Frustrated magnets are materials in which localized magnetic moments, or spins, interact through competing exchange interactions that cannot be simultaneously satisfied, giving rise to a large degeneracy of the system ground state. Under certain conditions, this can lead to the formation of fluid-like states of matter, so-called spin liquids, in which the constituent spins are highly correlated but still fluctuate strongly down to a temperature of absolute zero. The fluctuations of the spins in a spin liquid can be classical or quantum and show remarkable collective phenomena such as emergent gauge fields and fractional particle excitations. This exotic behaviour is now being uncovered in the laboratory, providing insight into the properties of spin liquids and challenges to the theoretical description of these materials.

Spin liquids in frustrated magnets

The proximity effect at superconductor-ferromagnet interfaces produces damped oscillatory behavior of the Cooper pair wave function within the ferromagnetic medium. This is analogous to the inhomogeneous superconductivity, predicted long ago by Fulde and Ferrell (P. Fulde and R. A. Ferrell, 1964, ``Superconductivity in a strong spin-exchange field,'' Phys. Rev. 135, A550--A563), and by Larkin and Ovchinnikov (A. I. Larkin and Y. N. Ovchinnikov, 1964, ``Inhomogeneous state of superconductors,'' Zh. Eksp. Teor. Fiz. 47, 1136--1146 [Sov. Phys. JETP 20, 762--769 (1965)]), and sought by condensed-matter experimentalists ever since. This article offers a qualitative analysis of the proximity effect in the presence of an exchange field and then provides a description of the properties of superconductor-ferromagnet heterostructures. Special attention is paid to the striking nonmonotonic dependence of the critical temperature of multilayers and bilayers on the ferromagnetic layer thickness as well as to the conditions under which ``$\ensuremath{\pi}$'' Josephson junctions are realized. Recent progress in the preparation of high-quality hybrid systems has permitted the observation of many interesting experimental effects, which are also discussed. Finally, the author analyzes the phenomenon of domain-wall superconductivity and the influence of superconductivity on the magnetic structure in superconductor-ferromagnet bilayers.

Proximity effects in superconductor-ferromagnet heterostructures

This review presents a summary and evaluation of the experimental properties of unconventional superconductivity in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ as they were known in the spring of 2002. At the same time, the paper is intended to be useful as an introduction to the physics of spin-triplet superconductivity. First, the authors show how the normal-state properties of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ are quantitatively described in terms of a quasi-two-dimensional Fermi liquid. Then they summarize its phenomenological superconducting parameters in the framework of the Ginzburg-Landau model, and discuss the existing evidence for spin-triplet pairing. After a brief introduction to the vector order parameter, they examine the most likely symmetry of the triplet state. The structure of the superconducting energy gap is discussed, as is the effect of symmetry-breaking magnetic fields on the phase diagram. The article concludes with a discussion of some outstanding issues and desirable future work. Appendixes on additional details of the normal state, difficulty in observing the bulk Fermi surface by angle-resolved photoemission, and the enhancement of superconducting transition temperature in a two-phase ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}\ensuremath{-}\mathrm{Ru}$ system are included.

The superconductivity of Sr 2 RuO 4 and the physics of spin-triplet pairing

This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both the existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.

http://export.arxiv.org/pdf/cond-mat/0606317

Fermi-liquid instabilities at magnetic quantum phase transitions

To make the transition from the quasi-long-range order in a chain of antiferromagnetically coupled S = 1/2 spins to the true long-range order that occurs in a plane, one can assemble chains to make ladders of increasing width. Surprisingly, this crossover between one and two dimensions is not at all smooth. Ladders with an even number of legs have purely short-range magnetic order and a finite energy gap to all magnetic excitations. Predictions of this ground state have now been verified experimentally. Holes doped into these ladders are predicted to pair and possibly superconduct.

https://science.sciencemag.org/content/sci/271/5249/618.full.pdf

Surprises on the Way from One- to Two-Dimensional Quantum Magnets: The Ladder Materials

Magnetic properties of Sr${\mathrm{Cu}}_{2}$${\mathrm{O}}_{3}$ and ${\mathrm{Sr}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{5}$, containing two-leg and three-leg $S=\frac{1}{2}$ ladders made of antiferromagnetic Cu-O-Cu linear bonds, were investigated. The susceptibility of the two-leg ladder material, Sr${\mathrm{Cu}}_{2}$${\mathrm{O}}_{3}$, is characteristic of thermal excitation from a nonmagnetic ground state with a spin gap of about 420 K, while the susceptibility of ${\mathrm{Sr}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{5}$, containing three-leg ladders, reflects a gapless spin excitation spectrum. The temperature dependence of the nuclear-spin lattice relaxation rate, $\frac{1}{{T}_{1}}$, of $^{63}\mathrm{Cu}$ NMR also indicates the existence of a spin gap only for Sr${\mathrm{Cu}}_{2}$${\mathrm{O}}_{3}$. The spin gap we observed for Sr${\mathrm{Cu}}_{2}$${\mathrm{O}}_{3}$ confirms a recent theoretical prediction for the magnetic behavior of spin = \textonehalf{} antiferromagnetically coupled Heisenberg chains.

Observation of a spin gap in SrCu2O3 comprising Ssin-12 quasi-1D two-leg ladders.

${}^{195}\mathrm{Pt}$ Knight shift (KS) measurements covering the superconducting multiple phases for major field ( $H$) orientations have been carried out on the high-quality single crystal ${\mathrm{UPt}}_{3}$. For $Hg5$ kOe, the KS does not change below the superconducting transition temperature ${T}_{c}$ down to 28 mK, regardless of major crystal orientations, which provides evidence that the odd-parity superconductivity with the parallel spin pairing is realized. By contrast, the KS decreases below ${T}_{c}$ for ${H}_{b}\ensuremath{\parallel}b$ axis and ${H}_{b}l5$ kOe and for ${H}_{c}\ensuremath{\parallel}c$ axis and ${H}_{c}l2.3$ kOe, whereas the KS for ${H}_{a}\ensuremath{\parallel}a$ axis is $T$ independent across ${T}_{c}$ down to ${H}_{a}\ensuremath{\sim}1.764$ kOe. These novel findings entitle ${\mathrm{UPt}}_{3}$ as the first spin-triplet odd-parity superconductor including a nonunitary pairing characterized by the two-component $\mathbf{d}$ vector like ${\mathbf{d}}_{b}+i{\mathbf{d}}_{c}$ at low $T$ and low $H$.

/pdf/nonunitary-spin-triplet-superconductivity-in-upt3-evidence-2zy5qg03g3.pdf

Nonunitary Spin-Triplet Superconductivity in UPt3 : Evidence from 195Pt Knight Shift Study

We have investigated a gap structure in a newly discovered superconductor, MgB2, through measurement of the (11)B nuclear spin-lattice relaxation rate, (11)(1/T(1)). (11)(1/T(1)) is proportional to the temperature (T) in the normal state, and decreases exponentially in the superconducting (SC) state, revealing a tiny coherence peak just below T(c). The T dependence of 1/T(1) in the SC state can be accounted for by an s-wave SC model with a large gap size of 2Delta/k(B)T(c) approximately 5 which suggests it is in a strong-coupling regime.

/pdf/evidence-for-strong-coupling-s-wave-superconductivity-in-1kuc51w5mi.pdf

Evidence for strong-coupling s-wave superconductivity in MgB2: (11)B NMR Study.

We report a $^{\mathrm{29}}\mathrm{S}\mathrm{i}$ NMR study on aligned single crystals of ${\mathrm{Y}\mathrm{b}\mathrm{R}\mathrm{h}}_{2}{\mathrm{S}\mathrm{i}}_{2}$ which shows behavior characteristic of a quantum critical point (QCP: ${T}_{\mathrm{N}}\ensuremath{\rightarrow}0$). The Knight shift $K$ and the nuclear spin-lattice relaxation rate $1/{T}_{1}$ of Si show a strong dependence on the external field $H$, especially below 5 kOe. At the lowest $H$ used in this measurement ($H\ensuremath{\sim}1.5\text{ }\text{ }\mathrm{k}\mathrm{O}\mathrm{e}$), it was found that $1/{T}_{1}T$ continues to increase down to 50 mK, whereas $K$ stays constant with a large magnitude below 200 mK. This result strongly suggests the development of antiferromagnetic fluctuations with finite $\mathbit{q}$ vectors that compete with $\mathbit{q}=0$ spin fluctuations in the vicinity of the QCP near $H=0.5\text{ }\text{ }\mathrm{k}\mathrm{O}\mathrm{e}$.

YbRh2Si2: Spin Fluctuations in the Vicinity of a Quantum Critical Point at Low Magnetic Field

From Ru- and Cu-NMR studies, we present evidence for coexistence of superconductivity and ferromagnetism in a cuprate superconductor ${\mathrm{RuSr}}_{2}{\mathrm{YCu}}_{2}{\mathrm{O}}_{8}$ (RuY1212). The observation of a large enhancement of a radio-frequency field for the Ru-NMR signal at zero field reveals the existence of a ferromagnetic (FM) component in the ordered ${\mathrm{RuO}}_{2}$ plane below a Curie temperature of ${T}_{M}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}150\mathrm{K}$. Just below the onset temperature of superconductivity ${T}_{c}^{\mathrm{onset}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}45\mathrm{K}$, a remarkable decrease of the nuclear spin-lattice relaxation rate ${1/T}_{1}$ was observed within the ordered ${\mathrm{RuO}}_{2}$ plane as well as the ${\mathrm{CuO}}_{2}$ plane, revealing that the superconducting gap coexists with the FM component in the ${\mathrm{RuO}}_{2}$ plane on a microscopic scale. In addition, from the observation of a sharp peak in ${}^{101}({1/T}_{1})$ at ${T}_{c}^{\mathrm{zero}}\ensuremath{\sim}23\mathrm{K}$ where the resistivity becomes zero, we suggest that the motion of self-induced vortices originating from fluctuations of the FM component induces the resistivity between ${T}_{c}^{\mathrm{onset}}$ and ${T}_{c}^{\mathrm{zero}}$ in RuY1212.

K. Ishida

Papers

Observation of a spin gap in SrCu2O3 comprising Ssin-12 quasi-1D two-leg ladders.

Nonunitary Spin-Triplet Superconductivity in UPt3 : Evidence from 195Pt Knight Shift Study

Evidence for strong-coupling s-wave superconductivity in MgB2: (11)B NMR Study.

YbRh2Si2: Spin Fluctuations in the Vicinity of a Quantum Critical Point at Low Magnetic Field

Nmr evidence for coexistence of superconductivity and ferromagnetic component in magnetic superconductor RuSr2YCu2O8: 99,101Ru and 63Cu NMR.