We present models where γ(+) and γ(-), the exponents of the susceptibility in the high- and low-temperature phases, are generically different. In these models, continuous symmetries are explicitly broken down by discrete anisotropies that are irrelevant in the renormalization-group sense. The Z(q)-invariant models are the simplest examples for two-component order parameters (N=2) and the model with icosahedral symmetry for N=3. We accurately compute γ(+)-γ(-) as well as the ratio ν/ν' of the exponents of the two correlation lengths present for T<T(c).

Critical Exponents Can Be Different on the Two Sides of a Transition: A Generic Mechanism

Ab initio band structure calculations are carried out for the higher borides MB6 and MB12. High-precision measurements of the elastic constants are performed for the compounds ZrB12, HoB12, ErB12, TmB12, LuB12, YB6 and LaB6 at low temperatures. The bulk properties of the borides are analyzed on the basis of the calculated equations of states and balanced crystal orbital overlap populations. Our calculations indicate that hexaborides with divalent metals, CaB6, SrB6, BaB6, and YbB6, are semiconductors with small energy gaps. The metallic MB6 hexaborides with trivalent M atoms are found to possess larger bulk moduli values. For dodecaborides the bulk moduli are found to be higher for MB12 with increased filling of the conduction band (ZrB12, HfB12, UB12) in comparison with M3+B12 compounds. The total energy calculations for different magnetic configurations in YbB12 point to the possibility of antiferromagnetic coupling between Yb3+ ions.

/pdf/electronic-structure-and-bulk-properties-of-mb6-and-mb12-1jptw652o8.pdf

Electronic structure and bulk properties of MB6 and MB12 borides

The high temperature phase transition in the three-layered ${P}^{\ensuremath{'}}3{\text{-Na}}_{x}{\text{CoO}}_{2}\phantom{\rule{0.3em}{0ex}}(x\ensuremath{\sim}0.62)$ has been investigated by means of heat capacity measurement, x-ray diffraction, and $^{23}\text{N}\text{a}$ magic angle spinning (MAS)--NMR spectroscopy in the 300--550 K range. The phase transition occurs nearby ${T}_{S}=350\text{ }\text{K}$. Below ${T}_{S}$, the unit cell is monoclinic (space group $C2/m$). Above ${T}_{S}$, the monoclinic cell is reversibly converted into a rhombohedral cell (space group $R3m$). The crystallographic change mainly manifests into Na rearrangement in the interslab from a low symmetry position to a higher symmetry position. A global picture for both systems of the $(x,y,z)$ off-center position of Na could be understood as a balance between on-site ${\text{Na}}^{+}{\text{-Co}}^{3+/4+}$ electrostatic repulsions ($z$ shift) and in-plane ${\text{Na}}^{+}{\text{-Na}}^{+}$ electrostatic repulsions ($xy$ shift). We suggest that ${\text{Na}}^{+}$ interlayer redistribution is the driving force of the phase transition. $^{23}\text{N}\text{a}$ MAS-NMR spectroscopy has been used to investigate changes in the environment and in the distribution of the sodium cations occurring by raising the temperature. The gradual suppression of the second-order quadrupolar interactions and the resulting new resonance is consistent with the sodium site exchange mechanism. Changes in the resistivity at ${T}_{S}$ suggest a strong coupling between the ${\text{Na}}^{+}$ and ${\text{CoO}}_{2}$ layers.

https://hal.archives-ouvertes.fr/hal-00286556/document

High-temperature phase transition in the three-layered sodium cobaltite P ′ 3 -Na x CoO 2 ( x ∼ 0.62 )

Topological effects on spin frustration in equilateral triangle S =3/2 spin tubes formed in CsCrF 4 were studied by magnetic susceptibility, heat capacity [ C ( T )], and electron spin resonance experiments. The experimental data show that there is no magnetic long-range order down to T =1.3 K, and that no spin gap due to a chiral spin structure appears. Furthermore, since the C ( T ) curve has a T -linear component, a gapless spin-liquid ground state in one-dimensional antiferromagnets, the so-called Tomonaga–Luttinger liquid, is realized. This is characteristic of equilateral triangle spin tubes with S = half-integer.

Spin-Liquid State Study of Equilateral Triangle $S=3/2$ Spin Tubes Formed in CsCrF4

https://arxiv.org/pdf/cond-mat/0412578.pdf

Structural phase transitions and sodium ordering in Na0.5CoO2: a combined electron diffraction and Raman spectroscopy study

We report the results of measurements of the dc susceptibility and the $^{23}\mathrm{N}\mathrm{a}$-NMR response of ${\mathrm{N}\mathrm{a}}_{2}{\mathrm{V}}_{3}{\mathrm{O}}_{7}$, a recently synthesized, nonmetallic low dimensional spin system. Our results indicate that, upon reducing the temperature to below 100 K, the ${\mathrm{V}}^{4+}$ moments are gradually quenched, leaving only one moment out of nine active. The NMR data reveal a phase transition at very low temperatures. With decreasing applied field $H$, the critical temperature shifts towards $T=0\text{ }\mathrm{K}$, suggesting that ${\mathrm{N}\mathrm{a}}_{2}{\mathrm{V}}_{3}{\mathrm{O}}_{7}$ may be regarded as an insulator reaching a quantum critical point at $H=0$.

Low-Dimensional SpinS=1/2System at the Quantum Critical Limit:Na2V3O7

We report the results of low-temperature measurements of the specific heat ${C}_{p}(T)$, ac susceptibility ${\ensuremath{\chi}}_{\mathrm{ac}}(T)$ and $^{23}\mathrm{Na}$ nuclear magnetic resonance NMR of ${\mathrm{Na}}_{2}{\mathrm{V}}_{3}{\mathrm{O}}_{7}$. At liquid He temperatures ${C}_{p}(T)$ exhibits a broad field-dependent Schottky-type anomaly. Below $1.5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ the ac magnetic susceptibility ${\ensuremath{\chi}}_{\mathrm{ac}}(T)$ follows a Curie-Weiss law and exhibits a cusp at $0.086\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ which indicates a phase transition at very low temperatures. These results support the previous conjecture that ${\mathrm{Na}}_{2}{\mathrm{V}}_{3}{\mathrm{O}}_{7}$ is close to a quantum critical point at ${\ensuremath{\mu}}_{0}H\ensuremath{\approx}0\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. The entire data set, including NMR spin-lattice relaxation ${T\phantom{\rule{0.1em}{0ex}}}_{1}^{\ensuremath{-}1}(T)$, reveals a complex magnetic behavior at low temperatures. We argue that it is due to a distribution of singlet-triplet energy gaps of dimerized V moments. The dimerization process evolves over a rather broad temperature range around and below $100\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. At the lowest temperatures the magnetic properties are dominated by the response of only a minor fraction of the V moments.

/pdf/unusual-magnetic-properties-of-the-low-dimensional-quantum-3nphojpvy2.pdf

Unusual magnetic properties of the low-dimensional quantum magnet Na2V3O7

We report the observation of an anomalous ${}^{27}\mathrm{Al}\ensuremath{-}\mathrm{NMR}$ response of a single grain ${\mathrm{Al}}_{72.4}{\mathrm{Pd}}_{20.5}{\mathrm{Mn}}_{7.1}$ icosahedral quasicrystal at low temperatures. In an external magnetic field of 6 T and upon decreasing temperature, we observe a sharp 100% increase of the resonance linewidth at 2.5 K. No further changes of the linewidth are observed down to 0.05 K. The linewidth enhancement is accompanied by a small but distinct increase of the spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}.$ These anomalies are absent in external fields of 2.5 T and below. Our observations indicate unusual variations in the stability of isolated magnetic moments in a quasiperiodic metallic environment.

Anomalous NMR response of quasicrystalline icosahedral Al 72.4 Pd 20.5 Mn 7.1 at low temperatures

We report the results of measurements of $^{27}$Al and $^{55}$Mn NMR spectra, the related spin-lattice relaxation rates, and the dc magnetic susceptibility of the stable decagonal quasicrystal Al$_{69.8}$Pd$_{12.1}$Mn$_{18.2}$. The temperature-variation of the magnetic susceptibility $\chi(T)$ reveals that the Mn ions carry only an average magnetic moment of approximately $2\mu_{\mathrm{B}}$, and confirms a spin-glass type freezing of the Mn-moments at $T_f=12$K. The NMR spectra reveal two partially resolved lines for the $^{27}$Al-nuclei, indicating that there are two different sets of environments for the Al-sites. The integrated intensity of the Mn line in the spectra suggests that about half of the Mn ions carry no magnetic moment. Below 50K, and upon decreasing the temperature, the $^{27}$Al NMR-linewidth $w$ and the spin-lattice relaxation rate $T_1^{-1}$ both grow with an increasingly negative slope, as it is often observed and interpreted as a critical "slowing down" of magnetic moments in systems approaching a spin-glass transition. Various features, such as a broad maximum in $T_1^{-1}(T)$ and a slope change in the $w(\chi)$ plot, both around 120K, suggest a gradual reduction of the number of Mn moments with decreasing temperature below 120K.

Anomalous magnetism in decagonalAl69.8Pd12.1Mn18.1

We report on measurements of the magnetic susceptibility χ ( T ) and 23 Na nuclear magnetic resonance (NMR) on polycrystalline samples of Na07CoO2 The χ ( T ) data suggest that for T > 75 K , the Co ions adopt an effective configuration of Co 34 +  The temperature evolution of 2D exchange 23 Na -NMR spectra and of the 23 Na spin-lattice relaxation time T 1 reveal significant anomalies between 230 and 300 K These features provide evidence for a crossover phenomenon or a phase transition and suggest that, upon decreasing temperature, a dramatic change occurs in the Co 3d–electron spin dynamics, starting just below 300 K and being completed at 230 K This phenomenom may involve a partial charge ordering within the Co subsystem

Unconventional charge ordering in Na0.70CoO2 below 300 K

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