Theory on the Stability of the Ferromagnetic Double Layer Structure and on the Peak Structure of the Magneto-Optical Spectra of CeSb

Abstract

We propose the pf +pd mixing model for CeSb to explain the stability of the ferromagnetic double layer structure in the magnetic ordering. The pd mixing causes the saddle type singular points, neighboring the ∆ axis, for the bands which gain energy through the pf hybridization with the occupied f state. The peak of the density of states due to this combined effect of the pf mixing and the pd mixing enhances the stability of the double layer structure. The same combined effect also causes the saddle type singular points in the joint density of states of the optical transition. The peak structure of the magneto-optical spectra which has been observed in experiments is explained by the present model.KEYWORDS: CeSb, magnetic order, double layer structure, optical conductivity, pf mixing model §1. Introduction Cerium monopnictides (CeX p , X p =P, As, Sb, Bi) are semimetals with the NaCl type lattice. Their electronic bands have hole surfaces originated from atomic X p p states around Γ, and electron surfaces originated from Ce 5d states around three equivalent X.1) In the temperature (T) and the magnetic field (H) diagram, 2, 3) CeX p 's show various types of magnetic ordered states. They consist of the ferromagnetic layers which stack antiferromagnetically. Many types of stacking sequences appear in the phase diagram. Among CeX p 's, CeSb 3) and CeBi 4, 5) have the type-IA antiferromagnetic (+ + −−) phase with nearly full (J z ≃ ±5/2) magnetic moment as the ground state of weak H case. Here '+' denotes the ferromagnetic layer with the magnetic moment parallel to the field, and '−' denotes the layer anti-parallel to the field.The pair of ferromagnetic layers (++ or −−) is widely observed as a unit of the magnetic structure in CeX p 's. We call it as the 'double layer structure', hereafter.The phase diagram of CeSb has been qualitatively reproduced by the ANNNI model.6-8) However, it is not clear how the parameters of the phenomenological model are related to those of the microscopic model.The origin of the ferromagnetic layer with nearly full moment was explained by the pf mixing model 9-16) proposed by Kasuya et al. The model also succeeded in explaining the origin of the antiferromagnetic stacking of the ferromagnetic layers. However, the stability of the double layer structure with sufficient energy gain has not been obtained.The pd mixing term between X p p bands and Ce d bands is neglected in the energy calculation of the original pf mixing model, because the pd mixing effect dis- * Contact address: NTT Energy and Environment Systems Laboratories, Tokyo 180-8585 appears on the ∆ axis where the pf mixing becomes maximum. Later, it was pointed out that the pd mixing term plays important role [17][18][19] to explain the Fermi surfaces of CeSb in the ferromagnetic phase [20][21][22][23][24][25] and + + − phase. 25, 26)In this paper, we employ the pf mixing model including the pd mixing effect, and examine the stability of the double layer structure in CeSb. Hereafter, we call the model as the pf +pd mixing model. I...

Band Calculation for Ce-Compounds on the basis of Dynamical Mean Field Theory

“…In the p − f mixing model, a part of the Γ 8 valence band which has the same symmetry with the occupied 4f band is pushed up above E F due to the hybridization in the ordered phase. [31][32][33][34] Such re-constructed electronic band structures in the ordered states are expected by Hatree-Fock-like static mean field theory, 38 and confirmed by experimental studies. [35][36][37] We need the DMFT band calculation in the paramagnetic phase.…”

“…[35][36][37] In the ordered states we can use the Hatree-Focklike static mean field approaches, and detailed comparison with experiments has been carried out. 34,38 However, in the paramagnetic phase we need DMFT band calculation. CeSb has a characteristic double peak structure in PES; the shallow-energy one is at about 0.8 eV below E F and the deep-energy one is at about 3 eV below E F .…”

Devil's staircase transition of the electronic structures in CeSb

“…Under the AF modulation, these bands should be transformed from a cubic to a tetragonal structure in the reduced Brillouin zone (BZ) (Fig. 1c), and the consequent band folding is theoretically expected to generate hybridization gaps at the Fermi energy (E F ) 16 . In addition, the theory has also pointed out importance of interactions between the localized 4f states and mobile electrons [17][18][19][20] , particularly intralayer hybridizations with the Sb 5p electrons (p-f mixing) 18,20 , to explain the anomalous properties of CeSb below T N .…”

Infrared spectroscopy under multiextreme conditions: Direct observation of pseudogap formation and collapse in CeSb

“…The energy of 0.4 eV is similar to the pf mixing energy (E(pf σ) =0.35 eV, E(pf π) =-0.245 eV) of CeSb. [2,12] This indicates that the Sb5p band modified by the Ce4f spin structure due to the pf mixing is the origin of the pseudo gap. The enhancement in the electrical resistivity originates from the decrease in the density of states on E F through the creation of the pseudo gap structure.…”

“…[10,11] The change in the Sb5p bands due to pf mixing in addition to the hybridization between the Sb5p and Ce5d orbitals plays an important role in the formation and stabilization of the double-layered magnetic structure. [12] The electronic structure of CeSb at high pressures has been investigated using infrared spectroscopy in our previous paper. [13] In the paper, the spectral changes of R(ω) due to two magnetic phase transition at P = 2.5 GPa were observed.…”