**5.1. 77Se-NMR measurements in** λ**–(BETS)2FeCl4**

### *5.1.1. 77Se-NMR spectrum*

Field-Induced Superconductors: NMR Studies of λ–(BETS)2FeCl4 13

ν

) from the above

φ

is counted from the center of the 77Se-NMR spectrum peak

*T H a bM T H*<sup>Τ</sup> ≈ − (2)

ν

φ

from our experiments is

at several temperatures. The angle

is dominated by the hyperfine field from the Fe3+ ion magnetization

min=13.6°.

*H*0 = 9 T. According to the crystal structure of λ–(BETS)2FeCl4, our calculation indicates that the direction of the Se-electron *pz* orbital is 76.4° from the *c-*axis. Thus the minimum angle

experiment is shown in Fig. 8 (a). In order to understand the origin of this resonance frequency, we also plotted it as a function of the 3d-Fe3+ ion magnetization (*Md*), which is a Brillouin function of temperature *T* and the total magnetic field (*H*T) at the Fe3+ ions. This is

(maximum). What it measures is the average of the local field in magnitude in total, including the direct hyperfine field from the conduction electrons and the indirect hyperfine field that coupled to the Fe3+ ions at the Lamar frequency of the 77Se nuclei (see details in

Figure 8 indicates that in the PM state above ~ 7 K at the applied field *H*0 = 9 T, a good fit to

<sup>0</sup> ( , ) ( , ), *<sup>d</sup>*

This result is a strong indication that the temperature *T* dependence of the77Se-NMR

It is important to notice that the sign of the contribution from *Md* is negative in Eq. (2). Thus, this also indicates that the hyperfine field from the Fe3+ ion magnetization is negative, i.e., opposite to applied magnetic field *H*0, as needed for the Jaccarino-Peter compensation

Now, to verify to validity of the Jaccarino-Peter mechanism, we need to find the field from the 3d Fe3+ ions at the Se π-electrons is (i.e., the π-d exchange field *H*πd) which is the central

According to the *H-T* phase diagram of λ–(BETS)2FeCl4 [Fig. 6 (c)], the magnitude of *H*πd = 33

basically describes the alignment direction of the applied magnetic field *H*0 relative to the

between *pz* and *H*0 during the rotation of the goniometer is

*5.1.2. Temperature dependence of the 77Se-NMR resonance frequency* 

shown in Fig. 8 (b), where the solid lines show the fit to the *Md*.

(uncertainty ± 3 kHz) is obtained using

ν

*5.1.3. Angular dependence of the 77Se-NMR resonance frequency* 

The angular dependence of the 77Se-NMR resonance frequency

shown in Fig. 9, which is plotted as a function of angle

where the fit parameters *a* = 73.221 MHz and *b* = 3.0158 [(mol.Fe/emu) .MHz].

ν

The resonance frequency

Section 5.1.4).

ν

resonance frequency

ν

goal of our 77Se-NMR measurements.

T (tesla) at temperature *T* = 5 K.

frequency

*Md*.

φ

sample lattice.

mechanism.

The temperature (*T)* dependence of the 77Se-NMR resonance frequency (

**Figure 7.** 77Se-NMR absorption spectrum at various temperatures with applied magnetic field

*H*0 = 9 T || *a'* in λ–(BETS)2FeCl4 [23].

The 77Se-NMR spectra of λ–(BETS)2FeCl4 at various temperatures are shown in Fig. 7. The spectrum has a dominant single-peak feature which is reasonable as a spin *I* = 1/2 nucleus for the 77Se, while it broadens inhomogeneously and significantly upon cooling (the linewidth increases from 90 kHz to 200 kHz as temperature is lowered from 30 K to 5 K). What the77Se-NMR spectrum measures is the local field distribution in total at the Se sites. Apparently, these spectrum data indicate that all the Se sites in the unit cell are essentially identical.

The sample used for the 77Se-NMR measurements was grown using a standard method [22] without 77Se enrichment (the natural abundance of 77Se is 7.5%). The sample dimension is *a*\*× *b*\*× *c* = 0.09 mm × 0.04 mm × 0.80 mm corresponding to a mass of ~ 7 μg with ~ 2.0 × 1015 77Se nuclei.

Due to the small number of spins, a small microcoil with a filling factor ~ 0.4 was used. For most acquisitions, 104–105 averages were used on a time scale of ~ 5 min for 104 averages. The sample and coil were rotated on a goniometer (rotation angle φ) whose rotation axis is along the lattice *c*-axis (the needle direction) and it is also perpendicular to the applied field *H*0 = 9 T. According to the crystal structure of λ–(BETS)2FeCl4, our calculation indicates that the direction of the Se-electron *pz* orbital is 76.4° from the *c-*axis. Thus the minimum angle between *pz* and *H*0 during the rotation of the goniometer is φmin=13.6°.
