Discussion and summary

CeCoGe3 has been studied using µSR, single crystal neutron diffraction, magnetic

susceptibility and powder inelastic neutron scattering. Single crystals grown by the flux method were measured using single crystal neutron diffraction in zero-field and the magnetic propagation vector is observed to change at each transition with

k = (0,0,1₂) for T < TN3, k = (0,0,5₈) for TN3 ≤ T < TN2, and k = (0,0,2₃)

for TN2 < T < TN1. A ferromagnetic component is also inferred between TN3

andTN1 from an increase in the intensity of the (110) reflection in this region. The

results indicate the that the moments align along the c axis in all three phases and are compatible with an equal moment, two-up, two down structure belowTN3

and two-up one down between TN2 and TN1. For these equal moment solutions,

magnetic refinements give moments of 0.405(5)µB/Ce at 2 K and no equal moment

structure could be deduced for the middle phase. This indicates a solution with unequal moments. Such spin-density wave type structures can arise in systems with competing interactions [116]. Further information about the structure in this phase would require a measurement of the magnitude of the ferromagnetic moment, which could be found by performing polarized neutron diffraction measurements. Thek = (0,0,1₂) propagation vector agrees with the dominant component observed in Ref. [175], but no evidence was found for the weaker k = (0,0,3₄). This shows that there appears to be sample dependence for single crystals, even though both samples were synthesized using the same method. This suggests that CeCoGe3 has

many competing magnetic phases and small variations in the crystal structure, site ordering or stoichiometry may promote different ground states.

The observation of a sharp drop in asymmetry, increase in the fluctuation rate and oscillations of the asymmetry in zero-field µSR spectra confirm the onset of long range magnetic order between 21 and 20 K. The internal fields were deduced from the frequency of the oscillations and the data were fitted with a model of the order parameter. The value of β may give information about the dimensionality of the system and order parameter [109]. The fact that the moments in all phases order along thecaxis and sharp metamagnetic transitions are observed in thecaxis susceptibility may suggest that the system is best described by an Ising model. The role of dimensionality is a very important topic in heavy-fermion superconductivity,

with the higher superconductingTc in CeTIn5 often being ascribed to a quasi-two-

dimensional electronic structure [13]. The CeT X3superconducting states have lower

values ofTc and in this would be further supported by a model withβ = 0.326 for

a three-dimensional Ising model. However, the only model which fitted the data wasβ = 0.5 for the mean field case, which does not reveal the universality class of the phase transition. This mean field model was also consistent with the size of the magnetic moments deduced from refinements of the neutron diffraction data at 2 and 14 K.

INS measurements were used to measure the CEF scheme as well the temper- ature dependence of low energy magnetic scattering. It is of particular use to com- pare the response to other CeT X3 compounds. INS measurements have previously

been made on CeRhGe3 [162] and CeRhSi3 [56]. At 2 and 10 K a well defined peak

in cuts ofSmag(Q, ω) at 4.5 meV gives the energy of the zone boundary magnons.

In CeRhGe3 a peak was observed at 3 meV and it orders at TN1 = 14.5 K. Both

the peak energy and TN1 scale similarly between CeRhGe3 and CeCoGe3 and the

higher values in the case of the latter indicate stronger intersite exchange interac- tions. Possible evidence is seen for a second low energy peak in CeRhGe3 which

may be evidence for anisotropic dispersions. However no evidence for a second peak is observed in CeCoGe3. Further characterization of the spin-waves and in partic-

ular anisotropic properties would be greatly aided by INS measurements of single crystals. TK deduced from the zero temperature width of the quasielastic linewidth

was similar in both compounds, being 11(3) K in CeCoGe3 and 12.6(3) CeRhGe3.

However Γ is linear with temperature up to 140 K in CeCoGe3 while it is nearly

temperature independent above 20 K in CeRhGe3. Although the first excited CEF

doublet is at a lower level in the latter (∼87 K), it is not clear that this entirely explains the difference in the temperature dependence at low temperatures.

From fitting single crystal magnetic susceptibility and INS data, a CEF scheme for CeCoGe3 has been proposed for the splitting of the J = 5₂ multi-

plet. The ground state is an admixture of±5₂

⟩

and ∓3₂

⟩

states and schemes with a ±1₂

⟩

ground state are not compatible with the data. A similar ground state was proposed for CeRhGe3, although the largest component was ±3₂

⟩ rather than ±5 2 ⟩

. In both cases a sizeableB₄4 leads to this mixing. B₂0 is negative for CeCoGe3

but positive for CeRhGe3.

The predicted moment is 1.01 µB/Ce along the c axis and therefore the

direction of the observed moment is correctly predicted but the magnitude is reduced compared to that predicted from the CEF model. In both CeRhGe3 and CeRhSi3

the moment is predicted to lie in theab plane. This is correct for CeRhSi3 but for

CeRhGe3, the change in orientation was ascribed to two-ion anisotropic exchange

interactions. These are not necessary to account for the moment direction CeCoGe3,

but the presence of a similar anisotropic exchange would further increase the energy cost of deviations of the moment from thec axis and may explain the strong Ising like behaviour observed in the magnetic phases.

The significant moment reduction is evidence for hybridization of the cerium 4f and conduction electrons and there is partial screening of the moments. In the case of CeRhGe3, a similar moment aligned along the c axis is observed through

neutron diffraction measurements but this is in agreement with the predicted⟨µz⟩. However, the moment reduction of CeCoGe3 is not as great as in CeRhSi3, where the

CEF model predicts a moment of 0.92µB/Ce but 0.12µB/Ce is observed in neutron

diffraction measurements [53]. A similar trend is observed in the linewidths of the CEF excitations. As shown in Table 4.2, the linewidths at 25 K were 1.6(3) and 2.9(3) meV for transitions from the ground state to ψ2 and ψ3. The correspond-

ing values for CeRhGe3 were 1.4(2) and 2.2(3) meV and therefore the excitation

to ψ3 is broader in CeCoGe3. However the CEF excitations were broader still in

CeRhSi3, where 3.9(2) and 9.2(4) meV are obtained [193]. These results indicate

that CeCoGe3 displays a degree of hybridization in between that of CeRhGe3 and

CeRhSi3. This agrees with CeRhSi3 being closer to quantum criticality, becom-

ing superconducting at 1.2 GPa and CeRhGe3 being further away, not displaying