Magnetic pyrochlore oxides

Within the past $20\text{years}$ or so, there has occurred an explosion of interest in the magnetic behavior of pyrochlore oxides of the type ${A_2}^{3+}{B_2}^{4+}{\mathrm{O}}_7$, where $A$ is a rare-earth ion and $B$ is usually a transition metal. Both the $A$ and $B$ sites form a network of corner-sharing tetrahedra which is the quintessential framework for a geometrically frustrated magnet. In these systems the natural tendency to form long-range ordered ground states in accord with the third law of thermodynamics is frustrated, resulting in some novel short-range ordered alternatives, such as spin glasses, spin ices, and spin liquids, and much new physics. This article attempts to review the myriad of properties found in pyrochlore oxides, mainly from a materials perspective, but with an appropriate theoretical context.

Figure 1

(Color online) Antiferromagnetically coupled spins arranged on a triangle or tetrahedron are geometrically frustrated.

Figure 2

(Color online) The $A$ and $B$ sublattices of the cubic pyrochlore materials. Either or both sublattices can be magnetic.

Figure 3

The coordination geometry of the $A$ site by O (shaded spheres) and ${\mathrm{O}}^{\prime }$ (open spheres) atoms. The ${\mathrm{O}}^{\prime }\text{−}A\text{−}{\mathrm{O}}^{\prime }$ unit is oriented normal to the average plane of a puckered six-membered ring. This bond is one of the shortest seen between a rare earth and oxygen ions.

Figure 4

Alternating kagome and triangular planar layers stacked along a [111] direction of the pyrochlore lattice.

Figure 5

(Color online) A structure-field or stability-field map for $A_2{B}_2{\mathrm{O}}_7$ materials. The $B=\mathrm{Pt}$ series are also high-pressure phases. Adapted from 300.

Figure 6

(Color online) Elements known to produce the $(3+,4+)$ cubic pyrochlore oxide phase.

Figure 7

Variation in unit cell constant and physical properties of the series $A_2{\mathrm{Mo}}_2{\mathrm{O}}_7$ with the $A^{3+}$ radius. From 2.

Figure 8

Variation of electrical resistivity and Mo-O1 distances with unit cell constant for oxygen deficient ${\mathrm{Gd}}_2{\mathrm{Mo}}_2{\mathrm{O}}_{7-x}$ single crystals. Top: Comparison of electrical resistivity data for three single crystals of as ${\mathrm{Gd}}_2{{\mathrm{Mo}}_{2-2x}}^{4+}{{\mathrm{Mo}}_{2x}}^{3+}{\mathrm{O}}_{7-x}$ a function of unit cell constant, $a_0$. Bottom: Variation in the Mo-O distance with increasing cell constant for ${\mathrm{Gd}}_2{\mathrm{Mo}}_2{\mathrm{O}}_{7-x}$ crystals.

Figure 9

Properties of an oxygen deficient single crystal of ${\mathrm{Sm}}_2{\mathrm{Mo}}_2{\mathrm{O}}_{7-x}$. (a) Metallic behavior. (b) Inverse susceptibility showing a positive ferromagnetic (FM) Curie-Weiss temperature. (c) Susceptibility showing $T_c=65\mathrm{K}$ and a zero field cooled (squares) and a field cooled (triangles) divergence at $50\mathrm{K}$. From 41.

Figure 10

(Color) Low temperature magnetic neutron powder diffraction data for ${\mathrm{Gd}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. Left: False color map of the temperature dependence of the magnetic diffraction from ${\mathrm{Gd}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. As temperature is lowered, the broad diffuse scattering centered at $1.2{\mathrm{\AA }}^{-1}$ sharpens into peaks. Right: Diffraction patterns at specific temperatures are shown along with tic marks indicating where Bragg reflections should be for the proposed ground state (see main text). At the lowest temperatures the $\frac{1}{2}\frac{1}{2}\frac{1}{2}$ reflection has some intensity and this is highlighted in the inset. From 297.

Figure 11

(Color online) Neutron powder diffraction pattern from ${\mathrm{Gd}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ at $0.1\mathrm{K}$ after a nuclear background $\left(1.4\mathrm{K}\right)$ data set was subtracted (336). Inset: one of the three ${\Gamma }_{7+}$ basis vectors that describe the data (see fit), consistent with the Palmer-Chalker model (223).

Figure 12

(Color online) Specific heat of ${\mathrm{Gd}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ from 233 (circles) and 30 (diamonds). The $T^2$ power law (dotted line) and a conventional $T^3$ power law (dashed line) for a three-dimensional antiferromagnet are plotted. The upturn seen below $150\mathrm{mK}$ results from the nuclear electric quadrupole interaction (233).

Figure 13

Ground state spin configuration determined for ${\mathrm{Er}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ (231). In a macroscopic sample six symmetry equivalent spin configurations will coexist.

Figure 14

Magnetic scattering from ${\mathrm{Tb}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ at $100\mathrm{mK}$. Inset: The proposed ordered spin-ice structure with spins canted off the ⟨111⟩ by 13°. The broad scattering at the base of the Bragg reflections is indicative of spin clusters which reach $\approx 200\mathrm{\AA }$ at base temperature. From 199.

Figure 15

Magnetic susceptibility and heat capacity results for various $A_2{\mathrm{Ru}}_2{\mathrm{O}}_7$ pyrochlores. Top: The temperature dependence of the susceptibility for Y and Lu ruthenate. Both data sets show the ${\mathrm{Ru}}^{4+}$ moments ordering at $\approx 75\mathrm{K}$. From 311. Bottom: Heat capacity measurements over the entire rare-earth ruthenate series showing how the ${\mathrm{Ru}}^{4+}$ ordering temperature increases as the size of the rare-earth ion decreases. From 144.

Figure 16

Temperature dependence of magnetic moments in ${\mathrm{Gd}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$ and ${\mathrm{Er}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$. Left: The temperature dependence of the Gd moment from Gd Mössbauer on ${\mathrm{Gd}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$. From 114. Right: The temperature dependence of the ${\mathrm{Ru}}^{4+}$ and ${\mathrm{Er}}^{3+}$ moments in ${\mathrm{Er}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$ as measured by neutron diffraction. From 313.

Figure 17

Specific heat of polycrystalline ${\mathrm{Ho}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$ as a function of temperature around the ${\mathrm{Ru}}^{4+}$ (inset) and ${\mathrm{Ho}}^{3+}$ (main) ordering temperatures. From 86.

Figure 18

Neutron spin echo spectra from ${\mathrm{Ho}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$ at $\left|\mathbf{Q}\right|=0.4{\mathrm{\AA }}^{-1}$ as measured on NG5 neutron spin echo spectrometer at NIST (left) and the dependence of the relaxation time on temperature (right) from two different positions in reciprocal space. The lines through the spectra on the left are a simple exponential, where the characteristic relaxation time is used in the Arrhenius plot on the right. From 86.

Figure 19

Ferromagnetism and giant megnetoresistance in ${\mathrm{Tl}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$. Top: Magnetic properties of ${\mathrm{Tl}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$ showing evidence for ferromagnetic order in $0.005\mathrm{T}$ (237). Bottom: Evidence for a giant magnetoresistance effect in ${\mathrm{Tl}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$ (278).

Figure 20

Bulk properties of ${\mathrm{Y}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$. Top left: dc susceptibility showing $T_c=16\mathrm{K}$ in $0.15\mathrm{mT}$ (circle), $0.56\mathrm{mT}$ (square), and $10\mathrm{mT}$ (triangle). Bottom left: Magnetization vs applied field at various temperatures (K) from top to bottom: 1.8, 5, 7.5, 10, 15, 20, 25, 30, 35, 40, 45, and $50\mathrm{K}$. Right: ac susceptibility. (C) ${\chi }^{\prime }=20\mathrm{Hz}$. The inset shows the ${\chi }^{\prime }$ maximum for various frequencies from top to bottom: 20, 100, 200, and $1000\mathrm{Hz}$. (D) ${\chi }^{″}$ at various frequencies from top to bottom: 20, 40, 80, 100, 200, 500, and $1000\mathrm{Hz}$. The curves are each shifted by $-0.1$ from the preceding one. From 249.

Figure 21

Heat capacity for ${\mathrm{Y}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$. Left: Comparison of the total heat capacity for ${\mathrm{Y}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$ reported by 249 (filled black squares) and 278 (open circles) and the diamagnetic material ${\mathrm{Y}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ (open squares). Right: The magnetic component of the heat capacity. Note the absence of a sharp peak and the linear dependence at low temperatures. From 249).

Figure 22

Neutron diffraction data for ${\mathrm{Y}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$ showing difference plots (data at $200\mathrm{K}$ subtracted) at various temperatures. Note the buildup of broad peaks at the 111 and 222 Bragg positions. From 249.

Figure 23

Comparison of the temperature dependence of the total SANS intensity data for the ferromagnet ${\mathrm{Tl}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$ and ${\mathrm{Y}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$ at $\left|\mathbf{Q}\right|=0.03{\mathrm{\AA }}^{-1}$ (237; 108). Similar results for ${\mathrm{Tl}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$ were obtained by 179.

Figure 24

Temperature dependence of the correlation lengths ${\xi }_1$ and ${\xi }_2$ for ${\mathrm{Y}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$, ${\mathrm{Ho}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$, and ${\mathrm{Yb}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$. From 108.

Figure 25

Bulk properties of ${\mathrm{Yb}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$ and ${\mathrm{Ho}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$. Left column is the real part of the ac susceptibility and right column is the magnetic component of the heat capacity. From 108.

Figure 26

Temperature dependence of magnetic Bragg peaks for ${\mathrm{Yb}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$ and ${\mathrm{Ho}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$ showing order-parameter-like behavior and an apparent $T_c$ of $38\left(1\right)\mathrm{K}$ for both. From 108.

Figure 27

Electrical resistivity for the $A_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ series. Top: Resistivity data for the $A_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ series showing the metal-insulator crossover between $A=\mathrm{Eu}$ and Gd (341). Bottom: Evidence for metal-insulator transitions with decreasing temperature for $A=\mathrm{Eu}$, Sm, and Nd but not for Pr. From 191.

Figure 28

Magnetic susceptibility for ${\mathrm{Sm}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ showing evidence for a magnetic anomaly near $120\mathrm{K}$. From 312.

Figure 29

Neutron powder diffraction results for ${\mathrm{Gd}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$. Top: The magnetic scattering at $1.7\mathrm{K}$ after a $90\mathrm{K}$ data set has been subtracted. The solid line is a fit to a model with collinear ferromagnetic coupling between Gd and Mo moments. Bottom: The temperature dependence of the ordered moments for the Gd and Mo sublattices. The inset shows the temperature development of the correlation lengths $\left(L\right)$ obtained from the widths of the Bragg peaks. From 197.

Figure 30

Proposed spin configurations [(a),(b) and (c),(d)] for the Mo and Nd moments from neutron diffraction on a single crystal of ${\mathrm{Nd}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$ at $4\mathrm{K}$. From 326.

Figure 31

Magnetic and electric (dc and Hall transport) properties of ${\mathrm{Nd}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$. (a) Temperature dependence of the bulk magnetic moment and the (200) magnetic reflection which tracks the development of the chiral order on the Nd sites in ${\mathrm{Nd}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$. (b) Temperature dependence of Hall conductivities for ${\mathrm{Nd}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$ and ${\mathrm{Gd}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$. Note the conventional behavior for $A=\mathrm{Gd}$ while the conductivity remains large and finite at low temperature for $A=\mathrm{Nd}$. From 307.

Figure 32

Susceptibility and heat capacity data for the spin glass, ${\mathrm{Y}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$. Left: dc magnetic susceptibility for ${\mathrm{Y}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$ at an applied field of $100\mathrm{Oe}$ (102). Right: (a) Heat capacity and (b) entropy for ${\mathrm{Y}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$. Note the broad maximum below $20\mathrm{K}$ and the linear dependence on temperature below $7\mathrm{K}$. From 235.

Figure 33

Spin dynamics in ${\mathrm{Y}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$. Left: Neutron spin echo results for ${\mathrm{Y}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$ at temperatures spanning $T_f=22.5\mathrm{K}$ determined from static magnetization data. Note that within this time window spin freezing is not fully established until $10\mathrm{K}$. From 89; 88. Right: Frequency dependent ac susceptibility ${\chi }^{\prime }$ for ${\mathrm{Y}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$ showing classical spin-glass behavior. From 205.

Figure 34

Nonlinear magnetization analyzed according to a scaling model for $T_f=22\mathrm{K}$, $\gamma =2.8$, and $\beta =0.75$. Inset shows a log-log plot which allows determination of the critical parameters with $\delta =4.73$ which follows from the scaling law with the above $\gamma$ and $\beta$ values. From 102.

Figure 35

The muon spin relaxation rate, $1∕T_1$, versus temperature. Note the critical slowing down near $T_f$ and the presence of a small but finite relaxation rate persisting to very low temperatures. From 66.

Figure 36

(Color online) Elastic neutron scattering for ${\mathrm{Y}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$ shown as the difference between data at 1.8 and $50\mathrm{K}$. The broad peak suggests the short-range order model shown in the inset. From 92.

Figure 37

Y-NMR data for ${\mathrm{Y}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$ showing multiple peaks arising below $200\mathrm{K}$, indicating the presence of multiple Y sites. From 154.

Figure 38

Diffuse magnetic elastic scattering for ${\mathrm{Tb}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$ at various temperatures (97).

Figure 39

The muon spin relaxation rate vs temperature for ${\mathrm{Tb}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$ in an applied field of $5\mathrm{mT}$. The inset shows the Tb moment fluctuation rate above the spin freezing point compared with neutron data indicated by the inverted triangles. From 66.

Figure 40

A phase diagram for $\left(A_{1-x}{A}_x^{\prime }\right){\mathrm{Mo}}_2{\mathrm{O}}_7$ pyrochlores. (a) $T_c$ or $T_f$. (b) Resistivity at $5\mathrm{K}$. (c) Magnetoresistance at $5\mathrm{K}$ and $T_c$ (d) Unit cell constant. From 151.

Figure 41

Illustration of the equivalence of the water ice rule “two protons near, two protons far” and the spin-ice rule “two spins in, two spins out.” The diagram (left) illustrates a water molecule in the tetrahedral coordination of the ice structure with proton positions located by displacement vectors that occupy a lattice of linked tetrahedra. In spin ice (right) the displacement vectors are replaced by rare-earth moments (“spins”) occupying the pyrochlore lattice, which is the dual lattice (i.e., the lattice formed by the midpoints of the bonds) of the oxide lattice in cubic ice.

Figure 42

Dipolar- spin-ice model: the scaled maximum eigenvalues ${\lambda }^{\max }\left(\mathbf{k}\right)∕D$ in the $\left(hhl\right)$ plane. The dipole-dipole interactions are treated with the Ewald approach. Here the exchange coupling $J$ in Eq. (1) was set to zero. While the spectrum is very flat, suggesting a weak propensity toward long-range order, a maximum at a unique ordering wave vector ${\mathbf{k}}_{\mathrm{ord}}=001$. From 99.

Figure 43

${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$: (a) Specific heat and (b) entropy vs temperature measured by 239. The recovered entropy at $10\mathrm{K}$ agrees reasonably well with Pauling’s entropy, $R∕2\ln (3∕2)$. The data are compared to that calculated by Monte Carlo simulations of 61 for the dipolar- spin-ice model with exchange $J_{\mathrm{nn}}=-1.24\mathrm{K}$ and dipolar coupling $D_{\mathrm{nn}}=2.35\mathrm{K}$. (c) ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$: The total specific heat is shown by the empty squares and the expected nuclear contribution by the solid line. The electronic contribution has been estimated by subtracting these two curves (open circles). Near to $0.7\mathrm{K}$, this subtraction is prone to a large error (see text). Dipolar- spin-ice simulation results are indicated by the filled circles. From 35.

Figure 44

(Color) ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$: Neutron scattering in the $hhl$ plane showing experimental data (upper panel; the sharp spots are nuclear Bragg scattering with no magnetic component) compared with Monte Carlo simulations of the near neighbor spin-ice model (middle panel) and the dipolar spin ice model (lower panel) (35). Blue indicates the weakest intensity and red-brown the strongest intensity.

Figure 45

Dipolar spin-ice model: the phase diagram. The antiferromagnetic ground state is an all-spin-in or all-spin-out configuration for each tetrahedron. The spin-ice configuration, which includes the ${\mathbf{k}}_{\mathrm{ord}}=001$ ground state, is a two-spin-in–two-spin-out configuration for each tetrahedron. The region encompassed between the quasivertical dotted lines displays hysteresis in the long-range ordered state selected (${\mathbf{k}}_{\mathrm{ord}}=000$ vs ${\mathbf{k}}_{\mathrm{ord}}=001$) as $J_{\mathrm{nn}}∕D_{\mathrm{nn}}$ is varied at fixed temperature $T$. From 194.

Figure 46

${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$: ac susceptibility (upper panel: ${\chi }^{\prime }$; lower panel; ${\chi }^{″}$) as a function of temperature at several frequencies, illustrating the “$15\mathrm{K}$ peak.” From 186.

Figure 47

(Color online) The magnetic entropy for ${\mathrm{Ho}}_{2+x}{\mathrm{Ti}}_{2-x}{\mathrm{O}}_{7-\delta }$ (integrated from below $T\approx 1–22\mathrm{K}$) as a function of stuffing at $H=0$ and $1\mathrm{T}$. The dashed lines represent the predicted ice entropy and total spin entropy values. Inset: The temperature dependence of the integrated entropy for few compositions at $H=0$ and $1\mathrm{T}$. From 169.

Figure 48

(Color) Inelastic neutron scattering from ${\mathrm{Ho}}_{2.3}{\mathrm{Ti}}_{1.7}{\mathrm{O}}_{7-\delta }$ (356). Data at $55\mathrm{mK}$, $700\mathrm{mK}$, and $10\mathrm{K}$, noting the appearance of a gapped spin excitation at low temperatures. Neutron spin echo results on stuffed (open symbols) and unstuffed (closed symbols) spin ice are depicted in the bottom right panel. Within the neutron time window, the spin ice appears static by $10\mathrm{K}$ (90% of the spin are static), but the stuffed spin ice has persistent dynamics.

Figure 49

(Color online) dc and ac susceptibility for ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. Left: The temperature dependence on the inverse molar susceptibility and the resulting fit to the Curie-Weiss law at high temperature $(T>250\mathrm{K})$. From 100. Right: The low-temperature $(T<0.5\mathrm{K})$ dependence of the magnetic susceptibility as a function of frequency. From 94.

Figure 50

Crystal field levels in ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ derived from inelastic neutron scattering data. Left: A typical constant $\left|\mathbf{Q}\right|$ scan at $2{\mathrm{\AA }}^{-1}$ revealing low-energy inelastic modes at $12\mathrm{K}$ on a powder sample of ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. Right: Schematic of the crystalline electric field levels. From 100.

Figure 51

(Color) Diffuse scattering from a single crystal of ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ at $50\mathrm{mK}$ (left) and $9\mathrm{K}$ (right) (91; 94). Sharp Bragg peaks can be seen at the appropriate reciprocal lattice positions in the $50\mathrm{mK}$ data set, but at $9\mathrm{K}$ these have been subtracted out using a high-temperature $\left(100\mathrm{K}\right)$ data set.

Figure 52

Cuts through the checkerboard board pattern of diffuse magnetic scattering (open symbols) along high-symmetry directions of the cubic lattice. To complement these data, the dispersion of the lowest-lying magnetic excitation, at $4\mathrm{K}$, is also plotted (closed symbols). Fits to the diffuse scattering are shown and discussed in the text. From 91.

Figure 53

(Color online) Temperature dependence of the muon relaxation rate in a field of ${\left({\mathrm{Tb}}_p{\mathrm{Y}}_{1-p}\right)}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. From 155.

Figure 54

Estimate fluctuation rate of the ${\mathrm{Yb}}^{3+}$ moment derived from muon (filled circles) and Mössbauer (open circles) spectroscopies. Note the constant nonzero rate below $200\mathrm{mK}$. From 136.

Figure 55

(Color online) Magnetic susceptibility and $\mu \mathrm{SR}$ relaxation times for ${\mathrm{Er}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$. Top: The temperature dependence of the inverse magnetic susceptibility from a powder sample of ${\mathrm{Er}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$. The inset shows the temperature dependence of the stretch exponential exponent $\beta$ for ${\mathrm{Er}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ showing the evolution from exponential ($\beta \sim 1$) to Gaussian ($\beta \sim 2$) curve shape across $T_N$. For ${\mathrm{Er}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$, the relaxation is exponential ($\beta \sim 1$) for the entire temperature range. From 166.

Figure 56

(Color online) dc susceptibility at a field of $20\mathrm{mT}$ applied along [111] for ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$. Note the $\ln \left(T\right)$ dependence expected for the Kondo effect and (inset) evidence for spin freezing. From 216.

Figure 57

Magnetic phase diagrams of the ${\mathrm{Gd}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ for three different orientations of an applied magnetic field. These phase boundaries roughly approximate those seen by 240) on a powder sample. From 227.

Figure 58

(Color) Neutron scattering with $\Delta E=\pm 0.5\mathrm{meV}$ from ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ at $1\mathrm{K}$. (a) Zero field, (b) $2\mathrm{T}$, and (c) $8.5\mathrm{T}$. (d) Constant $Q$ scans at $0.1\mathrm{K}$ indicating that the low-lying magnetic scattering (slow spin dynamics) is quenched as the field increases. From 258.

Figure 59

Pressure induced magnetic Bragg scattering from polycrystalline ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ at $<2\mathrm{K}$. The data show the pressure evolution of static correlations in the cooperative paramagnet. Insets: the Néel temperature, $T_N$ (left), and ordered magnetic moment at 1.4 K, $M$ (right), versus pressure. From 202.

Figure 60

Pressure dependence on the magnetic scattering from ${\mathrm{Gd}}_2{\mathrm{Mo}}_2{\mathrm{O}}_7$. Note the broadening of the reflection near $q=1{\mathrm{\AA }}^{-1}$ which is complete by $2.7\mathrm{GPa}$. From 197.