Experimental evidence for magnetic resonance in the antiferro‐quadrupole phase

Abstract

The existence of quadrupolar interaction driven magnetic ordering has been established for various rare earth intermetallic compounds [1][2][3][4]. In the studied cases the quadrupole magnetic moments at some critical temperature T Q become ordered whereas dipole (i.e. ordinary) magnetic moments remain disordered. With lowering temperature the magnetic dipoles may become ordered undergoing a ferromagnetic or antiferromagnetic transition inside the quadrupole phase at T D < T Q . Note that if the strength of the dipole interaction will be sufficient to change the inequality to opposite, T D > T Q , the ordering of dipoles will with necessity induce the ordering of quadrupoles and the one and only magnetic transition will occur. In the latter case, however, the quadrupole interactions may modify the characteristics of the dipolar transition [1][2][3].Cerium hexaboride is a well-known example of a compound where quadrupole magnetic interactions play an essential role [5 -10]. The dipole and quadrupole magnetic moments are associated with the Ce 3+ ions forming a simple cubic lattice [5,6]. In zero magnetic field the quadrupole ordering occurs at T Q = 3.2 K and precedes the formation of an antiferromagnetic phase (i.e. dipole ordering) at T D = 2.3 K. In the region T > T Q cerium hexaboride is a paramagnetic metal and demonstrates behaviour typical of a dense Kondo system. The application of the external magnetic field induces an enhancement of T Q and suppression of T D as shown in the magnetic phase diagram (inset in Fig. 1). This sequence of phase transitions in CeB 6 has been proved by means of neutron diffraction [5] and resonant X-ray scattering [6] studies as well as by specific heat [7], NMR [8], magnetisation [9,10] and transport measurements [11]. The microscopic nature of the quadrupole ordering still remains the subject of discussions [12]. However it is widely accepted that the crystal field splitting of the 2 F 5/2 level of Ce ion leads to the lowest in energy Γ 8 term, whose symmetry allows the existence of the quadrupole moment [12]. The neutron scattering evidence [5] of an antiferromagnetic component with a wave vector, , ] in the quadrupole phase implies two types of nonequivalent Ce ions having quadrupole moments +Q and -Q and arranged in an alternating three-dimensional structure. Thus the ordered phase of CeB 6 at T < T Q is referred as an antiferro-quadrupole phase [5 -12].The coupling between quadrupole moments and dipole moments suggests the study of the antiferro-quadrupole phase of CeB 6 by means of various magnetic techniques, not excluding a priori resonant measurements. However, for dense Kondo systems the spin fluctuations at the magnetic ions are generally believed to broaden the resonance For strongly correlated electronic systems in addition to magnetically ordered phases based on the interaction between magnetic dipoles magnetic ordering originating from the quadrupolar magnetic interactions is possible. Up to now any information about magnetic resonances specific to quadrupolar or...

Electron spin resonance in antiferro-quadrupolar-ordered CeB6

“…Recently, an ESR signal was observed at 60 GHz in the cubic compound CeB 6 in the temperature range from 1.8 K to 3.8 K for the magnetic field parallel to the [110] direction. 20,21 The resonance 22 has a Dysonian-like lineshape and a g-factor of 1.59. The compound has a Kondo temperature of the order of 1 K and displays antiferroquadrupolar order 23 where the resonance was observed.…”

“…[20][21][22] It is convenient to rotate the magnetization so that M * z is parallel to the magnetic field, i.e. we choose…”

Theory of Electron Spin Resonance in Ferromagnetically Correlated Heavy Fermion Compounds

“…Experimentally, however, only one ESR signal was observed at 60 GHz for 1.8 K < T < 3.8 K for B parallel to the [110] direction [11,12], rather than the four expected lines. The resonance [41] has a Dysonian-like lineshape, characteristic of a metallic environment, and a g-factor of 1.59.…”

“…Three of these resonances are quenched by the AFQ order at each site and the coherence of the wave functions reduces the signal to one resonance. The experimentally observed g-value [11,12,41] is about 1.6 and depends on the angle θ of the magnetic field with the crystallographic axis. The theoretical effective g-factor depends then on two angles, θ and ϕ, and the Knight shift.…”

“…However, recently, an ESR signal was found in single crystals of YbRh 2 Si 2 [4][5][6], YbIr 2 Si 2 [7], YbRh [8], YbCo 2 Zn 20 [9], CeRuPO [10], and CeB 6 [11,12] proving this common belief incorrect. The resonances are attributed to the Yb 3+ and Ce 3+ ions despite their rather large T K .…”