Hall Conductivity of a Spin-Triplet Superconductor

Kim, Wonkee; Marsiglio, F.; Ting, C. S.

doi:10.1103/physrevlett.100.227003

Cited by 17 publications

(26 citation statements)

References 19 publications

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“…(10) vanishes upon integration over the orientation of p, because v x is an odd function of p x , and v y is an odd function of p y . Even if an anisotropic model with ∆ x = ∆ y is considered [33], still a similar calculation gives a symmetric tensor Q xy = Q yx , which does not represent the Hall conductivity [25] and is not relevant for the experiment [1].…”

Section: Theoretical Model and General Discussionmentioning

confidence: 99%

“…This implies that the Hall conductivity σ xy in a clean chiral superconductor is zero, even though a non-zero value is nominally permitted by the TRSB. Kim et al [33] obtained a non-zero value of σ xy for an anisotropic superconducting pairing, but their calculated conductivity tensor is symmetric σ xy = σ yx . So, it does not represent the antisymmetric Hall conductivity (σ xy = −σ yx ) and does not contribute to the polar Kerr effect.…”

Section: Introductionmentioning

confidence: 99%

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Frequency and temperature dependence of the anomalous ac Hall conductivity in a chiralpx+ipysuperconductor with impurities

2009

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We calculate frequency and temperature dependence of the anomalous ac Hall conductivity induced by impurity scattering in a chiral px +ipy superconductor, such as Sr2RuO4, with spontaneous time-reversal-symmetry breaking in the absence of an external magnetic field. We consider two models of disorder, Gaussian and non-Gaussian, characterized by the second and third moments of the random impurity potential, respectively. Within both models, we find that the anomalous Hall conductivity has a finite real value at zero frequency, exhibits singularities at the threshold of photon absorption across the superconducting gap, and decays as some power of the high frequency ω. The Hall conductivity increases linearly with the decrease of temperature below the superconducting transition and saturates at zero temperature. Using our results for the high-frequency Hall conductivity, we estimate the polar Kerr angle for light reflection from the material and compare it with the experimental measurements in Sr2RuO4 by Xia et al., Phys. Rev. Lett. 97, 167002 (2006).

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Section: Theoretical Model and General Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Frequency and temperature dependence of the anomalous ac Hall conductivity in a chiralpx+ipysuperconductor with impurities

2009

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“…This fact, in principle, should allow to avoid the excitation of multiple modes and simplify the shape of the oscillation peak, i.e., reduces ∆f 10 . From non-linear oscillation models 11,12 , ∆f is expected to be proportional to the temperature T and to the nonlinearity of the system, i.e.,…”

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confidence: 99%

“…Indeed, the classical formula (see Eq. 1) for a (weakly) non linear oscillator 11,12 , should be modified by adding an extra constant term c 1 : ∆f = c 0 k b T + c 1 .…”

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confidence: 99%

Temperature dependence of microwave voltage emission associated to spin-transfer induced vortex oscillation in magnetic tunnel junction

Bortolotti

Dussaux

Grollier

et al. 2012

Applied Physics Letters

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The temperature dependence of a vortex-based nano-oscillator induced by spin transfer torque (STVO) in magnetic tunnel junctions (MTJ) is considered. We obtain emitted signals with large output power and good signal coherence. Due to the reduced non-linearities compared to the uniform magnetization case, we first observe a linear decrease of linewidth with decreasing temperature. However, this expected behavior no longer applies at lower temperature and a bottom limit of the linewidth is measured.PACS numbers: 75.40.Gb, 85.30.Mn Keywords: magnetic devices, spin-transfer-torque, tunnel magnetoresistance, magnetic vortex dynamics A spin polarized current can exert a large torque on the magnetization of a ferromagnet through a transfer of spin angular momentum 1 . This mechanism offers a new method to manipulate a magnetization, and potentially a stable precession can be reached 2 . By converting such dynamics into a high frequency voltage oscillation through the magnetoresistance effect, the concept of spin transfer-torque nano-oscillator (STNO) has been proposed as a promising device for new technological applications in IC-Technologies. However, despite compelling progresses 3-6 , present challenges remain to both increase the output power and improve the coherence of the emitted signal. Recently, we demonstrated 7,8 that, by considering a magnetic tunnel junction (MTJ) with a vortex ground state (free layer), the so-called spin transfer-torque vortex oscillator (STVO), we obtain large integrated power (P int ≃ 5 nW) for a small linewidth, i.e., full width at half maximum, ∆f < 1 MHz. However, although ∆f is considerably reduced compared to the uniform magnetization case, a major issue is still its origin, and consequently the origin of the phase noise.When the efficiency of the spin transfer-torque induced by I dc exceeds a critical value, the vortex core starts to precess and eventually reaches a stable gyrotropic motion. The frequency of such gyrotropic vortex mode 9 is well-separated from the frequencies of others modes (radial and azimuthal spin waves). This fact, in principle, should allow to avoid the excitation of multiple modes and simplify the shape of the oscillation peak, i.e., reduces ∆f 10 . From non-linear oscillation models 11,12 , ∆f is expected to be proportional to the temperature T and to the nonlinearity of the system, i.e.,Here, ν ∝ N , which is the non-linear frequency shift a) Corresponding author. Electronic address: paolo.bortolotti@thalesgroup.com coefficient N = df /dp, Γ G is the intrinsic damping coefficient and E(p) represents the energy of the autooscillation with power p. In the case of gyrotropic vortex oscillators, N is weak compared to MTJs with uniform magnetization 4 . Hence, we expect a quasi-linear dependence of ∆f with temperature.The samples are circular MTJs of 300 nm diameter, with a 10 nm NiFe thick free layer and a synthetic antiferromagnet (SAF) that acts as in-plane uniformly magnetized spin polarizer. The complete structure (with thickness in nm) is: PtMn(15) / C...

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“…Annealing of polycrystalline samples often results in the reduction of the frequency shift [4,5] but sometimes in its increase [5], while single crystals show no change [5]. The concentration of 3 He impurities, x 3 , in the initial liquid 4 He strongly affects the characteristic temperature T 0 at which the TO frequency is half-way between its high-and low-temperature values: T 0 ∼ 30 mK for x 3 = 10 −9 and increases to ∼ 300 mK for x 3 = 10 −5 [6]. All these observations suggest that the phenomenon is influenced by crystalline defects interacting with impurities.…”

mentioning

confidence: 99%

Simultaneous Measurements of the Torsional Oscillator Anomaly and Thermal Conductivity in SolidHe4

Zmeev

Golov

2011

Phys. Rev. Lett.

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In these torsional oscillator experiments, the samples of solid (4)He were characterized by measuring their thermal conductivity. Polycrystalline samples of helium of either high isotopic purity or natural concentration of (3)He were grown in an annular container by the blocked-capillary method and investigated before and after annealing. No correlation has been found between the magnitude of the low-temperature shift of the torsional oscillator frequency and the amount of crystalline defects as measured by the thermal conductivity. In samples with the natural (3)He concentration, a substantial excess thermal conductivity over the usual T(3) dependence was observed below 120 mK.

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Hall Conductivity of a Spin-Triplet Superconductor

Cited by 17 publications

References 19 publications

Frequency and temperature dependence of the anomalous ac Hall conductivity in a chiralpx+ipysuperconductor with impurities

Frequency and temperature dependence of the anomalous ac Hall conductivity in a chiralpx+ipysuperconductor with impurities

Temperature dependence of microwave voltage emission associated to spin-transfer induced vortex oscillation in magnetic tunnel junction

Simultaneous Measurements of the Torsional Oscillator Anomaly and Thermal Conductivity in SolidHe4

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