The tetragonal heavy-fermion metal YbRh2Si2 orders antiferromagnetically at T N = 70 mK and exhibits an unconventional quantum critical point (QCP) of Kondo-destroying type at B N = 60 mT, for the magnetic field applied within the basal (a, b) plane. Ultra-low-temperature magnetization and heat-capacity measurements at very low fields indicate that the 4f-electronic antiferromagnetic (AF) order is strongly suppressed by a nuclear-dominated hybrid order (“A-phase”) at T A ≤ 2.3 mK, such that quantum critical fluctuations develop at B ≈ 0 (Schuberth et al., Science, 2016, 351, 485–488). This enables the onset of heavy-fermion superconductivity (T c = 2 mK) which appears to be suppressed by the primary antiferromagnetic order at elevated temperatures. Measurements of the Meissner effect reveal bulk superconductivity, with T c decreasing under applied field to T c < 1 mK at B > 20 mT. The observation of a weak but distinct superconducting shielding signal at a temperature as high as 10 mK suggests the formation of insulated random islands with emergent A-phase order and superconductivity. Upon cooling, the shielding signal increases almost linearly in temperature, indicating a growth of the islands which eventually percolate at T ≈ 6.5 mK. Recent electrical-resistivity results by Nguyen et al. (Nat. Commun., 2021, 12, 4341) confirm the existence of superconductivity in YbRh2Si2 at ultra-low temperatures. The combination of the results of Schuberth et al. (2016) and Nguyen et al. (2021) at ultra-low temperatures below B N, along with those previously established at higher temperatures in the paramagnetic state, provide compelling evidence that the Kondo-destruction quantum criticality robustly drives unconventional superconductivity.

Following our recent discovery of superconductivity in YbRh $$_2$$ Si $$_2$$   at 2 mK, nearly coinciding with a hybrid electronic–nuclear magnetic moment ordering (Schuberth et al. in Science 351:485, 2016), we re-analyzed previous data on the magnetic susceptibility of CeCu $$_{6}$$ at ultra-low temperatures. We found that there is a direct analogy between the magnetic susceptibilities of both compounds which raises the question if there is the same hybrid transition in CeCu $$_{6}$$ , possibly also followed by superconductivity. Data taken some 20 years ago by groups in Garching and at Cornell University revealed an antiferromagnetic transition around 3 mK and further anomalies around 0.5 mK, very similar to the case of YbRh $$_2$$ Si $$_2$$ . If the above speculation is correct, it would suggest that superconductivity is a general phenomenon, occurring even in a heavy-fermion compound like CeCu $$_{6}$$ which for a long time was considered as “non-ordering.”

Following our recent discovery of superconductivity in YbRh _2 Si _2 at 2 mK, nearly coinciding with a hybrid electronic–nuclear magnetic moment ordering (Schuberth et al. in Science 351:485, 2016 ), we re-analyzed previous data on the magnetic susceptibility of CeCu _6 at ultra-low temperatures. We found that there is a direct analogy between the magnetic susceptibilities of both compounds which raises the question if there is the same hybrid transition in CeCu _6 , possibly also followed by superconductivity. Data taken some 20 years ago by groups in Garching and at Cornell University revealed an antiferromagnetic transition around 3 mK and further anomalies around 0.5 mK, very similar to the case of YbRh _2 Si _2 . If the above speculation is correct, it would suggest that superconductivity is a general phenomenon, occurring even in a heavy-fermion compound like CeCu _6 which for a long time was considered as “non-ordering.”

The smooth disappearance of antiferromagnetic order in strongly correlated metals commonly furnishes the development of unconventional superconductivity. The canonical heavy-electron compound YbRh2Si2 seems to represent an apparent exception from this quantum critical paradigm in that it is not a superconductor at temperature T ≥ 10 millikelvin (mK). Here we report magnetic and calorimetric measurements on YbRh2Si2, down to temperatures as low as T ≈ 1 mK. The data reveal the development of nuclear antiferromagnetic order slightly above 2 mK and of heavy-electron superconductivity almost concomitantly with this order. Our results demonstrate that superconductivity in the vicinity of quantum criticality is a general phenomenon.

AbstractMagnetic and caloric measurements on high‐quality YbRh2Si2 single crystals reveal the development of nuclear antiferromagnetic order slightly above 2 mK and of heavy‐electron superconductivity almost concomitantly with this order.

YbRh2Si2 is a widely studied heavy Fermion system with a variety of interesting properties, among them a quantum critical point at 60mT for B//a,b-plane 1. At low temperatures we previously found a new magnetically ordered phase below 2.2mK 2 taking place in the well known antiferromagnetic phase which starts at 70mK 3. In addition to this A phase, we now observe a second, weaker phase transition below 14mK and 5mT which we named B phase. To study these phases of YbRh2Si2 at the lowest possible temperatures, we measured the DC magnetization in magnetic fields up to 60mT using a home made rf SQUID magnetometer. The A phase is very robust and extends at least up to a magnetic field of 23mT. Above this field, it is suppressed to below our detection limit of 1mK. The A transition is characterized by a reduced magnetic susceptibility in the ordered state and there is zero magnetization in the limit B0. From these findings, we expect it to be an antiferromagnetic ordered state. The experiments were performed in our low temperature cryostat at the Walther Meissner Institute in Garching which includes a 0.9-mole PrNi5 nuclear demagnetization stage with a final temperature of 400 mu K. The temperatures of the nuclear stage were measured by pulsed NMR on a Cu rod thermally anchored to it. YbRh2Si2 single crystals of very high quality have been grown in an Indium flux at the MPI CPfS Dresden. The samples were clamped in a 5N Ag rod screwed to the nuclear stage and extending into the pick-up coil of a conventional flux transformer. Their temperatures were always close to that of the nuclear stage. In addition, we performed specific heat measurements with the semiadiabatic heat-pulse method. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

To determine the exact spin structure of the nuclear magnetic ordered phases of solid He-3, the U2D2 low field and the high field phases above 0.4 T, a European Research and Training Network for neutron scattering from the ordered solid was established which consisted of a collaboration with the Hahn Meitner Institute, Berlin, and other European and US groups. For this experiment it is crucial to grow a single crystal within the sinter needed for cooling the solid to temperatures of the order of 500 mu K and to keep it cold long enough to measure a magnetic neutron diffraction. The sinter is also necessary to absorb the major part (> 90%) of the heat generated by the neutron capture and decay reaction of the He-3 nucleus. In this work we studied the growth of crystals in Ag sinters of different pore sizes and with different growth speeds to find an optimal way to obtain single crystalline samples, or at least samples with only a few grains. We used SQUID magnetometry and NMR to measure the magnetization in the ordered phases. They were indicated by the known drop of the intensity, both in the NMR signal and in the dc magnetization, for the U2D2 phase, and by an increase of about 30% for the high field phase. The best results for cooling were obtained with sinters made from 700 angstrom "Japanese powder" with a packing fraction of 50% which were annealed at 130 degrees C after sintering and then had a calculated particle size of about 4200 A. In the dc magnetization we found a paramagnetic surface contribution from a few monolayers of 3He down to 500 mu K in addition to the bulk magnetization.

Solid 3He, in the bcc lattice between 34 and 100 bar, exhibits two nuclear magnetic ordered phases in the sub-mK temperature range, the so called U2D2 low (magnetic) field phase and the “high field phase” above 0.4 T. To determine the exact spin structure of these phases we started a project of neutron scattering from the ordered solid in collaboration with the Hahn-MeitnerInstitute, Berlin, and other European and US groups. For this experiment it is crucial to grow a single crystal within the sinter needed for cooling the solid to temperatures of the order of 500 μK (or even twenty times lowerin the case of the hcp lattice which is formed above 100 bar) and to keep it there long enough to measure a magnetic neutron reflection. We studied the growth of crystals in Ag sinters of different pore size and with different growth speeds to find an optimal way to obtain single crystalline samples. As a first diagnostic step we performed pulsed NMR measurements in the ordered phases of solid 3He in a sinter of 2700 Å particle size down to temperatures of 450 μKat various molar volumes. We could keep the samples in the orderedstate for as long as 140 h. The second method we used was SQUID magnetometry. For the low field phase TN was indicated by a drop of the intensity, both in the NMR signal and in the dc magnetization, whereas in the high field phase an increase of about 30% was observed below the ordering temperature. For the fabrication of the sinters a packing fraction of 50% and subsequent annealing proved to be very favorable to obtain cold ordered solid. Furthermore, we find that a paramagnetic surface contribution from a few monolayers of 3He exists down to 500 μK in addition to the bulk magnetization.

To obtain the exact spin structure of the nuclear magnetically ordered phases of solid 3He, which in the bee lattice are the U2D2 and the high field phase, both occurring below about 1 mK, we started a project of neutron scattering at the Hahn-Meitner Institut, Berlin. This experiment faces three main difficugties: to grow a single crystal within the sinter needed for cooling, to cool the solid to temperatures below 1 mK (or even much lower in the case of the hcp lattice), and to keep it there long enough, even under neutron irradiation. As a first step we have performed pulsed NMR measurements in the ordered phases of solid 3He in a Ag sinter of 700 Å particle size down to temperatures of 400 µK at various molar volumes. The samples remained in the ordered state for as long as 140 h. In the low field phase a strong reduction of the Larmor line to nearly zero intensity was observed. With a sample grown over 6 h at the megting curve around 50 bars three lines at the Larrnor frequency and on its high frequency side were observed which seem to indicate a partly crystalline U2D2 phase in our sinter. The origin of the strong intensity drop, however, is not clear and needs further investigation.

α-(BEDT-TTF) 2 KHg(SCN) 4 is considered to be in the charge-density-wave (CDW) state below 8 K.We present new magnetoresistance data suggesting that the material undergoes a series of field-induced CDW (FICDW) transitions at pressures slightly exceeding the critical pressure P c at which the zero-field CDW state is destroyed.Further, we argue that a novel kind of FICDW transitions, entirely determined by a superposition of the strong Pauli and quantizing orbital effects of magnetic field on the CDW wavevector, arises when the field is strongly tilted towards the conducting layers.These new transitions can take place even in the case of a relatively well nested Fermi surface.Finally we report on the superconducting (SC) state and its coexistence with the CDW in the title compound under quasi-hydrostatic pressure.Below P c the material is most likely a heterogeneous SC/CDW mixture, with the SC phase persisting down to ambient pressure.The SC onset temperature appears to drastically increase upon entering the SC/CDW coexistence region.

Simultaneous measurements of magnetic susceptibility from 0.5 to 10 mK and pressure from 2.88 to 3.54 MPa have been made in 3 He nano-clusters embedded in a 4 He matrix, following phase separation. The susceptibility of the 3.54 MPa, all-solid sample behaves similarly to that of bulk 3 He for v=21.3 cm 3 /mole, with a Weiss constant θ=− 250 μK. For the 2.88 MPa, liquid-droplet sample, θ= 140 μK, indicating a ferromagnetic tendency, similar to 2-D films at some coverages. At intermediate pressures, χ has a peak near 1.05 mK, but without a discontinuity. For all samples, χ had a solid-like contribution to the lowest temperatures. Magnetic ordering in nano-clusters appears to be different than the U2D2 phase of bulk 3 He.

In order to distinguish the superconducting phases of the title compounds we have studied their DC magnetic properties in low fields with a SQUID magnetometer. The magnetic penetration depth of UPt3 shows the second superconducting transition at Tc− when the field is applied along the c-axis, but not with H⊥c. This result, combined with a power law behavior of λ at low temperatures, is most consistent with the two-dimensional E2u order parameter symmetry. Below 20mK we find an additional diamagnetic signal which we ascribe to the normal state magnetism. For Sr2RuO4, supposedly a p-wave superconductor, we find a sharp single diamagnetic transition at 1.08K showing that our sample is of high quality, but there is no indication of an unusual superconducting behavior.

The magnetic susceptibility of He-3 nanoclusters embedded in a He-4 matrix has been measured from 0.5 to 10 mK at pressures from 2.88 to 3.54 MPa. Even the lowest pressure clusters have a solid fraction in the region of the phase diagram where bulk solid is unstable. At 3.54 MPa, theta = -250 muK, equal to that of bull; 3He for v = 21.3 cm(3)/mole. For 2.88 MPa, theta = 140 muK, indicating a ferromagnetic tendency, similar to 2D films at some coverages. At intermediate pressures, chi has a peak near 1.05 mK, but with no discontinuity. Magnetic ordering in nanoclusters appears to be different than the U2D2 phase of bull He-3.

We studied the anisotropic magnetic response of the internal superconducting phases of UPt3 and its anisotropic magnetic susceptibility with a capacitive torque meter which is very sensitive in high fields. Experiments were performed at temperatures down to 20 mK and at various angles between the c axis (hexagonal structure) and (B) over right arrow, ranging from 16 degrees to 82 degrees. The samples were four single crystals grown with different methods and subjected to different annealing procedures. The normal state susceptibility has a maximum around 20 K for (B) over right arrow in the a-b plane which we followed up to 14 T. It may arise from hybridized uranium ion states split by the hexagonal crystal field. The magnetization curves in the superconducting (SC) regime show strong irreversibilities which are highly sample dependent. They are not correlated with the internal SC phase lines but continue up to a line of fields that lies parallel to the B-c2 curve and even follows its kink at the tetracritical point (T*,B*). In the cleanest sample this line is shifted to fields well below the B-C internal phase line which then manifests itself in a pronounced kink of the magnetization curve indicating an enhanced Ginzburg-Landau parameter kappa. In another sample the B-C phase line between two of the three internal SC states could be detected even in the hysteretic region. The enhanced Ginzburg-Landau parameter kappa means a larger penetration depth and/or a shorter coherence length, clear evidence for the unconventional character of the B-C phase transition. With our cleanest sample we also observe an anomalous peak effect, a region of enhanced flux pinning near B-c2, which is probably related to the Fulde-Ferrell-Larkin-Ovchinnikov state. In yet another sample we find a crossing of the up-down magnetization curves, also near B-c2, but with reversed orientation of the magnetization loops. We interpret this in terms of different flux pinning in the two main crystal directions, possibly in relation to the peak effect which is, however, masked in this sample by strong irreversibilities.

In order to distinguish the UPt3 superconducting (s.c.) phases we have studied their magnetic properties at low fields in a SQUID magnetometer and up to fields >Hc2(0) with a capacitive torque-meter. With the SQUID we measure the magnetic penetration depth and find the second s.c. transition at Tc− when the field is applied along the c-axis, but not with H⊥ĉ. This result, combined with power-law behavior at low temperature T, is most consistent with the two-dimensional E2u s.c. order parameter. Below 20 mK we find an additional diamagnetic signal that we ascribe to the normal state magnetism. In high fields our torque measurements show a kink of the perpendicular magnetization component at the B–C phase line, pointing to an enhanced Ginzburg–Landau parameter in the C phase.

We have investigated the feasibility of neutron diffraction from solid 3He. The experiment will be performed at the HMI, first aiming for the properties of the antiferromagnetic ordering in the BCC phase and the ferromagnetic order in the HCP phase. Signal and beam heating considerations are essential to account for the enormous neutron absorption cross section of 3He. The study shows that neutron diffraction and transmission experiments are possible, relying on the experience gained from the neutron diffraction experiments on Cu and Ag at nanokelvin temperatures. A pressure cell has been developed which complies with the conflicting demands arising from the neutron and ultralow temperature aspects of the experiment. This work is a first step in an extensive effort to characterize 3He by neutron diffraction.

Simultaneous measurements of pressure and magnetic susceptibility have been made in 3 He nano-clusters embedded in a 4 He matrix, following phase separation of the mixture. Susceptibility measurements extend from 0.5 mK to 10 mK for three different samples, which either undergo partial melting upon further cooling, or separate with liquid already present. The magnetic behavior of the clusters indicates solid fractions of 77, 54, and 19%, respectively, for pressures of 3.36 MPa, 3.06 MPa, and 2.88 MPa. The susceptibility of the 3.36 MPa sample follows a Curie law to the lowest temperature. For 3.06 MPa, we observe a kink in χ at 1.1 mK, which is approximately the ordering temperature TN of the pure bulk 3 He if it existed at this pressure. However χ is almost constant down to 0.6 mK, with no drop at 1.1 mK, and no frequency shift, within our resolution of ∼10 Hz. Thus if there is magnetic ordering at 1.1 mK it is quite different than for bulk 3 He, not the U2D2 phase. For 2.88 MPa, χ follows a Curie-Weiss law with a positive Weiss θ=140 μK, indicative of a ferromagnetic tendency, similar to that seen in 2D films.