### Abstract

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
_{2}
Si
_{2}
, CeRu
_{2}
Si
_{2}
, and β-YbAlB
_{4}
. For YbRh
_{2}
Si
_{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
_{1}
T, and the Hall coefficient. For CeRu
_{2}
Si
_{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.

Original language | English |
---|---|

Article number | 084707 |

Journal | Journal of the Physical Society of Japan |

Volume | 78 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2009 Aug 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Heavy-fermion systems
- Quantum critical phenomena
- Quantum tricritical point
- Self-consistent renormalization theory
- Tricritical point

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

_{2}Si

_{2}, CeRu

_{2}Si

_{2}, and β-YbAIB

_{4}.

*Journal of the Physical Society of Japan*,

*78*(8), [084707]. https://doi.org/10.1143/JPSJ.78.084707

**Spin fluctuation theory for quantum tricritical point arising in proximity to first-order phase transitions : Applications to heavy-fermion systems, YbRh
_{2}
Si
_{2}
, CeRu
_{2}
Si
_{2}
, and β-YbAIB
_{4}.** / Misawa, Takahiro; Yamaji, Youhei; Imada, Masatoshi.

Research output: Contribution to journal › Article

_{2}Si

_{2}, CeRu

_{2}Si

_{2}, and β-YbAIB

_{4}',

*Journal of the Physical Society of Japan*, vol. 78, no. 8, 084707. https://doi.org/10.1143/JPSJ.78.084707

_{2}Si

_{2}, CeRu

_{2}Si

_{2}, and β-YbAIB

_{4}. Journal of the Physical Society of Japan. 2009 Aug 1;78(8). 084707. https://doi.org/10.1143/JPSJ.78.084707

}

TY - JOUR

T1 - Spin fluctuation theory for quantum tricritical point arising in proximity to first-order phase transitions

T2 - Applications to heavy-fermion systems, YbRh 2 Si 2 , CeRu 2 Si 2 , and β-YbAIB 4

AU - Misawa, Takahiro

AU - Yamaji, Youhei

AU - Imada, Masatoshi

PY - 2009/8/1

Y1 - 2009/8/1

N2 - 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 2 Si 2 , CeRu 2 Si 2 , and β-YbAlB 4 . For YbRh 2 Si 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 1 T, and the Hall coefficient. For CeRu 2 Si 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.

AB - 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 2 Si 2 , CeRu 2 Si 2 , and β-YbAlB 4 . For YbRh 2 Si 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 1 T, and the Hall coefficient. For CeRu 2 Si 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.

KW - Heavy-fermion systems

KW - Quantum critical phenomena

KW - Quantum tricritical point

KW - Self-consistent renormalization theory

KW - Tricritical point

UR - http://www.scopus.com/inward/record.url?scp=69149109450&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=69149109450&partnerID=8YFLogxK

U2 - 10.1143/JPSJ.78.084707

DO - 10.1143/JPSJ.78.084707

M3 - Article

AN - SCOPUS:69149109450

VL - 78

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 8

M1 - 084707

ER -