Observation of angular momentum compensation by using the Barnett effect
M. Imai1), H. Chudo1), Y. Ogata1), M. Ono1), K. Harii1), M. Matsuo1, 2, 3),
Y. Ohnuma2, 3), S. Maekawa1, 2, 3) and E. Saitoh1, 4)1): R.G. for Spin-energy transformation science, JAEA2): CEMS, RIKEN 3): Univ. Chinese Acad. of Sci. 4): The Univ. of Tokyo.

Ferrimagnets contain some kinds of magnetic ions, themagnetic moments of which are antiferromagnetically coupledwith each other as shown in Fig. 1(a). Their spontaneous
magnetization originates from the difference of magnetic
moments of sublattices. In some ferrimagnets, the size of thesublattice magnetic moments is balanced at a temperature called
the magnetization compensation temperature TM, resulting thatnet magnetization vanishes. In addition, when the gyromagnetic
ratio differs depending on the kind of ions, the net angularmomentum becomes zero at a temperature called the angularmomentum compensation temperature TA, which is considered
as a key characteristic of spintronics from the viewpoint of highspeed magnetic response. While TM can be easily measured bymagnetization measurements, TA has not been able to bemeasured directly as the temperature that the net angularmomentum is zero. In order to detect TA, the Barnett effect wasused in this work. We constructed a variable temperatureapparatus for measuring the Barnett effect, and determined TAof the ferrimagnetic insulator Ho3Fe5O12.
The Barnett effect is a phenomenon in which matter ismagnetized by mechanical rotation Ω [1], resulting from angularmomentum J of electrons in material aligns with the rotation
axis through the spin-rotation coupling (- J•Ω). The Barnetteffect does not apply when the net angular momentum ⟨Jnet⟩ = 0,
which is the definition of the angular momentum compensation.
Figure 1(b) shows a schematic illustration of ourexperimental setup [2]. The powder sample of Ho3Fe5O12 packed
in a capsule was floated by bearing air and rotated by blowing
driving air on the impeller. The magnetization MΩ induced bymechanical rotation was detected with a fluxgate magnetic
sensor through the stray magnetic field from the sample. To
realize the measurement under low temperatures, the system

was placed into a cryostat, and the rotor was driven by nitrogengas cooled through a heat exchanger.
Figure 2 shows that MΩ becomes zero at 135 and 240 K. The
former corresponds to TM determined by conventional
magnetization measurements. At TM, the angular momentum inthe sample aligns with Ω, but magnetization M is zero, resultingin MΩ = 0. The latter is TA. The bottom of Fig. 2 shows ⟨Jnet⟩
obtained from MΩ and M. At TA = 240 K, ⟨Jnet⟩ becomes zero.
We succeeded in observation of the temperature dependent net
angular momentum and determination of TA of Ho3Fe5O12 [2].
Furthermore, the gyromagnetic reversal state, where the angularmomentum and the magnetization are coupling inversely inordinary electrons, was realized at the temperatures between TMand TA.
The Barnett effect enables us to measure the net angularmomentum in materials and to determine TA, supporting toexploration of candidate materials for the high-speed magneticdevices utilizing fast-magnetization reversal at TA.

Fig.2 Temperature dependence of magnetization induced bymechanical rotation (top) and the net angular momentum of
Ho3Fe5O12 (bottom).

This work was supported by JST ERATO Grant No.
JPMJER1402, JSPS Grant-in-Aid for Scientific Research on
Innovative Areas Grant No. JP26103005, and JSPS KAKENHI
Grant Nos. JP16H04023, JP16K18353, JP15K05153 andJP17H02927.
Fig.1 Schematic illustration of ferrimagnet and experimental
setup. (a). Relationship between angular momentum and magneticmoment. (b) The apparatus for the Barnett effect measurement
using an air-driven rotor system.

References[1] S. J. Barnett, Phys. Rev. 6, 239 (1915).
[2] M. Imai et al., Appl. Phys. Lett. 113, 052402 (2018).