Aging dip and cumulative aging in hierarchical successive transition of stage-2 CoCl2_{2} graphite intercalation compound

Memory and aging behaviors in stage-2 CoCl$_{2}$ GIC ($T_{cu}$ = 8.9 K and $T_{cl}$ = 6.9 K) have been studied using low frequency ($f$ = 0.1 Hz) AC magnetic susceptibility ($\chi^{\prime}$ and $\chi^{\prime\prime}$) as well as thermoremnant magnetization. There occurs a crossover from a cumulative aging (mainly) with a partial memory effect for the domain-growth in the intermediate state between $T_{cu}$ and $T_{cl}$ to an aging and memory in a spin glass phase below $T_{cl}$. When the system is aged at single or multiple stop and wait processes at stop temperatures $T_{s}$'s below $T_{cl}$ for wait times $t_{s}$, the AC magnetic susceptibility shows single or multiple aging dips at $T_{s}$'s on reheating. The depth of the aging dips is logarithmically proportional to the wait time $t_{s}$. Very weak aging dip between $T_{cu}$ and $T_{cl}$ indicates the existence of a partial memory effect. The sign of the difference between the reference cooling and reference heating curves changes from positive to negative on crossing $T_{cl}$ from the high $T$-side. The time dependence of $\chi^{\prime}$ and $\chi^{\prime\prime}$ below $T_{cl}$ is described by a scaling function of $\omega t$. its a local maximum at 6.5 K just below $T_{cl}$, and drastically decreases with increasing $T$. The nature of the cumulative aging between $T_{cl}$ and $T_{cu}$ is also examined.Comment: 11 pages. 13 figures, 1 tabl

Ordered spin structures of β\beta-MnO2_{2} (rutile-type) systems with competing exchange interactions: numerical approach using equi-energy contour plot

Using numerical calculations of equi-energy contour plot of the Fourier transform of the spin Hamiltonian, we study the magnetic phase diagram ($J_{2}$ and $J_{3}$) of the rutile type $\beta$-MnO$_{2}$, where $J_{1}$ ($<0$) is fixed and is the antiferromagnetic interaction along the diagonal direction, $J_{2}$ is the interaction along the c axis, and $J_{3}$ is the interaction along the a axis. The magnetic phase diagram consists of the multricritical point (the intersection $J_{2}J_{3}=J_{1}^{2}$ and $J_{2}+J_{3}=2J_{1}$), the helical order along the c axis, the $(h=1/2,k=0,l=1/2)$ phase, the helical order along the a axis, and the phase $(h=0,k=0,l=1)$. The shift of the location of the magnetic Bragg peak in the $(h,0,l)$ reciprocal lattice plane is examined with the change of $J_{2}$ and $J_{3}$ in the phase diagram. The shift is discontinuous on the first-order phase transition, and is continuous on the second-order phase transition. The detail of our magnetic phase diagram is rather different from that reported by Yoshimori.Comment: 16 pages, 20 figure

A proper understanding of the Davisson and Germer experiments for undergraduate modern physics course

The physical interpretation for the Davisson-Germer experiments on nickel (Ni) single crystals [(111), (100), and (110) surfaces] is presented in terms of two-dimensional (2D) Bragg scattering. The Ni surface acts as a reflective diffraction grating when the incident electron beams hits the surface. The 2D Bragg reflection occurs when the Ewald sphere intersects the Bragg rods arising from the two-dimension character of the system. Such a concept is essential to proper understanding of the Davisson-Germer experiment for undergraduate modern physics course.Comment: 8 pages and 14 figure

Observation of a magnetic-field-induced Griffiths phase in three-dimensional Ising random magnet Nip_{p}Mg1−p_{1-p}(OH)2_{2} from absorption of AC magnetic susceptibility

The nature of the Griffiths phase in three-dimensional Ising random magnet Ni_{p}Mg_{1-p}(OH)_{2} (p = 0.10, 0.25, 0.315, 0.50, 0.80, and 1) is studied from the measurements of absorption (the out-of phase in AC magnetic susceptibility) in the field-cooled (FC) state. The temperature (T) dependence of absorption is measured in the vicinity of the critical temperature [N\'{e}el temperature for p = 0.50, 0.80, 1, and the spin glass transition temperature for p = 0.1, 0.25, 0.315] in the presence of an external magnetic field H. A broad peak is clearly observed for absorption vs T well above the critical temperature at H > 20 kOe. This result gives a piece of evidence for the magnetic-field induced Griffiths phase.Comment: 10 pages, 17 figure

Stretched exponential relaxation in three dimensional short-range spin glass Cu0.5_{0.5}Co0.5_{0.5}Cl2_{2}-FeCl3_{3} graphite bi-intercalation compound

Cu$_{0.5}$Co$_{0.5}$Cl$_{2}$-FeCl$_{3}$ graphite bi-intercalation compound is a three-dimensional short-range spin glass with a spin freezing temperature $T_{SG}$ ($= 3.92 \pm 0.11$ K). The time evolution of the zero-field cooled magnetization $M_{ZFC}(t)$ has been measured under various combinations of wait time ($t_{w}$), temperature ($T$), temperature-shift ($\Delta T$), and magnetic field ($H$). The relaxation rate $S_{ZFC}(t)$ [$=(1/H)$d$M_{ZFC}(t)$/d$\ln t$] shows a peak at a peak time $t_{cr}$. The shape of $S_{ZFC}(t)$ in the vicinity of $t_{cr}$ is well described by stretched exponential relaxation (SER). The SER exponent $b$ and the SER relaxation time $\tau_{SER}$ are determined as a function of $t_{w}$, $T$, $H$, and $\Delta T$. The value of $b$ at $T=T_{SG}$ is nearly equal to 0.3. There is a correlation between $\tau_{SER}$ and $1/b$, irrespective of the values of $t_{w}$, $T$, $H$, and $\Delta T$. These features can be well explained in terms of a simple relaxation model for glassy dynamics.Comment: 11 pages, 12 figures; submitted to Physical Review

Magnetic Ordering of CoCl_{2}-GIC: a Spin Ceramic -Hierarchical Successive Transitions and the Intermediate Glassy Phase-

Stage-2 CoCl$_{2}$-GIC is a spin ceramic and shows hierarchical successive transitions at $T_{cu}$ (= 8.9 K) and $T_{cl}$ (= 7.0 K) from the paramagnetic phase into an intra-cluster (two-dimensional ferromagnetic) order with inter-cluster disorder and then to an inter-cluster (three-dimensional antiferromagnetic like) order over the whole system. The nature of the inter-cluster disorder was suggested to be of spin glass by nonlinear magnetic response analyses around $T_{cu}$ and by studies on dynamical aspects of ordering between $T_{cu}$ and $T_{cl}$. Here, we present a further extensive examination of a series of time dependence of zero-field cooled magnetization $M_{ZFC}$ after the aging protocol below $T_{cu}$. The time dependence of the relaxation rates $S_{ZFC}(t) = (1/H)dM_{ZFC}(t)/d\ln t$ dramatically changes from the curves of simple spin glass aging effect below $T_{cl}$ to those of two peaks above $T_{cl}$. The characteristic relaxation behavior apparently indicates that there coexist two different kinds of glassy correlated regions below $T_{cu}$.Comment: 6 pages, 3 figures, Proceeding of HFM2006, J. Phys.: Condensed Matter (accepted for publication

Memory and aging effect in hierarchical spin orderings of stage-2 CoCl_{2} graphite intercalation compound

Stage-2 CoCl$_{2}$ graphite intercalation compound undergoes two magnetic phase transitions at $T_{cl}$ (= 7.0 K) and $T_{cu}$ (= 8.9 K). The aging dynamics of this compound is studied near $T_{cl}$ and $T_{cu}$. The intermediate state between $T_{cl}$ and $T_{cu}$ is characterized by a spin glass phase extending over ferromagnetic islands. A genuine thermoremnant magnetization (TRM) measurement indicates that the memory of the specific spin configurations imprinted at temperatures between $T_{cl}$ and $T_{cu}$ during the field-cooled (FC) aging protocol can be recalled when the system is re-heated at a constant heating rate. The zero-field cooled (ZFC) and TRM magnetization is examined in a series of heating and reheating process. The magnetization shows both characteristic memory and rejuvenation effects. The time $(t)$ dependence of the relaxation rate $S_{ZFC}(t)=(1/H)$d$M_{ZFC}(t)$/d$\ln t$ after the ZFC aging protocol with a wait time $t_{w}$, exhibits two peaks at characteristic times $t_{cr1}$ and $t_{cr2}$ between $T_{cl}$ and $T_{cu}$. An aging process is revealed as the strong $t_{w}$ dependence of $t_{cr2}$. The observed aging and memory effect is discussed in terms of the droplet model.Comment: 14 pages, 16 figures; submitted to Phys. Rev.

Successive superconducting transitions and Anderson localization effect in Ta2_{2}S2_{2}C

A complex carbide Ta$_{2}$S$_{2}$C consists of van der Waals (vdw)-bonded layers with a stacking sequence $...$ C-Ta-S-vdw-S-Ta-C- $...$ along the c axis. The magnetic properties of this compound have been studied from DC and AC magnetic susceptibility. Ta$_{2}$S$_{2}$C undergoes successive superconducting transitions of a hierachical nature at $T_{cl} = 3.61 \pm 0.01$ K [$H_{c1}^{(l)}(0) = 28 \pm 2$ Oe and $H_{c2}^{(l)}(0) = 7.7 \pm 0.2$ kOe] and $T_{cu} = 9.0 \pm 0.2$ K [$H_{c2}^{(u)}(0) = 6.0 \pm 0.3$ kOe]. The intermediate phase between $T_{cu}$ and $T_{cl}$, where $\delta \chi (= \chi_{FC} - \chi_{ZFC}) \approx 0$, is an intra-grain superconductive state occurring in the Ta-C layers in Ta$_{2}$S$_{2}$C. The low temperature phase below $T_{cl}$, where $\delta \chi$ clearly appears, is an inter-grain superconductive state. The magnetic susceptibility at $H$ well above $H_{c2}^{(l)}(0)$ is described by a sum of a diamagnetic susceptibility and a Curie-like behavior. The latter is due to the localized magnetic moments of conduction electrons associated with the Anderson localization effect, occurring in the 1T-TaS$_{2}$ type structure in Ta$_{2}$S$_{2}$C.Comment: 12 pages, 13 figures; submitted to Phys. Rev.

Specific heat of stage-2 MnCl2_{2} graphite intercalation compound: co-existence of spin glass phase and incommensurate short-range spin order

Stage-2 MnCl$_{2}$ GIC magnetically behaves like a quasi 2D $XY$ antiferromagnet on the triangular lattice. It shows a typical spin glass behavior below the spin freezing temperature $T_{SG}$ (= 1.1 K). The AC magnetic susceptibility shows a peak at $T$ = $T_{SG}$ at $H$ = 0. This peak shifts to the low temperature side with increasing $H$, according to the de Almeida-Thouless critical line. We have undertaken an extensive study on the $T$ dependence of specific heat in the absence of an external field $H$ and in the presence of $H$ along the $c$ plane. The magnetic specific heat $C_{mag}$ at $H$ = 0 shows no anomaly at $T_{SG}$, but exhibits double broad peaks around 5 K and 41 K. The magnetic specific heat $C_{mag}$ at $H$ = 0 is described by $C_{mag} \propto (1/T^{2})\exp(-\Delta/T)$ with $\Delta = 1.41 \pm 0.03$ K, while $C_{mag}$ at $H$ = 10 kOe is proportional to $T$. The entropy due to the broad peak around 5 K is 1/3 of the total entropy. The residual entropy is 63 % of the total entropy because of highly frustrated nature of the system. The magnetic neutron scattering indicates that a short range spin order associated with the incommensurate wave vector $| {\bf Q}_{incomm}|$ ($= 0.522 \AA^{-1}$ at 0.45 K) appears below 5 K and remains unchanged down to 63 mK. The in-plane spin correlation length is only 18 $\AA$ at 0.45 K. The low temperature phase below $T_{SG}$ is a kind of reentrant spin glass phase where the spin glass phase coexists with a short range spin order associated with $| {\bf Q}_{incomm}|$.Comment: 14 pages, 20 figure

Magnetic-field induced superconductor-metal-insulator transitions in bismuth metal-graphite

Bismuth-metal graphite (MG) has a unique layered structure where Bi nanoparticles are encapsulated between adjacent sheets of nanographites. The superconductivity below $T_{c}$ (= 2.48 K) is due to Bi nanoparticles. The Curie-like susceptibility below 30 K is due to conduction electrons localized near zigzag edges of nanographites. A magnetic-field induced transition from metallic to semiconductor-like phase is observed in the in-plane resistivity $\rho_{a}$ around $H_{c}$ ($\approx$ 25 kOe) for both $H$$\perp$$c$ and $H$$\parallel$$c$ ($c$: c axis). A negative magnetoresistance in $\rho_{a}$ for $H$$\perp$$c$ (0$<H\leq$3.5 kOe) and a logarithmic divergence in $\rho_{a}$ with decreasing temperature for $H$$\parallel$$c$ ($H$ $>$ 40 kOe) suggest the occurrence of two-dimensional weak localization effect.Comment: 9 pages, 9 figures; published in Phys. Rev. B 66, 014533 (2002