A few layers of helium three (3He) thin films adsorbed on an atomically flat graphite surface are ideal 2D Fermion systems with nuclear spin-1/2. Particularly, in the second layer, particle correlations can widely be changed from the dilute Fermi gas regime to the highly compressed solid by varying areal density of 3He (p). As a result, a rich quantum phase diagram with various exotic quantum phases is proposed [1,2]. They include an anomalous quantum fluid phase [3], the gapless quantum spin-liquid (QSL) state in the low-density commensurate solid (the 4/7 phase) [2,4] and a ferromagnetic state in the high-density incommensurate solid [2,5]. However, detailed density evolutions of the various phases have not been explored until today.

In this thesis, after introduction to 3He systems in two dimensions (2D) in Chap. 1 and 2 and describing experimental methods in Chap.3, results of a comprehensive heat-capacity measurement of the 2nd layer solid 3He adsorbed on graphite preplated with a monolayer 4He (3He/4He/gr) in a wide temperature (0.1 <= T <= 80 mK) and density (6.8 <= p <= 16.5 nm-2) range are discussed in Chap. 4. Here, I could disclose how the gapless QSL evolves into a frustrated ferromagnet through a first-order transition (possibly a commensurate-incommensurate (C-IC) transition) including density evolutions of the multiple-spin exchange (MSE) interactions up to six-spin exchanges [6]. In Chap. 5, results of similar heat-capacity measurements at very low densities for the 1st to 4th layers are given. Here, I could answer a long-standing question if 2D 3He systems self-condense or not. The answer is yes but with a surprisingly low critical liquid density (0.6-0.9 nm-2) ever found. In Chap. 6, I show results of nuclear magnetic resonance (NMR) measurements on the second layer 3He including the first experimental information on the spin dynamics of the gapless QSL.

Frustrated magnetism in the 2nd layer solid 3He (Chap. 4)

As was first pointed out by Thouless [7] nuclear magnetism of solid 3He can be frustrated by competition among the MSE interactions where exchanges of odd (even) number of atoms favour (anti-) ferromagnetism. This magnetic frustration manifests most exotically in the 4/7 phase as the gapless QSL state. We found that the 4/7 phase (p = 6.8 nm-2) is stable against adding 3He atoms up to 8.1 nm-2. With increasing density further, the heat-capacity double peak of the 4/7 phase below 1 mK characteristic of the gapless QSL dramatically changes to the ferromagnetic single peak at 3 mK in the density region of 8.1 <= p <= 9.5 nm-2. Measured heat capacities in this region are consistent with the two-phase coexistence model (C = (1 - x)Cc + xClc) between the 4/7 (C) and the incommensurate (IC) solid at p = 9.5 nm-2 (Fig. 1). This is the first thermodynamic evidence for this previously anticipated phase transition. In addition, a slightly positive deviation of the density evolution of x from the linear relation indicates that this would be somewhat more complicated by the domain-wall structure characteristic of the C-IC transition than the conventional two-phase coexistence.

Above 9.5 nm-2, the ferromagnetic IC solid is uniformly compressed with increasing density. Figure 2 shows measured heat capacities in this region normalized by the number of 3He atoms N and the effective exchange interaction Jc. The solid line in the figure is a theoretical calculation of the spin-1/2 Heisenberg ferromagnetic model on a 2D triangular lattice (HFT) [8]. The data at the highest density (14.45 nm-2) are represented very well by this HFT model. With decreasing density, the data show a remarkable deviation from the model. This is because of increasing contributions from the higher-order exchanges such as four- and six-spin exchanges (J4 and J6) at lower densities. Since the ground state of the IC solid is known to be ferromagnetic [5], we call this phase a frustrated ferromagnet. The inset of Fig. 2 shows density variations of the MSE parameters, -J = J2 -2J3, J6/J4 and -K/J, deduced by fitting our data to the high-T series expansion of heat capacity for the MSE Hamiltonian [9]. Here, Jn is the n-spin exchange interaction, and K = J4 -2J5. The MSE parameters are determined here with much higher precisions than the earlier study [10].

2D self-condensation of 3He on graphite (Chap. 5)

It is known that the attractive interatomic potential, repulsive zero-point energy and Fermi energy are severely countervailing each other in a 2D system of 3He. Therefore, it has been a long-standing question whether self-condensation exists or not in this system. Previous theoretical calculations suggest the absence of the self-condensation [11]. So far existing experimental studies show also no signature of the 2D condensation except one experiment, which is a heat-capacity study of submonolayer 3He floating on thin superfluid 4He films [12]. However, the subsequent heat-capacity, third sound and NMR measurements gave contradictory results.

To answer this question, I made detailed heat-capacity measurements of low-density monolayer 3He in the first four layers on graphite successively. At low enough temperatures (T << TF), heat capacity of a 2D Fermi fluid should be C = YT (Y = πkB2m*A/(3h2)). Here m* is effective mass of 3He quasiparticle and A is surface area of the system. In 2D, Y is independent of the number of atoms, and depends only on m* and A. Thus, if there exists a gas-liquid transition, Y will linearly decrease to zero with decreasing density. Measured Y values actually show such linear decreases at very low densities never explored before in the 2nd, 3rd [13] and 3rd + 4th layer 3He adsorbed on a monolayer 4He preplated graphite (coloured regions in Fig. 3). The heat capacity of the 1st layer 3He adsorbed directly on a bare graphite surface also show a similar linear decrease of Y followed by an initial development of a spin heat-capacity contribution with a weak T-dependence from amorphous 3He preferentially trapped on substrate heterogeneities. These four monolayer 3He systems have extremely different confinement potential, phonon velocities in underlayers, and substrate heterogeneity effect each other. Nevertheless the 2D condensation (puddling) was observed with a similar critical liquid density (0.6-0.9 nm-2) below which a uniform liquid 3He is unstable against the gas-liquid phase separation. Thus, I conclude that the self-condensation of 3He in 2D should be an intrinsic property. This provides a severe constrain for future theoretical many-body calculations for Fermions.

Pulsed-NMR studies of the 2nd layer 3He (Chap. 6)

The spin-spin relaxation time T2 of the 2nd layer 3He adsorbed on a monolayer 4He preplated graphite was measured in a wide temperature range (0.1 mK <= T <= 1.4 K). In the 4/7 phase, T2 is T-independent in a wide rage of 10 <= T <= 300 mK where it is determined by the exchange interactions (exchange plateau), while below 10 mK T2 decreases gradually with decreasing T down to 100 μK. This gradual T2 shortening is suggestive of the growth of short-range spin ordering when the system undergoes a gapless QSL state without long-range ordering. This would be the first direct experimental information on spin dynamics of such an exotic magnetic system. The density dependence of T2 at 100 mK shows a V-shaped minimum at the density of the 4/7 phase. These T- and p-dependences of T2 are qualitatively consistent with the quantum phase diagram determined from our heat-capacity measurements. However, quantitative analyses of the T2 data are difficult at this moment because of an observed unexpected magnetic-field (B) dependence of T2 (1/T2 ∝ B) [14]. The origin of this field-dependence is probably microscopic magnetic field inhomogeneities due to a mosaic angle spread of the platelet of Grafoil substrate and large diamagnetism of graphite. Future NMR measurements in much lower fields will resolve this problem.

Fig. 1: Magnetic heat capacities of the 2nd-layer solid 3He on graphite in the C-IC transition region. The solid lines are fittings to the conventional two-phase coexistence model. The inset shows an areal fraction of the C phase (x) obtained by the fittings.

Fig. 2: Specific heats C/NkB as functions of T/Jc in the frustrated ferromagnetic phase of the 2nd-layer 3He on graphite at various densities. The solid curve corresponds to a theoretical calculation of the spin-1/2 Heisenberg ferromagnetic model on a 2D triangular lattice [8]. The inset shows density variations of the multiple-spin exchange interactions. The filled circles are results in this work, and the others are those in earlier studies on pure 3He films [10].

Fig. 3: Density variations of the Y coefficients in the 2nd, 3rd and 4th layers of 3He on graphite. The filled circles (this work) and open triangles [3] are data for the 3He/4He/gr system. The crosses are for 3He/3He/gr [1]. The horizontal dashed line corresponds to the Y value of the ideal Fermi gas. The vertical solid line at 6.8 (13.9) nm-2 corresponds to promotion to the 3rd (4th) layer. The coloured regions are the self-condensed phase at each layer.

グラファイト表面に吸着されたヘリウム3原子は、強い吸着ポテンシャルによって運動が2次元面内に制限される。吸着量(面密度)を制御することにより、グラファイト上のヘリウム3は理想的な2次元フェルミ液体または2次元量子スピン系として振る舞う。本論文では、比熱およびNMRを実験手段として、グラファイト上ヘリウム3の2次元量子相に関する研究を行っている。

本論文は7章から構成されている。

第1章は序章であり、グラファイトの吸着ポテンシャルや、本研究で重要となるグラファイト上ヘリウム3の相図についての理解の現状が述べられている。

第2章は2次元ヘリウム3の基本的性質に関して述べられている。特に本論文の研究目的である2次元ヘリウム3流体の自己凝縮の可能性および固体相の核磁性に関する先行研究と問題点について説明がなされている。

第3章では実験方法について述べられている。本研究では核断熱消磁冷凍機を用い、100 μKから80 mKにわたり広範囲に温度変化を行っているのが特徴である。また吸着材のグラファイトとしては吸着表面積が極めて大きいグラフォイルを用いており、その表面積は556 m2である。本研究では1層目にヘリウム4を、2層目以降にヘリウム3を吸着させた試料を主に用いている。比熱測定は超伝導ヒートスイッチを用いた断熱法で行っている。またNMR測定の装置と原理についても述べられている。

第4章ではグラファイト上第2層ヘリウム3固体相の核磁性の全体像を明らかにするために、ヘリウム3の面密度を詳細に変化させて比熱測定を行った結果について説明している。ここで4/7相と呼ばれる整合相(反強磁性的スピン液体)がある面密度範囲で安定に存在すること、4/7相から不整合相(強磁性的)への転移が1次の構造相転移として起こることを見出している。また、不整合相の比熱が高密度極限で2次元ハイゼンベルグ強磁性の理論的予測によく合うことを示した。さらに不整合相の比熱の系統的な密度変化を高温展開の理論を用いて解析し、この相における多体交換相互作用の面密度依存性を先行研究よりも高い精度で得ることに成功している。

第5章では、2次元ヘリウム3の自己凝縮に関する実験結果を説明している。2次元面に束縛された希ガス原子の集団が有限温度で気相液相転移を起こすかどうかは統計力学的に興味深い問題である。ヘリウム3よりも量子性の弱い希ガス原子については、有限温度に気相液相転移の臨界点を持つことが既にわかっている。2次元ヘリウム3はちょうどクリティカルな条件にあり、有限温度に臨界点を持つかどうかについてこれまで理論実験共に論争が続いていた。本研究では、1層目~4層目ヘリウム3の低密度領域のフェルミ液体比熱の密度依存性を詳しく調べ、いずれも面密度が0.6-0.9 nm-2付近で自己凝縮、すなわち気相と液相に分離したと考えられる証拠を得ることに初めて成功した。

第6章では第2層ヘリウム3の固体相についてNMRによるスピンスピン緩和時間および磁化率の測定を行い、比熱測定で得られた相図を微視的に支持する結果を得ている。

第7章は全体のまとめに充てられている。

以上のように本研究はグラファイト上ヘリウム3の低温比熱の極めて詳細な面密度依存性のデータを提供するとともに、2次元ヘリウム3液体相および固体相の核磁性についての新たな知見を与えるものである。またこれらの成果は2次元ヘリウム3の理論に対する新たな発展を促すものとして評価できる。

なお本論文の4章と5章の一部(J. Low Temp. Phys. 158 (2010) 201, 544)および6章の一部(J. Phys.: Conference Series 掲載予定)は既に論文として公表済みまたは公表予定である。本論文はこれらの論文の共著者との共同研究による部分があるが、いずれも論文提出者が主体となって研究を行ったものであり、論文提出者の寄与が十分大きいと判断する。

以上をもって審査員一同は、本論文が博士(理学)の学位を授与するにふさわしいものであると認定した。