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25ISSN 2072-5981
Volume 17, Issue 2 Paper No 15202, 1-5 pages 2015
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© Kazan Federal University (KFU)*
"Magnetic Resonance in Solids. Electronic Journal" (MRSey) is a
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Editors
Vadim Atsarkin (Institute of Radio Engineering and Electronics, Moscow) Yurij Bunkov (CNRS, Grenoble) Mikhail Eremin (KFU, Kazan) David Fushman (University of Maryland,
College Park)
Hugo Keller (University of Zürich, Zürich) Yoshio Kitaoka (Osaka University, Osaka) Boris Malkin (KFU, Kazan) Alexander Shengelaya (Tbilisi State University, Tbilisi) Jörg Sichelschmidt (Max Planck Institute for Chemical Physics of Solids, Dresden) Haruhiko Suzuki (Kanazawa University,
Kanazava) Murat Tagirov (KFU, Kazan) Dmitrii Tayurskii (KFU, Kazan) Valentin Zhikharev (KNRTU, Kazan)
In Kazan University the Electron Paramagnetic Resonance (EPR) was discovered by Zavoisky E.K. in 1944.
*
Double magnetic resonance in MnCÛ3^
Yu.M. Bunkov1'2, A.V. Klochkov1, T.R. Safin1*, K.R. Safiullin1'3, M.S. Tagirov1'3 1 Kazan Federal University, Kremlevskaya 18, 420008 Kazan, Russia 2Institut Neel, CNRS et Universite Joseph Fourier, F-38042 Grenoble, France 3Institute of Perspective Research, TAS, L.Bulachnaya 36a, 420111 Kazan, Russia
* E-mail: imfador@gmail.com
(Received December 15, 2015; accepted December 25, 2015)
Results of experiments on MnCO3 investigations by double magnetic resonance are presented.
Additional mode of oscillation has been observed in a created Bose-Einstein condensation of
magnons state in MnCO3. The properties of observed signals are similar to Goldstone modes.
PACS: 71.45.-d, 74.25.nj, 75.50.Ee
Keywords: Bose-Einstein condensation, magnetic resonance, antiferromagnetics, magnons, MnCO3 1. Introduction
In this article magnetic resonance techniques for the resonance spin system excitation at an additional frequency are presented. This method may be applied when an additional, hidden, mode of resonance exists. The observation of magnetic resonance in Landau field is the best example of this case [1]. The Landau field is Fermi liquid corrections for liquid 3He, incorporated to explain the susceptibility of Fermi liquid. This imaginary field is always directed along the magnetization. Consequently it does not change the Larmor frequency of magnetic resonance. It is just directed along the magnetization, even if the magnetization is deflected and rotates around the external magnetic field. There are two components of magnetization in superfluid 3He - the magnetization of superfluid and normal parts of the liquid. The magnetization of both components are bound to each other and rotates in phase at the temperatures about 0.4 Tc and higher. But at the limit of lower temperatures the two components are unbounded and rotates separately around the common Landau field. The Landau field can be adjusted to the external field by changing the temperature or the pressure. In [1] it was found that the relaxation rate of common Larmor precession increases when the Landau field is equivalent to an external magnetic field. The mode of in-phase precession excites the mode of two components precession around the Landau field. By this experiment it was shown that the Landau field is a real molecular field but not an imaginary.
The double resonance is also observed in the systems with magnon Bose-Einstein condensation (BEC). The magnon BEC is a coherent quantum state of non-equilibrium magnons. It may be created during continuous-wave (CW) nuclear magnetic resonance (NMR) or after a pulsed NMR at the conditions when the minimum of magnon spectrum energy is lower than the chemical potential of excited magnons. In this case the macroscopic number of magnons occupy the lowest energy state according to the Bose statistics. The magnon BEC was first found in superfluid 3He in 1984 [2,3]. The BEC leads to the phenomena of spin superfluidity and related phenomena, like spin current Josephson Effect [4], critical spin supercurrent [5,6],
^This paper material was selected at XVIII International Youth Scientific School "Actual problems of magnetic resonance and its application", Kazan, 26 - 30 October 2015. The paper was recommended to publication in our journal and it is published after additional MRSej reviewing.
spin current Abrikosov vortex [7, 8], etc. All these phenomena show that the BEC state has some rigidity, and consequently the Goldstone and Highs modes of ground state excitation may exist. In the ordered (BEC) state, all spins precess coherently, which means that the whole macroscopic magnetization of the sample of volume V is precessing [9]:
Mx + iMy = M±eiMt+ia, M± = xHV sin $ (1)
where x is the magnetic susceptibility, a is the phase of precession, $ is an angle of magnetization deflection. The spatial oscillation of a corresponds to a new Bosonic excitation, the Goldstone modes of oscillation. These modes have the same nature as in cosmology and the particle physics [10]. The Goldstone modes of oscillation have been found in superfluid 3He-B [11-13].
In this work the BEC state was created by CW NMR. Then the phase modulation h (modulation index) of RF field on a frequency wm was applied. When this frequency wm is of the order of wm = C1;2/2L, where C1;2 is the combination of spin waves velocities at different directions and L is the spatial dimension of BEC state, the additional adsorption is observed. At the moment when wm corresponds to one of the Goldstone mode, the BEC signal shows the additional relaxation rate and at sufficient modulation amplitude can even be destroyed. Two different modes of Goldstone oscillation were observed in 3He-B by this method: the axial and plain modes [11-13]. The review of the different experiments with superfluid 3He-B may be found in [9,14,15]. There are few different magnon BEC states found in different states of superfluid 3He. One of them is found in superfluid 3He-A [16-18] in the conditions of strong orbital momentum orientation along the magnetic field [19,20]. Exactly the same BEC state was suggested for antiferromagnets with coupled nuclear-electron precession [21]. The BEC state in MnCO3 and CsMnF3 was found in the conditions of CW [22,23], pulsed NMR [24,25] and original switch-off method [26]. The experimental setup for this experiments one can found in [27,28].
2. Results and discussion
Single crystal MnCO3 was used as a sample in our experiments. The sample was grown by S.V. Petrov in the P.L. Kapitza Institute for physical problems RAS. The crystal has a tablet shape with radius 0.75 mm and 1 mm height. The experiments were performed at the temperature of 1.5 K, at 547.45 MHz frequency and magnetic field of 139.8 mT. Fig. 1 shows the calculated spectrum of nuclear-electron magnetic resonance (NEMR) in MnCO3.
We applied the RF field and swept down the magnetic field. At the point wrf the NMR signal appears. In the case of traditional linear NMR the signal should disappear at lower magnetic field values. But in the presence of Suhl-Nacamura interaction the frequency depends on the angle of magnetization deflection [30]:
wrf = Wni - Wp cos $, (2)
where wn1 is an unshifted NMR frequency, wp is the dynamic frequency shift parameter. This equation has a non-linear solution, when the NMR frequency matches with wrf at lower field as cos $ = (wn1 — wRF)/wne. In other words the system may rest at the resonance on the frequency wrf even at the lower field if the magnetization deflected on the $ angle. This solution is valid only for a region of a sample, where wn1 is the same. Usually the spin systems have an inhomogeneous broadening [15]. It means that the local wn1 is different for different parts of the sample. Consequently the long standing coherent precession is not possible. The induced precession is still possible but the amplitude of the signal should strongly depends on the amplitude of RF field. Indeed, in our case the amplitude of the signal is extremely large and does not depend on the amplitude of RF field. The signal has critical amplitude of RF field below
N
K (N
roRF
500
(0
400
300
1 1 1 1 1 1 1 1 a I2n= 640 MHz ■ nl ■
-Am=a)-a ---- RF -
".y . I.I. T= 1.5 K i . i
200
400
Bn(mT)
600
800
Figure 1. The frequency of NEMR in MnCO3 single crystal as a function of the external magnetic field [29]. The solid horizontal line corresponds to an unshifted NMR frequency. Arrow shows the magnetic field sweep direction in our experiments.
3
£5 O
Sh
O
te Xi oS
1 tO
3 <
1.0
0.8
0.6
0.4
0.2
0.0
1 i 1 i 1 i 1 i
■ vj
-0.5 rad "
-0.8 rad
- -1.0 rad "
-1.5 rad
- = 547.45 MHz " RF
Aco= 19.8 MHz
T= 1.5 K
- i . i , i , i
0 100 200 300 400
f (kHz)
Figure 2. The signal amplitude behavior at different modulation index in MnCO3. Arrows show the direction of phase modulation frequency sweep.
which it disappears. These properties of the signal correspond to a formation of BEC state of magnons in a complete agreement with Bose statistics. If one has pumped the significant number of non-equilibrium magnons with the density N = S(1 — cos 5), where S = ,
the number of magnons becomes bigger than the critical one and the magnons create a single coherent quantum state [9]. The critical angles for magnon BEC was calculated in [31] and correspond to 10°, which equivalent to Aw œ 2 MHz for the conditions of our experiments. The next step is to keep the magnon BEC signal at a given field and start to modulate in-phase RF field with a frequency wm. In the case of small modulation the small decrease of BEC signal is observed at the frequency about 100 kHz (see Fig. 2). If one increases the depth of modulation, the BEC signal become smaller at this frequency of double resonance. And finally at some critical amplitude of modulation the BEC signal is completely destroyed.
We performed the systematic studies of BEC signal decrease and found that its amplitude decrease linearly with increase of modulation index h, starting from some threshold value of modulation. We may suggest that we excited the Goldstone mode of BEC state. There is not yet clear theory of the Goldstone modes of BEC in MnCO3. Indeed we are able to estimate the frequency of this mode. The velocity of spin waves propagation for a small k is about C & 105 cm/s [32]. The dimensions L of the sample are about 1 mm. The frequency of Goldstone mode is about wm = C/2L & 5 ■ 105 rad/s & 100 kHz, in the order of the frequency we have observed.
3. Summary
The investigations of single crystal MnCO3 by CW magnetic resonance at the temperature of 1.5 K are presented. The nuclear-electron magnetic resonance signal dependence on the phase modulation index is obtained. The signal properties are very similar to Goldstone modes observed earlier in superfluid 3He-B. The frequency of Goldstone modes is the order of 100 kHz.
Acknowledgments
The work is performed according to the Russian Government Program of Competitive Growth of Kazan Federal University and partly supported by the Russian Foundation for Basic Research (project no. 14-02-31290 moLa).
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