ЖЭТФ, 2020, том 158, вып. 1 (7), стр. 100-102
© 2020
MAGNON BEC AT ROOM TEMPERATURE
AND ITS SPATIO-TEMPORAL DYNAMICS
S. O. Demokritov*
Institute for Applied Physics and Center for NanoTechnology, University of Muenster
48149, Muenster, Germany
Received January 30, 2020,
revised version January 30, 2020
Accepted for publication March 13, 2020
Contribution for the JETP special issue in honor of A. S. Borovik-Pomanov’s 100th anniversary
DOI: 10.31857/S0044451020070093
can be controlled using microwave pumping [4] or illu-
mination with light [5].
Bose-Einstein condensation (BEC), predicted in
To observe BEC of magnons, we took advanta-
1925 by Einstein describes a formation of a collective
ge of monocrystalline films of yttrium iron garnet
quantum state bosons. In fact, in a gas of noninter-
Y3Fe2(FeO4)3 (YIG) [6]. An intense electromagnetic
acting bosons the thermal equilibrium distribution of
pumping field was applied to YIG film with the thick-
particles over their energies ε is
ness of 5 μm placed into a spatially uniform static mag-
[
]-1
netic field H0 oriented in the film plane. As a result,
(ε-μ)
n(ε) = exp
-1
,
(1)
a lot of primary parametrically pumped magnons were
kBT
injected in YIG. The distribution of magnons over fre-
where ε is the energy of the particle, T is the tempera-
quencies was studied using the time- and space-resolved
ture, kB is the Boltzmann constant, and μ is the chem-
Brillouin light scattering (BLS) spectroscopy [7,8]. The
ical potential of the gas, grows with growing density of
measured BLS intensity I(f) is proportional to the re-
the particles. It is seen from Eq. (1) that μ cannot be
duced spectral density of magnons, I(f) ∝
D(f)n(f),
larger than the minimum energy of the particles εmin.
where
D(f) is the density of magnon states taking into
Correspondingly, there exist a critical density Nc:
account only the magnons accessible for BLS and n(f)
(
)3/2
is the magnon occupation function. Calculating
D(f)
m
Nc(T) = kBT
,
(2)
from the known magnon spectrum, the measured BLS
3.31ℏ2
intensity gives directly n(f).
where m is the boson mass. If the density is larger than
The BLS spectra recorded at different delay times
Nc, the gas is spontaneously divided into two fractions:
with respect of start of the pumping are shown in Fig. 1.
particles with the density Nc distributed according to
At small delay times, the data can be nicely fitted by
Eq. (1) and particles accumulated in the ground state.
Eq. (1) with μ being the fit parameter. One observes
The latter fraction represents BEC [1]. Experimen-
that the maximum value μ/h = fmin = 2.10 GHz is
tally, BEC was observed in diluted atomic alkali gases
reached already after 300 ns, the corresponding dis-
at ultra-low temperatures of 10-7 K [2,3].
tribution can be considered as the critical distribution
It is very straightforward idea to observe BEC in
nc(f). Further increase of the density of the pumped
gases of quasi-particles since in this case such ultra-low
magnons leads to BEC of magnons: magnons are col-
temperatures are not needed, because: (i) the effective
lected at εmin without changing the population of the
mass of quasi-particles can be essentially smaller than
states with higher frequencies as illustrated by the
that of atoms; (ii) a large number of quasi-particles
right-hand part of Fig. 1, showing the high-frequency
exists at non-zero temperatures due to thermal fluctu-
parts of the magnon distribution. This part excludes
ations; (iii) if necessary, the density of quasi-particles
a higher temperature for BLS spectra for t > 300 ns
* E-mail: demokrit@ uni-muenster.de
since variation of temperature varies magnon popula-
100
ЖЭТФ, том 158, вып. 1 (7), 2020
Magnon BEC at room temperature and its spatio-temporal dynamics
y, m
1.05
1.03
4
= 500 ns
1.01
2
3
0.99
0.97
60
2
0.95
400 ns
1
1
0
2
4
6
8
10
300 ns
/h = 2.10 GHz
z, m
Fig. 2. (Color online) Measured two-dimensional spatial map
of the BLS intensity proportional to the condensate density ob-
200 ns
2.05 GHz
tained at the maximum used pumping power. Dashed circles
0
show the positions of topological defects in the standing-wave
1.5
2.0
2.5
3.0
3.5
pattern
Frequency, GHz
Fig. 1. (Color online) BLS spectra from pumped magnons at
periodic modulation of the condensate density clearly
different delay times as indicated. Solid lines show the results
of the fit of the spectra based on the Bose-Einstein statistics
confirms the existence of two spatially coherent wave
with the chemical potential being a fit parameter. Note that
functions in the magnon condensate. Moreover, the
the critical value of the chemical potential is reached at 300 ns.
presence of topological defects marked by dashed cir-
The high-frequency part of the same spectrum is shown on the
cles is seen in Fig. 2. These defects correspond to sin-
right
gularities of the phase of the individual components ψ+
and ψ-.
To investigate second sound in magnon gas, we
tions at all frequencies. The difference between a dis-
added to the setup a control strip line. This line al-
tribution at a given time t>300 ns and the critical one
lows to create an additional spatially inhomogeneous
is non-zero in the region close to fmin, the width of
magnetic field ΔH induced by an electric current flow-
the region Δf ≈ 0.3 GHz being defined by the resolu-
ing in the line. If radio-frequency current flows through
tion of the spectrometer. Later experiments with the
the control line, it causes a periodic oscillation of the
ultimate resolution have shown that the intrinsic width
magnon density underneath of the control line, which
of the region is about 700 kHz [9], which corresponds
excites waves of magnon density propagating away from
to a high degree of coherence of the condensate, giving
the control line, as shown in Fig. 3, obtained by swee-
Δf < 10-6kBT/h.
ping the laser beam away from the control line, and
using the time- and space-resolved BLS spectroscopy.
Since the lowest-energy magnon state in in-plane
magnetized magnetic films is doubly degenerate, the
The color code in Fig. 3 reflects the magnon density,
condensation occurs at two non-zero values of the wave
with red/blue color corresponding to the highest/lowest
vector k = ±kmin = ±kBEC . Correspondingly, the
density. Propagating waves of the magnon density are
condensate comprises two spatially overlapping wave
indicated by straight lines of the constant density in
functions ψ+ and ψ-. Interference of two wave func-
Fig. 3, with the slope of the lines being proportional
tions with the opposite wave vectors should lead to a
to the phase velocity of the waves. By varying the fre-
quency of the exciting signal, we were able to measure
standing wave of the condensate density in the real
space, provided they are phase-locked to each other.
the dispersion of the second sound, which was analyzed
using a corresponding theoretical model [10].
Figure 2 illustrating a two-dimensional mapping of
the condensate density, clearly demonstrates a periodic
The magnon BEC takes place at the states, where
pattern along the direction of the static magnetic field
the phase velocity is rather large, the magnon group
created as a result of such interference. The detected
velocity at the ground state is zero. Therefore, the
101
S. O. Demokritov
ЖЭТФ, том 158, вып. 1 (7), 2020
z, m
The full text of this paper is published in the English
70
version of JETP.
60
50
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Fig. 3. (Color online) Spatio-temporal map (t is time from
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