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Recent interest in topological nature in condensed matter physics has revealed the essential role of Berry curvature in anomalous Hall effect (AHE). However, since large Hall response originating from Berry curvature has been reported in quite limited materials, the detailed mechanism remains unclear at present. Here, we report the discovery of a large AHE triggered by a pressure-induced magnetic phase transition in elemental $\alpha$-Mn. The AHE is absent in the non-collinear antiferromagnetic phase at ambient pressure, whereas a large AHE is observed in the weak ferromagnetic phase under high pressure despite the small averaged moment of $\sim 0.02 \mu_B$/Mn. Our results indicate that the emergence of the AHE in $\alpha$-Mn is governed by the symmetry of the underlying magnetic structure, providing a direct evidence of a switch between a zero and non-zero contribution of the Berry curvature across the phase boundary. $\alpha$-Mn can be an elemental and tunable platform to reveal the role of Berry curvature in AHE.

International audience; T he focus of much research on correlated-electron quantum materials is the competition between ordered and disordered electronic states, their tuning via quantum phase transitions and their possible relationship with unconventional superconductivity 1-6. Amongst these materials, URu 2 Si 2 occupies a special place, due to the richness of its quantum electronic properties and the challenge of understanding them 7. Discussions and controversies still exist about the nature of the 'hidden-order' (HO) phase, which is established below the temperature T 0 = 17.5 K. Efforts have been devoted to understand its order parameter, but so far none has been successful in determining it unambiguously. The transition at T 0 leads to strong physical responses, such as a large jump in the heat capacity 8 , an enhancement and a sudden gapping of intersite magnetic fluctuations 9,10 , a boost of the carrier mobility and a modification of the Fermi surface 11-14 and the opening of an electronic gap 15,16. While neutron diffraction experiments 17 showed a small antiferromagnetic (AF) moment below T 0 , most now accept that ambient-pressure antiferromagnetism is an extrinsic property induced by crystal defects and distortions 18. One proposal, motivated by Fermi-surface studies under pressure, is that the HO has the same periodicity of wavevector k 0 = (0 0 1) as the AF phase stabilized under pressure 19. The symmetry of the HO has also been considered: torque 20 and diffrac-tion 21 experiments lead to the proposal of a nematic behaviour in the HO phase. However, this picture faces a series of contradictory diffraction 22,23 , NMR 24 and thermodynamic 25 experiments, and the question of the symmetry remains open. Beyond experiments , many theories have tried to describe the HO within different approaches: localized, itinerant or dual (localized/itinerant) f-electrons, multipolar order, nematicity, spin liquid, 'hastatic' order and so on 26-30. It is difficult to find experimental evidence, in a direct and unambiguous manner, for the order parameters proposed by these models. To reveal the physics of the HO, an alternative route is to study how it can be destabilized by tuning external parameters 5. In the HO state, gapped low-energy magnetic fluctuations peaked at the wavevectors k 0 and k 1 = (0.6 0 0) (refs. 9,10) can be seen as precursors of long-range magnetic ordering with the same wavevectors and indicate nearby quantum phase transitions. In heavy-fermion paramagnets, such intersite magnetic fluctuations often indicate the proximity of a magnetically ordered phase. For instance, in the textbook CeRu 2 Si 2 case quantum magnetic fluctuations with wave-vector k 1 = (0.31 0 0) can be transformed into long-range magnetic order with the same wavevector by La doping 31. As well as doping, pressure and magnetic field are ideal tools to tune the electronic interactions. In URu 2 Si 2 , hydrostatic pressure 32-34 leads to a phase transition from the HO phase towards an AF state, with the wave-vector k 0 and the moments aligned along the c axis of the tetrago-nal crystal. At ambient pressure, under a magnetic field from 35 to 39 T applied along c, the HO is replaced by a spin-density wave (SDW), where the magnetic moments are ordered with the wave-vector k 1 and aligned along c (refs. 35,36). Remarkably, experiments under combined magnetic field and pressure, in the limited ranges 16 T/2 GPa (ref. 37) and 45 T/1 GPa (ref. 38), showed that a magnetic field applied to the pressure-induced AF phase induces a return to the HO phase 37 , and that the SDW phase shrinks and moves to higher fields under pressure 38. The relative stability of these different types of order is clearly complicated, and a full description of how URu 2 Si 2 evolves under combined pressure and magnetic field is needed. Here, we present the three-dimensional (3D) magnetic-field-pressure-temperature phase diagram of URu 2 Si 2. Its magnetoresis-tivity was measured in magnetic fields up to 60 T combined with pressures up to 4 GPa. We find a rich phase diagram indicating a subtle competition between the electronic interactions. The main features are the disappearance of the field-induced SDW phase and a squeezing out of the HO phase under high pressure. We emphasize that many of the boundaries of the 3D phase diagram are controlled by the field and pressure dependences of a single parameter characterizing the electronic correlations. The mystery of the hidden-order phase in the correlated electron paramagnet URu 2 Si 2 is still unsolved. To address this problem, one strategy is to search for clues in the subtle competition between this state and neighbouring magnetically ordered states. It is now well established that long-range antiferromagnetic order can be stabilized in this metal when it is under pressure and that a spin-density wave manifests when a magnetic field is applied along the easy magnetic axis c. However, the full boundaries of the hidden-order phase in the pressure-magnetic-field plane have not been determined so far. Here we present a systematic investigation of URu 2 Si 2 under combined high pressures and intense magnetic fields. The boundaries of the hidden-order, antiferromagnetic and spin-density-wave phases are mapped out, indicating an intricate three-dimensional phase diagram. We show that the field-induced spin-density-wave and hidden-order phases disappear in favour of antiferromagnetism at high pressure. Interestingly, a large number of phase boundaries are controlled by the field and pressure dependences of a single parameter. This gives new constraints for theories that model the electronic correlations and ordered phases in URu 2 Si 2. NAtURe PhySicS | VOL 16 | SEPTEMbER 2020 | 942-948 | www.nature.com/naturephysics 942

Alkali metal nanoclusters can be stabilized in the regular cages of zeolite crystals by the loading of guest alkali metals. Cages are connected by the sharing of windows of the framework, and arrayed in simple cubic, diamond and body centered cubic structures in zeolites A, X and sodalite, respectively. The s-electrons have the localized nature of nanoclusters with magnetic moments, and have mutual interactions through the windows of cages. They show exotic magnetism depending on the structure type of zeolites, the kind of alkali metals and the average loading density of alkali atoms per cage. In zeolite A, potassium clusters are formed in α-cages that have an inside diameter of 11 A. They exhibit ferromagnetic properties explained by the canted antiferromagnetism of the Mott insulator, where the 1p-like degenerate orbitals of clusters play an essential role in the magnetic properties. Na-K alloy clusters generated at supercages and β-cages of low-silica X (LSX) zeolite exhibit Neel’s N-type ferrimagnetism at specific loading densities of alkali metals. Alkali metal clusters in sodalite show the ideal Heisenberg antiferromagnetism of the Mott insulator.

We report the discovery of new superconducting and novel magnetic phases in CeIn$_3$ on the verge of antiferromagnetism (AFM) under pressure ($P$) through the In-nuclear quadrupole resonance (NQR) measurements. We have found a $P$-induced phase separation of AFM and paramagnetism (PM) without any trace for a quantum phase transition in CeIn$_3$. A new type of superconductivity (SC) was found in $P=2.28-2.5$ GPa to coexist with AFM that is magnetically separated from PM where the heavy fermion SC takes place. We propose that the magnetic excitations such as spin-density fluctuations induced by the first-order magnetic phase transition might mediate attractive interaction to form Cooper pairs.

Neutron diffraction experiments on the heavy-fermion superconductor PrOs 4 Sb 12 revealed that a small antiferromagnetic moment, parallel to [010] ( y -direction), is induced in the field-induced phase ( H ∥ z ). The analysis, based on the Γ 1 singlet ground state crystal field model, shows that antiferro-order of O y z -type quadrupole moments of Pr ions is formed in the field-induced phase. This strongly suggests that the crystal field ground-state of Pr ions in PrOs 4 Sb 12 is the Γ 1 singlet and the quadrupolar ordering is induced due to level crossing with an excited state under a magnetic field.

The effects of pressure on antiferromagnetic (AFM) and superconducting phase transitions of 112-type Ca$_{1-x}$La$_{x}$FeAs$_{2}$ were studied, and the in-plane electrical resistivity $\rho_{ab}$ was measured with an indenter-type pressure cell. The AFM phase transition temperatures of $T_{\rm N}$ = 47, 63, and 63 K at ambient pressure for $x$ = 0.18, 0.21, and 0.26 was suppressed by applying pressure $P$, with superconductivity emerging at critical pressures of $P_{\rm c}$ $\simeq$ 0, 1.5, and 3.4 GPa, respectively. Correspondingly, the slope of $T_{\rm N}$ against $P$ decreased as $dT_{\rm N}/P$ $\simeq$ $-$15 and $-$2 K/GPa for $x$ = 0.21 and 0.26, respectively. Thus, although the AFM phase was stabilized with La doping $x$, the AFM phase was suppressed by pressure, and superconductivity eventually emerged., Comment: 4 pages, 2 figures, Note added after publication: We noticed a paper by Yazhou Zhou et al. [Science Bulletin, 62, 857(2017)] reporting the pressure-induced superconductivity in the 112 system

We have measured the ac magnetic susceptibility in various fields and thermal expansion of single crystals of the heavy fermion compound ${\mathrm{CeCu}}_{6}$ at temperatures down to $250\ensuremath{\mu}\mathrm{K}$. The susceptibility of ${\mathrm{CeCu}}_{6}$ shows a peak at about 2 mK and has a large anisotropy. We also detected an anomaly of thermal expansion at the same temperature. The observed behaviors of the susceptibility and the thermal expansion in ${\mathrm{CeCu}}_{6}$ indicate the occurrence of an antiferromagnetic order.

We studied systematically a series of the ternary compounds RRhIn 5 (R: rare earth) which were grown in the single crystalline form by means of the flux method. Most of these compounds order antiferromagnetically at low temperatures, except for R = Y, La, Pr and Yb. The observed temperature dependence of the specific heat and the anisotropic features in the magnetic susceptibility and magnetization have been analyzed on the basis of the crystalline electric field (CEF) model, and an interesting relationship between the anisotropic exchange interaction and the CEF effect is obtained for RRhIn 5 compounds.

We report the novel phase diagram of superconductivity (SC) and antiferromagnetism (AFM) in heavy-fermion (HF) pressure( P )-induced superconductors CeRhIn 5 and CeIn 5 through nuclear-quadrupole-resonance (NQR) measurements under P . The P -induced superconductivity in CeRhIn 5 coexists with AFM on a microscopic level in P =1.5–1.9 GPa. By contrast, in CeIn 3 , the P -induced phase separation of AFM and paramagnetism (PM) takes place without any trace of a quantum phase transition. The outstanding finding is that SC sets in at both the phases magnetically separated into AFM and PM in P =2.28–2.5 GPa.

We report the discovery of novel phases in CeIn3 on the verge of antiferromagnetism (AFM) through the In-nuclear quadrupole resonance (NQR) measurements. We have found that even though a pressure (P)-induced phase separation into AFM and paramagnetism (PM) takes place, a novel superconductivity (SC), which is induced without strong spin fluctuations, has been found to coexist with AFM on a microscopic level. We propose that the magnetic excitations such as spin-density fluctuations induced by the first-order magnetic phase transition might mediate attractive interaction to form Cooper pairs.

The effects of Ni substitution on Ce(Cu1-xNix)2Si2 have been studied by specific heat and electrical resistivity measurements. The specific heat measurement has revealed that the enhanced quantum fluctuations around an antiferromagnetic quantum critical point are markedly suppressed by Ni substitution, and that the Fermi liquid state recovers in the Nirich region (x > 0.12). The characteristic T-linear dependence of the resistivity has been observed at approximately x ~ 0.10 together with a sign of superconductivity. The variation of n in the form of rho - rho0 = aT^n against Tmax^1, at which the resistivity peaks, coincides with the case of high-pressure experiments on pure CeCu2Si2. The anomalous T-linear behavior appears to occur in the crossover region from the Kondo regime to the valence fluctuation regime rather than in the conventional antiferromagnetic quantum critical region., 11 pages, 5 figures, to be published (J. Phys. Soc. Jpn)

We report on pressure-induced unconventional superconductivity (SC) in the heavy-fermion (HF) antiferromagnet ${\mathrm{CeIn}}_{3}$ by means of nuclear-quadrupole-resonance (NQR) studies conducted under a high pressure. The temperature $(T)$ and pressure $(P)$ dependences of the In-NQR spectra have revealed a first-order quantum-phase transition (QPT) from antiferromagnetism (AFM) to paramagnetism (PM) at a critical pressure ${P}_{\mathrm{c}}=2.46\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ at which AFM disappears with a minimum value of ${T}_{\mathrm{N}}({P}_{\mathrm{c}})=1.2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. High-energy x-ray scattering measurements under $P$ show a progressive decrease in the lattice density without any change in the crystal structure, whereas an increase in the NQR frequency $({\ensuremath{\nu}}_{\mathrm{Q}})$ indicates an increase in the hybridization between $4f$ electrons and conduction electrons, which stabilizes the HF-PM state. This competition between the AFM phase where ${T}_{\mathrm{N}}$ is reduced and the formation of the HF-PM phase triggers the first-order QPT at ${P}_{\mathrm{c}}=2.46\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. Despite the lack of an AFM quantum critical point in the $P\text{\ensuremath{-}}T$ phase diagram, we highlight the fact that unconventional SC occurs in both phases of AFM and PM. The measurements of the nuclear spin-lattice relaxation rate $1∕{T}_{1}$ in the AFM phase have provided evidence for the uniformly coexisting $\mathrm{AFM}+\mathrm{SC}$ phase. Remarkably, the significant increase in $1∕{T}_{1}$ upon cooling in the AFM phase has revealed the development of low-lying magnetic excitations down to ${T}_{\mathrm{c}}$ in the AFM phase; it is indeed relevant to the onset of the uniformly coexisting AFM+SC phase. In the HF-PM phase where AFM fluctuations are not developed, $1∕{T}_{1}$ decreases without the coherence peak just below ${T}_{\mathrm{c}}$, followed by a power-law-like $T$ dependence that indicates an unconventional SC with a line-node gap. Remarkably, ${T}_{\mathrm{c}}$ has a peak around ${P}_{\mathrm{c}}$ in the HF-PM phase as well as in the AFM phase. In other words, an SC dome exists with a maximum value of ${T}_{\mathrm{c}}=230\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$ around ${P}_{\mathrm{c}}$, indicating that the origin of the pressure-induced HF SC in ${\mathrm{CeIn}}_{3}$ is not relevant to AFM spin fluctuations but to the emergence of the first-order QPT in ${\mathrm{CeIn}}_{3}$. These phenomena observed in ${\mathrm{CeIn}}_{3}$ should be understood in terms of the first-order QPT because these new phases of matter are induced by applying $P$. When the AFM critical temperature is suppressed at the termination point of the first-order QPT, ${P}_{\mathrm{c}}=2.46\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, the diverging AFM spin-density fluctuations emerge at the critical point from AFM to PM. The results with ${\mathrm{CeIn}}_{3}$ leading to a new type of quantum criticality deserve further theoretical investigations.

The temperature dependence of the Hall coefficient of CeIn3 under high pressure has been investigated. The absolute value of the Hall coefficient shows an anomalous increase below T* ∼ 80 K at ambient pressure. The increase in T* with increasing pressure is similar to the pressure dependence of the characteristic temperature where the resistivity reaches its maximum. The temperature variations below T* at various pressures are well scaled on a single curve that is the formula based on the two-fluid model. No effect of the antiferromagnetic fluctuations observed in CeTIn5 (T = Co, Rh, and Ir) is observed above 2 K even near the critical pressure where antiferromagnetic ordering disappears.

We present detailed investigations on the effects of Ni substitution (x) on Ce(Cu1−xNix)2Si2 with x < 0.3, and a pressure (p) study for x = 0.04(2), 0.05(2), and 0.09(2) by resistivity measurements. The Cu–Ni substitution suppresses both antiferromagnetic fluctuations and superconductivity in CeCu2Si2, and leads to a dramatic crossover from the heavy-fermion (HF) regime to the intermediate-valence (IV) regime with progressive Ni doping. The crossover can be characterized by a marked increase in Kondo temperature evaluated from resistivity, specific heat, and susceptibility measurements. In high-pressure resistivity measurements, the Ni-doped system exhibits similar anomalies to those observed in CeCu2Si2, namely, T-linear dependence, an enhancement of residual resistivity, and a marked decrease in the A coefficient of the T2-resistivity. Furthermore, we observed an unexpected upturn anomaly in resistivity in the Ni-doped system under high pressure. By constructing the x–p phase diagram of Ce(Cu1−xNix)2Si2...

Systematic neutron-scattering experiments have been carried out in order to reveal the crystal and magnetic structures as well as the magnetic excitation in the Ce-based intermetallic compound ${\mathrm{CeAgSb}}_{2}.$ It was clarified that the Ag atoms in ${\mathrm{CeAgSb}}_{2}$ (space group: $\mathrm{P}4/nmm)$ occupy the 2b site, while Sb atoms occupy $2a$ and $2c$ sites, which have, to date, been controversial in literature. From the analysis of neutron powder-diffraction profile, we found the existence of the ferromagnetic component of about $0.41{\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{Ce}$ oriented along the c axis, consistent with the result of previous studies. On the other hand, however, no trace of the antiferromagnetic or spin-density wave peak was detected within our range of experimental accuracy. We observed a considerable spin-wave excitation below 3 meV. The dispersion relation was explained by the anisotropic Heisenberg model. This means that ${\mathrm{CeAgSb}}_{2}$ has a simple ferromagnetic structure. Furthermore, crystalline electric-field (CEF) excitations were observed at 5.2 and 12.5 meV in the paramagnetic state, which is indicative of the localized nature of the $\mathrm{Ce}\ensuremath{-}4f$ electron. Our analysis revealed that $|{J}_{z}=\ifmmode\pm\else\textpm\fi{}\frac{1}{2}〉$ is the ground state, while the first and second excited levels are mainly due to $|\ifmmode\pm\else\textpm\fi{}\frac{3}{2}〉$ and $|\ifmmode\pm\else\textpm\fi{}\frac{5}{2}〉,$ respectively. The observed ferromagnetic moment is in good agreement with the ground-state saturation moment, ${g}_{J}{\ensuremath{\mu}}_{\mathrm{B}}{J}_{\mathrm{z}}\ensuremath{\sim}0.43{\ensuremath{\mu}}_{\mathrm{B}}.$ The susceptibility, magnetization curve, and magnetostriction can be explained in terms of the CEF level scheme with anisotropic exchange interaction.

Evolution of the pressure-induced heavy fermion state and superconductivity in ${\mathrm{CeRhIn}}_{5}$ have been established by high-pressure Fermi surface studies using dHvA technique. The effective mass of the conduction electrons named branch ${\ensuremath{\beta}}_{2}$ increases from 5.5 ${m}_{0}$ at ambient pressure to 20 ${m}_{0}$ at 1.6 GPa where superconductivity sets in. This heavy electron mass continues to increase steeply up to 2.1 GPa, 45 ${m}_{0}$ at 2.1 GPa, with a concomitant increase of the superconducting transition temperature. However, the underlying Fermi surface remains approximately same even at 2.1 GPa, strongly suggesting that antiferromagnetic fluctuations of Ce moments do not contribute to the volume of the Fermi surface, but enhance the cyclotron mass of the conduction electrons.

EuGa4 and EuAl4 crystallize in the BaAl4-type tetragonal structure. The antiferromagnetic order was observed at 15 and 16.5K in EuGa4 and EuAl4, respectively.1,2) The magnetic susceptibilities in EuGa4 and EuAl4 well follow the Curie–Weiss law with effective moments of 7.97 and 8.02 B, respectively, which are consistent with the theoretical value of 7.94 B for a Eu-divalent electronic state.1,3) In the electrical resistivity and thermoelectric power measurements under pressure, a shoulderlike change was observed below about 100K at 1GPa in EuGa4. Moreover, a similar resistivity hump was observed below TCDW 1⁄4 140K at ambient pressure in EuAl4. The authors in Ref. 2 considered that this transition corresponds to the emergence of a charge density wave (CDW). In this study, we measured the magnetoresistance and Hall effect to clarify whether this is indeed based on CDW transition. Single crystals of EuAl4 were grown by the Al self-flux method. The transverse magnetoresistance and Hall resistivity were measured with an AC resistance bridge. The magnetic field H was applied along the [010] and [001] directions. The electrical current flow J was parallel to the [100] direction. Figure 1 shows a Kohler plot for the transverse magnetoresistance in the configurations of H k 1⁄2001 and J k 1⁄2100 . Kohler’s rule, i.e., = 1⁄2 ðHÞ ð0Þ = ð0Þ 1⁄4 fðH= ð0ÞÞ, holds when the temperature dependences of the scattering relaxation time are the same for all carriers. The = above 150K, namely, at 150, 160, and 200K, is well scaled on a single curve, which indicates that Kohler’s rule is satisfied above TCDW. On the other hand, the = below 140K deviates from Kohler’s rule, indicating that the carrier density and/or the scattering mechanism change below TCDW. In the two-band model, the transverse magnetoresistance and Hall resistivity are expressed as xx 1⁄4 ex hxð ey þ hyÞ þ ð exR 2 h þ hxReÞH ð ex þ hxÞð ey þ hyÞ þ ðRe þ RhÞH2 ; ð1Þ yx 1⁄4 ðRe hx hy þ Rh ex eyÞ þ ReRhðRe þ RhÞH 2 ð ex þ hxÞð ey þ hyÞ þ ðRe þ RhÞH2 H; ð2Þ where ei ( hi) and Re (Rh) are the resistivity along the i 1⁄4 xor y-direction and the Hall coefficient of the electron (hole) band, respectively.4) The Hall coefficient of each band is inversely proportional to the carrier density as Re 1⁄4 1=nee and Rh 1⁄4 1=nhe, where ne and nh are the electron and hole densities, respectively. The resistivity of each band is ei 1⁄4 1=ne eie ( hi 1⁄4 1=nh hie), where ei ( hi) is the mobility of the electron (hole). The transverse magnetoresistance increases quadratically, = H, for a compensated metal (ne 1⁄4 nh) at a high field limit (!c 1), whereas it tends to saturate for an uncompensated metal (ne 61⁄4 nh). Here, !c is the cyclotron frequency and is the scattering relaxation time. !c is roughly estimated using the relation = ð!c Þ2, which is obtained from the free-electron model. There is one EuAl4 unit in a body-centered tetragonal primitive cell. Considering that Eu is divalent, as proved by the magnetic susceptibility data,3) EuAl4 is a compensated metal with an even number of valence electrons. The experimentally obtained H-dependent magnetoresistance of up to = 2:5 10 2 (!c 0:16), shown as the solid curve in Fig. 1, reveals that EuAl4 is a compensated metal above TCDW. On the other hand, the = below TCDW gradually deviates at higher fields from the initial H dependence, as shown by the broken curve in Fig. 1 and the broken line in the inset of Fig. 1, at 100K. The deviation at 100K occurs at = 8 10 3 (!c 0:09). This behavior corresponds to the tendency toward saturation at higher fields, although the high field limit (!c 1) is not satisfied. Therefore, the transverse magnetoresistance indicates that EuAl4 is a compensated metal above TCDW and changes into an uncompensated metal below TCDW. The present experimental result and the hump of μ just below TCDW indicate that ne or nh starts to decrease below TCDW. Figure 2 shows the temperature dependence of the Hall coefficient RH determined at 0 T, shown by solid circles for H k 1⁄2010 and by solid squares for H k 1⁄2001 . The phase transitions at TCDW 1⁄4 140K and TN 1⁄4 14K are well observed. RH is temperature independent and negative above TCDW for both field directions. This means that the anomalous Hall coefficient, which is related to the magnetic susceptibility, is negligible in EuAl4. The negative RH for the compensated metal indicates e > h. The absolute value of RH increases with decreasing temperature below TCDW. The Hall resistivity is proportional to the magnetic field above TCDW, for example, at 200K, as shown in the inset of Fig. 2. On the other hand, the Hall resistivity gradually deviates downward from the linear field dependence with decreasing 0.06

We report the pressure $(P)$-temperature $(T)$ phase diagram of antiferromagnetism and superconductivity in ${\mathrm{CeRhIn}}_{5}$ and ${\mathrm{CeIn}}_{3}$ revealed by the ${}^{115}\mathrm{In}$ nuclear-spin-lattice-relaxation ${(T}_{1})$ measurement. In the itinerant magnet ${\mathrm{CeRhIn}}_{5},$ we found that the N\'eel temperature ${T}_{N}$ is reduced at $Pg~1.23\mathrm{GPa}$ with an emergent pseudogap behavior. In ${\mathrm{CeIn}}_{3},$ the localized magnetic character is robust against the application of pressure up to $P\ensuremath{\sim}1.9\mathrm{GPa},$ beyond which the system evolves into an itinerant regime in which the resistive superconducting phase emerges. We discuss the relationship between the phase diagram and the magnetic fluctuations.

That the $4f$ electrons in the rare-earth antiferromagnetic compound ${\mathrm{CeRh}}_{2}{\mathrm{Si}}_{2}$ should be considered as localized electrons at cerium sites has been confirmed by comparing a de Haas--van Alphen experiment to the result of energy band calculations for ${\mathrm{LaRh}}_{2}{\mathrm{Si}}_{2}.$ When pressure p is applied to the compound, the N\'eel temperature ${T}_{\mathrm{N}1}=36 \mathrm{K}$ decreases and finally becomes zero at ${p}_{\mathrm{c}}\ensuremath{\simeq}1.0$--1.1 GPa. The topology of the Fermi surface is found to be almost unchanged up to 1.0 GPa, but the cyclotron effective mass increases with increasing pressure. Above 1.1 GPa, the topology of the Fermi surface changes abruptly. A new Fermi surface is explained by the $4f$-itinerant-band model. The corresponding cyclotron mass is large, being about ${22m}_{0}.$

We have studied the de Haas–van Alphen (dHvA) effect under pressure for an antiferromagnet CeRhIn5, where the antiferromagnetic state is changed into the superconducting state at higher pressures than 1.6 GPa . It is clarified from the present dHvA experiment that the topology of the Fermi surface is unchanged up to 2.1 GPa but the cyclotron mass increases strongly above 1.6 GPa . Superconductivity is found to be realized in this heavy fermion state.

High-field magnetization measurements in a heavy fermion antiferromagnet CeRh2Si2 were performed under high pressures at various temperatures to study the nature of the metamagnetism. Metamagnetic transitions were observed not only in the antiferromagnetic state but also in the paramagnetic state at various pressures. The metamagnetism in CeRh2Si2 does not originate from the rearrangement of antiferromagnetic moments but from the recovery of the local moment from the Kondo singlet state by applying high magnetic fields.

A series of ternary compounds RRhIn 5 (R: rare earth) has been grown in the single crystalline form by means of the flux method. The magnetic properties of these compounds were investigated by meas...