Antiferroquadrupolar Research Articles

Search for heavy quasiparticles in the resistivity ofPrOs4Sb12in magnetic fields: Comparison withPr0.7La0.3Os4Sb12

We study the resistivity $\ensuremath{\rho}(T)$ of ${\text{PrOs}}_{4}{\text{Sb}}_{12}$ and ${\text{Pr}}_{0.7}{\text{La}}_{0.3}{\text{Os}}_{4}{\text{Sb}}_{12}$ in magnetic fields between 2.7 and 16 T and at temperatures $20\text{ }\text{mK}\ensuremath{\le}T\ensuremath{\le}1\text{ }\text{K}$. ${\text{PrOs}}_{4}{\text{Sb}}_{12}$ is known to exhibit field-induced antiferroquadrupolar (AFQ) order while there is no evidence for such order in the specific heat of ${\text{Pr}}_{0.7}{\text{La}}_{0.3}{\text{Os}}_{4}{\text{Sb}}_{12}$. We find the resistivity of ${\text{Pr}}_{0.7}{\text{La}}_{0.3}{\text{Os}}_{4}{\text{Sb}}_{12}$ to be consistent with the accepted crystalline electric field (CEF) model. The model predicts a low-temperature plateau in $\ensuremath{\rho}(T)$ in fields smaller or larger than the CEF level-crossing field of approximately 9 T, as is also observed in ${\text{PrOs}}_{4}{\text{Sb}}_{12}$. However, further analysis suggests that for ${\text{PrOs}}_{4}{\text{Sb}}_{12}$ in fields below 5 T, this plateau is not a CEF effect but is rather due either to a crossover to a state characterized by a small electronic effective mass ${m}^{\ensuremath{\ast}}$ or to the existence of two resistivity contributions, one increasing and the other decreasing with temperature. In fields between 4 and 6 T, $\ensuremath{\rho}(T)$ shows a shallow minimum. A Kadowaki-Woods analysis of $\ensuremath{\rho}(T)$ of ${\text{PrOs}}_{4}{\text{Sb}}_{12}$ over a restricted temperature range implies that ${m}^{\ensuremath{\ast}}$ depends strongly on magnetic field, increasing when the field approaches the boundary of the AFQ region. However, for all fields investigated, ${\ensuremath{\partial}}^{2}\ensuremath{\rho}/\ensuremath{\partial}{T}^{2}$ for $T\ensuremath{\rightarrow}0$ remains small compared with its value in canonical heavy fermions. In the AFQ regime (only), the resistivity has different temperature dependences in fields parallel and perpendicular to the principal crystal direction of current flow, suggesting an increase in the orbital contribution to the resistivity in the ordered phase.

Thomson scattering from the antiferroquadrupolar ordering phase in TmTe

On the basis of the recently established crystal electric field level scheme of Γ8 − Γ6 − Γ7, we investigate the Thomson scattering intensity of the superstructure reflections with h,k,l = 2n + 1 in the Γ3-type (O22, O02) antiferroquadrupolar (AFQ) ordering phase of TmTe. The intensities show strong dependence on G and the direction of the applied magnetic field H. These dependences on G and H similar to those found in the AFQ phase of CeB6, another AFQ material with Γ5-type (Oyz, Ozx, Oxy) order parameter having the Γ8 ground states, may provide us a useful tool to distinguish the component of the AFQ order of Γ3-type and Γ5-type.

Magnetic Phase Diagrams of Dy0.8Gd0.2B2C2 with the Antiferroquadrupolar Ordering in the Antiferromagnetic Phase

Gd substitution for Dy in DyB 2 C 2 that undergoes an antiferroquadrupolar (AFQ) ordering at T Q =24.7 K and an antiferromagnetic (AFM) one at T N =15.3 K enhances the AFM interaction and weakens the AFQ interaction. In Dy 0.8 Gd 0.2 B 2 C 2 , the AFQ transition occurs at T Q =17.6 K below the AFM one at T N =19.0 K. However, the strong competition between the AFQ and AFM interactions supresses the development of the AFQ order parameter below T Q and causes an anomalous behavior in field-induced transitions. The magnetic phase diagrams of Dy 0.8 Gd 0.2 B 2 C 2 drawn from the experimental results of specific heat and magnetization have anomalous phase boundaries originating from this competition.

Quadrupole Ordering in Clathrate Compound Ce3Pd20Si6

Low-temperature elastic properties of the clathrate compound Ce 3 Pd 20 Si 6 were investigated using ultrasonic measurements. Pronounced softening of elastic constants ( C 11 - C 12 )/2 and C 44 with decreasing temperature indicates a precursor of electric quadrupole ordering due to a Γ 8 quartet ground sate with an orbital degeneracy for 8c site of a Ce ion. A minimum of ( C 11 - C 12 )/2 at T C =170 mK indicates a transition from paramagnetic phase I to an ordered phase III. Applied magnetic fields induce an antiferro-quadrupole (AFQ) ordered phase II with highly anisotropic character depending on the field direction, which resembles the AFQ phase with O x y -type order parameter in CeB 6 with the Γ 8 ground sate. The order paramater of the phase III may be characterized by either magnetic dipole or magnetic octupole. The Γ 7 ground state at 4a site may fall into a singlet screened by conduction electrons at low temperatures without long-range magnetic ordering.

Anisotropic Phase Diagram for Quadrupole Ordering and Possible Crystal Field Level Structure in TmTe

The origin of an anisotropic phase diagram for the antiferro-quadrupolar (AFQ) order in TmTe is studied using a realistic J = 7/2 multiplet model, based on a previous analysis for the classical limit J →∞. Assuming the Γ 3 -type AFQ order parameters, a quantitative comparison of the phase diagram with the experiments is presented for a few candidates of the crystal field (CF) level schemes. It is shown that a scheme with a sequence from low- to high-energy levels, Γ 8 -Γ 6 -Γ 7 , naturally explains the observed field dependence and anisotropy of the phase diagram. The resonant x-ray scattering signals in the AFQ phase are studied to explore a possibility of identifying the order parameter and the CF scheme experimentally.

Simultaneous Occurrence of an Antiferroquadrupolar and a Ferromagnetic Transitions in Rare-Earth Palladium Bronze CePd3S4

Neutron powder diffraction experiments have been performed on CePd 3 S 4 as well as measurements of magnetic and transport properties on a single-crystalline sample. Magnetic susceptibility increases markedly below T C = 6.3 K and a spontaneous magnetization appears below T C . The logarithmic temperature dependence of electrical resistivity implies that CePd 3 S 4 is classified into a Kondo-lattice compound whose Kondo temperature is comparable to T C . Magnetic susceptibility is analyzed satisfactorily with a crystalline electric field model that the 4 f ground state of Ce 3+ is the Γ 8 quartet with the excited Γ 7 doublet located at 630 K. The magnetic structure of CePd 3 S 4 was determined to be a canted structure with a canting angle of 51°. Such a canted structure is a result of the ferromagnetic (FM) ordering and simultaneous [100]-type antiferroquadrupolar (AFQ) ordering at T C . The smaller magnetization values and an unexpectedly high T C can be explained by the simultaneous occurrence of AFQ an...

Spin Gap State ofS= 1/2 Heisenberg Antiferromagnet YbAl3C3

YbAl 3 C 3 has been investigated in detail, which was previously reported to show an antiferroquadrupolar (AFQ) ordering at an extremely high ordering temperature of 80 K. The present study has revealed that the specific heat, magnetic susceptibility, and electrical resistivity of the single crystalline YbAl 3 C 3 clearly exhibit the characteristic features of the first order transition around 77 K. In addition, we have discovered that LuAl 3 C 3 also exhibits a sharp peak in the specific heat around 110 K, which most likely corresponds to the 77 K transition of YbAl 3 C 3 . Therefore, the 77 K transition of YbAl 3 C 3 is considered to be irrelevant to the nature of the 4 f -electrons such as the AFQ ordering but is ascribed to a structural one. Low temperature physical properties of YbAl 3 C 3 below 77 K is indicative of a spin gap and a nonmagnetic ground state. A new model is proposed, in which the adjacent spins on the triangular lattice of Yb 3+ ions are antiferromagnetically coupled to form a dimer by the structural transition at 77 K. The spin gap behavior at low temperatures can be well explained by an isolated dimer model with a singlet–triplet energy gap of about 15 K.

Specific heat of praseodymium palladium bronze, PrPd 3S 4

We report the results of the specific-heat measurements on single crystalline samples of PrPd 3S 4. A second-order phase transition was observed at T Q=1.5 K. The T Q shifts to higher temperatures with increasing magnetic field for B<1.5 T, while it decreases for B>1.5 T. Such a re-entrant behavior of T Q in magnetic fields strongly suggests that an antiferroquadrupolar (AFQ) ordering occurs at T Q.

Analysis of hyperfine interactions in NMR studies of Pr skutterudites

The splitting of NMR signal, which is analyzed in terms of the invariant hyperfine coupling between the nuclear spin and the multipolar moments of magnetic ions, gives important information about the multipolar ordering. The NMR splitting of P nuclei is analyzed for the low-temperature phase of PrFe 4P 12, whose nature has been controversial. Two scenarios are examined: one is a modulation of the hyperfine coupling caused by the antiferro-quadrupole (AFQ) ordering; another is the hyperfine coupling due to a monopole-type ordering.

Antiferroquadrupolar Ordering and Anisotropic Magnetic Phase Diagram of Dysprosium Palladium Bronze, DyPd3S4

From the measurements of magnetization and specific heat, we constructed B – T phase diagrams of single-crystalline DyPd 3 S 4 which is known to exhibit antiferroquadrupolar (AFQ) and antiferromagnetic (AFM) ordering at low temperatures. The phase diagrams are found to be highly anisotropic and re-entrant, which are typical of rare-earth compounds exhibiting multipolar ordering. The crystalline electric field (CEF) scheme of Dy 3+ in DyPd 3 S 4 was deduced from the specific heat and magnetization measurements of the Y-diluted compounds Dy 1- x Y x Pd 3 S 4 (0.1≤ x ≤0.9) and discussed in detail. The CEF ground state was determined to be the orbitally-degenerated quartet Γ 67 (1) , and the overall splitting width was estimated to be about 104 K. No correlation was found between the anisotropy of T Q and that of the Zeeman splitting width of the ground quartet Γ 67 (1) .

A New Multipolar Ordering Compound, Rare-Earth Palladium Bronze PrPd3S4

Specific heat and magnetization measurements were performed on single crystalline PrPd 3 S 4 . A λ-type anomaly at T M = 1.56 K in the specific heat shifts to higher temperatures by magnetic fields, begins to shift to lower temperatures above 2 T, and disappears above 3.6 T. The 4 f ground state of Pr 3+ was deduced to be a magnetic triplet. Below T M , the magnetic susceptibility increases while no spontaneous magnetization appears. These results strongly reveal that PrPd 3 S 4 shows a multipolar ordering at T M . The most probable ordering state for PrPd 3 S 4 is an antiferroquadrupolar (AFQ) ordering since the B – T phase diagrams are of the “re-entrant” type, which is typical for AFQ ordering compounds.

Unusual Enhancement of Magnetization by Pressure in the Antiferro-Quadrupole-Ordered Phase in CeB6

The effect of pressure on CeB 6 was investigated by the measurement of the magnetization ( M ) under pressure, and we obtained the following results. The effect of pressure on M in phase I is very small. By applying pressure, T Q is enhanced, but T N and the critical field from the antiferromagnetic (AFM) phase III to the antiferro-quadrupole (AFQ) phase II ( H c III–II ) are suppressed, as previously reported. The magnetization curve in phase III shows the characteristic shoulder at H ∼ H c III–II /2 at ambient pressure. This shoulder becomes much more pronounced by applying pressure. Both H c III–II and the magnetic field, where a shoulder is seen in the magnetization curve in phase III, are largely suppressed by pressure. In phase II, the M – T curve at a low magnetic field exhibits an unusual concave temperature dependence below T Q down to T N . Thus, we found that the lower the magnetic field, the larger the enhancement of M in both phases III and II. To clarify the origin of the unusual pressure ef...

Comments on the Hidden Order in Phase IV of CexLa1-xB6

We have studied the effect of the O x y -antiferro-quadrupole (AFQ), T x y z -antiferro-octupole (AFO), and AF exchange interactions on the Γ 5 u -AFO order, which is a strong candidate of the orde...

Electrical Resistivity Measurements on PrPb3under High Pressures

PrPb 3 shows antiferroquadrupolar (AFQ) ordering below T Q = 0.4 K. Recently, Onimaru et al. revealed the existence of spatially modulated AFQ structure by neutron diffraction technique. Suggestively, an indirect RKKY-type quadrupolar interaction should play an important role in this system. In the present work, in order to examine stability of the AFQ ordered state in pressure, we carried out electric resistivity measurements under high pressures up to 7.3 GPa and at temperatures down to 0.3 K. We found that a kink observed at T Q in ρ( T ) gradually rose with increasing pressures up to 5 GPa, indicating that the AFQ ordered state would be stabilized by applying pressure. However, further increases in pressure above 5 GPa result in disappearance of the kink which should be observed at T Q .

Possible Antiferro-Octupolar Order in Antiferromagnetic TbB2C2 Examined by Gd Substitution

We have examined the effects of Gd substitution on the anomalous antiferromagnetic (AFM) properties of TbB 2 C 2 having field-induced antiferro-quadrupolar (AFQ) ordered phases. The Gd substitution induces drastic changes in the magnetic properties. The AFM structure characteristic to TbB 2 C 2 , the anomalous increase in magnetic susceptibility below T N , and the strong preference of AFM domains disappear with the substitution of low Gd content of less than 10%. We propose a promising assumption that an antiferro-octupolar (AFO) ordering occurs at T N simultaneously with AFM ordering in TbB 2 C 2 . The fragility of anomalous properties originates in the fragility of the antiferro-octupolar interaction against the substitution of Gd 3+ ions with L =0.

Frustrating Quadrupolar Interaction and Possible Pressure Effects in PrOs4Sb12

The skutterudite superconductor PrOs 4 Sb 12 exhibits a field-induced phase transition that is interpreted as an antiferro-quadrupolar (AFQ) ordering in the low-lying singlet–triplet crystal field levels. In this paper, we investigate the properties of the possible AFQ state in lower magnetic fields which can be realized with hydrostatic and uniaxial pressures. Making use of a new pseudo-spin description, we show that the AFQ model at zero field is well approximated as the quantum four-state Potts model with macroscopic ground-state degeneracy. Some consequences of this mapping and the resulting magnetic field effects on the AFQ state are discussed. In particular, it is shown that a type of uniaxial strains can stabilize the AFQ state in low fields by relaxing the frustration in the Potts limit. Based upon such findings, we study the mean field solutions of the original AFQ model as a function of the magnetic field. The evolutions from the field-induced order to the zero-field one are elucidated by changi...

Understanding the quadrupolar structures of [formula omitted

UPd 3 exhibits four phase transitions below T 0 = 7.8 K , attributed to a succession of antiferroquadrupolar (AFQ) orderings of the 5 f 2 uranium ions localised on the quasi-cubic sites of the dhcp crystal structure. From earlier polarised neutron diffraction measurements in a magnetic field, we proposed that the order parameter of the phase below T 0 is Q x 2 - y 2 and a model for the order parameters of the four phases was subsequently developed. This model has now been tested experimentally with measurements of the azimuthal dependence of the intensities of the quadrupolar reflections in the different phases, by means of X-ray resonant scattering (XRS) studies at ESRF. The results indicate that the order parameter, in zero field, of the phase below T 0 is Q zx . Our model provides an explanation for these apparently contradictory results. New measurements of the heat capacity of UPd 3 at low temperatures have revealed the entropy changes at each of the four transitions. We find that the entropy changes ( Δ S ) at T 0 and T + 1 = 6.9 K are minimal, whereas Δ S is large at T - 1 = 6.7 K . From this information together with the new XRS results, we have extended our model to provide an explanation of the AFQ structures of UPd 3 .

Ultrasonic investigations of antiferro-quadrupole ordering in [formula omitted

We have investigated elastic properties of a single crystal PrPb 3 showing antiferro-quadrupole (AFQ) ordering at T Q = 0.4 K using ultrasonic measurements. Since the crystalline-electric-field (CEF) ground state of PrPb 3 is a non-Kramers Γ 3 doublet having quadrupolar moments O 2 0 and O 2 2 , the temperature dependence of a transverse ( C 11 - C 12 ) / 2 mode shows a curie-type softening with decreasing temperature toward T Q . Furthermore, an anomaly accompanying a lock-in transition of AFQ ordering was observed in ( C 11 - C 12 ) / 2 on PrPb 3 at 250 mK . In the case of Pr 0.98 La 0.02 Pb 3 , ( C 11 - C 12 ) / 2 exhibits softening with decreasing temperature and shows a broad minimum at 330 mK . We have observed a large attenuation of the ( C 11 - C 12 ) / 2 mode in applying magnetic fields up to 13 T .

Field-induced quadrupolar order and possible pressure effect in [formula omitted

The skutterudite superconductor PrOs 4 Sb 12 exhibits a field-induced phase transition that is interpreted as an antiferro-quadrupolar (AFQ) ordering in the low-lying singlet-triplet crystal field levels. In this paper, we study theoretically the effect of uniaxial strains on the field-induced AFQ order using the pseudo-spin model introduced previously. It is shown that the strains stabilize the AFQ state in lower magnetic fields by relaxing the competing AFQ interaction. The characteristic evolution from the field-induced order to the zero-field one is elucidated by changing the strength of the strains.

Magnetic phase diagrams of [formula omitted] in high magnetic fields

We have performed ultrasonic measurements under high magnetic fields up to 30 T by using the hybrid magnet at the National Institute for Materials Science to investigate the magnetic phase diagram for antiferroquadrupole (AFQ) phase II in Ce x La 1 - x B 6 . With increasing Ce concentration x from x = 0.50 , the AFQ phase transition temperatures T Q indicate an almost linear increase in various fields. The large magnetic anisotropy of AFQ phase II, in which T Q H ∥ [ 0 0 1 ] is much smaller than T Q H ∥ [ 1 1 0 ] and T Q H ∥ [ 1 1 1 ] in high magnetic fields, is revealed in x = 0.75 , 0.60 as well as in x = 0.50 . These experimental results support the theoretical calculation based on the Γ 5 -type AFQ ordering and the magnetic field induced octupole T xyz .