Hall coefficient in heavy fermion metals

Abstract

Experimental studies of the antiferromagnetic (AF) heavy fermion metal YbRh2Si2 in a magnetic field B indicate the presence of a jump in the Hall coefficient at a magnetic-field tuned quantum state in the zero temperature limit. This quantum state occurs at B ≥ Bc0 and induces the jump even though the change of the magnetic field at B = Bc0 is infinitesimal. We investigate this by using the model of heavy electron liquid with the fermion condensate. Within this model the jump takes place when the magnetic field reaches the critical value Bc0 at which the ordering temperature TN (B = Bc0) of the AF transition vanishes. We show that at B → Bc0, this second order AF phase transition becomes the first order one, making the corresponding quantum and thermal critical fluctuations vanish at the jump. At T → 0 and B = Bc0, the Grüneisen ratio as a function of temperature T diverges. We demonstrate that both the divergence and the jump are determined by the specific low temperature behavior of the entropy S(T ) ∝ S0 + a √ T + bT with S0, a and b are temperature independent constants.PACS numbers: 71.10. Hf, 71.27.+a, 71.10.Hf, The most outstanding puzzle of heavy fermion (HF) metals is what determines their universal behavior which drastically differs from the behavior of ordinary metals. It is wide accepted that the fundamental physics observed in the HF metals is controlled by quantum phase transitions. A quantum phase transition is driven by control parameters such as composition, pressure, number density x of electrons (holes), magnetic field B, etc, and takes place at a quantum critical point (QCP) when the temperature T = 0. In the case of conventional quantum phase transitions (CQPT) the physics is dominated by thermal and quantum fluctuations near CQP. This critical state is characterized by the absence of quasiparticles. It is believed that the absence of quasiparticle-like excitations is the main cause of the non-Fermi liquid (NFL) behavior, see e.g. [1]. However, theories based on CQPT fail to explain the experimental observations of the universal behavior related to the divergence of the effective mass M * at the magnetic field tuned QCP, the specific behavior of the spin susceptibility, its scaling properties, etc.It is possible to explain the observed universal behavior of the HF metals on the basis of the fermion condensation quantum phase transition (FCQPT) which takes place at x = x F C and allows the existence of the Landau quasiparticles down to the lowest temperatures [2]. It is the quasiparticles which define the universal behavior of the HF metals at low temperatures [2,3]. In contrast to the conventional Landau quasiparticles, these are characterized by the effective mass which strongly depends on temperature T , applied magnetic field B and the number density x of the heavy electron liquid of HF metal. Thus, we come back again to the key role of the of the effective * E-mail: vrshag@thd.pnpi.spb.ru mass.On the other hand, it is plausible to probe the other properties of the heavy electron liquid w...

Scaling behavior of heavy fermion metals

“…( 136) cannot be satisfied at sufficiently low temperatures T ≤ T crit because of the temperature-independent term S 0 . Hence, the second order antiferromagnetic phase transition becomes the first order one at T = T crit [183,184] as shown by the arrow in Fig. 40.…”

“…(137) that the discontinuity in the Hall coefficient is determined by the anomalous behavior of the entropy, which can be attributed to S 0 . Hence, the discontinuity tends to zero as r → 0 and disappears when the system is on the disordered side of FCQPT, where the entropy has no temperature-independent term [186]. We now turn to the magnetization which is determined by Eq.…”

Magnetic Field as an Important Tool in Exploring the Strongly Correlated Fermi Systems and Their Particle–Hole and Time-Reversal Asymmetries

“…Thus, the outstanding puzzle of HF compounds originating from their universal behavior, which drastically differs from the behavior of ordinary metals and superconductors, is resolved [14][15][16][17]23,25], and the fundamental physics of HF compounds are controlled by the topological FCQPT (see, e.g., [15][16][17]20,27]). It is plausible to probe the other properties of HF compounds, which are not directly determined by the effective mass M * and cannot be explained within the framework of theories based on conventional quantum phase transitions (see, e.g., [15,20,24,[28][29][30][31]). An important feature explained within the framework of the FC theory is the crossover from NFL behavior to LFL behavior under the application of magnetic field B, pressure P, etc.…”

“…Due to the same reason, the residual resistivity ρ 0 (B) under the application of magnetic field B is strongly reduced, and the behavior of the resistivity ρ(T) changes from ρ(T) ∝ T to ρ(T) ∝ T 2 [17,32]. Moreover, the dependence of the magnetic field on the Hall coefficient R H (B) provides information about the QCP, determining the properties of HF metals [31]. Experiments have shown that the Hall coefficient R H (B) in the antiferromagnetic HF metal YbRh 2 Si 2 in magnetic fields B undergoes a jump in the zero-temperature limit under the application of magnetic field B, tuning the metal from the antiferromagnetic to the paramagnetic state at B = B c0 [33].…”

Nature of the quantum critical point as disclosed by extraordinary behavior of magnetotransport and the Lorentz number in the heavy-fermion metal YbRh2Si2

“…As a result, the Hall coefficient experiences a sharp jump because R H (B) ∝ 1/p 3 F in the AF phase and R H (B) ∝ 1/p 3 f in the paramagnetic phase. Assuming that R H (B) is a measure of the Fermi momentum [37,39] (as is the case with a simply connected Fermi volume), we obtain [7,40]…”