Terms Of Crystalline Electric Field Research Articles

Giant crystal-electric-field effect and complex magnetic behavior in single-crystallineCeRh3Si2

Single-crystalline CeRh3Si2 was investigated by means of x-ray diffraction, magnetic susceptibility, magnetization, electrical resistivity, and specific heat measurements carried out in wide temperature and magnetic field ranges. Moreover, the electronic structure of the compound was studied at room temperature by cerium core-level x-ray photoemission spectroscopy (XPS). The physical properties were analyzed in terms of crystalline electric field and compared with results of ab-initio band structure calculations performed within the density functional theory approach. The compound was found to crystallize in the orthorhombic unit cell of the ErRh3Si2 type (space group Imma -- No.74, Pearson symbol: oI24) with the lattice parameters: a = 7.1330(14) A, b = 9.7340(19) A, and c = 5.6040(11) A. Analysis of the magnetic and XPS data revealed the presence of well localized magnetic moments of trivalent cerium ions. All physical properties were found to be highly anisotropic over the whole temperature range studied, and influenced by exceptionally strong crystalline electric field with the overall splitting of the 4f1 ground multiplet exceeding 5700 K. Antiferromagnetic order of the cerium magnetic moments at TN = 4.70(1)K and their subsequent spin rearrangement at Tt = 4.48(1) K manifest themselves as distinct anomalies in the temperature characteristics of all investigated physical properties and exhibit complex evolution in an external magnetic field. A tentative magnetic B-T phase diagram, constructed for B parallel to the b-axis being the easy magnetization direction, shows very complex magnetic behavior of CeRh3Si2, similar to that recently reported for an isostructural compound CeIr3Si2. The electronic band structure calculations corroborated the antiferromagnetic ordering of the cerium magnetic moments and well reproduced the experimental XPS valence band spectrum.

Effective Crystalline Electric Field Potential in a j– j Coupling Scheme

We propose an effective model on the basis of a $j$-$j$ coupling scheme to describe local $f$-electron states for realistic values of Coulomb interaction $U$ and spin-orbit coupling $\lambda$, for future development of microscopic theory of magnetism and superconductivity in $f^n$-electron systems, where $n$ is the number of local $f$ electrons. The effective model is systematically constructed by including the effect of a crystalline electric field (CEF) potential in the perturbation expansion in terms of $1/\lambda$. In this paper, we collect all the terms up to the first order of $1/\lambda$. Solving the effective model, we show the results of the CEF states for each case of $n$=2$\sim$5 with $O_{\rm h}$ symmetry in comparison with those of the Stevens Hamiltonian for the weak CEF. In particular, we carefully discuss the CEF energy levels in an intermediate coupling region with $\lambda/U$ in the order of 0.1 corresponding to actual $f$-electron materials between the $LS$ and $j$-$j$ coupling schemes. Note that the relevant energy scale of $U$ is the Hund's rule interaction. It is found that the CEF energy levels in the intermediate coupling region can be quantitatively reproduced by our modified $j$-$j$ coupling scheme, when we correctly take into account the corrections in the order of $1/\lambda$ in addition to the CEF terms and Coulomb interactions which remain in the limit of $\lambda$=$\infty$. As an application of the modified $j$-$j$ coupling scheme, we discuss the CEF energy levels of filled skutterudites with $T_{\rm h}$ symmetry.

Construction of a microscopic model forf-electron systems on the basis of aj−jcoupling scheme

We construct a microscopic model for f-electron systems, composed of f-electron hopping, Coulomb interaction, and crystalline electric field (CEF) terms. In order to clarify the meaning of one f-electron state, here the j-j coupling scheme is considered, since the spin-orbit interaction is generally large in f-electron systems. Thus, the f-electron state at each site is labelled by $\mu$, namely, the z-component of total angular momentum j. By paying due attention to f-orbital symmetry, the hopping amplitudes between f-electron states are expressed using Slater's integrals. The Coulomb interaction terms among the $\mu$-states are written by Slater-Condon or Racah parameters. Finally, the CEF terms are obtained from the table of Hutchings. The constructed Hamiltonian is regarded as an orbital degenerate Hubbard model, since it includes two pseudo-spin and three pseudo-orbital degrees of freedom. For practical purposes, it is further simplified into a couple of two-orbital models by discarding one of the three orbitals. One of those simplified models is here analyzed using the exact diagonalization method to clarify ground-state properties by evaluating several kinds of correlation functions. Especially, the superconducting pair correlation function in orbital degenerate systems is carefully calculated based on the concept of off-diagonal long-range order. We attempt to discuss a possible relation of the present results with experimental observations for recently discovered heavy fermion superconductors CeMIn$_5$ (M=Ir, Co, and Rh), and a comprehensive scenario to understand superconducting and antiferromagnetic tendencies in the so-called ``115'' materials such as CeMIn$_5$, UMGa$_5$, and PuCoGa$_5$ from the microscopic viewpoint.

Spin reorientation and crystal field in a single crystal

Magnetization measurements performed on a single crystal of the tetragonal ferrimagnetic compound are presented together with their quantitative analysis. Between K and a spin reorientation temperature K, the spontaneous magnetization is along the crystallographic c direction. Below the spontaneous magnetization progressively shifts away from c and is directed between this axis and the [100] direction. The results are rather well accounted for by considering the iron sublattice characteristics measured on a single crystal and diagonalising the rare earth Hamiltonian through a system of coupled equations. A set of crystalline electric field (CEF) parameters and Er-Fe exchange field coefficient is proposed. It is shown that the spin reorientation does not come from a competition between iron anisotropy and the effect of the second order CEF parameter acting on the rare earth, as is frequently observed in this type of compounds. It results rather from the interaction between (i) the effect of these two contributions both of which favour the c axis, and (ii) that of the fourth order CEF terms, in particular , which favour an intermediate direction of magnetization. The relative importance of this latter contribution is greatest at low temperature.

Magnetization spin reorientation and crystalline electric field coefficients of RCo5 ( R = Pr, Nd, Tb, DyandHo) compounds

By means of the single-ion crystalline electric field (CEF) model we have investigated the spin reorientation of RCo 5 ( R = Pr, Nd, Tb, Dy and Ho) compounds and discussed the contributions of high order CEF terms B 0 4 and B 0 6 to magnetocrystalline anisotropy. In addition, viewof the anisotropic competition of sublattice R and Co, we have fitted the temperature dependence of the easy cone angle θ, which is the angle between the easy direction of the magnetization and the c-axis. The CEF coefficients B m n are obtained by fitting the experimental data. The variations of the total free energy F tot for each RCo 5 compound changing with angle θ are presented.

Heat capacity of (R 1− xPr x)Ba 2Cu 3O 7 (R=Y, Gd)

We present specific heat measurements of (R, Pr)Ba 2Cu 3O 7 (R=Y, Gd) in external fields up to 11 T. The results are analyzed in terms of crystalline electric field (CEF) effects and indicate that in these systems Pr appears to be trivalent rather than tetravalent.

Magnetic properties of Nd/sub 2/Fe/sub 13.8/Mo/sub 0.1/Nb/sub 0.1/B/sub 1-x/C/sub x/ alloys

The effect of carbon substitution on the magnetic properties of Nd/sub 2/Fe/sub 13.8/Mo/sub 0.1/Nb/sub 0.1/B/sub 1-x/C/sub x/ (with x=0, 0.2, 0.4, 0.6, 0.8) was studied. The anisotropy field was measured from 77 K to 379 K using the singular point detection technique. It was found that both the anisotropy field and the critical field increase with increasing carbon content. A slight decrease of both Curie temperature and saturation magnetization were observed. The increase of anisotropy field may be due to a variation of the crystal field behavior due to Nd ions when boron is substituted by carbon. The increase of critical field with increasing carbon content may be due to the variation of high-order crystalline electric field terms. >

Origin of magnetic anisotropy in R2Fe14B (R=rare earth) compounds: Crystalline electric field model calculations (abstract)

The tetragonal R2Fe14B compounds have attracted a great deal of attention because of the permanent magnet applications of the Nd-Fe-B system. Nd2Fe14B shows a spin reorientation from an axial arrangement at 300 K to a conical-type structure below 140 K. In contrast, Pr2Fe14B remains axial down to 4.2 K. We show that this behavior in the Pr and Nd compounds results from an interplay of crystalline electric field (CEF) effects and the R-Fe exchange interaction. There are two inequivalent R sites ( f and g) in these compounds which are magnetically further split into f 1, f 2 and g1,g2 sites. The CEF parameters B02 and B22 for each site are taken from the 155Gd Mössbauer measurements in Gd2Fe14B and the R-Fe exchange field is estimated from the Gd magnetization.1 These parameters are suitably scaled for the rare-earth ion under consideration. It is shown that with the known values of B02, B22, and Hex and with B04 =0.118 K for Nd (which corresponds to B04 =0.35 K for Pr), the four-site calculation, employing these three CEF terms, predicts a spin reorientation in Nd2Fe14B at about 130 K but an axial behavior in Pr2Fe14B at all temperatures.

Magnetic properties of equiatomic rare earth cadmium compounds

The magnetization processes obtained in monocrystalline samples are presented for the ferromagnetic compounds of the equiatomic rare earth cadmium series. They are discussed in terms of crystalline electric field and bilinear and quadrupolar pair interactions. A close similarity appears with the isomorphous series with zinc. The importance of quadrupolar interactions is emphasized. They are, for instance, strong enough in DyCd to enforce the fourfold axis as easy magnetization direction instead of the threefold one which would be driven by the only crystalline electric field. A discussion of the magnetic properties of dysprosium compounds having the CsCl-type structure is then given.

Magnetic excitations in HoNi2

Using inelastic neutron scattering we have studied the magnetic excitations in HoNi2. Several modes have been observed in the [001] direction showing that the magnetic excitations in this compound are governed by crystal field effects. The acoustic mode is the only one which is weakly dispersive. The JHo-Ho interaction deduced is very weak and leads to a calculated Curie temperature much smaller than the experimental one. This shows that although the nickel is not magnetic it could contribute to the magnetic ordering. An analysis of the complete results in terms of crystalline electric field and Heisenberg type exchange interaction fails to account simultaneously for magnetization and inelastic neutron measurement.