Thulium

Principles of Surgical Technique

The thulium (Tm) laser has a wavelength of 2013 nm and a penetration depth of 0.25 mm, using water as the absorbing chromophore [48]. Unlike holmium, energy is released in a visible continuous wave [48]. Two forms of thulium lasers are currently used in clinical practice—Tm-YAG (Revolix) and Tm-fiber (Vela XL) [1]. Similar to holmium, the thulium laser can be used for vaporization, resection, or enucleation. First used for BPH in 2005 by Xia et al., a Tm:YAG laser was used for a procedure known as thulium laser resection of the prostate (TmLRP-TT) in which thulium laser is used to resect the prostate into small tissue chips [49]. Another version is known as thulium vaporesection of the prostate (ThuVARP), referring to a combination of vaporization and resection [6,50]. In 2009, Bach et al. then adopted enucleation which became Thulium VapoEnucleation of the prostate (ThuVEP) initially, analogous to HoLEP. This has been further refined to become thulium laser enucleation of the prostate (ThuLEP), in which the incision is apical rather than the original three-lobe HoLEP/ThuVEP, and blunt enucleation is used more, for dissection to the surgical capsule [6,51].

Abstract

The high-power thulium laser was first introduced in 2005 for the treatment of benign prostatic hyperplasia (BPH) (Barbalat et al., 2016). The thulium laser has several properties that confer some theoretical advantages over other lasers used for the treatment of BPH. In ex-vivo animal studies comparing the potassium-titanyl-phosphate and thulium lasers, similar hemostatic properties were observed with a shallower coagulation zone for thulium lasers (Wendt-Nordahl et al., 2008). Thulium vapoenucleation, thulium laser resection - tangerine technique, thulium laser enucleation, and thulium vaporization are techniques for thulium laser prostatectomy that have been described. Studies using the 70–150-W thulium laser systems demonstrated good efficacy of these procedures with low morbidity and few complications in prostates of small to medium sizes (Gross et al., 2013). More recent studies show safety and efficacy in treatment of large prostates and in patients taking oral anticoagulation (Wei et al., 2014; Macchione et al., 2013; Pearce et al., 2016). Comparative studies have been published comparing thulium laser prostatectomy to monopolar transurethral resection of prostate (TURP), bipolar TURP, and holmium laser enucleation of prostate (HoLEP) (Barbalat et al., 2016). In general, thulium laser prostatectomy appears to have longer operative times, but shorter catheterization times, shorter hospital stay, and lower transfusion rates compared to standard and bipolar TURP. Outcomes of HoLEP and thulium enucleation techniques appear to be similar. Overall, thulium laser prostatectomy appears to be very safe and effective with low morbidity (Gilling, 2013).

1.1 Magnetic Order in Rare-earth Elements

As with all physical systems, it is possible to define a Hamiltonian. The spin Hamiltonian is composed of terms intended to represent the possibility of strong anisotropic behavior through crystal field and magnetic exchange. These terms are often linked to the crystal lattice through magnetoelastic coupling. Consideration of the spin Hamiltonian is beyond the scope of the current article, and the reader is referred to Jensen and Mackintosh (1991) and references therein.

The elements chosen for discussion are thulium and erbium. The crystal structure for each of these elements is hexagonal close-packed (h.c.p.), with the three orthogonal symmetry directions being the a, b, and c axes. The crystal field for each element is such that the preferred orientation of the magnetic moments is along different directions. In the case of thulium, the moment is constrained to the c-axis. In erbium, the moments are found to develop first along the c-axis, and then an additional moment develops along the a-axis. In each case, the propagation wave vector for the antiferromagnetic structures is parallel to the c-axis. The RKKY-exchange energy (Jensen and Mackintosh 1991) is found to increase going from thulium to erbium. The main consequences of this are an increase in the Néel temperature, and a decrease in the role played by the crystal field within the Hamiltonian.

5.4.7 Tm-doped lasers

Development of room-temperature solid-state lasers in the 2 μm spectral range received renewed attention at the end of the 1990s because of potential applications in medicine and optical communications. A significant absorption band of water and carbon dioxide around 2 μm wavelength (water vapor maxima for λ = 1.88 μm, 1.91 μm, and 2.14 μm; carbon dioxide for λ = 1.96 μm, 2.01 μm, and 2.06 μm) induced researchers to look for laser-generating radiation in this region. Laser radiation from this spectral range can be used also in radar and Light Detection And Ranging (LIDAR) technology for applications such as distance measurement, determining the composition of the atmosphere, measuring the speed of moving air masses, and, due to its high absorption in water (see Fig. 5.14), in medicine. Suitable active media for the construction of lasers generating radiation in this region are materials (matrix YAG, YAP, GdVO₄, YLF, Sc₂O₃, YSGG, etc.) doped with the trivalent lanthanide rare-earth ion of thulium (Tm^3 +). An overview of lasers with trivalent Tm^3 + ions is presented in Table 5.13.

5.14. Tm:YAG laser emission on the basis of the absorption of radiation in water.

Table 5.13. Thulium-doped lasers

Laser material	Lifetime (ms)	Laser emission (nm)	Characteristics
Cr:Tm:Y3Al5O12 (YAG)	10	2020	Efficient flashlamp-pumped thulium laser (Quarles et al.,1990)
Tm:Y3Al5O12 (YAG)	10	2020	Efficient diode-pumped thulium laser (Li et al., 1999)
Tm:YAlO3 (YAP, YAlO)	6	1870–2036	Tunable diode-pumped thulium laser with polarized output(Cerny et al., 2006b)
Tm:GdVO4	3	1860–1990	Material with large gain, suitable for diode pumping (Cerny et al., 2006a)
Tm:LiYF4 (YLF)	16	1910–2070	Polarized output (Schellhorn, 2008)
Tm:Glass	2–5	1934	Efficient fiber laser

Another possibility of pumping is coherent, by laser radiation. The first-generation pumping of the Tm:YAG laser was reached by a Ti:sapphire system tuned for the needed wavelength. After laser diodes in the required region appeared, many laser systems were investigated. For this type of pumping the sensitizer is not needed.

The advantages of thulium-doped active material are broad emission lines (it is possible to cover a range of wavelengths from 1800 to 2200 nm) and high quantum efficiency for diode pumping, enabled by resonant ion–ion interactions. Another advantage of this ion is its long lifetime in the excited state (up to 11 ms for Tm:YAG); the active element with ions of Tm^3 + is suitable for energy storage and generation of Q-switched pulse (Powell, 1998; Sorokina and Vodopyanov, 2003).

Conventional materials with Tm^3 + ions are Tm:YAG and Tm:YAP. It has been investigated with flashlamps as well as diode pumping. As a result, power of dozens of watts was obtained (Stoneman and Esterowitz, 1990, 1995; Beach et al., 1996; Honea et al., 1997; Bollig et al., 1998; Tsunekane et al., 1999; Elder and Payne, 1998a,b; Li et al., 1999; Matkovskii et al., 2002). Because the absorption bands of these materials are narrow, a special laser diode with convenient pumping wavelength has to be chosen to reach the optimal output efficiency.

8.1 Y₃Al₅O₁₂ (YAG)

Owing to its application as a laser crystal yttrium aluminum garnet is very widely used. It acts as the host crystal for impurity ions, which take part in amplified stimulated emission of radiation (LASER). Pure YAG has very good characteristics as a host crystal. It is transparent for radiation in the region of 0.3–4.2 μm. It has excellent thermochemical properties—a small coefficient of thermal expansion and large thermal conductivity. Moreover it has good mechanical properties: Poisson’s ratio (0.25), Young’s modulus (3.17×104 kgmm⁻²), a high value of hardness (Table 2), and chemical resistance (it is soluble only in boiling H₃PO₄) and a good stability of the liquid phase. The melting point is 1970 °C. One disadvantage of YAG is that it grows with a convex growth interface, which develops facets. Only the crystal volume outside the facet core is usable. The dopant ions incorporated in YAG are mainly Ln³⁺. Laser action cannot be obtained from all of them. So far some crystals have industrial applications:

(a) YAG:Nd—(emission at 1.064 μm) crystals with a diameter up to 5 cm, usually produced by the Czochralski method. In practice, the neodymium concentration is not higher than 1.3 at.% (Y_2.961Nd_0.039Al₅O₁₂). Higher dopant concentrations are not recommended. The distribution coefficient for neodymium is k_Nd=0.18, which means that supercooling occurs at the crystallization interface, and the pulling rate has to be very small (0.5–0.8 mmh⁻¹). Another consequence of the small distribution coefficient is the steep neodymium concentration gradient along the crystal.

(b) YAG:Ho,Tm,Cr—(emission at about 2.1 μm). Holmium is the optically active ion, with chromium and thulium as sensitizers. An optimal composition is: Ho³⁺–0.36 at.%, Tm³⁺–5.9 at.%, Cr³⁺–0.85 at.%. The stoichiometry in this case is: {Y_3−x−yHo_xTm_y}[Cr_zAl_2−z](Al₃)O₁₂, where x=0.0108, y=0.177, z=0.017. The distribution coefficients for Ho, Tm, and Cr are 1, 1.1, and 2.5, respectively. Therefore holmium ions are homogeneously distributed throughout the crystal; thulium ions have a near-homogeneous distribution whereas the chromium concentration steadily decreases while growing the crystal. This can cause variations in the thulium/chromium ratio that are detrimental to the lasing properties. This effect can be overcome by crystallizing only a small part of the melt. The ratio crystal weight/melt weight should not be bigger than 0.2. The Cr³⁺ ions impart an intense green color to the crystals.

(c) YAG:Er—erbium and yttrium oxides form a solid solution, so the crystals can be obtained with any concentration of erbium. It may be grown at a rate of several mm/h. The distribution coefficient of erbium in YAG is k_Er=1. The crystal is a pink in color, and for laser applications additions of 1.5 at.% of erbium (giving emission at 1.53 μm) or 33–50 at.% (giving emission at 3.94 μm) are used.

(d) YAG:Cr⁴⁺—a garnet which differs from the Ln³⁺ model. This nonstandard oxidation state of chromium is obtained by co-doping the crystal with Mg²⁺ or Ca²⁺. The composition of this garnet can be written as $\{{\text{Y}}_{3-x}-{\text{Ca}}_x^{2+}\}[{\text{Al}}_{2-y}{\text{Cr}}_{y-z}^{3+/4+}]({\text{Al}}_{3-z}{\text{Cr}}_z^{4+})$, where 0⩽z<y, which shows the distribution of different ions in particular sites in the crystal lattice. The proportion of chromium ions changes very easily, being very sensitive to the growth atmosphere. Annealing the crystal (temperature 1000–1300 °C) in reducing or oxidizing atmosphere changes the coloration of the crystal from green (Cr³⁺) to black (Cr⁴⁺). Cr⁴⁺ ions (located on tetrahedral sites) strongly absorb visible radiation, but they also have a weaker absorption band with a maximum at 1 μm. Therefore the YAG:Cr⁴⁺ crystal weakly absorbs the laser radiation of YAG:Nd (1.064 μm). Following strong irradiation, the crystal becomes transparent for a while, and in one pulse it emits all the accumulated energy. Such a crystal is called a saturable absorber. These properties of YAG:Cr⁴⁺ make it an ideal passive modulator (Q-switch) for YAG:Nd laser crystals.

(e) YAG:V³⁺—the effect of saturable absorption also occurs with YAG:V³⁺ crystals, and is similarly caused by V³⁺ ions at tetrahedral sites. It is not possible to obtain such a crystal directly by the CZ or B-S methods. However, the effect of saturable absorption for λ≈1.3 μm laser emission can be obtained after annealing the as-grown crystal in a reducing atmosphere.

2 TL Spectra

TL spectra have been measured in order to investigate the valence of the Ln ion-doped K₃Na(SO₄)₂ matrix. The TL spectrum of yttrium, lanthanum, or lutetium ion-doped K₃Na(SO₄)₂ consists of a broad, weak peak (about 400 nm) owing to the K₃Na(SO₄)₂ matrix. In praseodymium, neodymium, gadolinium, or thulium ion-doped K₃Na(SO₄)₂, the TL spectrum consists of peaks assigned to the f–f transitions of each Ln³⁺ ion, i.e., the ¹D₂→³H₄ transition of Pr³⁺, the ²G_5/2→⁴I_13/2 and ²H_5/2→⁴I_9/2 transitions of Nd³⁺, the ⁶P_7/2→⁸S transition of Gd³⁺, and the ¹D₂→³H₆, ¹D₃→³H₄, ¹G₄→³H₆, ¹G₄→³H₄, and ¹G₄→³H₅ transitions of Tm³⁺. The TL intensity of the f–f transition peaks varies according to the following sequence: Gd³⁺⪡Pr³⁺, Nd³⁺<Tm³⁺. This is in contrast to the ESR signal intensity (Fig. 2).

The TL spectrum of samarium ion-doped K₃Na(SO₄)₂ is affected by the glow peak temperature, i.e., a broad peak owing to the 4f⁵5d→4f⁶ transition of Sm²⁺ and three sharp peaks owing to the ⁴G_5/2→⁶H_5/2, ⁴G_5/2→⁶H_7/2, and ⁴G_5/2→⁶H_9/2 transitions of Sm³⁺ are observed near 380 K and near 430 K, respectively. The TL spectrum of europium ion-doped K₃Na(SO₄)₂ consists of a broad, strong peak owing to the 4f⁶5d→4f⁷ transition of Eu²⁺.

5 Heavy-fermion Compounds

In the series of rare-earth metals, three are anomalous in the sense that they do not have a stable valence of 3. Cerium has a very peculiar phase diagram with intermediate valence phases, while europium and ytterbium metals are divalent under normal conditions of temperature and pressure. Thus, as discussed below, many cerium and ytterbium alloys or compounds and only a few europium-based systems have an anomalous behavior.

An anomalous behavior has also been observed in alloys or compounds containing three other rare earths which are trivalent normal metals: praseodymium (4f²), samarium (4f⁵), and thulium (4f¹²). However, no anomalous behavior has been detected and consequently the normal trivalent character remains very stable even at very high pressures in systems with the other rare earths and in particular with the heavy ones (gadolinium, terbium, dysprosium, holmium, and erbium) (Coqblin 1977).

Examples of anomalous behavior are known for systems containing praseodymium, samarium, or thulium. For example, PrSn₃ and TmS show a decrease of the magnetic resistivity characteristic of the Kondo effect. SmS shows, under pressure, a metal–insulator transition that is accompanied by a valence change. TmSe, which is insulating at low temperatures in the antiferromagnetic domain, has an intermediate valence, roughly equal to 2.5 at stoichiometry and varying with the departure from stoichiometry. A semiconducting or low carrier behavior has also been observed in other compounds, such as CeNiSn, SmB₆, and cerium or ytterbium pnictides.

We now discuss cerium and ytterbium compounds that have a Kondo or heavy-fermion behavior. In fact, there are more than 100 of such compounds, which are reviewed elsewhere (Coqblin et al. 1996). Moreover, there are several types of cerium and ytterbium systems, depending on the valence (i.e., intermediate valence and Kondo systems have clearly different behaviors), on the existence of a magnetic moment (yielding a Curie–Weiss law at sufficiently high temperatures), and on the existence of a magnetic order at low temperatures. For example, when x increases, the compound CeSi_x passes through several situations: first a Kondo system which orders antiferromagnetically at low temperatures, then the Néel temperature tends to zero and the compound is no longer magnetically ordered but still magnetic at high temperatures, and finally a nonmagnetic intermediate valence state is reached (Lee et al. 1987).

We now discuss the case of Kondo systems that have a heavy-fermion behavior. Table 1 gives some examples of heavy-fermion compounds of cerium, ytterbium, and uranium, with the corresponding values of the crystalline field splittings deduced from the high-temperature behavior, the Néel temperatures when the compounds order, and the very low-temperature values of γ. In fact, it is difficult in some cases to estimate the values of γ, which are not really constant at low temperatures. In spite of these possible difficulties, the values of γ given in Table 1 are very large and characteristic of the heavy-fermion behavior. The cerium compounds that order magnetically at low temperatures generally show an antiferromagnetic order and only some of them (such as Ce₃Al₁₁ in Table 1) order ferromagnetically.

A similar behavior is observed in ytterbium compounds, except that the effect of pressure is reversed. When pressure is applied, the system goes from a nonmagnetic to a magnetically ordered state, and the Néel temperature increases with pressure, as, for example, observed in YbCu₂Si₂ (Jaccard et al. 1999). There are also examples of heavy-fermion compounds of uranium. Table 1 includes the compound U(Pt_0.95Pd_0.05)₃ that orders antiferromagnetically at 6 K because the parent compound UPt₃ seems to have a very peculiar short-range magnetic order, as observed by sophisticated neutron scattering or muon spectroscopy experiments (Koike et al. 1999). The three uranium compounds listed in Table 1 have a fascinating behavior, because they combine a heavy-fermion behavior with an antiferromagnetic order and a superconducting state; this last point is discussed in Sect. 7. Finally, very large values of γ have been found in the two compounds YMn₂ and LiV₂O₄ containing 3d transition elements. Table 1 gives the corresponding values of γ for these compounds as well as, for example, for the actinide compound NpSn₃, which orders antiferromagnetically at low temperatures. The heavy-fermion character of actinide systems is also a very interesting subject that can be connected to the multichannel Kondo effect (see also Heavy-fermion Systems).

Evolution of Holmium Laser Enucleation of the Prostate

Though Ho:YAG laser use in urology dates back to the late 1980s for use in fragmenting renal calculi, the first application of the holmium energy source to treat BPH was reported by Drs. Gilling and Chun in 1995.^3,4 The authors first reported strong clinical outcomes using a dual approach of Nd:YAG for incision and Ho:YAG for ablation but subsequently abandoned the use of Nd:YAG because holmium ablation offered superior features more suitable to application in treating BPH. HoLAP was compared in a randomized controlled trial (RCT) to TURP and found to be superior in some ways (shorter catheterization time), comparable with similar improvements in Qmax and International Prostate Symptom Score (IPSS) scores and no difference in the postoperative sexual dysfunction and inferior in other parameters, namely the procedure took 20 min longer on average than TURP.⁵ This limits this technique to prostates that are less than 60 ccs. Holmium ablation has decreased in popularity but the concept remains valid and has been adopted by newer technologies including photovaporization of the prostate (PVP), thulium vaporization of the prostate, and higher power holmium lasers (100 and 120 W).^6,7

The next iteration of holmium laser application in BPH was HoLRP, developed to reduce operative times to durations that more closely resemble TURP. HoLRP relies on using a Ho:YAG laser to incise pieces of prostatic tissue piece by piece until exposing the surgical capsule rather than ablating half-millimeter layers of tissue. The success of HoLRP has been more thoroughly studied and a metaanalysis by Tooher et al. HoLRP is as effective in improving Qmax and quality of life scores as TURP.⁸ However, HoLRP patients experienced shorter catheterization duration and decreased transfusion rates when compared to the TURP group.⁹ Additionally, Frauendorfer et al. found that HoLRP was nearly one-fourth less expensive than TURP and in less than 100 cases the initial capital investment in a Ho:YAG laser could be recouped.¹⁰ Like HoLAP, the primary weakness of HoLRP was operative time, which was found to be as high as 30% longer than TURP. Fragmenting the lobes of the prostate with repeated holmium incision, while virtually bloodless, takes significantly longer than the electrocautery applied in TURP. Accordingly, HoLRP has fallen out of favor for treating BPH except in certain scenarios such as reoperation for adenomatous regrowth.

HoLEP allows the surgeon to completely dissect out the adenoma by using the Ho:YAG laser to incise along the capsule to shell out the lobes of the adenoma en bloc. The shelled-out lobes are then deposited into the bladder for morcellation. This technique relies on an entirely new component of technology, the transurethral power morcellator, to avoid having to remove bits of the prostate piecemeal through the urethra. A morcellator uses reciprocating blades to simultaneously shred and suction. First reported by Fraundorfer and Gilling in 1998 on a series of 14 patients where both suprapubic and transurethral morcellation was used. The results demonstrated favorable outcomes for patients with average glad size of 98.6 ccs and with an average surgical duration of 98 min. Twelve of the patients were discharged the next day without a catheter and at 1 month, Qmax was 25.2 mL/s and mean IPSS was 7.2.¹¹ In the same year, a report on a larger group of 64 patients was published that reported similarly, compelling outcomes: greater than 90% discharged next day catheter-free and Qmax of 23.4 mL/s, and a reduction in IPSS from 23.0 to 8.6 after 1 month.^12,13 The size of the prostate, while potentially extending operation time, does not affect perioperative clinical outcomes such as length of stay, Qmax, postvoid residual, and catheterization time.^14–16

1.2 Theoretical Models

The theoretical treatment of pressure effects on magnetic properties of solids has been performed within models of both localized and band magnetism (see also Localized 4f and 5f Moments: Magnetism and Itinerant Electron Systems: Magnetism (Ferromagnetism)).

Calculations of the s–d interaction in transition metals are able to describe the volume dependence of the d-band width as W∼R⁻⁵ which leads to λ=5/3 (Heine 1967). The pressure (volume) dependence of the band width W given by the parameter λ controls all the pressure-induced changes of the magnetic characteristics of the transition metal ferromagnets in the theoretical concept, where only single-particle excitations have been taken into consideration.

Since the late 1980s the band calculations based on the local spin density approximation (LSDA) (see Density Functional Theory: Magnetism) have revealed the instabilities of the transition-metal moments in the volume instability ranges (Moruzzi and Marcus 1988). The theoretically predicted existence of two ferromagnetic states, very close in energy, for iron in the f.c.c. crystal structure, and the verification of the Fe-moment stability in the more open b.c.c. crystal structure, explains the anomalous magnetovolume effects in Invar alloys (f.c.c.) as well as the almost total insensitivity of the b.c.c.-Fe to external pressures (see Invar Materials: Phenomena and references therein).

2 Experimental Evidence of Intermediate Valence

In general, the lattice parameters of an isotypic series of rare-earth intermetallics smoothly decrease from lanthanum to lutetium. This is attributed to the lanthanide contraction and ascribed to the fact that though the electron count of the 4f shell increases, it cannot completely screen the increase in the nuclear charge and, therefore, the outer electrons become constricted. However, compounds with cerium, samarium, europium, thulium, or ytterbium may significantly deviate from this simple dependence since their valency can be larger or smaller than three, thus cause a decrease or an increase of the unit cell volume, respectively.

2.1 Samarium and Thulium Monochalcogenides

The monochalcogenides SmS, SmSe, and SmTe crystallize in the f.c.c. structure and are characterized by a semiconducting behavior owing to an energy gap E_g between the 4f⁶ and the 5d state of about 0.15, 0.45, and 0.65 eV, respectively (Wachter 1994). CF interaction of cubic symmetry splits the 5d orbital into the lower lying t_2g band and the e_g band.

The magnetic susceptibility of this series behaves like an inhomogeneous mixing of Sm²⁺ and Sm³⁺, but the finite values for T → 0 imply that the ground state is homogeneous. The valence fluctuations render the mixture homogeneous; hence the f⁵ spin memory is lost when the configuration fluctuates (Lawrence et al. 1981).

Pressure applied to such narrow bandgap systems can give rise to a semiconductor-metal instability. In fact, a first order transition was deduced for SmS at p_c=6.5 kbar (Jayaraman et al. 1970), accompanied by a volume change of about 20%. Slightly above p_c, SmS turns golden as the plasma edge moves into visible and IV occurs. For SmSe and SmTe the pressure-induced valence transition is continuous and is found at significant higher values of pressure, i.e., 45 and 60 kbar, respectively (Bucher et al. 1971).

The approach of the ions due to applied pressure cause the Coulomb potential to increase. Thus CF splitting of the 5d band grows and eventually leads to an overlap with the 4f⁶ state. Accordingly, the bandgap closes and 4f electrons empty into the d states. Upon the enhanced number of conduction electrons, the lattice starts to shrink, so CF splitting strengthens further, resulting in some avalanche effect and a first order phase transition. Since the reduced lattice parameter stiffens the lattice as a whole, the trivalent state is not attained. Rather, the process stops at ν=2.75 (Kaindl et al. 1984) where the gain in electronic energy is compensated by the increase of the lattice energy. In the case of SmSe and SmTe, the gap in the density of states at E_F closes before the lattice softens, and consequently only a second-order phase transition is observed.

In the case of Tm, both EC, i.e., Tm²⁺ (J=7/2) and Tm³⁺ (J=6) result in a magnetic ground state. Such systems can exhibit long-range magnetic order even in the IV state, which is in contrast to those based on cerium, samarium, europium, or ytterbium. The thulium monochalcogenides are of particular interest. Binary compounds range from metallic trivalent TmS over IV TmSe to semiconducting divalent TmTe.

A sketch of the electronic structure and the density of states of this series is shown in Fig. 2 (Wachter 1994).There is a cross-over from metallic (TmSe) to isolating behavior (TmTe). The latter exhibits the divalent 4f¹³ EC, where the localized 4f state is separated by an energy gap E_g∼0.3 eV from the bottom of the 5d-t_2g band.

Figure 2. Electronic structure and density of states of the Tm monochalcogenides normalized to the Fermi energy E_F (dotted line). The dashed lines through the density of state peaks serve as a guide to the eyes.

When proceeding from TmTe to TmSe or TmS, the lattice constant shrinks, thus producing chemical pressure onto the Tm cation. Therefore, crystal field splitting of the 5d band increases. The bottom of the conduction band (mostly 5d-t_2g states) may then overlap with the 4f¹³ level and 4f electrons will spill into the conduction band.

Stoichiometric TmSe orders antiferromagnetically below T_N=2.9 k (Bjerrum-Moller et al. 1977). The electrical resistivity in both the paramagnetically and the magnetically ordered state shows thermally activated behavior. According to Luttinger’s theorem, TmSe should be a metal since the compound is an odd electron system in both EC, 4f¹³ and 4f¹²5d. Antiferromagnetic order below 2.9 k, however, enlarges the magnetic unit cell which contains an even number (26) of electrons. The hybridization gap can then exist with E_F just in the center, and the system should behave isolating. However, at μ₀H=0.5 T, TmSe becomes ferromagnetic, thus the folding of the Brillouin zone vanishes. Consequently, TmSe behaves metallic and the system is an IV ferromagnet (Batlogg et al. 1977).

As for many other IV compounds with the Fermi level within the hybridization gap, pressure applied to TmSe (p_c∼30 kbar) will close the bandgap primarily due to the growing overlap of the crystal field split 5d band with the 4f¹³state (Wachter 1994).

Besides, the pseudobinary TmSe_1−xTe_x allows to realize a novel feature in condensed matter physics, the excitonic insulator, which is characterized by a Bose-Einstein condensation of quasi-particles into a coherent exciton phase (Neuenschwander and Wachter 1990). Figure 3 shows the pressure dependence of the electrical resistivity of TmSe_0.45Te_0.55 at high and low temperatures and the Hall constant. The most striking feature with respect to the resistivity at T=4 k is that after the expected initial decrease of ρ(p), a rapid rise in a narrow pressure range from about 5 kbar to 8 kbar occurs. Beyond this pressure, the resistivity decreases again and furthermore exhibits a first order phase transition near p=14 kbar.

Figure 3. (a) Pressure dependence of the resistivity of TmSe_0.45Te_0.55 at 300 k (lower curve) and at 4.2 k (upper curve). At 300 k the semiconducting to metal transition is at p_c=11.5 kbar and for T=4.2 k at p_c∼14 kbar. (b) Pressure-dependent Hall constant R_H at 4.2 k.

2.2 Cerium and Ytterbium Systems

A large number of cerium compounds and alloys exhibit an EC ranging between the 4f¹ and the 4f⁰ state, thus behaving as IV materials. The most striking feature of IV, however, occurs in f.c.c. cerium as a response to applied pressure. At a temperature-dependent critical pressure (p_c=7 kbar at room temperature, Franceschi and Olcese 1969) cerium crosses over from the γ state (lattice parameter a=5.15 Å) to the α state (a=4.85 Å). This transition is accompanied by a volume change of about 15% which does not, however, distort the cubic crystal symmetry. While the γ state is primarily trivalent (4f¹(5d6s)³), the α state behaves almost tetravalent (4f⁰(5d6s)⁴), with a valence ν=3.67 (Koskenmaki 1978).

Intermediate valence in ytterbium systems is constrained by divalent ytterbium (EC 4f¹⁴) and trivalent Yb (EC 4f¹³). While the former is a nonmagnetic state, the latter is magnetic with a total angular momentum J=7/2. Pressure can be used to subtly tune the valence of the ytterbium ion and eventually drive it towards the trivalent magnetic ground state. For proper ytterbium compounds and alloys, intermediate valence is then completely adjustable from the Yb²⁺ towards Yb³⁺ state (Bauer et al. 1995).

In addition to pressure, temperature may also cause a dramatic alteration of the ytterbium valence. A temperature driven first order type of transition, as shown in Fig. 4, has been observed for YbCu₄In (Felner and Nowik 1986). The particular transition temperature T_ν, however, depends sensitively on details of the stoichiometry (Löffert et al. 1999). Qualitatively, the high-temperature state corresponds to the magnetic Yb³⁺ while the low-temperature state is the nonmagnetic Yb²⁺. Quantitatively, however, the valence at T_ν only changes by about 0.2, and the principal effect observed is the nearly complete Kondo compensation of the local moment of ytterbium. This scenario is rendered also from the change of the Kondo temperature, which is small for T>T_ν (T_K⁺∼25 k), but substantially larger for T<T_ν (T_K⁻∼500 k) (Cornelius et al. 1997).Concomitantly, there is a large change in the carrier density which occurs at the phase transition, from trivalent semimetallic behavior at high temperature to IV metallic behavior at low temperatures. Although the change of the volume at T=T_ν (about 0.5%) is reminiscent of the γ−α transition of cerium, a “Kondo volume expansion” in YbCu₄In would require an extraordinary and unrealistic large Grüneisen parameter Ω=−δlnT_K/δlnV∼4000 in order to match the conditions of the Kondo volume collapse of cerium.

Figure 4. Temperature-dependent resistivity ρ (left axis) and lattice constant a (right axis) of YbCu₄In.