Schottky specific heat of the lightly Mn-substituted electron-doped SrTiO₃

SrTiO₃ shows various exotic phenomena such as superconductivity,¹ ferroelectrics,² large n-type thermoelectric response,^3,4 an anomalous photoelectronic process,⁵ and quantum paraelectrics,⁶ while it is known as a prototype of an n-type oxide semiconductor. The end compound, SrTiO₃, is a good insulator with the band gap of about 3.2 eV,⁷ and the electrons can be ideally doped into it by the La³⁺ substitution for Sr²⁺, the Nb⁵⁺ one for Ti⁴⁺, or the oxygen vacancy.^1,8 The SrTiO₃ has some structural instabilities, leading to the unique dielectric properties,^2,6 and the structure is sensitive to a subtle ion substitution,² an external pressure,⁹ or strain.¹⁰ Since other structural instability is expected to be introduced by substituting a magnetic ion such as a Jahn-Teller active Mn³⁺ ion, it is interesting to investigate the effect of the Mn substitution on the thermal and electronic properties.

Although it has been reported that the valence of Mn ion is tetravalence in SrTi_1−yMn_yO₃,¹¹ we expect that it becomes trivalence when the Mn ions are substituted at the Ti sites in the electron-doped compound such as Sr_1−xLa_xTiO₃. Actually, recently, we have observed the increase of lattice parameters of Sr_1−xLa_xTiO₃ with the substitution of Mn for Ti^12,13 which is thought to originate from the production of Mn³⁺ ions at the Ti site, and have found that the Mn substitution effectively reduces the thermal conductivity and improves the thermoelectric property of Sr_1−xLa_xTiO₃.^12,13 Furthermore, we have also found a large Schottky specific heat (C_Sch) of the Mn 3d electrons at the low temperature and its large magnetic field dependence.¹⁴ 

In this proceeding, we will briefly summarize our previous results.^12–14 We will show that the observed C_Sch for the lightly Mn-substituted electron-doped SrTiO₃, Sr_1−xLa_xTi_1−yMn_zO₃ for y = 0.02 and 0.04, is well explained by a conventional model of Schottky specific heat with the existence of Mn³⁺ ions except for the fact that the number of spins of Mn ions seems to be about 30% smaller than a nominal value. Furthermore, we will discuss the origin of the enhancement of effective mass of itinerant electrons which is determined by subtracting the C_Sch component from the specific heat (C). All results have already been published in refs. 12–14.

The details of experiments have been described elsewhere.^12–14 The single crystals were grown by a floating zone method. According to the inductively coupled plasma mass spectroscopy (ICP) measurements, a part of Mn ions were lost in the grown crystal, so the chemical formula is expressed as Sr_1−xLa_xTi_1−yMn_zO₃ (SLTMO), where y is the nominal value of Mn ions and z is the actual value of Mn ions determined by the ICP measurement. Specific heat was measured in a magnetic field up to 9 Tesla by a relaxation method by using a physical property measurement system (PPMS) of Quantum Design Incorporated.

Figure 1 shows the C/T versus T plots for Sr_0.95La_0.05Ti_0.96Mn_0.023O₃ (SLTMO for y = 0.04) in 0, 3, 6, and 9 Tesla, as an example of results of low temperature specific heat (low-T C) measurements in magnetic fields for SLTMO. As shown in Fig. 1(a), the C in 0 Tesla shows the large upturn at the low-T below 5 K. The upturn is proportional to 1/T², which suggests an existence of some Schottky component in the high T limit. Actually, the low-T C in 0 Tesla is well fitted to the following relation,

where γT expresses the electronic specific heat, and βT³ and ηT⁵ usually express the harmonic and anharmonic lattice specific heat. The evolution of γ with the La substitution (x) in Sr_1−xLa_xTiO₃ has already been reported previously.¹⁵ If we assume that the observed C_Sch are assigned to C_Sch of the ⁵⁵Mn nucleus (I = 5/2), the values of hyperfine fields (H_hyp) for y = 0.02 and 0.04 are estimated to be about 390 and 560 Tesla, respectively, by using spin quantum numbers deduced from the magnetization measurements. The deduced H_hyp values are one order of magnitude larger than those observed in antiferromagnetic and ferromagnetic La_1−xSr_xMnO₃¹⁷ where the Mn cations occupy all the B sites in the similar perovskite structure.

Then, we speculate that the observed C_Sch is the one for the localized spins of the Mn 3d electrons in a weak internal magnetic field (H_int) via the itinerant electrons. In this case, the H_int values roughly estimated by using the average spin quantum number (S_ave) deduced when we assume the compounds to be in a Curie paramagnetic state¹³ are about 0.2 Tesla for these compounds. Such a C_Sch with the low H_int should be easily modulated by external magnetic fields. Actually, as shown in Fig. 1(a), the large changes of C_Sch were observed in external magnetic fields (H_ext) up to 9 Tesla. The changes by magnetic fields are qualitatively reproduced by a conventional model (the dashed lines in Fig. 1(a)), as follows;

where H_all = H_int + H_ext, and the coefficients n₂ and n_5/2 are the fractions of Mn³⁺ (S = 2) and Mn²⁺ (S = 5/2) components (n₂ + n_5/2 = 1), respectively, deduced from the S_ave by using the relation, S_ave(S_ave +1) = n₂ × 2(2+1) + n_5/2 × 2.5(2.5+1). The deduced n₂ and n_5/2 are about 0.74 and 0.26 for y = 0.02, and about 0.52 and 0.48 for y = 0.04, respectively.

Furthermore, as expressed by the solid lines in Fig. 1(b), the calculated tC_Sch for the y = 0.04 with t = 0.67 well reproduce the changes by applying magnetic fields. Although not shown, the calculated tC_Sch for y = 0.02 with t = 0.7 also well reproduces the changes.¹⁴ In other words, about 30% number of the localized Mn 3d spin seems to disappear at the low-T for both compounds. The disappearance of the Mn 3d spin may relate to the observations that the magnetizations are suppressed and deviates from the Curie law at the low-T.¹³ 

It should be noted that, comparing the calculated C_Sch with using different S (as an example, the calculations for y = 0.04 in 3 Tesla are shown in the Fig. 1(b)), the Mn ions are apparently not Mn⁴⁺ (S = 3/2) ions in both compounds. It is likely that they are Mn³⁺ (S = 2) ions or mixtures of Mn³⁺ and Mn²⁺ ions.

The (C − tC_Sch)/T in 0 and 9 Tesla are almost consistent with each other.¹⁴ The γ (≡ lim_T→0(C − tC_Sch)/T) deduced from Fig. 2 increases from about 2.5 to 7 mJ/K² mol with the increase of y from 0 to 0.04. Such an increase of γ in spite of the reduction of the electron concentration by the Mn substitution¹³ indicates a renormalization of the effective mass of the electron, although the compounds are far away from the Mott transition of Sr_1−xLa_xTiO₃¹⁵ and LaTiO_3−δ.¹⁶ 

Taking into account the possibility of the disappearance of part of the Mn 3d spins, such an enhancement of the effective mass of the electron may originate from the Kondo coupling between part of the localized spins and the itinerant electrons.¹⁴ However, since the estimated Kondo temperature is far below room temperature even if all of the magnetic entropy of the disappeared localized Mn 3d spins contributes to the renormalization of the effective mass, the scenario at the low-T can not fully explain the enhancement¹³ of Seebeck coefficients at room temperature. According to the recent inelastic neutron scattering measurements,¹⁸ momentum-independent increase in the low-energy spectral weight below about 10 meV is effectively induced by the La-Mn co-doping, which indicates dynamical and local structural fluctuations caused by the Jahn-Teller instability in Mn³⁺ ions maybe coupled with the incipient ferroelectric nature of SrTiO₃. While such a low-energy phonon excitation should cause the low thermal conductivity for the La-Mn co-doped compounds, it may contribute to the observed enhancement of the effective mass of the electron through some electron-lattice coupling.

Large changes of the low temperature specific heat (low-T C) for the lightly Mn-substituted electron-doped SrTiO₃, Sr_0.95La_0.05Ti_1−yMn_zO₃ (SLTMO), with y = 0.02 and 0.04, were found by applying magnetic fields up to 9 Tesla. The changes in the low-T C are qualitatively explained by the conventional model of the Schottky specific heat (C_Sch) of the localized spins of the Mn 3d electrons except for the fact that the C_Sch is by about 30% suppressed, suggesting that the number of Mn 3d spins is reduced. It may originate from the occurrence of Kondo coupling between the itinerant electrons and part of the localized Mn 3d spins, which, together with some coupling between the electron and the lattice, may contribute to the observed renormalization of the effective mass of the electron.

This work is supported by JST CREST Grant Number JPMJCR15Q2, Japan.