text:
\section{\label{Intro} INTRODUCTION}

The rare earth pyrochlore oxides $R_2B_2$O$_7$ ($R$ is a trivalent rare earth and $B$ a tetravalent transition metal or Ge, Sn, Pb) containing magnetic networks of corner-sharing tetrahedra are well known for their exotic ground state (arising from the combined effect of crystal field anisotropy and dipolar and exchange interactions) and have been an interesting topic of research for the past few decades \cite{Gardner2010, Castelnovo2012, Gingras2014, Ramirez1999, Siddharthan1999,Hertog2000,Bramwell2001}. The research interests in these systems were invigorated after the discovery of spin-ice behavior in Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$ \cite{Ramirez1999, Siddharthan1999, Hertog2000, Bramwell2001}. The crystal field induced Ising anisotropic ground state (where the spins are forced to point along the local $\langle 111 \rangle $ direction) of these classical spin-ice materials along with ferromagnetic dipolar interactions give rise to a `two-in/two-out' configuration (the so called `ice rule') of rare earth moments \cite{Harris1997}. The two-in/two-out spin configuration of these classical spin-ices is equivalent to the arrangement of protons in water ice, thereby they also possess low-temperature Pauling residual entropy $(1/2) R \ln(3/2)$ \cite{Ramirez1999}. The fundamental excitations at the heart of spin-ice physics are the emergent magnetic monopoles arising from the creation and anihilation of `three-in/one-out' or `one-in/three-out' spin configurations \cite{Castelnovo2008}. The experimental observation of Dirac strings via neutron scattering have provided evidence of these magnetic monopoles \cite{Castelnovo2008, Morris2009, Fennell2009}. The monopole dynamics provides further insights to the emergent magnetic phases in spin-ice materials \cite{Castelnovo2008, Fennell2009, Morris2009, Jaubert2009, Bramwell2009}.

The titanate pyrochlores Tb$_2$Ti$_2$O$_7$ and Yb$_2$Ti$_2$O$_7$ also present interesting magnetic ground states. Tb$_2$Ti$_2$O$_7$ is a spin-liquid system that shows a cooperative critical paramagnetic ground state \cite{Gardner1999, Gardner2001, Molavian2007}. Yb$_2$Ti$_2$O$_7$ exhibits the characteristic features of quantum spin-ice (QSI) behavior \cite{Ross2011, Pan2016}. The ground state of Yb$_2$Ti$_2$O$_7$ is however very much sample dependent ranging from ferromagnetic order to disorder. A Higgs transition from a magnetic Coulomb liquid state to a ferromagnetic state (the Higgs phase of magnetic monopoles) has been suggested for ferromagnetically ordered Yb$_2$Ti$_2$O$_7$ \cite{Chang2012}. The quantum fluctuations play an important role in quantum spin-ice materials. While in a classical spin-ice system, because of strong magnetic anisotropy, only Ising interactions exist, in a quantum spin-ice system the magnetic anisotropy is not so strong and significant non-Ising terms exist in the Hamiltonian, therefore quantum fluctuations strongly dominate the spin dynamics in QSI systems. In order to have strong quantum fluctuations the dipolar interaction has to be small which one would naively expect to be the case with the materials having rare earth ions with smaller moments. This condition is fulfilled for Yb$^{3+}$, and because of the smaller dipolar interaction the ground state of Yb$_2$Ti$_2$O$_7$ is mainly dominated by exchange interactions \cite{Ross2011}.

Pr$^{3+}$ and Ce$^{3+}$ have much smaller magnetic moments compared to Dy$^{3+}$ and Ho$^{3+}$, therefore the pyrochlore systems containing Pr and Ce is expected to fullfill the condition of smaller dipolar interaction. As the dipolar interaction is proportional to the square of magnetic moment, the dipolar interaction in Pr-pyrochlores (say Pr$_2$Sn$_2$O$_7$)  will be only  $\sim 9\%$ of that in Dy$_2$Ti$_2$O$_7$. Indeed the Pr-pyrochlores Pr$_2$Sn$_2$O$_7$ \cite{Zhou2008} and Pr$_2$Zr$_2$O$_7$ \cite{Kimura2013}, and Ce-pyrochlore Ce$_2$Sn$_2$O$_7$ \cite{Sibille2015} have been found to show the characteristic features of a quantum spin-ice/spin-liquid system. Pr$_2$Ir$_2$O$_7$ on the other hand shows a metallic spin-liquid ground state \cite{Nakatsuji2006} that is situated close to a quantum critical point \cite{Tokiwa2014}. Of particular interest are the Pr-based pyrochlores which have a non-Kramers doublet as ground state. Lee {\it et al}.\ \cite{Lee2012} used a gauge mean-field theoretical approach to suggest that the QSI phase in a system with a non-Kramers doublet ground state [such as in Pr$_2B_2$O$_7$  ($B$ = Zr, Sn, Ir)]  is more stable than in a system with a Kramers doublet ground state.

The hafnate pyrochlore Pr$_2$Hf$_2$O$_7$ is another potential Pr-based system for the study of possible quantum spin-ice behavior. Pr$_2$Hf$_2$O$_7$ is reported to form in a cubic pyrochlore ($Fd\bar3m$) structure \cite{Karthik2012}. A recent muon spin relaxation study on Pr$_2$Hf$_2$O$_7$ by Foronda {\it et al}.\ \cite{Foronda2015} found muon-induced anisotropic local distortion for which they proposed a splitting of the non-Kramers doublet of Pr$^{3+}$. Extending our work on pyrohafnates \cite{Anand2015} here we report the physical properties of Pr$_2$Hf$_2$O$_7$ which indeed seems to be a potential candidate for quantum spin-ice behavior. Our investigations using various complementary techniques exclude long-range magnetic ordering down to 90~mK\@.  The ac magnetic susceptibility $\chi_{\rm ac}(T)$ shows a rather broad frequency dependent anomaly near 0.2~K at 160~Hz. The frequency dependent behavior of this anomaly at such a low temperature is a reminiscence of spin-ice dynamics. With a $J$ value of 4, Pr$^{3+}$ has a $(2J+1 = 9)$-fold degenerate ground state which under the action of crystal electric field (CEF) can split into a combination of singlets and doublets. In order to determine whether the CEF-split ground state of Pr$^{3+}$ is consistent with spin-ice physics we performed an inelastic neutron scattering measurement and found that Pr$_2$Hf$_2$O$_7$ indeed has a well isolated Ising anisotropic doublet ground state. The CEF ground state of Pr$_2$Hf$_2$O$_7$ thus meets the requirements for quantum spin-ice behavior. A recent work by Sibille {\it et al}. \cite{Sibille2016} also reports a quantum spin-ice behavior in Pr$_2$Hf$_2$O$_7$.

\section{\label{ExpDetails} EXPERIMENTAL DETAILS}

The polycrystalline Pr$_2$Hf$_2$O$_7$ sample was prepared at the Crystal Lab, Helmholtz-Zentrum Berlin (HZB) by solid-state reaction method using the high purity materials: Pr$_6$O$_{11}$ (99.99\%, Alfa Aesar)  and HfO$_2$ (99.95\%, Alfa Aesar). A single phase sample was obtained by firing the stoichiometric mixture of Pr$_6$O$_{11}$ and HfO$_2$ at 1300~$^\circ$C for 50~h followed by three more successive grindings, pelletizings and firings at 1500~$^\circ$C for 50~h\@. The polycrystalline La$_2$Hf$_2$O$_7$ sample was prepared using La$_2$O$_3$ (99.999\%, Alfa Aesar) and HfO$_2$  as detailed in Ref.~\cite{Anand2015}. The phase purity and quality of the samples were checked by room temperature powder x-ray diffraction using the Bruker-D8 laboratory-based x-ray diffractometer.

A large single crystal of Pr$_2$Hf$_2$O$_7$ was successfully grown by the Floating-zone technique in a four mirror type high-temperature optical floating zone furnace (Crystal Systems corp.\ FZ-T-12000-X-VII-VPO-PC) equipped with Xenon arc lamps, in flowing argon atmosphere. The quality of the single crystal was checked by Laue diffraction. The single crystal was also oriented by the Laue method and cut into small pieces for magnetic measurements.

The magnetic measurements down to 2~K and up to 14~T were performed using a Quantum Design superconducting quantum interference device vibrating sample magnetometer (SQUID-VSM) and VSM option of a Quantum Design physical properties measurement system (PPMS) at Mag Lab, HZB. The heat capacity measurements down to 1.8~K were performed by the adiabatic-relaxation technique using the PPMS at Mag Lab, HZB.  The ac susceptibility measurements down to 90~mK were performed  at Helmholtz-Zentrum Dresden-Rossendorf using compensated coil-pair susceptometer built in a He-3/4 dilution refrigerator using a SR830 lock-in amplifier. We also made an attempt to measure the resistivity but the resistance was found to be beyond the measurement range of PPMS indicating an insulating behavior. The resistance measurement using a multimeter further confirmed the insulating ground state of Pr$_2$Hf$_2$O$_7$.

The high-resolution synchrotron x-ray diffraction measurements were performed on the MS-beamline \cite{Willmott2013} at Paul Scherrer Institute (PSI), Switzerland. The sample was very finely ground and filled into a thin capillary (0.3~mm in diameter).  In order to minimize the profile shape dependence on capillary diameter and reduce the effect of preferred orientation the sample was rotated continuously. X-rays of energy 25~keV were used for the measurement. The exact wavelength of the x-rays (0.4957 {\AA}) and the instrument profile parameters were determined by measurements on the standard LaB$_6$ powder (NIST) under the identical experimental condition.

The inelastic neutron scattering measurements were performed on the high neutron flux beamline MERLIN at the ISIS facility of the Rutherford Appleton Laboratory, Didcot, U.K. \cite{Bewley2006, Bewley2009}. About 20~g powder samples each of Pr$_2$Hf$_2$O$_7$ and La$_2$Hf$_2$O$_7$ were used for the INS measurements. The powder samples were mounted inside a thin-walled aluminum can using a thin wrapper of aluminum foil in a cylindrical geometry with diameter approximately 40~mm and height 40~mm, which was then mounted into a closed-cycle refrigerator using \mbox{He-4} exchange gas. The measurements were carried out at 10~K, 100~K and 300~K using neutrons of incident energies $E_i = 18.9$~meV, 40.1~meV, 86.3~meV, 136.0~meV and 195.0~meV.

\section{\label{Structure} Crystallography}

\begin{figure}
\includegraphics[width=\columnwidth, keepaspectratio]{Fig01.eps}
\caption {(Color online) Synchrotron powder x-ray diffraction pattern of polycrystalline Pr$_2$Hf$_2$O$_7$ recorded at room temperature. The solid line through the experimental points is the Rietveld refinement profile calculated for the ${\rm Eu_2Zr_2O_7}$-type face-centered cubic (space group $Fd\bar{3}m$) pyrochlore structure. The short vertical bars mark the Bragg peaks positions and the lowermost curve represents the difference between the experimental and calculated intensities. Inset: An expanded scale view showing the details of the refinement in a small angle range at high $2\theta$.}
\label{fig:XRD}
\end{figure}

The room temperature high-resolution synchrotron powder XRD pattern of polycrystalline Pr$_2$Hf$_2$O$_7$ is shown in Fig.~\ref{fig:XRD} along with the structural Rietveld refinement profile. For Rietveld refinement we used the software FullProf \cite{Rodriguez1993}. The refinement revealed no impurity phase and confirmed the reported ${\rm Eu_2Zr_2O_7}$-type face-centered cubic  (space group $Fd\bar{3}m$) pyrochlore structure. In this structure both Pr and Hf form individual three-dimensional networks of corner-shared tetrahedra. The Wyckoff positions (atomic coordinates) of Pr, Hf, O1 and O2 are 16d (1/2,1/2,1/2), 16c (0,0,0), 48f ($x_{\rm O1}$,1/8,1/8) and 8b (3/8,3/8,3/8), respectively. The lattice parameter $a = 10.6728(1)$~\AA\ and the $x$-coordinate of O1 $x_{\rm O1} = 0.3351(4)$ obtained from the refinement agree very well with the reported values \cite{Karthik2012}. The agreement factors for the refinement are $\chi^2 = 10.1$, $R_{\rm p} = 2.91\%$ and $R_{\rm wp} = 3.66\%$. We also checked for possible Pr/Hf site mixing and refined the occupancies of atoms which did not make any noticeable improvement in the fit or agreement factors. From our synchrotron data we anticipate that Pr/Hf site mixing and/or oxygen deficiency, if present, are less than 0.5\%. This suggests a well-ordered pyrochlore structure for Pr$_2$Hf$_2$O$_7$ consistent with the previous report  \cite{Karthik2012} and with the prediction based on the ratio of the cation radii $r_{\rm Pr}/r_{\rm Hf} \approx 1.59 $ which is well within the range of 1.36--1.71 required for a stable ordered pyrochlore phase  \cite{Gardner2010}.

\section{\label{Sec:ChiMH} DC Magnetic Susceptibility and Magnetization}

\begin{figure}
\includegraphics[width=\columnwidth, keepaspectratio]{Fig02.eps}
\caption{(Color online) Zero-field-cooled magnetic susceptibility $\chi$ of polycrystalline Pr$_2$Hf$_2$O$_7$ plotted as inverse magnetic susceptibility $\chi^{-1}$ as a function of temperature $T$ for $2~{\rm K} \leq T \leq 300$~K measured in magnetic field $H= 1.0$~T\@. The solid curve is the crystal field susceptibility corresponding to the crystal field parameters obtained from the analysis of inelastic neutron scattering data. Upper inset: Low-$T$ $\chi(T)$ for $H= 0.1$~T and 1.0~T and $2~{\rm K} \leq T \leq 25$~K\@. Lower inset: $\chi^{-1}(T)$ for $H=0.1$~T and $2~{\rm K} \le T \leq 25$~K\@. The solid red line is the fit of the $\chi^{-1}(T)$ data by the modified Curie-Weiss law fitted over $12~{\rm K} \leq T \leq 25$~K and the dashed line is an extrapolation.}
\label{fig:MT}
\end{figure}

The zero-field-cooled (ZFC) dc magnetic susceptibility $\chi(T)$ data of polycrystalline Pr$_2$Hf$_2$O$_7$ are shown in Fig.~\ref{fig:MT}. It is clear from Fig.~\ref{fig:MT} that at $T \geq 2$~K the $\chi(T)$ data show no anomaly related to magnetic phase transition. As can be seen from the upper inset of Fig.~\ref{fig:MT}, the magnitude of $\chi$ at low-$T$ is rather large. The ZFC and field-cooled (FC) $\chi(T)$ data (not shown) do not show any thermal hysteresis above 2~K\@. The $\chi(T)$ data follow modified Curie-Weiss behavior, $\chi(T) =  \chi_0 + C/(T-\theta_{\rm p})$ (lower inset of Fig.~\ref{fig:MT}). A fit of ZFC $\chi^{-1}(T)$ data (measured in magnetic field $H=0.1$~T) in $12~{\rm K} \leq T \leq 25$~K gives $\chi_0 = 5.02(6) \times 10^{-3}$ emu/mol\,Pr, $C = 0.81(1)$~emu\,K/mol\,Pr and $\theta_{\rm p} = -0.01(2)$~K\@. Upon correcting the $\chi(T)$ data for demagnetization effects (approximating the sample by a sphere) we obtain $\chi_0 = 5.02(6) \times 10^{-3}$ emu/mol\,Pr, $C = 0.81(1)$~emu\,K/mol\,Pr and $\theta_{\rm p} = +0.06(2)$~K\@. The positive $\theta_{\rm p}$ suggests the effective interaction in Pr$_2$Hf$_2$O$_7$ to be ferromagnetic in nature. The $C$ value yields an effective moment of $\mu_{\rm eff} \approx 2.54\, \mu_{\rm B}$/Pr which is significantly lower than the expected paramagnetic state value of $\mu_{\rm eff} = g_J\sqrt{J(J+1)} = 3.58 \, \mu_{\rm B}$/Pr for free Pr$^{3+}$ ions ($g_J = 4/5$ and $J = 4$). The reduced value of $\mu_{\rm eff}$ reflects the Ising anisotropic nature of magnetic ground state. A fit of the $H=1.0$~T $\chi^{-1}(T)$ data in $50~{\rm K} \leq T \leq 300$~K yields $\mu_{\rm eff}  \approx 2.91 \, \mu_{\rm B}$/Pr which is also smaller than the free ion value and can be attributed to crystal field effect.

\begin{figure}
\includegraphics[width=\columnwidth, keepaspectratio]{Fig03.eps}
\caption{(Color online) Isothermal magnetization $M$ of polycrystalline Pr$_2$Hf$_2$O$_7$ as a function of applied magnetic field $H$ for $0 \leq H \leq 7$~T measured at the indicated temperatures. The solid curve is the fit of 2~K $M(H)$ data by Eq.~(\ref{MH-Ising}) with an effective longitudinal $g$-factor $g_{\parallel}= 4.78(1)$.}
\label{fig:MH}
\end{figure}

The isothermal magnetization $M(H)$ data of polycrystalline Pr$_2$Hf$_2$O$_7$ at five different temperatures between 2~K and 50~K are shown in Fig.~\ref{fig:MH}. For $T\geq 20$~K the $M(H)$ isotherms are almost linear in $H$ and become nonlinear at $T\leq 10$~K\@. The nonlinearity can be attributed to the saturation behavior of magnetization which is best reflected in $M(H)$ curve at 2~K\@. At 2~K, the near saturation value of magnetization is $M \approx 1.15\, \mu_{\rm B}$/Pr at 5~T which is  only about 36\% of the theoretical saturation magnetization $M_{\rm sat} = g_J J\,\mu_{\rm B} = 3.2\,\mu_{\rm B}$/Pr for free Pr$^{3+}$ ions. However, the observed $M$ is consistent with the local $\langle 111 \rangle$ Ising anisotropic behavior. We fitted the $M(H)$ data by \cite{Bramwell2000, Xu2015}
\begin{equation}
\langle M \rangle = \frac{(k_{\rm B} T)^2}{g_{\parallel}\mu_{\rm B} H^2 S} \int_0^{g_{\parallel}\mu_{\rm B} H S/k_{\rm B} T} x \tanh(x) \,dx
\label{MH-Ising}
\end{equation}
that describes the $H$ dependence of powder-averaged $M$ in the paramagnetic state of an Ising pyrochlore within effective spin $S = 1/2$ model. Here $g_{\parallel}$ is the longitudinal $g$-factor and the transverse $g$-factor $g_\perp$ is assumed to be zero. The fit of $M(H)$ data at 2~K (shown by solid red line in Fig.~\ref{fig:MH}) gives $g_{\parallel} = 4.78(1)$, accordingly the paramagnetic state moment is expected to be $m = g_{\parallel} S\,\mu_{\rm B} \approx 2.4\,\mu_{\rm B}$/Pr which is very close to the $\mu_{\rm eff} \approx 2.54\, \mu_{\rm B}$/Pr obtained above from $\chi(T)$.  Further it is seen that while Eq.~(\ref{MH-Ising}) predicts a saturation tendency at high $H$ (see the fit in Fig.~\ref{fig:MH}), the $M(H)$ data show a weak increase, this departure is clearly noticed at $H> 6$~T\@. Such a behavior of $M(H)$ hints for the presence of spin fluctuations/non-Ising contribution.

The nearest neighbor dipole-dipole interaction $D_{\rm nn}$ corresponding to our Ising ground state moment $\mu_{\rm eff} = 2.54\, \mu_{\rm B}$/Pr can be estimated using the relation $D_{\rm nn} = ({5}/{3})({\mu_0}/{4\pi}) {\mu_{\rm eff}^2}/{r_{\rm nn}^3}$ \cite{Bramwell2001,Hertog2000}, $\mu_0$ being the magnetic permeability of free space and $r_{\rm nn }= (a/4)\surd 2$ the nearest neighbor distance. For Pr$_2$Hf$_2$O$_7$ the lattice parameter $a = 10.6389(1)$~\AA, therefore $D_{\rm nn} \approx 0.12$~K\@. An estimate of effective magnetic interaction $J_{\rm eff}$ can be obtained from the value of Weiss temperature, $\theta_{\rm p} = z J_{\rm eff} S(S+1)/3k_{B}$ ($z=6$ is the number of the nearest neighbor) which for $\theta_{\rm p} = +0.06$~K and $S=1/2$ (effective spin) yields $J_{\rm eff} = +0.04$~K (in our notation a positive sign indicates ferromagnetic interaction and a negative sign the antiferromagnetic interaction). The effective interaction $J_{\rm eff} = J_{\rm nn} + D_{\rm nn}$ where $J_{\rm nn}$ is the nearest neighbor exchange interaction which for $J_{\rm eff} = +0.04$~K and $D_{\rm nn} \approx +0.12$~K would imply $J_{\rm nn} \approx -0.08$~K\@. As expected, the exchange interaction is thus antiferromagnetic in nature. A more realistic estimate of $J_{\rm nn}$ can be obtained from heat capacity $C_{\rm p}(T)$. The height or the temperature of the peak of $C_{\rm p}(T)$ has been found to give very reasonable estimate of $J_{\rm nn}$ \cite{Gardner2010,Hertog2000,Melko2004} which does not suffer from the issue of choice of fitting range of temperature that causes a little variation in the value of $\theta_{\rm p}$. Sibille {\it et al}. \cite{Sibille2016} reported a value of $C_{\rm p} \approx 3.2$~J/mol\,K near the peak around 1.8~K\@.  The $C_{\rm peak} \approx 3.2$~J/mol\,K corresponds to $J_{\rm nn}/D_{\rm nn} \approx 0.7$ in the phase diagram of dipolar spin ice  \cite{Hertog2000} which for $D_{\rm nn} \approx +0.12$~K yields $J_{\rm nn} \approx -0.08$~K\@. We thus see that both $\theta_{\rm p} $ and $C_{\rm peak}$ give a very consistent estimate of the antiferromagnetic exchange interaction in Pr$_2$Hf$_2$O$_7$.

\section{\label{Sec:ACsus} AC Magnetic Susceptibility}

\begin{figure*}
\includegraphics[width=6.5in, keepaspectratio]{Fig04.eps}
\caption {(Color online) (a) Real  $\chi'$ and imaginary $\chi''$  parts of zero-field-cooled ac magnetic susceptibility $\chi_{\rm ac}$ of polycrystalline Pr$_2$Hf$_2$O$_7$ as a function of temperature $T$ for $0.09~{\rm K} \leq T \leq 0.5$~K measured at indicated frequencies and ac magnetic fields (in zero dc field). (b) Single-spin relaxation time $\tau_{\rm spin}(T) = \chi''(T)/\omega  \chi'(T)$ of Pr$_2$Hf$_2$O$_7$. Also shown is the $\tau_{\rm spin} (T)$ for Ho$_2$Ti$_2$O$_7$ \cite{Thomas}. The open circles are the data points of Pr$_2$Hf$_2$O$_7$ normalized and scaled to the spin-freezing temperature of Ho$_2$Ti$_2$O$_7$. (c) Sample temperature $T_{\rm sample}$ as a function of time $t$ showing the thermal relaxation in polycrystalline Pr$_2$Hf$_2$O$_7$. The orange solid  lines are the fits of the $T_{\rm sample}(t)$ data. (d) Thermal relaxation time $\tau_{\rm sample}(T)$ obtained from the fitting of $T_{\rm sample}(t)$ in (c).  }
\label{fig:Chiac}
\end{figure*}

The ac magnetic susceptibility $\chi_{\rm ac}$ of polycrystalline Pr$_2$Hf$_2$O$_7$ measured at frequencies 16~Hz, 160~Hz and 1.6~kHz is shown in Fig.~\ref{fig:Chiac}(a). Both real $\chi'$ and imaginary $\chi''$ parts of $\chi_{\rm ac}(T)$ show broad peaks. The peak position depends on the frequency, with increasing frequency the peak position shifts to higher temperatures. At 16~Hz $\chi'(T)$ shows a peak near 0.16~K which shifts to 0.18 K at 160 Hz and 0.28~K at 1.6~kHz. The frequency dependent ac susceptibility clearly indicates very slow spin dynamics and is reminiscent of spin-ice behavior. This kind of frequency dependent $\chi_{\rm ac}(T)$ associated with spin-freezing has also been observed in the classical spin-ice systems Dy$_2$Ti$_2$O$_7$  \cite{Matsuhira2001} and Ho$_2$Ti$_2$O$_7$ \cite{Matsuhira2000} and dynamic spin-ice systems Pr$_2$Sn$_2$O$_7$ \cite{Matsuhira2004} and Pr$_2$Zr$_2$O$_7$ \cite{Kimura2013}. Sibille {\it et al}.\ [29]  also found a similar frequency dependent peak in ac susceptibility of Pr$_2$Hf$_2$O$_7$. Through the $\chi_{\rm ac}$ measurements at several frequencies they suggested cooperative spin-dynamics in this compound.

We have determined the single-spin relaxation time $\tau_{\rm spin}$ according to the Casimir-du Pr\'e relation in the paramagnetic limit \cite{Casimir1938}, $\tau_{\rm spin} = \chi''/\omega  \chi'$, the $T$ dependence of which is shown in Fig.~\ref{fig:Chiac}(b). For comparison, $\tau_{\rm spin} (T)$ of Ho$_2$Ti$_2$O$_7$ \cite{Thomas} is also shown in Fig.~\ref{fig:Chiac}(b). The single-spin relaxation time is a sensitive and direct measure of the spin dynamics of magnetic materials, in particular in the vicinity of the spin-freezing temperature. The $\tau_{\rm spin} (T)$ of Pr$^{3+}$ magnetic moments of Pr$_2$Hf$_2$O$_7$ scales pretty well with that of Ho$^{3+}$ in Ho$_2$Ti$_2$O$_7$ by multiplying with the ratio of their spin-freezing temperatures. We thus see that $\tau_{\rm spin} (T)$ of Pr$_2$Hf$_2$O$_7$ follows qualitatively and quantitatively the temperature dependent single-spin relaxation time observed for the spin-ice compound Ho$_2$Ti$_2$O$_7$.

We also see a distinct thermal relaxation behavior in Pr$_2$Hf$_2$O$_7$. However, the ac susceptibility of the sample has a reproducible temperature dependence and serves as an internal sample thermometer. Susceptibility data have been taken during stepwise heating up and cooling of the mixing chamber of the used He-3/4 fridge over long periods. At very low temperatures, the temperature has been kept constant for days [relaxed susceptibility-temperature data points are shown in Fig.~\ref{fig:Chiac}(a)].

The sample temperature $T_{\rm sample}$ deduced from the $\chi_{\rm ac}$ data is shown in Fig.~\ref{fig:Chiac}(c) as a function of time $t$. The $T_{\rm sample}(t)$ represents the thermal relaxation in polycrystalline Pr$_2$Hf$_2$O$_7$. The $T_{\rm sample}(t)$ data in Fig.~\ref{fig:Chiac}(c) show a very slow thermal relaxation in Pr$_2$Hf$_2$O$_7$. We fit the $T_{\rm sample}(t)$ data by $T_{\rm sample}(t) = T_0 + \Delta T \exp(-t/\tau_{\rm sample})$, the fits are shown by orange solid  lines in Fig.~\ref{fig:Chiac}(c). The mean thermal relaxation time $\tau_{\rm sample}(T)$ obtained from the fit is shown in Fig.~\ref{fig:Chiac}(d). The $\tau_{\rm sample}$ is very large and increases very rapidly as $T$ decreases, following a power law behavior, $\tau_{\rm sample}(T) = R_{\rm thermal}(T) C_{\rm sample}(T) \sim 1/T^\alpha$ with $\alpha=4.5$. The observed thermal relaxation time of the sample exceeds the typical time windows of standard heat-capacity measurements. As the thermal coupling resistance $R_{\rm thermal}(T) $ is expected to follow a $1/T^3$ power law due to phononic transport in the low-temperature limit, the sample relaxation time of Pr$_2$Hf$_2$O$_7$ allows for an estimate of the temperature dependence of the heat capacity, $C_{\rm sample}(T) \sim 1/ T^{1.5}$ in the investigated temperature interval (0.1--0.25~K). This increase of heat capacity with decreasing temperature at low-$T$ indicates that, in contrast to observations in classical spin-ice materials, the spin entropy drops in the temperature range of spin freezing. In consequence, the ice entropy might not be conserved in Pr$_2$Hf$_2$O$_7$. We interpret this observation as a hint for the occurence of quantum fluctuations in the low-temperature limit.

\section{\label{Sec:HC}Heat Capacity}

The $C_{\rm p}(T)$ data of polycrystalline Pr$_2$Hf$_2$O$_7$ are shown in Fig.~\ref{fig:HC} for 1.8~K~$\leq T \leq$~300~K\@. As can be seen from Fig.~\ref{fig:HC} the $C_{\rm p}(T)$ data do not show any anomaly at $T\geq1.8$~K, though an upturn feature is seen at $T \leq 10$~K which is shown in detail in the upper inset of Fig.~\ref{fig:HC}. The magnetic contribution to heat capacity $C_{\rm mag}(T)$ estimated after subtracting the lattice contribution (equivalent to formula mass and unit cell volume corrected $C_{\rm p}(T)$ of La$_2$Hf$_2$O$_7$) is shown in the lower inset of Fig.~\ref{fig:HC}. A broad Schottky type peak near 50~K is seen in $C_{\rm mag}(T)$ data. The $T$ dependence of $C_{\rm mag}$ is described by the crystal field. The crystal field contribution to heat capacity $C_{\rm CEF}(T)$ calculated according to the CEF level scheme deduced from the analysis of INS data (Sec.~\ref{INS}), shown by solid red curve in the lower inset of Fig.~\ref{fig:HC}, agrees well with the $C_{\rm mag}(T)$.

\begin{figure}
\includegraphics[width=\columnwidth, keepaspectratio]{Fig05.eps}
\caption{\label{fig:HC} (Color online) (a) Heat capacity $C_{\rm p}$ of polycrystalline Pr$_2$Hf$_2$O$_7$ as a function of temperature $T$ for 1.8~K~$\leq T \leq$~300~K measured in zero field. The solid curve is the fit by Debye+Einstein models of lattice heat capacity plus crystal field contribution as deduced from inelastic neutron scattering (INS) data. Upper inset: Expanded view of \mbox{low-$T$} $C_{\rm p}(T)$ data over $1.8~{\rm K} \leq T \leq 15$~K\@. Lower inset: Magnetic contribution to heat capacity $C_{\rm mag}(T)$ of Pr$_2$Hf$_2$O$_7$. The solid curve represents the crystal-field contribution to heat capacity according to the CEF level scheme deduced from the INS data.}
\end{figure}

The room temperature value of  $C_{\rm p} \approx 228$ J/mol\,K is substantially lower than the expected high-$T$ limit Dulong-Petit value, reflecting the large value of Debye temperature $\Theta_{\rm D}$. We estimate $\Theta_{\rm D}$ by fitting the $C_{\rm p}(T)$ data by a combination of the Debye and Einstein models of lattice heat capacity added to the fixed crystal field contribution $C_{\rm CEF}(T)$. The fit of $C_{\rm p}(T)$ data by CEF+Debye+Einstein models \cite{Anand2015a} is shown by the solid red curve in Fig.~\ref{fig:HC} which gives $\Theta_{\rm D} = 790(7)$~K and Einstein temperature $\Theta_{\rm E} = 158(2)$~K with 66\% weight to Debye term and 34\% to Einstein term.  The obtained $\Theta_{\rm D}$ is similar to that of the related pyrohafnates La$_2$Hf$_2$O$_7$ ($\Theta_{\rm D} = 792(5)$~K) and Nd$_2$Hf$_2$O$_7$ ($\Theta_{\rm D} = 785(6)$~K) \cite{Anand2015}.

\begin{figure*}
\includegraphics[width=\textwidth, keepaspectratio]{Fig06.eps}
\caption {(color online) Inelastic neutron scattering response, a color-coded map of the intensity, energy transfer ($E$) versus momentum transfer ($Q$) for Pr$_2$Hf$_2$O$_7$ (upper panel)  and La$_2$Hf$_2$O$_7$ (lower panel) measured at 10~K with the incident energy $E_i=40$~meV, 86~meV and 136~meV. The arrow mark the position of CEF excitations in Pr$_2$Hf$_2$O$_7$. The corresponding energy positions in La$_2$Hf$_2$O$_7$ are also marked. }
\label{fig:INS1}
\end{figure*}

\section{\label{INS} Inelastic Neutron Scattering and Crystal Field Excitations}

The bulk properties measurement discussed above, particularly the ac susceptibility data hint for spin-ice like behavior. Therefore in order to check if the ground state is consistent with the physics of spin-ice which requires a doublet as ground state we determine the crystal field states using inelastic neutron scattering. Figure~\ref{fig:INS1} shows the color-coded contour maps of the INS response from powder Pr$_2$Hf$_2$O$_7$ and La$_2$Hf$_2$O$_7$ showing energy transfer $E$ versus wave vector $Q$ for neutrons of incident energy $E_i=40.1$~meV, 86.3~meV and 136.0~meV at 10~K\@. A comparison of the contour maps of Pr$_2$Hf$_2$O$_7$ and La$_2$Hf$_2$O$_7$ clearly show five dispersionless excitations in Pr$_2$Hf$_2$O$_7$ at around 9.1~meV, 56.5~meV, 82.2~meV, 94.5~meV and 109.5~meV at low-$Q$. Since La$_2$Hf$_2$O$_7$ does not show strong phonon scattering at low-$Q$, these low-$Q$ excitations of Pr$_2$Hf$_2$O$_7$ seems to have magnetic origin due to the crystal field excitations from  Pr$^{3+}$.

With a $J$ value of 4, the ground state (GS) of Pr$^{3+}$ possesses nine-fold degeneracy, when this $^3H_4$ GS multiplet is subject to a CEF interaction with $D_{3d}$ symmetry (point symmetry $\bar{3}m$) due to the pyrochlore structure, it splits into three doublets and three singlets, designated by the symmetry decompositions 3$\Gamma_3^+ + 2 \Gamma_1^+ + \Gamma_2^+$ in the irreducible representations of $D_{3d}$. Accordingly there ought to be five CEF excitations from the GS multiplet which we clearly see in the INS spectra at 10~K\@. For a $D_{3d}$ symmetry with $z$ axis along the local cubic $\langle$111$\rangle$ direction, the CEF Hamiltonian is given by
\begin{equation}
\begin{split}
H_{\rm{CEF}}= & B_0^2C_0^2+B_0^4C_0^4+B_3^4(C_{-3}^4+C_3^4)\\
             & +B_0^6C_0^6+B_3^6(C_{-3}^6+C_3^6)+B_6^6(C_{-6}^6+C_6^6),
\end{split}
\end{equation}
where $B_q^k$ are the crystal field parameters and $C_q^k$ the tensor operators \cite{cfbook}.

\begin{figure}
\includegraphics[width=\columnwidth, keepaspectratio]{Fig07.eps}
\caption {(Color online) $Q$-integrated inelastic magnetic scattering intensity $S_{\rm M}(Q,\omega)$ versus energy transfer $E$ of Pr$_2$Hf$_2$O$_7$ integrated over (a) momentum $Q$ range [2.5--3]~{\AA $^{-1}$} for $E_i=18.9$~meV, and (b) $Q$ range [4--5]~{\AA $^{-1}$} for $E_i=136.0$~meV, showing all five transitions within the ground state multiplet $^3H_4$ of Pr$^{3+}$ at 10~K\@. The solid lines are the fits of the data according to the crystal field model discussed in the text.}
\label{fig:INS2}
\end{figure}

The $Q$-integrated one-dimensional energy cuts of the INS response from the low-$Q$ region (where the phonon contributions are relatively weaker) were made to obtain the scattering intensity $S(Q,\omega)$. The magnetic scattering $S_{\rm M}(Q,\omega)$ from Pr$_2$Hf$_2$O$_7$ was obtained by subtracting the phonon contribution using the INS data of nonmagnetic reference La$_2$Hf$_2$O$_7$. The plots of $S_{\rm M}(Q,\omega)$ versus $E$ are shown in Fig.~\ref{fig:INS2} where $S_{\rm M}(Q,\omega)= S(Q,\omega)_{\rm Pr_2Hf_2O_7} - \alpha\, S(Q,\omega)_{\rm La_2Hf_2O_7} $ with $\alpha=0.8$ being the ratio of the neutron scattering cross sections of Pr$_2$Hf$_2$O$_7$ and La$_2$Hf$_2$O$_7$. The five CEF excitations near 9.1~meV, 56.5~meV, 82.2~meV, 94.5~meV and 109.5~meV are clearly visible in the $S_{\rm M}(Q,\omega)$ plots in Fig.~\ref{fig:INS2}.

\begin{figure}
\includegraphics[width=\columnwidth, keepaspectratio]{Fig08.eps}
\caption {(Color online) (a) $\phi $-integrated inelastic scattering intensity $S(\langle \phi \rangle,\omega)$ versus energy transfer $E$ of Pr$_2$Hf$_2$O$_7$ and La$_2$Hf$_2$O$_7$  for $E_i=136.0$~meV integrated over scattering angle  $9^\circ \leq \phi \leq 11^\circ$ together with the scaled phonon backgound $S(\langle \phi \rangle,\omega)$ from $\langle \phi \rangle$ range $119^\circ \leq \phi \leq 121^\circ$ of Pr$_2$Hf$_2$O$_7$. (b) Magnetic scattering intensity $S_{\rm M}(\langle \phi \rangle,\omega)$ versus $E$ of Pr$_2$Hf$_2$O$_7$ for $\langle \phi \rangle$ range $9^\circ \leq \phi \leq 11^\circ$, showing four transitions within the ground state multiplet $^3H_4$ of Pr$^{3+}$ at 10~K\@. The solid line is the fit of the data according to the crystal field model discussed in text. The apparent peak near 45~meV is an artifact due to phonon.}
\label{fig:INS3}
\end{figure}

The $S(Q,\omega)$ of La$_2$Hf$_2$O$_7$ does not account well for the phonon background of Pr$_2$Hf$_2$O$_7$, particularly at low $E$ the phonon contributions to the INS response of the two compounds are quite different. This aspect of the INS data is evident in the $\phi$-integrated energy cuts $S(\langle \phi \rangle,\omega)$ shown in Fig.~\ref{fig:INS3}(a). For a better estimate of the phonon background we adopted the approach suggested by Boothroyd {\it et al}.\ \cite{Boothroyd2003}. Accordingly the low-angle phonon background is estimated from the high-angle scattering of Pr$_2$Hf$_2$O$_7$ itself where the magnetic scattering is negligibly small. For this the high-angle Pr$_2$Hf$_2$O$_7$ spectrum was scaled by a factor equal to the ratio of the high- to low-angle La$_2$Hf$_2$O$_7$ spectra. The scaled phonon background estimated this way from the Pr$_2$Hf$_2$O$_7$ data in $119^\circ \leq \phi \leq 121^\circ$ is shown in Fig.~\ref{fig:INS3}(a). A substantial difference between the phonon background from the La$_2$Hf$_2$O$_7$ spectrum and scaled high-angle Pr$_2$Hf$_2$O$_7$ spectrum is obvious from Fig.~\ref{fig:INS3}(a). The $\phi$-integrated magnetic scattering $S_{\rm M}(\langle \phi \rangle,\omega)$ estimated using this scaled background is shown in Fig.~\ref{fig:INS3}(b). The corresponding $Q$ is obtained using the relation $\hbar^2 Q^2/2m_{\rm n} = E_i + E_f - 2(E_iE_f)^{1/2} \cos\phi$, where $E_f = E_i -E$ and $m_{\rm n}$ is the rest mass of neutron.

In order to obtain quantitative information of the CEF states we analyzed the magnetic INS data using the software SPECTRE \cite{SPECTRE} which allowed us to use the intermediate-coupling free ion basis states for diagonalizing the $H_{\rm CEF}$. We employed the complete set of 91 intermediate coupling basis states following the approach used for the related Pr-based system Pr$_2$Sn$_2$O$_7$ \cite{Princep2013}. For least-square fitting of the observed INS excitations (energies and relative intensities) the CEF parameters of Pr$_2$Sn$_2$O$_7$ were used as the starting parameters. The results of our analysis of INS data are summarized in Table~\ref{tab:cf}. The fits of INS data are shown in Figs.~\ref{fig:INS2}(a), \ref{fig:INS2}(b) and \ref{fig:INS3}(b). We used a Lorentzian shape peak function for fitting the magnetic INS specta. Further details of our analysis can be found in our recent paper on Nd$_2$Zr$_2$O$_7$ \cite{Xu2015} where we employed a similar approach for analyzing the INS data by the crystal field model.

\begin{table}
\caption{\label{tab:cf} Observed  and calculated  crystal-field transition energies ($E$) and integrated intensities ($I$) within the ground state multiplet $^3H_4$ of Pr$_2$Hf$_2$O$_7$ at 10~K\@. The intensities are relative to the highest observed peak. The best-fit crystal field parameters $B_q^k$  are:  $B^2_0 = 33.8$~meV, $B^4_0 = 426.0 $~meV, $B^4_3 = 192.7 $~meV, $B^6_0 = 165.3 $~meV, $B^6_3 = -111.8 $~meV, and $B^6_6 = 178.6$~meV. The goodness-of-fit parameter $\chi^2=3.12$. }
\begin{ruledtabular}
\begin{tabular}{ccccc}
Levels         & $E_{obs}$ (meV)& $E_{cal}$ (meV)&$I_{obs}$&$I_{cal}$\\
\hline
$\Gamma_3^+$    &  0            & 0        &            & \\
$\Gamma_1^+$    & 9.1(1)      & 8.82   &   -          & - \\
$\Gamma_3^+$    & 56.5(2)    & 56.63  & 0.42(10)     & 0.55\\
$\Gamma_1^+$    & 82.2(3)    & 82.11  & 0.39(8) &0.47\\
$\Gamma_3^+$    & 94.5(3)    & 94.56  & 1.0      &1.0\\
$\Gamma_2^+$    & 109.5(4)  & 109.46 & 0.33(6) & 0.38\\
\end{tabular}
\end{ruledtabular}
\end{table}

The CEF parameters $B_q^k$ obtained from the analysis are: $B^2_0 = 33.8$~meV, $B^4_0 = 426.0 $~meV, $B^4_3 = 192.7 $~meV, $B^6_0 = 165.3 $~meV, $B^6_3 = -111.8 $~meV, and $B^6_6 = 178.6$~meV. The CEF analysis of INS data reveal the ground state to be a doublet, first excited state a singlet at 8.82~meV, second excited state a doublet at 56.63~meV, third excited state a singlet at 82.11~meV,  fourth excited state a doublet at 94.56~meV and fifth excited state a singlet at 109.46~meV. The CEF level scheme of Pr$_2$Hf$_2$O$_7$ is found to be very similar to that of Pr$_2$Sn$_2$O$_7$ \cite{Princep2013} and Pr$_2$Zr$_2$O$_7$ \cite{Kimura2013}.

The wavefunction of the ground state non-Kramers doublet is found to be
\begin{subequations}
\begin{equation}
\begin{split}
\Gamma_{3}^+  = & \ 0.823|^3H_{4},\pm 4 \rangle \pm 0.513|^3H_{4}, \pm 1 \rangle - 0.136|^3H_{4},\pm2 \rangle \\
                 &       + 0.139|^1G_{4}, \pm 4 \rangle \pm 0.087|^1G_{4}, \pm 1 \rangle   \\
                &      \mp 0.058|^3H_{5},\pm 4 \rangle    \mp 0.050|^3H_{5},\pm 2 \rangle \\
\end{split}
\end{equation}
and that of the first excited singlet
\begin{equation}
\begin{split}
\Gamma_1^+   =\  & 0.173|^3H_{4}, 3 \rangle + 0.950|^3H_{4}, 0 \rangle - 0.173|^3H_{4}, -3 \rangle \\
               &  + 0.162|^1G_{4}, 0 \rangle + 0.038|^3F_2, 0 \rangle.
\end{split}
\end{equation}
\label{eq:wavefunctions}
\end{subequations}
A significant mixing of $|^3H_{4},\pm 4 \rangle$ with $|^3H_{4},m_J\neq\pm4 \rangle$ terms as well as with $^1G_{4}$ and $^3H_{5}$ is found in the ground state. Based on the CEF ground state wavefunction we estimate $g_\parallel = 4.80$ and $g_\perp =0$ which are consistent with the values deduced from the magnetic measurements. The ground state wave function gives the magnetic moment of $2.4~\, \mu_{\rm B} $/Pr which is close to the effective moment obtained from the Curie-Weiss analysis of magnetic susceptibility.

The crystal field parameters obtained from the analysis of INS data are able to reproduce the powder dc susceptibility as well as the magnetic contribution to the heat capacity. The magnetic susceptibility calculated from these CEF parameters is shown in Fig.~\ref{fig:MT}, which show an excellent agreement with the experimental data and thus supports the obtained CEF states and parameters. The anisotropic CEF suceptibility yields $\chi_\parallel/\chi_\perp \sim 45 $ at 10~K where $\chi_\parallel$ is the susceptibility parallel to $\langle 111 \rangle$ and $\chi_\perp$ is perpendicular to $\langle 111 \rangle$. This value of $\chi_\parallel/\chi_\perp $ is very close to that of Pr$_2$Sn$_2$O$_7$ for which $\chi_\parallel/\chi_\perp \sim 60 $ at 10~K \cite{Princep2013}. The $\chi_\perp$ is purely Van-Vleck like therefore $\chi_\parallel/\chi_\perp $ increases very rapidly as $T \rightarrow 0$, e.g.\ at 3.5~K  $\chi_\parallel/\chi_\perp \sim 120 $. The $C_{\rm CEF}(T)$ calculated from the CEF parameters is shown in the lower inset of Fig.~\ref{fig:HC} (solid red line), in good agreement with $C_{\rm mag}(T)$ data, thus further supporting the deduced CEF level scheme. Our CEF level scheme (CEF parameters, eigenvalues and wavefunction) are in good agreement with the recent results by Sibille {\it et al}.\ \cite{Sibille2016}, though the values of observed CEF excitations and deduced $B_q^k$ parameters are slightly different.

\section{\label{PrHfO_SC} Single crystal P\lowercase{r}$_2$H\lowercase{f}$_2$O$_7$ }

\begin{figure}
\includegraphics[width=\columnwidth, keepaspectratio]{Fig09.eps}
\caption{(Color online) Zero-field-cooled magnetic susceptibility $\chi$ of single crystal Pr$_2$Hf$_2$O$_7$ as a function of temperature $T$ for $2~{\rm K} \leq T \leq 50$~K for the three crystallographic directions [100], [110] and [111], measured in magnetic field $H= 0.1$~T\@. Inset: Inverse susceptibility $\chi^{-1}(T)$ for $H=0.1$~T and $2~{\rm K} \le T \leq 25$~K\@. The solid red line is the fit of the $\chi^{-1}(T)$ data by the modified Curie-Weiss law in $12~{\rm K} \leq T \leq 25$~K and the dashed line is an extrapolation.}
\label{fig:MT_SC}
\end{figure}

The ZFC $\chi(T)$ of single crystal Pr$_2$Hf$_2$O$_7$ is shown in Fig.~\ref{fig:MT_SC} for the $H$ applied along the three crystallographic directions [100], [110] and [111]. Consistent with the $\chi(T)$ of the polycrystalline sample the $\chi(T)$ of the single crystal does not show any anomaly. The $\chi(T)$ for $H$ along [100], [110] and [111] show very similar $T$ dependence with similar magnitude. In order to estimate the $\theta_{\rm p}$ and $\mu_{\rm eff}$ the $\chi(T)$ data at $12~{\rm K} \leq T \leq 25$~K were analyzed by modified Curie-Weiss behavior, the representative fit for [111] direction is shown in the inset of Fig.~\ref{fig:MT_SC}). The fit parameters are listed in Table~\ref{tab:CW_chi}. The $C$ values yield $\mu_{\rm eff} \approx 2.51\, \mu_{\rm B}$/Pr for the single crystal which, as expected, is very similar to that obtained for the polycrystalline sample.

\begin{table}
\caption{\label{tab:CW_chi} Parameters obtained from the analysis of magnetic susceptibility of Pr$_2$Hf$_2$O$_7$ by modified Curie-Weiss law. }
\begin{ruledtabular}
\begin{tabular}{cccc}
$H$ direction          & $\chi_0$            &  $C$                   & $\theta_{\rm p}$\\
                             &  (emu/mol\,Pr)   & (emu\,K/mol\,Pr) &  (K) \\
\hline
$[100]$    & $4.9(1)   \times 10^{-3}$      & 0.79(1)      &   $-0.81(4)$     \\
$[110]$    & $4.8(1)   \times 10^{-3}$      & 0.79(1)      &   $-0.93(5)$      \\
$[111]$    &  $4.9(1)   \times 10^{-3}$     & 0.79(1)      &   $-0.86(5)$     \\
\end{tabular}
\end{ruledtabular}
\end{table}

\begin{figure}
\includegraphics[width=\columnwidth, keepaspectratio]{Fig10.eps}
\caption{(Color online) Isothermal magnetization $M$ of single crystal Pr$_2$Hf$_2$O$_7$ as a function of applied magnetic field $H$ for $0 \leq H \leq 14$~T measured at 2~K for the three crystallographic directions [100], [110] and [111].}
\label{fig:MH_SC}
\end{figure}

The isothermal $M(H)$ data of single crystal Pr$_2$Hf$_2$O$_7$ measured at 2~K are shown in Fig.~\ref{fig:MH_SC}. The $M(H)$ data reflect the Ising anisotropy. For a system with $\langle 111 \rangle$ Ising anisotropy, the saturation magnetizations $M_s $ are given by \cite{Fukazawa2002}: $g' J' \mu_{\rm B}(1/\sqrt 3)$ for [100] (two-in/two-out), $g' J' \mu_{\rm B}(\sqrt{2/3} \times2)/4$ for [110] (one-in/one-out, two free) and $g' J' \mu_{\rm B}(1+1/3\times 3)/4$ for [111] (three-in/one-out). The observed magnetizations at $H=14$~T are $M_{[100]} = 1.46\,\mu_{\rm B}$/Pr, $M_{[110]} = 1.21 \,\mu_{\rm B}$/Pr and $M_{[111]} = 1.34 \,\mu_{\rm B}$/Pr. The observed anisotropic $M$ gives the ratio  $M_{[100]}/M_{[110]}$ = 1.21  and $M_{[100]}/M_{[111]}$ = 1.09  which are in line with Ising anisotropy but somewhat smaller than the theoretically expected ratios of $\sqrt2$ and $2/\sqrt3$, respectively. With $g' J' \mu_{\rm B} \approx 2.51\, \mu_{\rm B} $, the effective moment, one would estimate $M_{[100]} = 1.45\,\mu_{\rm B}$/Pr, $M_{[110]} = 1.02 \,\mu_{\rm B}$/Pr and $M_{[111]} = 1.26 \,\mu_{\rm B}$/Pr. Thus we see that while the observed $M_{[100]} $ and $M_{[111]}$ are close to their expected values, the observed $M_{[110]}$ is significantly higher than the expected value. The deviations from the Ising picture possibly indicates the presence of additional non-Ising terms in the Hamiltonian.  Further we also notice that the $M$ is not saturated even at 14~T field which could be due to the mixing of ground state multiplet and/or non-Ising contributions.

\section{\label{Conclusion} Summary and Conclusions}

We have synthesized polycrystalline and single crystal samples of the pyrohafnate compound Pr$_2$Hf$_2$O$_7$ and investigated  their structural and physical properties by means of synchrotron x-ray diffraction, dc magnetic susceptibility, isothermal magnetization, ac susceptibility, heat capacity and inelastic neutron scattering measurments. The high-resolution synchrotron x-ray diffraction revealed the well-ordered pyrochlore ($Fd\bar{3}m$) structure with Pr/Hf site mixing and/or oxygen deficiency (if present) at a level lower than 0.5\%. Our ac susceptibility measurments down to 90~mK did not reveal any evidence for a magnetic transition to a long range ordered phase. The $\chi_{\rm ac}(T)$ is found to show a frequency dependent broad peak, a characteristic feature of spin-freezing in spin-ice systems, indicating slow spin dynamics in Pr$_2$Hf$_2$O$_7$ at low temperature.  The single-spin relaxation time for Pr$_2$Hf$_2$O$_7$ is found to be very similar to that of the spin-ice Ho$_2$Ti$_2$O$_7$.

The dc magnetic susceptibility and magnetization data show the Ising anisotropic features commonly observed in 227 pyrochlore spin-ice systems. The single crystal magnetic data clearly reveal this Ising anisotropic behavior, which is most obvious from the field dependence of directional dependent isothermal magnetization data. The inelastic neutron scattering data reveal five well defined magnetic excitations which are well accounted for by a model based on crystal electric field, accordingly we have determined the crystal field states of Pr$^{3+}$. The CEF ground state is a well isolated non-Kramers doublet. The CEF suceptibility yields $\chi_\parallel/\chi_\perp \sim 120 $ at 3.5~K revealing an Ising type anisotropy. The ground state wavefunction shows significant mixing of $|^3H_{4},\pm 4 \rangle$ state with other multiplets. Such a mixing can cause quantum fluctuations. The single crystal $M(H)$ data reflect the presence of non-Ising contribution which are very favorable for quantum spin-ice behavior.

The key observations from our investigations are i) a weakly ferromagnetic interaction as inferred from the Weiss temperature, ii) crystal field ground state is a doublet well-separated from the first excited state, iii) low-$T$ magnetism described by an effective pseudospin-1/2 model,   iv) anisotropic g-tensor, v) Ising-type anisotropy, and vi) slow spin dynamics. All these indicate that the magnetic ground state of Pr$_2$Hf$_2$O$_7$ is consistent with spin-ice physics. In addition, there is some indication for the presence of a non-Ising contribution that would imply a dynamic spin-ice behavior instead of classical spin-ice behavior. The magnetic properties of Pr$_2$Hf$_2$O$_7$ are very similar to those of the dynamic spin-ice systems Pr$_2$Sn$_2$O$_7$  \cite{Zhou2008,Princep2013} and Pr$_2$Zr$_2$O$_7$ \cite{Kimura2013}. Recent investigations by Sibille {\it et al}.\ [29] also concludes in favor of a quantum spin-ice behavior in Pr$_2$Hf$_2$O$_7$ where they also implied low energy inelastic neutron scattering in addtion to ac susceptibility for the study of spin dynamics in this compound. Further investigations are required to explore the quantum spin-ice ground state of Pr$_2$Hf$_2$O$_7$.

\acknowledgements
We acknowledge Helmholtz Gemeinschaft for funding via the Helmholtz Virtual Institute (Project No. VH-VI-521) and DFG through Research Training Group GRK 1621 and SFB 1143. We also acknowledge the support of the HLD-HZDR, a member of the European Magnetic Field Laboratory (EMFL).

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text:
David O. Smith
President and COO
David O. Smith, President and COO at LightGrid, LLC, is a Subject Matter Expert (SME) focusing on Network Optimization and Modernization, enterprise capabilities, network deployment, and network decommissioning.
Mr. Smith has supported the Department of Defense (DoD) for over 15 years and is currently supporting the Defense Information Systems Agency (DISA) Infrastructure Executive (IE) as Network Architect. He currently supports DISA's 100G IP Core Upgrade, Global IP Transport, and DISN Network Optimization efforts.
Before Mr. Smith started with LightGrid, he worked for Science Application International Corporation (SAIC) as a project lead. David managed transition teams consisting of engineers, implementation teams, and site survey teams to transition telecommunication networks from service providers to an in- house government owned and managed large scale optical based core infrastructure.Prior to SAIC, Mr. Smith worked for Booz Allen Hamilton. He worked with several DoD clients to resolve interoperability issues within the Defense Information Systems Network (DISN)/ Government Information Grid – Bandwidth expansion (GIG-BE) framework. Mr. Smith has also lead DISA's three Metro Area Network (MAN) decommissioning projects as the Program Lead for Network Services.
Mr. Smith is a graduate of The Johns Hopkins University, where he earned a M.S. in Information and Telecommunication Systems in Business. He also earned a B.S. in Computer and Information Sciences from Shepherd University. Mr. Smith was also published by the Information Assurance Technology Analysis Center (IATAC) IANewsletter, "GIG-BE – Improving the Warfighter's Information Pipline".
Mr. Smith is involved in several charities, including the National Kidney Foundation and Project Healing Waters.

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Local artist's hard work pays off as he bags awesome award nomination
2 months ago 144 views by Desere Davis
- Thabiso 'Masaladi' Zakwe is a budding artist who has earned himself a spot in the music world next to big names such as Lady Zamar and Simmy
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Everbilt Sliding Barn Door Track Hardware Kit 72 in. Everbilt's Decorative Sliding Door Hardware adds an upscale look to ordinary doors and doorways in the home, office or place of business by incorporating barn door style doors and functionality. Ideal for closets, interior doors and room dividers. The set includes all mounting hardware and hanging components needed for 1 door. The high density plastic wheels provide a smooth, quiet operation and a high quality feel.
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: 2.44 in Builders Hardware Product Type: Wall Mount Door Hardware Color/Finish: Dark oil-rubbed bronze Hardware Finish Family: Bronze Material: Steel. The item "Everbilt Sliding Barn Door Track Hardware Kit 72 in. Steel Oil-Rubbed Bronze" is in sale since Monday, January 28, 2019. This item is in the category "Home & Garden\Home Improvement\Building & Hardware\Doors & Door Hardware\Other Door Hardware". The seller is "*happyvalleysales" and is located in Multiple Locations.


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Our Naturals bakeware starts out as a solid coil of aluminum, weighing several thousand pounds. The coil is fed into a press, which first performs a 'blanking' operation to cut out the rough shape of the pan. Next, it is roughly formed to resemble the shape of the finished pan. Finally, a galvanized steel rim, which gives rigidity to the pan, is added, and the edges of the pan are curled around the steel rim to encapsulate it fully. Our galvanized steel rims are formed on-site at Nordic Ware too; they begin as long metal rod and go through a series of bending maneuvers to be properly sized for each pan. After all of the metalworking is complete, the pan is sent to be washed and packed. One of the great aspects of manufacturing with pure aluminum is that it is highly recyclable, so any scrap metal that is produced during our production process can be re-melted down and used again.
Nordic Ware was founded in 1946 by a determined wife, Dotty, and her resourceful husband Dave, newly back from the second world war. With only $500 in their pockets, a few good ideas and a desire to create a business of their own, a humble kitchenware company was launched from the basement of their home in Minneapolis, Minnesota. In the beginning, Nordic Ware's product line was only a handful of items, all of which were specialty Scandinavian ethnic cookware products. But times have changed! 70 years later with a good measure of perseverance added, Nordic Ware is still proudly manufacturing the vast majority of its products in Minneapolis. We're proud to say that we're still family-owned and operated, with three generations involved in our business, and each year we add innovative items to our expansive kitchenware line.
With wife Dotty at his side, Dave Dalquist returned from WWII to start a business. From humble beginnings in a basement, Nordic Ware has become an internationally distributed kitchenware brand with a variety of product lines, hundreds of products and millions of fans!
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Yes, you can use this under a broiler or at 450+ degree F to roast vegetables, and yes, cooked-on oil comes clean and doesn't affect the stickiness of the pan. This is all aluminum, with (allegedly) steel around the edges so it doesn't warp at high temperatures. Very heavy duty pan.
A little history: when I moved out on my own for the 1st time, my mom gave me a no name aluminum sheet pan. I have abused this thing for about 10 years. My mom had it for probably 20 before me. I have a little family of my own now and my husband likes roasted veggies, but I have found that I often make broccoli and potatoes or fries or homemade chicken nuggets in the same night. I have go thru a few other sheets pans looking for a sturdy one to accompany my old beat up one. They all would twist or warp over 400 degrees like it was their job. Didn't seem like the price made a difference. I had cheap ones and then expensive ones. They all went funny at 400. I assumed all pans did that these days and almost gave up, but then I found this one. Two, actually. So now I have three awesome pans. I use the old one and one new one for veggies, and the third exclusively for baking cookies so it will stay cleaner and stick free.
Note: these are not "non-stick", they are just not sticky because the metal is really smooth. If you're afraid of chemicals leeching into your foods from non-stick coatings, these are a good choice. Use a fat (oil, shortening) to make foods easy to remove from the pan.
1.0 out of 5 starsConsuming Heavy Metals is not part of my diet.
i enjoyed the large surface area of the pans, able to fit a lot of potatoes (fried potatoes) at one time.
Sheets (BS) not a health seminar so i will sum it my simply saying i am now eliminating anything potentially contributing to having heavy metals in my system. i am not saying these baking sheets are the cause of my issues but i will no longer be using these baking sheets, and i will show you why. Most of the time i use these BS twice a day for about two months.
I've been cooking with these BS since April 2018 it is now November 8th 2018. I've now discarded them.
5.0 out of 5 starsI'm finally writing this review 1/2 a year after purchasing because I recently handwashed the pan and it almost looks like new!
I've never owned one of these before so I put it in the dishwasher not knowing that I wasn't supposed to ......... I'm sure you can guess how it turned out. However, I was sure that would not change the usefulness of the pan so I've continued to use it anyways. With a sheet of aluminum foil on top and a light spray of cooking oil all my food has come out of the toaster oven perfectly! The sturdiness of the pan and the even cooking were the reason I bought the pan and the trip through the dishwasher didn't ruin that one bit.
I'm finally writing this review 1/2 a year after purchasing because I recently handwashed the pan and it almost looks like new! It seems that the cooking spray has been leaking through the foil and months of baking the oils has seasoned the pan. I imagine all these reviews with photos saying the pan is junk probably ran it thru the dishwasher and never tried to figure out why.
5.0 out of 5 starsJelly roll is the size to buy!
I love the jelly roll size. Two of these fit perfectly in the oven on the rack. They are much easier to clean than one huge pan, plus easier to store inside cabinets. It is very well-made with measurements exactly as described. These are by far the most frequently used item in my kitchen.
3.0 out of 5 starsThe logo is unnecessary and just annoys me!
I love sheet pans similar this and have owned many in my lifetime. Everyone else I know must love them too, as my supply of five sheet pans had dwindled down to two. I needed more - so I ordered these since they were so well reviewed. When they got here I was really disappointed in two things: specifically they feel a little lighter weight than the ones I've owned in the past, and they have a sizable raised logo that stretches across about a third of the bottom of pan – which is exactly what I don't want – I don't want one more place for gunk to get stuck.
3.0 out of 5 starsLooked nice upon arrival. Great size.
I like this cooking sheet!!! I like being able to bake a whole salmon filet without it drooping over the edges or having to cut it! I like being able to cook 2 full racks of spare ribs with pleny of room to spare! I like that it fits in my oven nicely with just enough room left for heat to circulate! I like being able to cook a $#!t-load of cookies in one go!
I bought a silicone baking mat to go in this, so I don't have to work so hard to keep it clean. I keep them both lightly oiled regardless of what the recipe calls for-- it makes it easier to clean this.
It did warp the first time I used it, baking at only 400F. Also on the outer edge, the metal is bent around to form a nice lip but it isn't completely sealed so it forms a small tube where it will be easy for grease/dirt/germs to accumulate so watch out!


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text:
Inflammatory myofibroblastic tumor of the right frontal lobe
Xuejian Wang1,
Zhifeng Wang1,
Yang Chen1 &
Ming Qian1
Chinese Neurosurgical Journal volume 3, Article number: 12 (2017) Cite this article
We aim to present an unique case of inflammatory myofibroblastic tumor (IMT) of the brain parenchyma and study the clinical presentation, imagine characteristic, intraoperative findings, and histopathology features of IMT in the brain parenchyma.
A 36-year-old female with IMT come to see doctor presented with a 3-month history of progressively worsening weakness in the left upper limb along with alalia. Serial magnetic resonance imaging studies revealed a lesion within the right frontal lobe. The lesions were locally clear boundary with peripheral tissues. A right frontotemporal craniotomy was performed and the specimens were detected by immunohistochemical staining and light microscopy. Through the microscope, the tumor was composed of large number of chronic inflammatory cells and spindle cells. From immunohistochemical stains, it demonstrated CD34 (+), SMA (+), Vimentin (+), and actin (+) were positive meanwhile S-100(-) was negative.
IMT of the right frontal lobe is a rare lesions. Surgical resection is the best and the most effective treatment.
Inflammatory myofibroblastic tumor (IMT) is a disease characterized by tumorous lesions formed by inflammatory cells and myofibroblastic spindle cells that occur primarily in the viscera and soft tissues of children and young adults [1]. IMT is most commonly seen in the lungs, omentum and mesentery. IMT of the brain is rare. We herein present a case of IMT located in the frontal lobe.
A 36-year-old man was admitted in December 2013 with progressively worsening weakness in the left upper limb along with alalia. Two months before admission, she had undergone a history of mild head injury. Physical examination is in good condition.
CT of the brain showed (Fig. 1a): a lesion located in the right frontal lobe, slightly more mixed density, size 3 cm, peripheral edema; T1 and T2-weighted Magnetic resonance imaging (MRI) showed: a low or iso-intensity area at the same site in T1-weighted MRI (Fig. 1c), a high and low mixed signal at the same site in T2-weighted MRI (Fig. 1d–f), with homogeneous enhancement by Gd-DTPA (Fig. 1g–i); MRS (Fig. 1b) showed no peak of Cho and NAA.
A 36-year-old man was admitted in December 2013 and diagnosed as IMT after surgery. a CT of the brain showed a mass located in the right frontal lobe, slightly more mixed density, size 3 cm, peripheral edema; b MRS showed no peak of Cho and NAA; c T1-weighted Magnetic resonance imaging (MRI) showed a low or iso-intensity area at the same site; d-f T2-weighted Magnetic resonance imaging (MRI) showed a high and low mixed signal at the same site; g-i MR image showing an homogeneous enhancement by gadolinium diethylenetriaminepenta-acetic acid (Gd DTPA) in the right frontal lobe
A right frontotemporal craniotomy was performed. The tumor located in a right frontal lobe with a clear boundary, and partly adhered to the dura. Tumor mass is toughening and had to be block excised.
Pathological examination
Histologically, the tumor specimen predominantly consisted of mature myofibroblast cells, with a large number of inflammatory cells infiltration, and distribution of collagen fibers. Myofibroblast cells are spindle, of red dye cytoplasm and round or oval nuclei. Most of inflammatory cells are plasma cells and lymphocytes, which are in diffused distribution or gather into oven. Spindle tumor cell is rare nuclear division, no obvious heteromorphism which accord with inflammatory myofibroblast cells.
Immunohistochemical analysis: Immunostaining demonstrated that the spindle cells reacted with vimentin and smooth muscle actin. CD34+, vimentin (+), actin (+), SMA+, Ki-67 positive rate < 5%, desmin (+), GFAP-, S-100(-), EMA-, ALK-1-, CD117-.
According to these findings, a histopathological diagnosis of IMT was made.
Postoperative CT: the tumor was total resected, with no residual tumor, and swelling is improving than before. In the one year of follow-up after the patient's discharge, there has been no any tumor progression or recurrence.
Inflammatory myofibroblastic tumor (IMT) is a disease characterized by spindle cell neoplasm composed of lymphocytes, plasma cells, and so on. IMT is rare in clinical, which mainly located in the lungs. IMT has been defined by many different names, including inflammatory pseudotumor (IPT) and plasma cell granuloma, highlighting the complexity and variable histological characteristics of these tumors. Pettinato and colleagues in 1990 first put forward the concept of inflammatory myofibroblastic tumor (IMT) [2]. In the 2002, World Health Organization (WHO) classification of soft tissue tumors, these lesions were renamed [3].
The etiology of these 'tumors' is not certain and the current acquaintance of the pathophysiology of this disease is based on an abnormal response by the myofibroblast to trauma, tissue injury, surgery, inflammation and so on. Our patient admitted to hospital with a history of head injury in before two month age, which may be the inducing factors of this disease. Some cases have been associated with tuberculosis or malignancy as satellite lesions, and some suggested to be associated to cocaine consumption [4–6] and even by viral infection such as Epstein–Barr virus [4, 7]. There have been reported IMT in the spleen may be associated with EBV infection [8]. In addition, there are scholars believe that abnormal autoimmune mechanism may be related to the occurrence of a muscle fiber mother cell tumor. Plasma cell granuloma might be responsible for the immunological abnormalities because symptom of plasma cell granuloma was resolved as soon as the tumor was removed [9, 10]. Recent studies have confirmed that the chromosome 2p23 of IMT case is rearrangement, which hints the of the monoclonal hyperplasia characteristics of IMT and supports this lesion as true tumor rather than inflammatory pseudotumor [11, 12]. However, the lack of p53 detection in IMT gone with the low proliferation index (Ki67 < 10%) hints that IMT may be a low-grade tumor, if at all [13].
Making a diagnosis of IMT requires a histopathological examination because the radiological and clinical findings are generally nonspecific [1]. Research suggests electron microscopic observation is special. Under the electron microscope, this tumor cells are of ultra microstructure characteristics of fibroblast and myofibroblast cell, show the bipolar or irregular cellular processes, well-differentiated rough endoplasmic reticulum, and filament bundle of the surrounding cytoplasm, discontinuous base board structures and pinocytosis vesicles surrounding cells. Immunohistochemical can assist the diagnosis to this disease. Spindle cells of IMT is performance for different degrees of positive reaction to the following antibody: vimentin, SMA, MSA (muscle-specific actin). Positive reaction of vimentin is usually very strong, but its specificity is not high, because the vimentin can be found in all normal mesenchymal tissue and most sarcoma. Specificity of SMA is good, whose positive reaction is thought to be important marker to IMT. A small part of IMT is of positive reactions to epithelial membrane antigen, CK, CD68, CD30, α-antitrypsin, α-anticoagulant protease or melting bacteria enzymes, and so on, but no specificity to diagnosis [14]. This case was proved as IMT by immunohistochemical staining with Vim+, SMA+, actin+, desmin (partly cells +).
Steroids have been used to treat unresectable lesions and got some success. Other medical treatment choice, however, are less effective, including radiotherapy and/or adjuvant chemotherapy and treatment with immunosuppressive and anti-inflammatory drugs. Treated with high-dose corticosteroid anti-inflammatory drug, some patients symptoms can subside, but withdrawal symptoms once drug discontinuance. Methotrexate, azathioprine, vinca alkaloids, cyclophosphamide and cyclosporine have been used; however, the response is variable and often poor [15–18]. Fumiko et al. report a successful treatment case of an unresectable inflammatory myofibroblastic tumor of the frontal bone by methotrexate and cyclooxygenase-2 inhibitor [1]. In summary to the existing literature, there is a consensus that total surgical excision is the most effective therapeutic option in cases in which the tumors are surgically accessible.
Our patient received only surgical excision therapy. This patient got a good postoperative outcome with no recurrent signs according to follow-up MR imaging for about one year. However, it must be carefully observed especially for recurrent signs of the tumor.
CT:
IMT:
Inflammatory myofibroblastic tumor
IPT:
Kusunoki-Nakamoto F, Matsukawa T, Tanaka M, Miyagawa T, Yamamoto T, Shimizu J, Ikemura M, Shibahara J, Tsuji S. Successful treatment of an unresectable inflammatory myofibroblastic tumor of the frontal bone using a cyclooxygenase-2 inhibitor and methotrexate. Intern Med. 2013;52(5):623–8.
Pettinato G, Manivel JC, De Rosa N, Dehner LP. Inflammatory myofibroblastic tumor (plasma cell granuloma). Clinicopathologic study of 20 cases with immunohistochemical and ultrastructural observations. Am J Clin Pathol. 1990;94(5):538–46.
Jeon YK, Chang KH, Suh YL, Jung HW, Park SH. Inflammatory myofibroblastic tumor of the central nervous system: clinicopathologic analysis of 10 cases. J Neuropathol Exp Neurol. 2005;64(3):254–9.
Boutarbouch M, Arkha Y, Rifi L, Derraz S, El Ouahabi A, El Khamlichi A. Intradural cervical inflammatory pseudotumor mimicking epidural hematoma in a pregnant woman: case report and review of the literature. Surg Neurol. 2008;69(3):302–5.
Hytiroglou P, Brandwein MS, Strauchen JA, Mirante JP, Urken ML, Biller HF. Inflammatory pseudotumor of the parapharyngeal space: case report and review of the literature. Head Neck. 1992;14(3):230–4.
Karatsis P, Wyman A, Sweetland HM, Bull AD, Rogers K. Inflammatory pseudotumour of the liver. Eur J Surg Oncol. 1993;19(4):384–7.
Arber DA, Kamel OW, van de Rijn M, Davis RE, Medeiros LJ, Jaffe ES, Weiss LM. Frequent presence of the Epstein-Barr virus in inflammatory pseudotumor. Hum Pathol. 1995;26(10):1093–8.
Oz Puyan F, Bilgi S, Unlu E, Yalcin O, Altaner S, Demir M, Cakir B. Inflammatory pseudotumor of the spleen with EBV positivity: report of a case. Eur J Haematol. 2004;72(4):285–91.
Coffin CM, Humphrey PA, Dehner LP. Extrapulmonary inflammatory myofibroblastic tumor: a clinical and pathological survey. Semin Diagn Pathol. 1998;15(2):85–101.
Figarella-Branger D, Gambarelli D, Perez-Castillo M, Garbe L, Grisoli F. Primary intracerebral plasma cell granuloma: a light, immunocytochemical, and ultrastructural study of one case. Neurosurgery. 1990;27(1):142–7.
Coffin CM, Patel A, Perkins S, Elenitoba-Johnson KS, Perlman E, Griffin CA. ALK1 and p80 expression and chromosomal rearrangements involving 2p23 in inflammatory myofibroblastic tumor. Mod Pathol. 2001;14(6):569–76.
Rabban JT, Zaloudek CJ, Shekitka KM, Tavassoli FA. Inflammatory myofibroblastic tumor of the uterus: a clinicopathologic study of 6 cases emphasizing distinction from aggressive mesenchymal tumors. Am J Surg Pathol. 2005;29(10):1348–55.
Meis-Kindblom JM, Kjellström C, Kindblom LG. Inflammatory fibrosarcoma: update, reappraisal, and perspective on its place in the spectrum of inflammatory myofibroblastic tumors. Semin Diagn Pathol. 1998;15(2):133–43.
Coffin CM, Watterson J, Priest JR, Dehner LP. Extrapulmonary inflammatory myofibroblastic tumor (inflammatory pseudotumor). A clinicopathologic and immunohistochemical study of 84 cases. Am J Surg Pathol. 1995;19(8):859–72.
Dishop MK, Warner BW, Dehner LP, Kriss VM, Greenwood MF, Geil JD, Moscow JA. Successful treatment of inflammatory myofibroblastic tumor with malignant transformation by surgical resection and chemotherapy. J Pediatr Hematol Oncol. 2003;25(2):153–8.
Favini F, Resti AG, Collini P, Casanova M, Meazza C, Trecate G, Ferrari A. Inflammatory myofibroblastic tumor of the conjunctiva: response to chemotherapy with low-dose methotrexate and vinorelbine. Pediatr Blood Cancer. 2010;54(3):483–5.
Sacco O, Gambini C, Gardella C, Tomà P, Rossi UG, Jasonni V, Bush A, Rossi GA. "Atypical steroid response" in a pulmonary inflammatory myofibroblastic tumor. Pediatr Pulmonol. 2010;45(7):721–6.
Trojan A, Stallmach T, Kollias S, Pestalozzi BC. Inflammatory myofibroblastic tumor with CNS involvement. Onkologie. 2001;24(4):368–72.
We didn't receive any financial support to analyze this data and we didn't have any financial interest in any materials or devices described.
This research supported by: (1) Young Medical Project of Nantong City Health Bureau (WQ2014016); (2) Traditional Chinese medicine science and technology project in Jiangsu province (No. YB2015113); (3) the science and technology program of Nantong city (no. : MS12015016).
All data generated or analyzed during this study are included in this published article.
Conceived and designed: Xuejian Wang, Yang Chen. Performed: Zhifeng Wang, Ming Qian. Analyzed the data: Xuejian Wang. Wrote the paper: Xuejian Wang. All authors read and approved the final manuscript.
Written informed consent was obtained from the patient for publication of this case report and any accompanying images.
This research has been approved by the ethics committee of the Second Hospital affiliated to Nantong University(2016002). Informed consent has been obtained and this report was processed according to the principles expressed in the Declaration of Helsinki.
Department of Neurosurgery, the Second Hospital affiliated to Nantong University, Nantong University, Nantong, Jiangsu, 226001, People's Republic of China
Xuejian Wang
, Zhifeng Wang
, Yang Chen
& Ming Qian
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Correspondence to Xuejian Wang.
Wang, X., Wang, Z., Chen, Y. et al. Inflammatory myofibroblastic tumor of the right frontal lobe. Chin Neurosurg Jl 3, 12 (2017) doi:10.1186/s41016-017-0076-5
Inflammatory myofibroblastic tumor (IMT)


The Contemporary Writers Series brings nationally and internationally known writers to our campus to share their work and to discuss their art with Canisius students in an informal setting. Past guests to Canisius include Pulitzer Prize winners, National Book Award winners, McArthur "genius" grant winners, and a Nobel Laureate: Richard Russo, George Saunders, Edwidge Danticat, Sharon Olds, Ann Patchett, Junot Diaz, Paul Muldoon, Tracy Kidder, Tracy K. Smith, Alice McDermott, and Seamus Heaney, among others.
Founded with a grant from the John R. Oishei Foundation and continued through the Peter Canisius Distinguished Teaching Professorship Program, the writer series is generously supported today by the Hassett, Scoma, and Lowery Endowments; The National Endowment for the Arts; and with the cooperation of The Buffalo & Erie County Public Library, Just Buffalo Literary Center, The Center for Urban Education, and Talking Leaves Books.
Michael Longley was born in Belfast, educated at the Royal Belfast Academical Institute, and studied Classics at Trinity College Dublin. He is the author of ten collections of poetry, most recently Angel Hill, and has been awarded the Whitbread Poetry Award, the Hawthornden Prize, the T.S. Eliot Prize, the International Griffin Poetry Prize, and the Irish Times Poetry Prize. He served as Ireland Professor of Poetry from 2007 to 2010, and was honored with the title of Commander of the Order of the British Empire (CBE) in 2010.
Lynda Barry was born in Wisconsin, grew up in Seattle, and earned a degree in fine arts from Evergreen State College. She is a painter, cartoonist, writer, illustrator, playwright, editor, commentator, teacher, and the author of 21 books, including The Good Times Are Killing Me, Cruddy, One! Hundred Demons!, and What It Is. She has received two William Eisner awards, the American Library Association's Alex Award, the Wisconsin Library Association's RR Donnelly Award, the Washington State Governor's Award, the Holtz Center for Science & Technology Outreach Fellowship, and the 2017 Milton Caniff Lifetime Achievement Award from the National Cartoonists Society. Currently she is Associate Professor in Interdisciplinary Creativity, Director of the Image Lab at the Wisconsin Institutes for Discovery, and the Chazen Family Distinguished Chair in Art at the University of Wisconsin-Madison.
Bao Phi was born in Vietnam, grew up in Minneapolis, and graduated from Macalester College with a degree in English. He is a poet, spoken-word artist, and community activist. a two-time Minnesota Grand Slam champion and a National Poetry Slam finalist, and his work has appeared in a variety of journals and anthologies, including Best American Poetry, selected by Billy Collins. He is the author of two collections of poetry, Sông I Sing and Thousand Star Hotel and a children's book, A Different Pond. He is Program Director at The Loft Literary Center in Minneapolis, where he coordinates a number of programs, including the Equilibrium series, which was awarded an Anti-Racism Initiative award.
Bao Phi Performs "You Bring Out the Vietnamese in Me"
Colson Whitehead is The New York Times bestselling author of The Noble Hustle, Zone One, Sag Harbor, The Intuitionist, John Henry Days, Apex Hides the Hurt, and The Colossus of New York. His most recent novel, The Underground Railroad, was winner of the Pulitzer Prize for Fiction, the National Book Award, American Bookseller's Association Adult Fiction Book of the Year, and an Oprah Book Club selection.
Belinda McKeon attended Trinity College, Dublin and University College Dublin and earned an MFA from Columbia University. Her first novel, Solace, won the 2012 Faber Prize and was voted Irish Book of the Year. Her second novel, Tender, was named a Kirkus Reviews Best Book of 2015. Her essays and journalism have appeared in The New York Times, The Paris Review, The Guardian, A Public Space and elsewhere. She lives in Brooklyn and teaches at Rutgers University.
Diana Goetsch was born in Brooklyn, grew up in North Point, Long Island, and earned degrees from Wesleyan University and New York University. She is the author (as Douglas Goetsch) of Nameless Boy, The Job of Being Everybody, and several other volumes of poems. Her work has appeared in The New Yorker, Poetry, The Gettysburg Review, The American Scholar, Best American Poetry, The Pushcart Prize and numerous other journals and anthologies. Among her honors are fellowships from the National Endowment for the Arts, the New York Foundation for the Arts, and the Donald Murray Prize. She's taught English and creative writing in New York City public schools and to incarcerated teens in the Bronx. She is the founder of Jane Street Press. Currently Goetsch writes a column entitled "Life in Transition" for The American Scholar, lives in New York, and works as a freelance teacher of writing.
The American Scholar "Between People"
fayobserver "Diana Goetsch: Moving beyond 'tolerance'"
Vermont Studio Center "Resident Profile: Diana Goetsch"
Cuppa Pulp & CILK119 Interview "No Such Thing as a Nice Little Old Lady"
Emma Donoghue was born in Dublin. She earned an undergraduate degree from University College Dublin and a Ph.D. in 18th-century literature from Cambridge. She has written for the screen, stage, and radio, as well as writing historical and contemporary novels and short stories. Her novel Room was an international bestseller, published in 39 countries, a New York Times Best Book of 2010, and a finalist for the Man Booker, Commonwealth, and Orange Prizes. Her film adaptation won Best First Screenplay at the Independent Spirit Awards and an Oscar Nomination for Best Adapted Screenplay. Her most recent book is The Wonder, to be published in September by Little Brown. She lives in London, Ontario, with her partner, son, and daughter.
Emma Donoghue reads from "A Short Story"
"Emma Donoghue: The How I Write Interview"
Cristina Henríquez earned her undergraduate degree from Northwestern University and is a graduate of the Iowa Writers' Workshop. She is the author of a story collection, Come Together, Fall Apart, and two novels: The World in Half and The Book of Unknown Americans, a New York Times and Washington Post Notable Book, an NPR Great Read, and named one of the best books of the year by Oprah.com and School Library Journal.
Anne Enright was born in Dublin. She is the author of a memoir of motherhood, three short story collections, and six novels, most recently The Green Road. Her work has appeared in The New Yorker, Granta, The Paris Review, and The Penguin Book of Irish Fiction, and her novel The Gathering won the 2007 Man Booker Prize. In January 2015, she was named the inaugural Laureate for Irish Fiction.
Theo Dorgan was born in Cork and completed a BA in English and Philosophy and an MA in English at University College Cork. He is the author of two works of nonfiction, Sailing for Home: A Voyage from Antigua to Ireland and Time on the Ocean: A Voyage from Cape Horn to Cape Town; a novel, Making Way; and several collections of poetry, most recently, Nine Bright Shiners, named 2015 winner of the Irish Times-Poetry Now award. He is a former director of Poetry Ireland and a member of Aosdána, Ireland's academy of the arts.
Kevin Kling was born in Osseo, Minnesota, and graduated from Gustavas Adolphus College. He is a playwright, storyteller, regular contributor to NPR's All Things Considered, and the author of two story collections. He performs his stories across the county and around the world, works with theaters including The Guthrie and the Interact Ensemble of Artists with Disabilities, and plays the tuba in the trio Bad Jazz.
"The Evolution of One Person's Prayer"


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text:
Q: GA4 Track Total Revenue I'm trying to track Revenue with the new GA4 but i'm having a hard time understanding how.
Show image
Can anyone please help?
Thank you!

A: The "value" parameter in tagging populates the "Revenue" metric in reports. For example if you upload the purchase event from this example (https://developers.google.com/analytics/devguides/collection/ga4/ecommerce#purchase):
gtag('event', 'purchase', {
  affiliation: 'Google Store',
  coupon: 'SUMMER_FUN',
  currency: 'USD',
  items: [{
    item_id: 'SKU_12345',
    item_name: 'jeggings',
    coupon: 'SUMMER_FUN',
    discount: 2.22,
    affiliation: 'Google Store',
    item_brand: 'Gucci',
    item_category: 'pants',
    item_variant: 'black',
    price: 9.99,
    currency: 'USD',
    quantity: 1
  }, {
    item_id: 'SKU_12346',
    item_name: 'jeggings',
    coupon: 'SUMMER_FUN',
    discount: 2.22,
    affiliation: 'Google Store',
    item_brand: 'Gucci',
    item_category: 'pants',
    item_variant: 'gray',
    price: 9.99,
    currency: 'USD',
    quantity: 1
  }],
  transaction_id: 'T_12345',
  shipping: 3.33,
  value: 21.09,
  tax: 2.22
})

Then, GA4 will show a Total Revenue of $21.09.

In the Monetization Overview Report, GA4 will show this $21.09 is specifically categorized as Ecommerce revenue.

redpajama_set_name: RedPajamaStackExchange


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