Spin relaxation in Kondo lattices

Abstract

A model of spin relaxation in Kondo lattices is proposed to explain the presence of an electron spin resonance (ESR) signal in the heavy fermion compounds YbRh 2 Si 2 and YbIr 2 Si 2 . Coupled equations for dynamical susceptibilities of Kondo ions and conduction electrons are derived by means of the functional derivative method. The perturbational scaling approach reveals the collective spin motion of Yb-ions with conduction electrons in the bottleneck regime. A common energy scale due to the Kondo effect regulates the temperature dependence of the different kinetic coefficients and results in a mutual cancelation of all divergent parts in a collective spin mode. The angular dependence of the ESR linewidth is shown to be in a qualitative agreement with experimental data on YbRh 2 Si 2 and YbIr 2 Si 2 . Linewidth contributions other than the Kondo interaction are also discussed. Theoretical modelOur basic theoretical model includes the kinetic energy of conduction electrons, the Zeeman energy, the Kondo interaction of Yb-ions with conduction electrons, and the coupling between the Yb-ions via conduction electrons (RKKY interaction).A free Yb 3+ ion has a 4f 13 configuration with one term 2 F. The spin-orbit interaction splits the 2 F term into two multiplets: 2 F 7/2 with J = 7/2 and 2 F 5/2 with J = 5/2, where J is the value of the total momentum J = L + S with L and S as the orbital and spin momentum of the ion. The excited multiplet 2 F 5/2 is separated from the ground state 2 F 7/2 by about 1 eV. Since this value is much larger than the energy of the crystal electric field (CEF), we consider in the following the ground multiplet only. It is reasonable to express the Zeeman energy of the i-th Yb-ion ZJ H for the lowest multiplet J = 7/2 via the total electronic momentum of the ion. Using the Lande g-factor g J , we have ( 2 ).As a matter of fact all these results are simple consequences of the well known the Wigner-Eckart theorem.The same arguments can be used to reveal the anisotropy of the RKKY interaction between the Kondo ions. Although this interaction appears in the second order of the Kondo interaction (3) it is convenient to consider it independently. The result is given, in particular, in [8]. Starting with the isotropic exchange Hamiltonian for two Kondo ions 2 ( 1) ij RKKY RKKY ex ij i j ij J i j RKKY J ij ij J J Jg J Jg g g J Jg g g J J g J J J J J θ θ

Crystal electric field parameters for Yb3+ion in YbRh2Si2

“…YbRh 2 Si 2 and YbIr 2 Si 2 belong to the class of heavy-fermions Kondo-lattice compounds which attracted the interest of scientists due to the very peculiar magnetic, thermal and transport properties. The discovery of electron paramagnetic resonance (EPR) in the Kondo lattices YbRh 2 Si 2 and YbIr 2 Si 2 below the thermodynamically measured Kondo temperatures was very unexpected [1][2][3] and stimulated different approaches for its explanation [4][5][6][7]. In particular, in [6,7] is shown that the idea of a collective spin motion of quasi-localized Yb f-electrons and wide-band electrons successfully explains the EPR signal existence.…”

“…The discovery of electron paramagnetic resonance (EPR) in the Kondo lattices YbRh 2 Si 2 and YbIr 2 Si 2 below the thermodynamically measured Kondo temperatures was very unexpected [1][2][3] and stimulated different approaches for its explanation [4][5][6][7]. In particular, in [6,7] is shown that the idea of a collective spin motion of quasi-localized Yb f-electrons and wide-band electrons successfully explains the EPR signal existence. In [8] the static magnetic susceptibility of YbRh 2 Si 2 and YbIr 2 Si 2 were also successfully studied, based on entirely local properties of Yb 3+ ions in a tetragonal crystal electric field (CEF).…”

Magnetic properties and spin kinetics of a heavy-fermion Kondo lattice

“…To consider the spin dynamics in the Kondo lattice under discussion we use the model including the kinetic energy of conduction electrons, the Zeeman energy, the Kondo interaction between Yb ions and conduction electrons, and the coupling between the Yb ions via conduction electrons (RKKY interaction) [23][24][25][26][27][28][29][30]. The physics of lowenergy spin excitations at temperatures 200 K T  can be described by the lowest Kramers doublet.…”

“…σσ σσ Γ = Σ Calculations of these coefficients up to the third order in the Kondo interaction give [24] ( )…”

Kondo lattice with heavy fermions: peculiarities of spin kinetics

“…The discovery of electron spin resonance (ESR) in the Kondo lattice YbRh 2 Si 2 below the Kondo temperature T K ≈ 25 K [1] (T K revealed by specific heat data [2] and by transport measurements [3]) was a great surprise to the condensed matter physics community and stimulated different approaches for its explanation [4][5][6][7][8]. According to the picture based on the single ion Kondo effect, the magnetic moments of the Yb ions are screened by conduction electrons at T < T K and the ESR linewidth is of the order ν = k B T K /2π h = 500 GHz.…”