Introduction

Strongly correlated electron systems (SCES) exhibit many interesting quantum phenomena such as unconventional superconductivity and metal–insulator transitions. SCES include high-temperature superconductors1,2,3,4, heavy fermions5,6,7,8, and organic conductors9. Electron–phonon interactions are important in metals and SCES. An unconventional isotope effect has been reported for high-temperature cuprate superconductors10,11. Electron–phonon interactions are ubiquitous in materials so it is important to investigate the role of electron–phonon coupling in SCES.

The isotope effect of the ferromagnetic transition in La1−xCaxMnO3 has been investigated12,13. A large oxygen isotope effect was observed for La1−xCaxMnO3 upon 18O substitution with the largest Curie Temperature (Tc) shift of Tc(16O) = 222.7 K to Tc(18O) = 202.0 K observed when x = 0.20. This shift may be caused by strong electron–lattice coupling and has some relation with large magnetoresistance14,15. It has been suggested that the ferromagnetic transition of La1−xCaxMnO3 is caused by the double-exchange interaction16,17,18 and its strong electron–lattice interaction originating from the Jahn–Teller effect19.

The isotope effect in the ferromagnetic insulating state of Pr1−xCaxMnO3, which is also a material that exhibits colossal magnetoresistance, has been investigated20. The Tc of Pr1−xCaxMnO3 was lowered upon isotope substitution 16O → 18O; for example, Tc(16O) = 112 K shifted to Tc(18O) = 106 K when x = 0.2. It is expected that this isotope effect arises from strong electron–phonon coupling21,22. The effect of isotope on Tc has also been examined for the ferromagnetic superconductor RuSr2GdCu2O823. A small decrease of Tc of ~0.35 K was obtained through the isotope effect, which also influenced superconducting transition temperature. As for strontium ruthenates, an anomalous isotope effect was observed for the superconducting transition temperature of the spin-triplet superconductor Sr2RuO424. Raman spectra of SrRuO3 films showed anomalous temperature dependence near the ferromagnetic transition temperature25. This indicates that the electron–phonon interaction plays a role in the ferromagnetism of SrRuO3. There has been an attempt to measure the isotope effect in the weak itinerant ferromagnet ZrZn226. However, the isotope effect of Tc was not determined because the shift of Tc was small and there was uncertainty arising from different impurity levels. To date, a distinct isotope effect of itinerant ferromagnets has not been observed.

In this article, we report the isotope effect of Tc of the itinerant ferromagnet SrRuO3, which is a metal27,28 and with Tc of ~160 K29,30. We observe for the first time that the ferromagnetic transition temperature of SrRuO3 is increased about 1 K upon 18O isotope substitution. This positive isotope effect needs a new analogy to explain the ferromagnetic interaction in itinerant electron systems. A softening of the oxygen vibration modes is induced by isotope substitution (16O → 18O), which is clearly indicated by Raman spectroscopy. The Raman spectra also confirm that almost all the oxygen atoms (more than 80%) are substituted.

The increase of atomic mass caused by isotope substitution leads to a decrease of the Debye frequency ωD. In fact, the Raman spectra of SrRuO3 before and after oxygen isotope substitution clearly indicate that the main vibration frequency of 16O at 372 cm−1 is lowered to 351 cm−1 for 18O. This shift is consistent with ωD being proportional to 1/√M, where M is the mass of an oxygen atom. Thus, our experiments confirm that the isotope shift of Tc is induced by the decrease of the frequency of the oxygen vibration mode. Our results reveal a small increase of Tc on 18O substitution, which is in contrast to the typical oxygen isotope effects of materials showing colossal magnetoresistance. The oxygen isotope effect in SrRuO3 arises from the electron–phonon interaction described by the electron–phonon coupled field theory31 because there is no lattice distortion such as the Jahn–Teller effect. We present a theory to account for the isotope effect with the positive shift of Tc in itinerant ferromagnets by considering the spin-fluctuation theory for ferromagnets32. The decrease of ωD increases the relative strength of the Coulomb interaction U. This results in a positive isotope shift of Tc in accordance with our experimental results.

Experiment

The matrix of SrRuO3 was synthesized by the conventional solid-state reaction method from a stoichiometric mixture of SrCO3 and RuO2. The starting materials were calcined at 800 °C for 24 h and then sintered at 1000 °C for 48 h in air, resulting in a dense pellet. Oxygen isotope substitution was performed by annealing. To ensure oxygen isotope substitution, samples were first annealed under the following conditions. Samples were places in two independent quartz tubes in a furnace and exposed to 16O2 or 18O2 gas at atmospheric pressure. Samples in both 16O2 and 18O2 gas were annealed at 1000 °C for 91 h, cooled in the furnace to room temperature and then annealed again at 1000 °C for 90 h. Raman spectroscopy of the samples confirmed that >80% of the oxygen atoms were substituted (Fig. 1).

Figure 1
figure 1

Intensity of Raman scattering as a function of frequency for SrRuO3 samples with different oxygen isotopes at room temperature.

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DC and AC magnetization measurements were conducted to determine Tc. DC magnetization measurements were carried out by a superconducting quantum interference device magnetometer (Quantum Design Inc., MPMS2) up to 5 Tesla at temperatures T from 5 to 300 K. AC magnetic susceptibility was measured using a Hartshorn bridge circuit. The AC magnetic field produced by the primary coil was 1 Oe and the frequency of the AC signal was 180 Hz.

The oxygen phonon modes are observed at room temperature. A softening of the oxygen vibration modes was confirmed by Raman spectroscopy. We resubstituted an 18O-substituted sample with 16O to produce a sample indicated as 16OR. The Raman spectrum of 16OR is also shown in Fig. 1.

The magnetic field dependence of magnetization of SrRuO3 samples substituted with oxygen 16O, 18O, and 16OR at T = 5 K are presented in Fig. 2. These three magnetization curves show almost the same magnetization process.

Figure 2
figure 2

Magnetization as a function of magnetic field for SrRuO3 samples with different oxygen isotopes at temperature T = 5 K.

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The temperature dependences of AC magnetic susceptibility of SrRuO3 samples substituted with 16O, 18O and 16OR are illustrated in Fig. 3. A shift of peak position caused by 18O substitution is clearly observed. The shift shows that ∆Tc is ~1 K. Therefore, the ferromagnetic transition temperature of SrRuO3 was increased by about 1 K by 18O substitution. The temperature dependence of magnetization at 1 kOe for SrRuO3 following oxygen isotope substitution is depicted in Fig. 4. The ferromagnetic transition temperature of SrRuO3 is increased by 18O substitution. Again, the shift indicates that ∆Tc is ~1 K. This agrees with the shift estimated from the AC magnetic susceptibility measurements.

Figure 3
figure 3

AC magnetic susceptibility as a function of temperature T for SrRuO3 samples with different oxygen isotopes.

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Figure 4
figure 4

Magnetization as a function of temperature T for the original SrRuO3 sample with 16O under an applied magnetic field H = 1 kOe.

Inset is the temperature dependence of magnetization of SrRuO3 following oxygen isotope substitution with 16O at H = 1 kOe.

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Disscussion

Let us examine the isotope effect theoretically. An important point is that the decrease of ωD increases the relative strength of the Coulomb interaction U. This leads to the positive shift of Tc in accordance with experiments. This is stated theoretically as follows. In the study of magnetism, the Hubbard model is of fundamental importance32,33,34,35,36,37. The isotope effect in an itinerant ferromagnet was investigated before using the RPA theory38,39. We consider a model with Hubbard on-site Coulomb repulsion and electron–phonon interaction. Tc is determined through solution of the gap equation. The Hamiltonian is given by

where ckσ and c†kσ are Fourier transforms of the annihilation and creation operators ciσ and c†iσ at site i, respectively. Here, niσ = c†iσciσ is the number operator, and ξk = ε k − μ is the dispersion relation measured from the chemical potential μ. The electron field ψσ and the phonon field ϕ are defined, respectively, as follows:

where V is the volume of the system. We denote the number of electrons with spin σ as nσ = (1/, where N is the number of sites. In the mean-field theory, the magnetization is determined by where Ekσ is the electron dispersion relation including the corrections in Fig. 5, which are given as

Figure 5
figure 5

Lowest-order electron self-energy corrections. The second term arises from the electron–phonon vertex correction.

The dashed line indicates the Coulomb interaction and the wavy line shows the phonon propagator.

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where g = −γ2, and ρ(μ0) is the density of states at the Fermi level. The vertex correction is of the order of ωD/EF in accordance with the Migdal theorem40,41,42. For the magnetization ∆ ≡ n↑ − n↓, we obtain the equation up to the order of ∆ of, where Ueff = U + Ugρ(μ0)(ωD/2εF)ln(εF/ωD). With the help of the Sommerfeld expansion, Tc in the mean-field approximation is given by

where R is a constant. It has been suggested that the vertex correction like that shown in Fig. 6(b) is important in evaluating Tc 39. We examined this by calculating the diagrams in Fig. 6(a,b) numerically, and found that the contribution in Fig. 6(b) is smaller than that in Fig. 6(a) by more than one order of magnitude. The sum of all particle–hole ladder diagrams will increase the term in Fig. 6(b), but this is restricted to a very small region just near the critical value of U. Thus, from the formula of Tc in Eq. (5) we obtain the positive isotope shift of Tc: ∂Tc/∂M > 0. The positive isotope shift of Tc is also obtained by taking the spin fluctuation effect into account32,43,44. The isotope coefficient α = −∂ ln Tc/∂ ln M is given as

Figure 6
figure 6

Contributions to the susceptibility χ+− (a) without and (b) with the electron–phonon vertex correction.

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This indicates that α is negative and Tc increases with M.

Conclusion

We examined the isotope effect of Tc in itinerant ferromagnet SrRuO3. First, Tc was estimated from DC and AC magnetization measurements. We found that Tc increases upon oxygen isotope substitution of 16O for 18O. This results in an inverse isotope effect of ∂ ln Tc /∂ ln M < 0. This finding is in contrast to the results obtained for Mn oxides that show colossal magnetoresistance. The isotope effect of Tc occurs through the electron–phonon interactions, especially the electron–phonon vertex correction.

We summarize the results and significance of our work as follows. (1) The inverse isotope effect of the Curie temperature was observed clearly in an itinerant ferromagnetic material for the first time. (2) Our result shows that the electron-phonon interaction is ubiquitous in the world, even in ferromagnetic materials. (3) The positive shift of the Curie temperature can be understood based on a theoretical model of the Coulomb interaction and the electron-phonon interaction. (4) We have established the experimental procedure to substitute isotope oxygen 18O for 16O. This technique would be helpful in searching new functional materials.

Additional Information

How to cite this article: Kawanaka, H. et al. Enhancement of ferromagnetism by oxygen isotope substitution in strontium ruthenate SrRuO3. Sci. Rep. 6, 35150; doi: 10.1038/srep35150 (2016).