and b axes reach the saturation value of the Er magnetic moment at x 150 kOe [68X2].
Drulis, M. Drub
- Thulium
- Lutetium
- References for 2.1
- Alloys between rare earth elements
- Introduction
- Alloys between light rare earth elements
- Alloys between heavy and light rare earth elements .1 General remarks
Average magnetic moment per Er atom, pEr, for H parallel to the c-axis as a function of the magnetic field for different temperatures in Y:Er diluted alloys. Spin wave dispersion relation for Er metal along the c-direction at 4.2 K for wave vectors parallel (open circles) and antiparallel (solid circles) to the ferromagnetic component of the conical structure. Temperature dependence of the attenuation of longitudinal ultrasound along the c-axis of Er at different frequencies near the sinusoidal paramagnetic phase transition.
Temperature dependence of the microwave resonance field Er at 35.3 GHz with the magnetic field along the c axis, with the b axis perpendicular to the disk. Temperature dependence of the modulation wave vector Q parallel to the c-axis Tm determined by neutron diffraction investigation. The out-of-plane reflections shown in the figure with open circles reflect the asphericity of the magnetic moment density distribution [69B4].
Graph of the inverse magnetic susceptibility, l/X*, as a function of temperature for the c and b axes of Tm crystals, which gives the paramagnetic Curie temperatures, Ob = - 17 K and 0.=41 K, respectively [69 R 1- J. Temperature dependence of the electrical resistivity, e, for the a, b, and c axes of single crystal Tm between 1.3 and 300 K. For each alloy system, a chronological list of relevant references precedes the data presentation.
For each of the alloying systems between light rare earth elements, figures and tables are provided in which data on the specified properties are given. In this section, the magnetic data for alloys between heavy and light rare earth elements are represented. NCel temperatures TN for hcp heavy rare earth-La alloys are not expressed by a universal curve for the average de Gennes factor unlike the alloys between heavy rare earth elements (see Fig. 13).
