NMR as a local probe for ferromagnetic quantum criticality in Fe- based systems

October 24, 2018

M. Majumder, P. Khuntia, A. Gippius¹, A. Strydom², C. Petrovic³, H. Yasuoka, M. Brando, H. Tjeng, F. Steglich, Y. Grin and M. Baenitz

¹Physics Department, University of Johannesburg,
PO Box 524, Auckland Park 2006, South Africa
²Department of Physics, Moscow State University,
119991, Moscow, Russia
³Condensed Matter Physics, Brookhaven National Laboratory
Upton, NY 11973-5000, New York, USA

Quantum criticality stemming from ferromagnetic (FM) exchange is a rare occurrence, and has been discussed among 4f- and 5f-electron systems such as CeFePO [1,2], YbNi₄P₂ [3,4] or UCoGe [5], and in weak itinerant ferromagnets like ZrZn₂ and NbFe₂ [6]. Our ongoing NMR study on various 3d-electron systems is focused mainly on the local fluctuations around a quantum critical point (QCP) and aims in particular to expose the real nature of the magnetic fluctuations (antiferromagnetic (afm) - versus ferromagnetic (fm) - correlations) by temperature- and field- scaling. Among Fe-based systems our search for new quantum critical matter has various approaches. The first is to study weak itinerant 3d- paramagnets at the verge of magnetic order, the second one is on Fe containing cage systems (aluminides) and the third one is on doped Fe-based semimetals.

TaFe₂ is a weak itinerant paramagnet with C14 - Laves phase structure and it was speculated that it resides already at a critical point at the verge of magnetic order [7]. In close collaboration with the Department of Inorganic Chemistry (G. Kreiner) we found that TaFe₂ could be tuned towards antiferromagnetism via vanadium substitution (see institute report 2009-2012). Here ⁵¹V NMR (J=7/2) was successfully applied over a wide stoichiometry range. NMR provided microscopic evidence for dominating fm- correlation at small V- substitution levels, whereas towards higher concentrations itinerant Fe-based long range afm- order was found.

Ternary (Y/Yb)-Fe- aluminides are also weakly ferromagnetic and we have shown that YFe₂Al₁₀ is located directly at the fm QCP [8], whereas YbFe₂Al₁₀ exhibits afm correlations among partly Kondo screened Fe-3d- moments at low temperatures [9]. Here the 3d- component of the spin lattice relaxation rate (SLRR) ²⁷R_3d at the Al-site as a measure of the q-averaged complex dynamic susceptibility shows that ²⁷R_3d = ²⁷(1/T₁T)_3d is proportional to χ(T)/T^0.5 which is in turn proportional to χ(T)² as a consequence of the heavy fermion formation in the Korringa framework (Fig1 (a) & (b) ). Additional support comes from the comparison of the field dependence of the SLRR ²⁷R_3d (H) with the specific heat Sommerfeld coefficient γ = C(H)/T. Here we find that ²⁷R_3d (H) is proportional to H^-n which is in turn proportional to γ(H)²,is found to be valid for our data which is very consistent with the theory. Furthermore Kondo – lattice behaviour has been seen in low temperature resistivity measurements which is quite surprising. Usually in an iron-based intermetallic compound the 3d orbitals of nearest-neighbor iron atoms overlap; they form a band of delocalized electronic states and give rise to band, rather than local-moment magnetism. Consequently, one does not expect to find an iron-based "Kondo-lattice" system as realized in numerous lanthanide/actinide-based intermetallics with extremely localized 4f/5f shells. YbFe₂Al₁₀ is an exceptional system because the Yb-derived 4f- electrons form a nonmagnetic, intermediate-valent state at low temperatures (with a Yb valence of 2.38) which appears to be a prerequisite for the observed typical Kondo-lattice phenomena in the 3d-electron system [9]. This work was done in close collaboration with the Department of Correlated Matter (H. Tjeng) where detailed hard X-ray photoemission studies are performed to determine precisely the Yb valence as function of temperature [9].

Fig. 1 (a) 27(1/T1T) versus T for YbFe2Al10 in various applied magnetic fields. The solid line represents a calculation base on a model which includes a 3d- and a 4f – component. Fig.1 (b) shows the linear relation between the square root of the 3d part of the SLRR and the bulk susceptibility and Fig. 1 (d) displays the field dependence of the SLRR at T = 2 K. Fig. 1 (c) gives the fluctuation time of the intermediate Yb3-δ ion [9]. — Fig. 1 (a) ²⁷(1/T₁T) versus T for YbFe₂Al₁₀ in various applied magnetic fields. The solid line represents a calculation base on a model which includes a 3d- and a 4f – component. Fig.1 (b) shows the linear relation between the square root of the 3d part of the SLRR and the bulk susceptibility and Fig. 1 (d) displays the field dependence of the SLRR at T = 2 K. Fig. 1 (c) gives the fluctuation time of the intermediate Yb^3-δ ion [9].

Fig. 1 (a) ²⁷(1/T₁T) versus T for YbFe₂Al₁₀ in various applied magnetic fields. The solid line represents a calculation base on a model which includes a 3d- and a 4f – component. Fig.1 (b) shows the linear relation between the square root of the 3d part of the SLRR and the bulk susceptibility and Fig. 1 (d) displays the field dependence of the SLRR at T = 2 K. Fig. 1 (c) gives the fluctuation time of the intermediate Yb^3-δ ion [9].

Fig. 2 Temperature dependence of 71(1/T1T) measured at the Ga2- site of FeGa3-xGex for various Ge concentrations x. The solid lines correspond to a two component model with a (T-independent) conduction electron part and a (T-dependent) 3d-spin part. The dashed lines indicate the power laws of the bare spin part. Fig.1 (b) shows the T-4/3 power law in 71(1/T1T)3d for the critical sample and Fig. 1 (c) shows the 71(1/T1T)3d proportional χ relation for the ordered x=0.2 sample for T > TC [13]. — Fig. 2 Temperature dependence of ⁷¹(1/T₁T) measured at the Ga2- site of FeGa_3-xGe_x for various Ge concentrations x. The solid lines correspond to a two component model with a (T-independent) conduction electron part and a (T-dependent) 3d-spin part. The dashed lines indicate the power laws of the bare spin part. Fig.1 (b) shows the T^-4/3 power law in ⁷¹(1/T₁T)_3d for the critical sample and Fig. 1 (c) shows the ⁷¹(1/T₁T)_3d proportional χ relation for the ordered x=0.2 sample for T > T_C [13].

Fig. 2 Temperature dependence of ⁷¹(1/T₁T) measured at the Ga2- site of FeGa_3-xGe_x for various Ge concentrations x. The solid lines correspond to a two component model with a (T-independent) conduction electron part and a (T-dependent) 3d-spin part. The dashed lines indicate the power laws of the bare spin part. Fig.1 (b) shows the T^-4/3 power law in ⁷¹(1/T₁T)_3d for the critical sample and Fig. 1 (c) shows the ⁷¹(1/T₁T)_3d proportional χ relation for the ordered x=0.2 sample for T > T_C [13].

Signatures of “Kondo–type” of correlations are also found in some magnetic semimetals. FeSi, FeSb₂ and FeGa₃ attracted great attention because of their non-magnetic ground state and their very good thermoelectric performance. The pure undoped semimetals are already at the verge of magnetism and show signs of magnetic correlations at low temperatures. [10,11] Metallic behavior and Fe-based magnetism could be introduced by controlled substitutions on the Fe- or the framework- site. In Fe(Te,Sb)₂ we use Sb-NQR to study the magnetic fluctuations and in addition the NQR line width itself to monitor the degree of disorder due to the alloying. Along this line we started to work on Ge- substituted FeGa₃ in close collaboration with the Department of Chemical Metal Science [13]. We performed Ga-NQR to monitor the disorder upon Ge- substitution and to probe the magnetic fluctuations at zero magnetic field via the spin lattice relaxation rate SLRR.

Surprisingly upon Ge-substitution in FeGa₃ afm correlations evolve and “heavy” 3d- electrons form. For T→ 0, ⁷¹(1/T₁T) and the Sommerfeld ratio γ=(C/T) are strongly enhanced (γ ~ 70 mJ/molK²). Towards higher Ge- concentrations a crossover to a (short-range) ferromagnetically ordered state was found. Whereas the low concentrations (x = 0.05, 0.1) samples show a good agreement with the Korringa theory for renormalized (heavy) fermions with ⁷¹R = ⁷¹(1/T₁T) proportional χ(T)/T^0.5 proportional χ(T)² the largest concentration (x = 0.2) sample exhibits a behaviour typical for an itinerant weak ferromagnet with ⁷¹R = ⁷¹(1/T₁T) proportional χ(T) (Fig. 2.) For the critical concentration (x = 0.15) an extreme pronounced T^-4/3power law was found over two orders in magnitude which indicates ferromagnetic 3D quantum critical fluctuations in the H=0 limit [13]. In conclusion the Ga-NQR SLRR provides microscopic evidence at H=0 and under the absence of disorder for a crossover from antiferromagnetic- to ferromagnetic- correlations upon Ge-substitution and the presence of pronounced 3D ferromagnetic fluctuations.

In summary it should be stressed that the microscopic magnetic resonance spectroscopy reveals effects due to local disorder in the structure and simultaneously is capable of probing anisotropic spin fluctuations due to extended afm- and fm- as well as local Kondo- type correlations across the magnetic H-T phase diagram. The most promising route towards new 3d-based correlated electron systems is probably the “disorder free” tuning of 3d-based semi metals (for example like β-FeSi₂ or CrSi₂ [14]) towards magnetism.

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