Non-Fermi Liquid Behavior in a Weak ItinerantFerromagnet MnSiName: Nirmal GhimireE-mail: [email protected]: Elbio DagottoSolid State Physics II, Spring 2010Department of Physics and AstronomyUniversity of Tennessee at KnoxvilleApril 20, 2010AbstractMnSi is a weak itinerant helimagnet with a relatively low ordermagnetic moment. Temperature dependance of resistivity shows thatit enters non-Fermi liquid state above a critical pressure pcwhich re-mains to be understood. The observed partial magnetic order abovepcindicates novel metallic state. Here, Fermi liquid and non-Fermiliquid theories are discussed with the main focus on the temperaturedependance of resistivity. Experimental evidence for the non-Fermiliquid behavior of MnSi has been presented and the partial magneticorder has been discussed.1 IntroductionThere are two basic theories of magnetism-localized moment theory anditinerant electron theory. In localized moment theory, the valence electronsare attached to the atoms and cannot move about the crystal. The valenceelectrons contribute a magnetic moment which is localized at the atom. Inthe itinerant electron magnetic theory, electrons responsible for magneticeffects are ionized from the atoms and are able to move through the crystal.There are materials for which one or the other model is a rather good ap-proximation [1]. There are models in terms of which these theories can beunderstood. Heisenberg model and Stoner model explain respectively local-ized and itinerant magnetic systems quite well. Yet there are some materials1with intermediate magnetic properties called near or weak ferromagnets inwhich the above mentioned theories become inadequate [2].In 1957 Landau came up with a model for the metallic state combiningthe Pauli exclusion principle with the effects of screening of the columbicinteraction named Fermi Liquid Theory (FLT) [3]. Among the many mate-rials obeying FLT are the nearly and weakly ferromagnetic d-electron metalsin which conduction bands derive from the substantial overlap of d-orbitalswhile the effects of spin-orbit coupling are weak [4]. There is a model consis-tent with the FLT which is developed for the ferromagnetic d-metals calledFerromagnetic Fermi Liquid theory (FFL). The general validity of the FFL,however, is in doubt. Non-fermi liquid behavior has been observed on theweakly magnetic d-electron compound MnSi [5].In this paper, I present a brief description of the fermi liquid and non-fermiliquid theory and the experimental observation in MnSi indicating the non-fermi liquid behavior.2 Fermi Liquid TheoryLandau developed the idea of quasiparticle excitation of interacting Fermisystems. This theory is known as Fermi Liquid Theory (FLT). Fermi liq-uids have spin12excitations and obey Fermi statistics. Examples are3He,electrons in metals and heavy nuclei. Landau gave the phenomenologicaldescription of FLT and formal derivation was later done by Abrikosov andKhalantikov [6].An electron in a metal collects around itself a screening cloud of other elec-trons, there by becoming a quasiparticle with some effective mass m∗. Thenumber of quasi particles is equal to the number of free electrons N. Thequasiparticles have momentum of p =¯hk, spin projection12, and obey Pauliexclusion principle. In ground state, like the free electrons, the quasipar-ticles fill the fermi sea up to the Fermi momentum. There is one to onecorrespondence between the free particle and quasi particle regarding thequantities like Fermi momentum (eqn 1), Fermi velocity (eqn 2), energy of asingle (quasi) particle (eqn 3) and density of state at the Fermi level (eqn 4),the quasi particle taking the effective mass (m∗) in place of mass of electron(m) in free electron model.pf= ¯h(3π2N)13(1)vf=pfm∗(2)2ε(p) =p22m∗(3)dndε=3Nm∗p2f(4)In FLT the interaction of quasiparticles is taken into account as a self con-sistent field of surrounding particle. The consequence is that energy of thesystem is not equal to the sum of energies of the N quasiparticles, but it isa functional of the distribution function. The energy of the quasiparticle iswritten as:E = εo(p, σ) + δεmeanfield(p,σ)(5)where, εo(p, σ) is the energy of the quasiparticle at T = 0 and δεmeanfield(p,σ)isthe mean field effect of the interaction with other quasi particles given by:δεmeanfield(p,σ)=12Sσ′∫f(p, σ; p′, σ′)δn(p, σ)2dpxdpydpz(2π¯h)3(6)The function f(p, σ; p′, σ′) is related to the scattering amplitude of two quasiparticles, and verifies time reversal symmetry i.e f (p, σ; p′, σ′)=f(p′, σ′; p, σ);δn(p, σ) = n-nF ermiand accounts for small deviations of the density of statesfrom the equilibrium value nF ermi. The quasiparticles are associated withlow energy excitations of the interacting system of electrons with a long lifetime near the Fermi energy, and hence it was created to explain the lowtemperature (T < TF ermi). The total energy is given by:E = Eo+∑p,σ∫δε(p, σ)δn(p, σ) (7)which shows that total energy is not just the sum of energies of each quasiparticle. The prediction for the temperature dependance of magnetic sus-ceptibility χ, specific heat [6] and electric resistivity ρ [7] is given by:χ = χo; χo= χo(m∗) (8)C = γoT ; γo= γo(m∗(9)ρ = ρo+ AT2(10)33 Non-Fermi Liquid SystemIn 1991 Seaman et al.[8] came up with measurement of specific heat, mag-netic susceptibility and electrical resistivity on Y1−xUxP d3system that stronglydisagreed with the Fermi-Liquid model of Landau. The Non-Fermi Liquid(NFL) behavior is characterized by weak power and logarithmic divergencein temperature dependance of the physical properties of these materials atlow temperature which take the following form [9]:ρ(T ) ∼ ρo[1 − a(TTo)n] (11)C(T )T∼ −[bRTo]ln(b′TTo)orT−1+λ(12)χ(T ) ∼ χo[1 − c(TTo)12]or − ln(TTo)orT−1+λ(13)where, a can be positive or negative, |a|, b, b′, and c are constants of theorder of unity, n lines in the range 1≤n≤1.6 and λ ≤ 1.A number of models have been proposed to account for the NFL behaviorobserved in d-and f-electron systems. The underlying physics of this modellies in the single-impurity multichannel kondo model and quantum criticalpoint theories [10].4 Non-Fermi Liquid State in MnSiMnSi is a d-transitional metal with a cubic crystallographic structure(a=4.588˚A [2]. Figure 1 shows the crystal structure of MnSi. There are 4 Mn ionsand 4 Si ions in a unit cell. The position of