Spin fluctuation theory for quantum tricritical point arising in proximity to first-order phase transitions: Applications to heavy-fermion systems, YbRh₂Si₂, CeRu₂Si₂, and β-YbAIB₄

We propose a phenomenological spin fluctuation theory for antiferromagnetic quantum tricritical point (QTCP), where a first-order phase transition changes into a continuous transition at zero temperature. Under magnetic fields, ferromagnetic quantum critical fluctuations develop around the antiferromagnetic QTCP in addition to antiferromagnetic fluctuations, which is in sharp contrast with the conventional antiferromagnetic quantum critical point. For itinerant electron systems, we show that the temperature dependence of critical magnetic fluctuations around the QTCP is given as χ _q T_-3/2 (χ ₀ T_-3/4) at the antiferromagnetic ordering (ferromagnetic) wave number q = Q (q = 0). The convex temperature dependence of χ _0-1 is a characteristic feature of the QTCP, which has never been seen in the conventional spin fluctuation theory. We propose a general theory of quantum tricriticality that has nothing to do with the specific Kondo physics itself, and solves puzzles of quantum criticalities widely observed in heavyfermion systems such as YbRh ₂Si ₂, CeRu ₂Si ₂, and β-YbAlB ₄. For YbRh ₂Si ₂, our theory successfully reproduces quantitative behaviors of the experimentally obtained ferromagnetic susceptibility and magnetization curve when suitable phenomenological parameters are chosen. The quantum tricriticality is also consistent with singularities of other physical properties such as specific heat, nuclear magnetic relaxation time 1/T ₁T, and the Hall coefficient. For CeRu ₂Si ₂ and β-YbAlB ₄, we point out that the quantum tricriticality is a possible origin of the anomalous diverging enhancement of the uniform susceptibility observed in these materials.