Tricritical point of a ferromagnetic transition in UGe<sub>2</sub>

Kabeya, Noriyuki; Iijima, Ryosuke; Osaki, E.; Ban, S.; Imura, Keiichiro; Deguchi, K.; Aso, Naofumi; Homma, Yoshiya; Shiokawa, Yoshinobu; Sato, Noriaki

doi:10.1088/1742-6596/200/3/032028

Cited by 12 publications

(14 citation statements)

References 11 publications

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“…Accordingly, α p at the first-order transition has a δ-function contribution that reflects the same "latent volume" as the corresponding δ-function contribution to the compressibility. This is consistent with the experiment by Kabeya et al [12], who observed a pronounced negative peak in α p at the transition, which they attributed to a broadened first-order transition.…”

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confidence: 93%

Third Law of Thermodynamics and The Shape of the Phase Diagram for Systems With a First-Order Quantum Phase Transition

Kirkpatrick

Belitz

2015

Phys. Rev. Lett.

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The third law of thermodynamics constrains the phase diagram of systems with a first-order quantum phase transition. For zero conjugate field, the coexistence curve has an infinite slope at T = 0. If a tricritical point exists at T > 0, then the associated tricritical wings are perpendicular to the T = 0 plane, but not to the zero-field plane. These results are based on the third law and basic thermodynamics only, and are completely general. As an explicit example we consider the ferromagnetic quantum phase transition in clean metals, where a first-order quantum phase transition is commonly observed.First-order phase transitions are ubiquitous in nature, the solid-to-liquid and liquid-to-gas transitions being the most commonly observed ones. Another common example of a first-order transition is the ferromagnetic transition below the Curie temperature as a function of an external magnetic field. First-order transitions are characterized by a coexistence curve in the phase diagram along which the two phases coexist in thermodynamic equilibrium. (The coexistence curve may be the projection of a higher-dimensional coexistence manifold into a particular plane in the phase diagram.)It has long been known that the curvature of the coexistence curve is determined by the discontinuities of certain observables across it. The Clapeyron-Clausius (CC) equation relates the slope of the coexistence curve in the pressure-temperature (p -T ) plane to the discontinuities of the entropy and the volume [1]:where ∆s = s 1 − s 2 and ∆v = v 1 − v 2 with s 1,2 and v 1,2 the specific entropy and volume per particle, respectively, in the two phases. For definiteness, let 1 and 2 label the ordered and disordered phases, respectively, and for later reference we indicate that an appropriate external field H, if any, is held constant in taking the derivative. The CC equation (1) and its analogs in different planes of the phase diagram are very general, as they rely only on basic thermodynamic arguments. In this Letter we show that for quantum phase transitions, when combined with the third law of thermodynamics, they provide interesting constraints on the shape of the phase diagram. We will consider a pressure-driven transition at T = 0 that is first order, remains first order at low T , and turns second order at higher T via a tricritical point (TCP). The schematic phase diagram in the space spanned by T , p, and H, where H is the field conjugate to the order parameter, is shown in Fig. 1. As we will see, the detailed shape of this phase diagram at low T is constrained by thermodynamics. Our arguments leading to this conclusion are completely general; however, as an explicit example we will discuss the quantum ferromagnetic transition in clean metals [2]. Another example of a first-order quantum phase transition with a TCP in the phase diagram is the Ising antiferromagnet dysprosium arXiv:1504.00644v3 [cond-mat.stat-mech] 9 Jul 2015

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confidence: 93%

Third Law of Thermodynamics and The Shape of the Phase Diagram for Systems With a First-Order Quantum Phase Transition

Kirkpatrick

Belitz

2015

Phys. Rev. Lett.

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“…Indications of the FM wings have been reported recently from thermal expansion measurements realized via a strain gauge [31]. The detection via resistivity can be realized down to very low temperature while the use of strain gauge is limited to above 1.5 K. As visible on Fig.…”

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confidence: 64%

Tricritical Point and Wing Structure in the Itinerant FerromagnetUGe2

Taufour

Aoki²,

Knebel³

et al. 2010

Phys. Rev. Lett.

159

171

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Precise resistivity measurements on the ferromagnetic superconductor UGe2 under pressure p and magnetic field H reveal a previously unobserved change of the anomaly at the Curie temperature. Therefore, the tricritical point (TCP) where the paramagnetic-to-ferromagnetic transition changes from a second order to a first order transition is located in the p-T phase diagram. Moreover, the evolution of the TCP can be followed under the magnetic field in the same way. It is the first report of the boundary of the first order plane which appears in the p-T-H phase diagram of weak itinerant ferromagnets. This line of critical points starts from the TCP and will terminate at a quantum critical point. These measurements provide the first estimation of the location of the quantum critical point in the p-H plane and will inspire similar studies of the other weak itinerant ferromagnets.

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“…The tricritical temperature has been measured to be T tc ≈ 24 K (Kotegawa et al, 2011b;Taufour et al, 2010), but values as high as T tc ≈ 31 K have been reported (Huxley et al, 2007) with a tricritical pressure p tc ≈ 13 kbar. Kabeya et al (2010) found a somewhat smaller value of ≈ 12.5 kbar from measurements of the linear thermal expansion coefficient. The tricritical wings have been mapped out in detail, see Fig.…”

Section: Uranium-based Compoundsmentioning

confidence: 92%

“…The experimental coexistence curve appears to be extremely steep in many FM systems, see, e.g., Figs. 5, 10, and the phase diagrams for ZrZn 2 measured by Uhlarz et al (2004) and Takashima et al (2007), but determining the coexistence curve from different observables can lead to different detailed shapes (Kabeya et al, 2010). Studies of the detailed shape, by pressure-cycling in the p -T plane, or field-cycling in the p -H plane, would be interesting.…”

Section: B Open Problemsmentioning

confidence: 99%

Metallic quantum ferromagnets

et al. 2016

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We give an overview of quantum phase transitions (QPTs) in metallic ferromagnets, discussing both experimental and theoretical aspects. These QPTs can be classified with respect to the presence and strength of quenched disorder: Clean systems generically show a discontinuous, or first-order, QPT from a ferromagnetic to a paramagnetic state as a function of some control parameter, as predicted by theory. Disordered systems are much more complicated, depending on the disorder strength and the distance from the QPT. In many disordered materials the QPT is continuous, or second order, and Griffiths-phase effects coexist with QPT singularities near the transition. In other systems the transition from the ferromagnetic state at low temperatures is to a different type of long-range order, such as an antiferromagnetic or a spin-density-wave state. In still other materials a transition to a state with glass-like spin dynamics is suspected. The review provides a comprehensive discussion of the current understanding of these various transitions, and of the relation between experiment and theory.

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Tricritical point of a ferromagnetic transition in UGe₂

Cited by 12 publications

References 11 publications

Third Law of Thermodynamics and The Shape of the Phase Diagram for Systems With a First-Order Quantum Phase Transition

Third Law of Thermodynamics and The Shape of the Phase Diagram for Systems With a First-Order Quantum Phase Transition

Tricritical Point and Wing Structure in the Itinerant FerromagnetUGe2

Metallic quantum ferromagnets

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Tricritical point of a ferromagnetic transition in UGe2

Cited by 12 publications

References 11 publications

Third Law of Thermodynamics and The Shape of the Phase Diagram for Systems With a First-Order Quantum Phase Transition

Third Law of Thermodynamics and The Shape of the Phase Diagram for Systems With a First-Order Quantum Phase Transition

Tricritical Point and Wing Structure in the Itinerant FerromagnetUGe2

Metallic quantum ferromagnets

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Tricritical point of a ferromagnetic transition in UGe₂